TSTP Solution File: ITP114^1 by cocATP---0.2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : ITP114^1 : TPTP v7.5.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n017.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 13:24:13 EDT 2021
% Result : Unknown 0.92s
% Output : None
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.11 % Problem : ITP114^1 : TPTP v7.5.0. Released v7.5.0.
% 0.12/0.12 % Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.33 % Computer : n017.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % DateTime : Fri Mar 19 06:08:08 EDT 2021
% 0.12/0.33 % CPUTime :
% 0.12/0.34 ModuleCmd_Load.c(213):ERROR:105: Unable to locate a modulefile for 'python/python27'
% 0.12/0.34 Python 2.7.5
% 0.47/0.65 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox2/benchmark/', '/export/starexec/sandbox2/benchmark/']
% 0.47/0.65 FOF formula (<kernel.Constant object at 0xa27998>, <kernel.Type object at 0xa27d40>) of role type named ty_n_t__Set__Oset_It__Extended____Real__Oereal_J
% 0.47/0.65 Using role type
% 0.47/0.65 Declaring set_Extended_ereal:Type
% 0.47/0.65 FOF formula (<kernel.Constant object at 0xa27908>, <kernel.Type object at 0xa441b8>) of role type named ty_n_t__Extended____Real__Oereal
% 0.47/0.65 Using role type
% 0.47/0.65 Declaring extended_ereal:Type
% 0.47/0.65 FOF formula (<kernel.Constant object at 0xa27cf8>, <kernel.Type object at 0xa44c68>) of role type named ty_n_t__Extended____Nat__Oenat
% 0.47/0.65 Using role type
% 0.47/0.65 Declaring extended_enat:Type
% 0.47/0.65 FOF formula (<kernel.Constant object at 0xa27908>, <kernel.Type object at 0xa44f38>) of role type named ty_n_t__Real__Oreal
% 0.47/0.65 Using role type
% 0.47/0.65 Declaring real:Type
% 0.47/0.65 FOF formula (<kernel.Constant object at 0xa27cf8>, <kernel.Type object at 0xa44d88>) of role type named ty_n_t__Num__Onum
% 0.47/0.65 Using role type
% 0.47/0.65 Declaring num:Type
% 0.47/0.65 FOF formula (<kernel.Constant object at 0xa27908>, <kernel.Type object at 0xa441b8>) of role type named ty_n_t__Nat__Onat
% 0.47/0.65 Using role type
% 0.47/0.65 Declaring nat:Type
% 0.47/0.65 FOF formula (<kernel.Constant object at 0xa4e5a8>, <kernel.Type object at 0xa44dd0>) of role type named ty_n_tf__a
% 0.47/0.65 Using role type
% 0.47/0.65 Declaring a:Type
% 0.47/0.65 FOF formula (<kernel.Constant object at 0xa44cf8>, <kernel.DependentProduct object at 0x2b8b6ffc1c20>) of role type named sy_c_Extended__Nat_Oenat
% 0.47/0.65 Using role type
% 0.47/0.65 Declaring extended_enat2:(nat->extended_enat)
% 0.47/0.65 FOF formula (<kernel.Constant object at 0xa44fc8>, <kernel.Constant object at 0xa44f38>) of role type named sy_c_Extended__Nat_Oinfinity__class_Oinfinity_001t__Extended____Real__Oereal
% 0.47/0.65 Using role type
% 0.47/0.65 Declaring extend1289208545_ereal:extended_ereal
% 0.47/0.65 FOF formula (<kernel.Constant object at 0xa44d88>, <kernel.DependentProduct object at 0xa4af80>) of role type named sy_c_Extended__Nat_Othe__enat
% 0.47/0.65 Using role type
% 0.47/0.65 Declaring extended_the_enat:(extended_enat->nat)
% 0.47/0.65 FOF formula (<kernel.Constant object at 0x2b8b6ffc1c20>, <kernel.Constant object at 0xa44f38>) of role type named sy_c_Extended__Real_Oereal_OMInfty
% 0.47/0.65 Using role type
% 0.47/0.65 Declaring extended_MInfty:extended_ereal
% 0.47/0.65 FOF formula (<kernel.Constant object at 0x2b8b6ffc1488>, <kernel.Constant object at 0xa44f38>) of role type named sy_c_Extended__Real_Oereal_OPInfty
% 0.47/0.65 Using role type
% 0.47/0.65 Declaring extended_PInfty:extended_ereal
% 0.47/0.65 FOF formula (<kernel.Constant object at 0x2b8b6ffc1488>, <kernel.DependentProduct object at 0xa4a638>) of role type named sy_c_Extended__Real_Oereal_Oereal
% 0.47/0.65 Using role type
% 0.47/0.65 Declaring extended_ereal2:(real->extended_ereal)
% 0.47/0.65 FOF formula (<kernel.Constant object at 0x2b8b6ffc1488>, <kernel.DependentProduct object at 0xa4a290>) of role type named sy_c_Extended__Real_Oereal_Osize__ereal
% 0.47/0.65 Using role type
% 0.47/0.65 Declaring extended_size_ereal:(extended_ereal->nat)
% 0.47/0.65 FOF formula (<kernel.Constant object at 0xa44f38>, <kernel.DependentProduct object at 0xa4a5f0>) of role type named sy_c_Extended__Real_Oereal__of__enat
% 0.47/0.65 Using role type
% 0.47/0.65 Declaring extend1771934483f_enat:(extended_enat->extended_ereal)
% 0.47/0.65 FOF formula (<kernel.Constant object at 0xa44fc8>, <kernel.DependentProduct object at 0xa4a6c8>) of role type named sy_c_Extended__Real_Oreal__of__ereal
% 0.47/0.65 Using role type
% 0.47/0.65 Declaring extend1716541707_ereal:(extended_ereal->real)
% 0.47/0.65 FOF formula (<kernel.Constant object at 0xa44d88>, <kernel.DependentProduct object at 0xa4a680>) of role type named sy_c_Groups_Oabs__class_Oabs_001t__Extended____Real__Oereal
% 0.47/0.65 Using role type
% 0.47/0.65 Declaring abs_ab1260901297_ereal:(extended_ereal->extended_ereal)
% 0.47/0.65 FOF formula (<kernel.Constant object at 0xa44fc8>, <kernel.DependentProduct object at 0xa4aab8>) of role type named sy_c_Groups_Ouminus__class_Ouminus_001t__Extended____Real__Oereal
% 0.47/0.65 Using role type
% 0.47/0.65 Declaring uminus1208298309_ereal:(extended_ereal->extended_ereal)
% 0.47/0.65 FOF formula (<kernel.Constant object at 0xa44fc8>, <kernel.DependentProduct object at 0xa4aa70>) of role type named sy_c_Groups_Ouminus__class_Ouminus_001t__Real__Oreal
% 0.47/0.65 Using role type
% 0.47/0.65 Declaring uminus_uminus_real:(real->real)
% 0.47/0.65 FOF formula (<kernel.Constant object at 0xa4a680>, <kernel.Constant object at 0xa4aa70>) of role type named sy_c_Groups_Ozero__class_Ozero_001t__Extended____Nat__Oenat
% 0.47/0.66 Using role type
% 0.47/0.66 Declaring zero_z491942557d_enat:extended_enat
% 0.47/0.66 FOF formula (<kernel.Constant object at 0xa4a5f0>, <kernel.Constant object at 0xa4aa70>) of role type named sy_c_Groups_Ozero__class_Ozero_001t__Extended____Real__Oereal
% 0.47/0.66 Using role type
% 0.47/0.66 Declaring zero_z163181189_ereal:extended_ereal
% 0.47/0.66 FOF formula (<kernel.Constant object at 0xa4a638>, <kernel.Constant object at 0xa4aa70>) of role type named sy_c_Groups_Ozero__class_Ozero_001t__Nat__Onat
% 0.47/0.66 Using role type
% 0.47/0.66 Declaring zero_zero_nat:nat
% 0.47/0.66 FOF formula (<kernel.Constant object at 0xa4a680>, <kernel.Constant object at 0xa4aa70>) of role type named sy_c_Groups_Ozero__class_Ozero_001t__Real__Oreal
% 0.47/0.66 Using role type
% 0.47/0.66 Declaring zero_zero_real:real
% 0.47/0.66 FOF formula (<kernel.Constant object at 0xa4a5f0>, <kernel.DependentProduct object at 0xa4ab00>) of role type named sy_c_Lower__Semicontinuous__Mirabelle__mxyexokbxt_Olsc_001tf__a_001t__Extended____Real__Oereal
% 0.47/0.66 Using role type
% 0.47/0.66 Declaring lower_1616484581_ereal:((a->extended_ereal)->Prop)
% 0.47/0.66 FOF formula (<kernel.Constant object at 0xa4a950>, <kernel.DependentProduct object at 0xa4a680>) of role type named sy_c_Lower__Semicontinuous__Mirabelle__mxyexokbxt_Olsc__hull_001tf__a
% 0.47/0.66 Using role type
% 0.47/0.66 Declaring lower_881475195hull_a:((a->extended_ereal)->(a->extended_ereal))
% 0.47/0.66 FOF formula (<kernel.Constant object at 0xa4a5a8>, <kernel.DependentProduct object at 0xa4a758>) of role type named sy_c_Num_Onumeral__class_Onumeral_001t__Extended____Nat__Oenat
% 0.47/0.66 Using role type
% 0.47/0.66 Declaring numera280919179d_enat:(num->extended_enat)
% 0.47/0.66 FOF formula (<kernel.Constant object at 0xa4a560>, <kernel.DependentProduct object at 0xa4aa70>) of role type named sy_c_Num_Onumeral__class_Onumeral_001t__Extended____Real__Oereal
% 0.47/0.66 Using role type
% 0.47/0.66 Declaring numera1793320307_ereal:(num->extended_ereal)
% 0.47/0.66 FOF formula (<kernel.Constant object at 0xa4a680>, <kernel.DependentProduct object at 0xa4a7e8>) of role type named sy_c_Num_Onumeral__class_Onumeral_001t__Nat__Onat
% 0.47/0.66 Using role type
% 0.47/0.66 Declaring numeral_numeral_nat:(num->nat)
% 0.47/0.66 FOF formula (<kernel.Constant object at 0xa4a758>, <kernel.DependentProduct object at 0xa4a7a0>) of role type named sy_c_Num_Onumeral__class_Onumeral_001t__Real__Oreal
% 0.47/0.66 Using role type
% 0.47/0.66 Declaring numeral_numeral_real:(num->real)
% 0.47/0.66 FOF formula (<kernel.Constant object at 0xa4aa70>, <kernel.DependentProduct object at 0xa4ad40>) of role type named sy_c_Orderings_Oord__class_Oless__eq_001_062_I_Eo_Mt__Extended____Nat__Oenat_J
% 0.47/0.66 Using role type
% 0.47/0.66 Declaring ord_le291126163d_enat:((Prop->extended_enat)->((Prop->extended_enat)->Prop))
% 0.47/0.66 FOF formula (<kernel.Constant object at 0xa4a680>, <kernel.DependentProduct object at 0xa4a488>) of role type named sy_c_Orderings_Oord__class_Oless__eq_001_062_I_Eo_Mt__Extended____Real__Oereal_J
% 0.47/0.66 Using role type
% 0.47/0.66 Declaring ord_le637473275_ereal:((Prop->extended_ereal)->((Prop->extended_ereal)->Prop))
% 0.47/0.66 FOF formula (<kernel.Constant object at 0xa4a758>, <kernel.DependentProduct object at 0xa4a440>) of role type named sy_c_Orderings_Oord__class_Oless__eq_001_062_I_Eo_Mt__Nat__Onat_J
% 0.47/0.66 Using role type
% 0.47/0.66 Declaring ord_less_eq_o_nat:((Prop->nat)->((Prop->nat)->Prop))
% 0.47/0.66 FOF formula (<kernel.Constant object at 0xa4aa70>, <kernel.DependentProduct object at 0xa4ae18>) of role type named sy_c_Orderings_Oord__class_Oless__eq_001_062_I_Eo_Mt__Real__Oreal_J
% 0.47/0.66 Using role type
% 0.47/0.66 Declaring ord_less_eq_o_real:((Prop->real)->((Prop->real)->Prop))
% 0.47/0.66 FOF formula (<kernel.Constant object at 0xa4a680>, <kernel.DependentProduct object at 0xa4a440>) of role type named sy_c_Orderings_Oord__class_Oless__eq_001t__Extended____Nat__Oenat
% 0.47/0.66 Using role type
% 0.47/0.66 Declaring ord_le1863327750d_enat:(extended_enat->(extended_enat->Prop))
% 0.47/0.66 FOF formula (<kernel.Constant object at 0xa4ad40>, <kernel.DependentProduct object at 0xa4a7a0>) of role type named sy_c_Orderings_Oord__class_Oless__eq_001t__Extended____Real__Oereal
% 0.47/0.66 Using role type
% 0.47/0.66 Declaring ord_le824540014_ereal:(extended_ereal->(extended_ereal->Prop))
% 0.47/0.66 FOF formula (<kernel.Constant object at 0xa4ae18>, <kernel.DependentProduct object at 0xa4a758>) of role type named sy_c_Orderings_Oord__class_Oless__eq_001t__Nat__Onat
% 0.47/0.67 Using role type
% 0.47/0.67 Declaring ord_less_eq_nat:(nat->(nat->Prop))
% 0.47/0.67 FOF formula (<kernel.Constant object at 0xa4a440>, <kernel.DependentProduct object at 0xa4aa70>) of role type named sy_c_Orderings_Oord__class_Oless__eq_001t__Num__Onum
% 0.47/0.67 Using role type
% 0.47/0.67 Declaring ord_less_eq_num:(num->(num->Prop))
% 0.47/0.67 FOF formula (<kernel.Constant object at 0xa4a7a0>, <kernel.DependentProduct object at 0xa4a680>) of role type named sy_c_Orderings_Oord__class_Oless__eq_001t__Real__Oreal
% 0.47/0.67 Using role type
% 0.47/0.67 Declaring ord_less_eq_real:(real->(real->Prop))
% 0.47/0.67 FOF formula (<kernel.Constant object at 0xa4a758>, <kernel.DependentProduct object at 0xa4ad88>) of role type named sy_c_Orderings_Oorder__class_OGreatest_001t__Extended____Nat__Oenat
% 0.47/0.67 Using role type
% 0.47/0.67 Declaring order_1628344639d_enat:((extended_enat->Prop)->extended_enat)
% 0.47/0.67 FOF formula (<kernel.Constant object at 0xa4aa70>, <kernel.DependentProduct object at 0xa4a200>) of role type named sy_c_Orderings_Oorder__class_OGreatest_001t__Extended____Real__Oereal
% 0.47/0.67 Using role type
% 0.47/0.67 Declaring order_1158471719_ereal:((extended_ereal->Prop)->extended_ereal)
% 0.47/0.67 FOF formula (<kernel.Constant object at 0xa4a4d0>, <kernel.DependentProduct object at 0xa4a0e0>) of role type named sy_c_Orderings_Oorder__class_OGreatest_001t__Nat__Onat
% 0.47/0.67 Using role type
% 0.47/0.67 Declaring order_Greatest_nat:((nat->Prop)->nat)
% 0.47/0.67 FOF formula (<kernel.Constant object at 0xa4ad40>, <kernel.DependentProduct object at 0xa4ac20>) of role type named sy_c_Orderings_Oorder__class_OGreatest_001t__Real__Oreal
% 0.47/0.67 Using role type
% 0.47/0.67 Declaring order_Greatest_real:((real->Prop)->real)
% 0.47/0.67 FOF formula (<kernel.Constant object at 0xa4a440>, <kernel.DependentProduct object at 0xa4a758>) of role type named sy_c_Orderings_Oorder__class_Oantimono_001t__Extended____Nat__Oenat_001t__Extended____Nat__Oenat
% 0.47/0.67 Using role type
% 0.47/0.67 Declaring order_2047034162d_enat:((extended_enat->extended_enat)->Prop)
% 0.47/0.67 FOF formula (<kernel.Constant object at 0xa4a7a0>, <kernel.DependentProduct object at 0xa4aa70>) of role type named sy_c_Orderings_Oorder__class_Oantimono_001t__Extended____Nat__Oenat_001t__Extended____Real__Oereal
% 0.47/0.67 Using role type
% 0.47/0.67 Declaring order_1147259034_ereal:((extended_enat->extended_ereal)->Prop)
% 0.47/0.67 FOF formula (<kernel.Constant object at 0xa4af38>, <kernel.DependentProduct object at 0xa4a4d0>) of role type named sy_c_Orderings_Oorder__class_Oantimono_001t__Extended____Nat__Oenat_001t__Nat__Onat
% 0.47/0.67 Using role type
% 0.47/0.67 Declaring order_442688004at_nat:((extended_enat->nat)->Prop)
% 0.47/0.67 FOF formula (<kernel.Constant object at 0xa4ab90>, <kernel.DependentProduct object at 0xa4ad40>) of role type named sy_c_Orderings_Oorder__class_Oantimono_001t__Extended____Nat__Oenat_001t__Real__Oreal
% 0.47/0.67 Using role type
% 0.47/0.67 Declaring order_182315744t_real:((extended_enat->real)->Prop)
% 0.47/0.67 FOF formula (<kernel.Constant object at 0xa4acf8>, <kernel.DependentProduct object at 0xa4a440>) of role type named sy_c_Orderings_Oorder__class_Oantimono_001t__Extended____Real__Oereal_001t__Extended____Nat__Oenat
% 0.47/0.67 Using role type
% 0.47/0.67 Declaring order_680161354d_enat:((extended_ereal->extended_enat)->Prop)
% 0.47/0.67 FOF formula (<kernel.Constant object at 0xa4a878>, <kernel.DependentProduct object at 0xa4a7a0>) of role type named sy_c_Orderings_Oorder__class_Oantimono_001t__Extended____Real__Oereal_001t__Extended____Real__Oereal
% 0.47/0.67 Using role type
% 0.47/0.67 Declaring order_1408494002_ereal:((extended_ereal->extended_ereal)->Prop)
% 0.47/0.67 FOF formula (<kernel.Constant object at 0xa4a368>, <kernel.DependentProduct object at 0xa4af38>) of role type named sy_c_Orderings_Oorder__class_Oantimono_001t__Extended____Real__Oereal_001t__Nat__Onat
% 0.47/0.67 Using role type
% 0.47/0.67 Declaring order_523806444al_nat:((extended_ereal->nat)->Prop)
% 0.47/0.67 FOF formula (<kernel.Constant object at 0xa4a320>, <kernel.DependentProduct object at 0xa4ab90>) of role type named sy_c_Orderings_Oorder__class_Oantimono_001t__Extended____Real__Oereal_001t__Real__Oreal
% 0.47/0.67 Using role type
% 0.47/0.67 Declaring order_1800387528l_real:((extended_ereal->real)->Prop)
% 0.47/0.67 FOF formula (<kernel.Constant object at 0xa4abd8>, <kernel.DependentProduct object at 0xa4acf8>) of role type named sy_c_Orderings_Oorder__class_Oantimono_001t__Nat__Onat_001t__Extended____Nat__Oenat
% 0.47/0.68 Using role type
% 0.47/0.68 Declaring order_1660553314d_enat:((nat->extended_enat)->Prop)
% 0.47/0.68 FOF formula (<kernel.Constant object at 0xa4a3b0>, <kernel.DependentProduct object at 0xa4a878>) of role type named sy_c_Orderings_Oorder__class_Oantimono_001t__Nat__Onat_001t__Extended____Real__Oereal
% 0.47/0.68 Using role type
% 0.47/0.68 Declaring order_736687562_ereal:((nat->extended_ereal)->Prop)
% 0.47/0.68 FOF formula (<kernel.Constant object at 0xa4a248>, <kernel.DependentProduct object at 0xa4a368>) of role type named sy_c_Orderings_Oorder__class_Oantimono_001t__Nat__Onat_001t__Nat__Onat
% 0.47/0.68 Using role type
% 0.47/0.68 Declaring order_1631207636at_nat:((nat->nat)->Prop)
% 0.47/0.68 FOF formula (<kernel.Constant object at 0xa4a908>, <kernel.DependentProduct object at 0xa4a320>) of role type named sy_c_Orderings_Oorder__class_Oantimono_001t__Nat__Onat_001t__Real__Oreal
% 0.47/0.68 Using role type
% 0.47/0.68 Declaring order_106095024t_real:((nat->real)->Prop)
% 0.47/0.68 FOF formula (<kernel.Constant object at 0x2b8b6ffc3098>, <kernel.DependentProduct object at 0xa4abd8>) of role type named sy_c_Orderings_Oorder__class_Ostrict__mono_001t__Extended____Nat__Oenat_001t__Extended____Nat__Oenat
% 0.47/0.68 Using role type
% 0.47/0.68 Declaring order_2106278841d_enat:((extended_enat->extended_enat)->Prop)
% 0.47/0.68 FOF formula (<kernel.Constant object at 0xa4a8c0>, <kernel.DependentProduct object at 0xa4afc8>) of role type named sy_c_Orderings_Oorder__class_Ostrict__mono_001t__Extended____Nat__Oenat_001t__Extended____Real__Oereal
% 0.47/0.68 Using role type
% 0.47/0.68 Declaring order_1180956065_ereal:((extended_enat->extended_ereal)->Prop)
% 0.47/0.68 FOF formula (<kernel.Constant object at 0xa4a320>, <kernel.DependentProduct object at 0xa4df38>) of role type named sy_c_Orderings_Oorder__class_Ostrict__mono_001t__Extended____Nat__Oenat_001t__Nat__Onat
% 0.47/0.68 Using role type
% 0.47/0.68 Declaring order_1622825661at_nat:((extended_enat->nat)->Prop)
% 0.47/0.68 FOF formula (<kernel.Constant object at 0xa4abd8>, <kernel.DependentProduct object at 0xa4df38>) of role type named sy_c_Orderings_Oorder__class_Ostrict__mono_001t__Extended____Nat__Oenat_001t__Real__Oreal
% 0.47/0.68 Using role type
% 0.47/0.68 Declaring order_135436057t_real:((extended_enat->real)->Prop)
% 0.47/0.68 FOF formula (<kernel.Constant object at 0xa4a8c0>, <kernel.DependentProduct object at 0xa4d4d0>) of role type named sy_c_Orderings_Oorder__class_Ostrict__mono_001t__Extended____Real__Oereal_001t__Extended____Nat__Oenat
% 0.47/0.68 Using role type
% 0.47/0.68 Declaring order_713858385d_enat:((extended_ereal->extended_enat)->Prop)
% 0.47/0.68 FOF formula (<kernel.Constant object at 0xa4a320>, <kernel.DependentProduct object at 0xa4def0>) of role type named sy_c_Orderings_Oorder__class_Ostrict__mono_001t__Extended____Real__Oereal_001t__Extended____Real__Oereal
% 0.47/0.68 Using role type
% 0.47/0.68 Declaring order_555877177_ereal:((extended_ereal->extended_ereal)->Prop)
% 0.47/0.68 FOF formula (<kernel.Constant object at 0xa4a8c0>, <kernel.DependentProduct object at 0xa4d4d0>) of role type named sy_c_Orderings_Oorder__class_Ostrict__mono_001t__Extended____Real__Oereal_001t__Nat__Onat
% 0.47/0.68 Using role type
% 0.47/0.68 Declaring order_476926757al_nat:((extended_ereal->nat)->Prop)
% 0.47/0.68 FOF formula (<kernel.Constant object at 0xa4abd8>, <kernel.DependentProduct object at 0xa4d3f8>) of role type named sy_c_Orderings_Oorder__class_Ostrict__mono_001t__Extended____Real__Oereal_001t__Real__Oreal
% 0.47/0.68 Using role type
% 0.47/0.68 Declaring order_1560271745l_real:((extended_ereal->real)->Prop)
% 0.47/0.68 FOF formula (<kernel.Constant object at 0xa4a8c0>, <kernel.DependentProduct object at 0xa4db00>) of role type named sy_c_Orderings_Oorder__class_Ostrict__mono_001t__Nat__Onat_001t__Extended____Nat__Oenat
% 0.47/0.68 Using role type
% 0.47/0.68 Declaring order_693207323d_enat:((nat->extended_enat)->Prop)
% 0.47/0.68 FOF formula (<kernel.Constant object at 0xa4a8c0>, <kernel.DependentProduct object at 0xa4d950>) of role type named sy_c_Orderings_Oorder__class_Ostrict__mono_001t__Nat__Onat_001t__Extended____Real__Oereal
% 0.47/0.68 Using role type
% 0.47/0.68 Declaring order_689807875_ereal:((nat->extended_ereal)->Prop)
% 0.47/0.68 FOF formula (<kernel.Constant object at 0xa4d200>, <kernel.DependentProduct object at 0xa4d5f0>) of role type named sy_c_Orderings_Oorder__class_Ostrict__mono_001t__Nat__Onat_001t__Nat__Onat
% 0.47/0.68 Using role type
% 0.47/0.68 Declaring order_769474267at_nat:((nat->nat)->Prop)
% 0.47/0.69 FOF formula (<kernel.Constant object at 0xa4d560>, <kernel.DependentProduct object at 0xa4d440>) of role type named sy_c_Orderings_Oorder__class_Ostrict__mono_001t__Real__Oreal_001t__Extended____Nat__Oenat
% 0.47/0.69 Using role type
% 0.47/0.69 Declaring order_1962034751d_enat:((real->extended_enat)->Prop)
% 0.47/0.69 FOF formula (<kernel.Constant object at 0xa4d320>, <kernel.DependentProduct object at 0xa4def0>) of role type named sy_c_Orderings_Oorder__class_Ostrict__mono_001t__Real__Oreal_001t__Extended____Real__Oereal
% 0.47/0.69 Using role type
% 0.47/0.69 Declaring order_946214183_ereal:((real->extended_ereal)->Prop)
% 0.47/0.69 FOF formula (<kernel.Constant object at 0xa4db90>, <kernel.DependentProduct object at 0xa4d200>) of role type named sy_c_Rings_Odivide__class_Odivide_001t__Extended____Real__Oereal
% 0.47/0.69 Using role type
% 0.47/0.69 Declaring divide595620860_ereal:(extended_ereal->(extended_ereal->extended_ereal))
% 0.47/0.69 FOF formula (<kernel.Constant object at 0xa4d050>, <kernel.DependentProduct object at 0xa4da28>) of role type named sy_c_member_001t__Extended____Real__Oereal
% 0.47/0.69 Using role type
% 0.47/0.69 Declaring member1900190071_ereal:(extended_ereal->(set_Extended_ereal->Prop))
% 0.47/0.69 FOF formula (<kernel.Constant object at 0xa4df38>, <kernel.DependentProduct object at 0xa4d6c8>) of role type named sy_v_f
% 0.47/0.69 Using role type
% 0.47/0.69 Declaring f:(a->extended_ereal)
% 0.47/0.69 FOF formula (<kernel.Constant object at 0xa4d200>, <kernel.DependentProduct object at 0xa4d170>) of role type named sy_v_g
% 0.47/0.69 Using role type
% 0.47/0.69 Declaring g:(a->extended_ereal)
% 0.47/0.69 FOF formula (<kernel.Constant object at 0xa4da28>, <kernel.Constant object at 0xa4d170>) of role type named sy_v_x____
% 0.47/0.69 Using role type
% 0.47/0.69 Declaring x:a
% 0.47/0.69 FOF formula (forall (X:a), ((ord_le824540014_ereal (g X)) (f X))) of role axiom named fact_0_assms
% 0.47/0.69 A new axiom: (forall (X:a), ((ord_le824540014_ereal (g X)) (f X)))
% 0.47/0.69 FOF formula ((ord_le824540014_ereal ((lower_881475195hull_a g) x)) (g x)) of role axiom named fact_1_calculation
% 0.47/0.69 A new axiom: ((ord_le824540014_ereal ((lower_881475195hull_a g) x)) (g x))
% 0.47/0.69 FOF formula (forall (X2:extended_ereal), ((ord_le824540014_ereal X2) X2)) of role axiom named fact_2_order__refl
% 0.47/0.69 A new axiom: (forall (X2:extended_ereal), ((ord_le824540014_ereal X2) X2))
% 0.47/0.69 FOF formula (forall (X2:extended_enat), ((ord_le1863327750d_enat X2) X2)) of role axiom named fact_3_order__refl
% 0.47/0.69 A new axiom: (forall (X2:extended_enat), ((ord_le1863327750d_enat X2) X2))
% 0.47/0.69 FOF formula (forall (X2:nat), ((ord_less_eq_nat X2) X2)) of role axiom named fact_4_order__refl
% 0.47/0.69 A new axiom: (forall (X2:nat), ((ord_less_eq_nat X2) X2))
% 0.47/0.69 FOF formula (forall (X2:real), ((ord_less_eq_real X2) X2)) of role axiom named fact_5_order__refl
% 0.47/0.69 A new axiom: (forall (X2:real), ((ord_less_eq_real X2) X2))
% 0.47/0.69 FOF formula (forall (S:set_Extended_ereal), ((ex extended_ereal) (fun (X3:extended_ereal)=> ((and (forall (Xa:extended_ereal), (((member1900190071_ereal Xa) S)->((ord_le824540014_ereal X3) Xa)))) (forall (Z:extended_ereal), ((forall (Xa2:extended_ereal), (((member1900190071_ereal Xa2) S)->((ord_le824540014_ereal Z) Xa2)))->((ord_le824540014_ereal Z) X3))))))) of role axiom named fact_6_ereal__complete__Inf
% 0.47/0.69 A new axiom: (forall (S:set_Extended_ereal), ((ex extended_ereal) (fun (X3:extended_ereal)=> ((and (forall (Xa:extended_ereal), (((member1900190071_ereal Xa) S)->((ord_le824540014_ereal X3) Xa)))) (forall (Z:extended_ereal), ((forall (Xa2:extended_ereal), (((member1900190071_ereal Xa2) S)->((ord_le824540014_ereal Z) Xa2)))->((ord_le824540014_ereal Z) X3)))))))
% 0.47/0.69 FOF formula (forall (S:set_Extended_ereal), ((ex extended_ereal) (fun (X3:extended_ereal)=> ((and (forall (Xa:extended_ereal), (((member1900190071_ereal Xa) S)->((ord_le824540014_ereal Xa) X3)))) (forall (Z:extended_ereal), ((forall (Xa2:extended_ereal), (((member1900190071_ereal Xa2) S)->((ord_le824540014_ereal Xa2) Z)))->((ord_le824540014_ereal X3) Z))))))) of role axiom named fact_7_ereal__complete__Sup
% 0.47/0.69 A new axiom: (forall (S:set_Extended_ereal), ((ex extended_ereal) (fun (X3:extended_ereal)=> ((and (forall (Xa:extended_ereal), (((member1900190071_ereal Xa) S)->((ord_le824540014_ereal Xa) X3)))) (forall (Z:extended_ereal), ((forall (Xa2:extended_ereal), (((member1900190071_ereal Xa2) S)->((ord_le824540014_ereal Xa2) Z)))->((ord_le824540014_ereal X3) Z)))))))
% 0.55/0.71 FOF formula (forall (A:extended_ereal) (F:(extended_ereal->extended_ereal)) (B:extended_ereal) (C:extended_ereal), (((ord_le824540014_ereal A) (F B))->(((ord_le824540014_ereal B) C)->((forall (X3:extended_ereal) (Y:extended_ereal), (((ord_le824540014_ereal X3) Y)->((ord_le824540014_ereal (F X3)) (F Y))))->((ord_le824540014_ereal A) (F C)))))) of role axiom named fact_8_order__subst1
% 0.55/0.71 A new axiom: (forall (A:extended_ereal) (F:(extended_ereal->extended_ereal)) (B:extended_ereal) (C:extended_ereal), (((ord_le824540014_ereal A) (F B))->(((ord_le824540014_ereal B) C)->((forall (X3:extended_ereal) (Y:extended_ereal), (((ord_le824540014_ereal X3) Y)->((ord_le824540014_ereal (F X3)) (F Y))))->((ord_le824540014_ereal A) (F C))))))
% 0.55/0.71 FOF formula (forall (A:extended_ereal) (F:(extended_enat->extended_ereal)) (B:extended_enat) (C:extended_enat), (((ord_le824540014_ereal A) (F B))->(((ord_le1863327750d_enat B) C)->((forall (X3:extended_enat) (Y:extended_enat), (((ord_le1863327750d_enat X3) Y)->((ord_le824540014_ereal (F X3)) (F Y))))->((ord_le824540014_ereal A) (F C)))))) of role axiom named fact_9_order__subst1
% 0.55/0.71 A new axiom: (forall (A:extended_ereal) (F:(extended_enat->extended_ereal)) (B:extended_enat) (C:extended_enat), (((ord_le824540014_ereal A) (F B))->(((ord_le1863327750d_enat B) C)->((forall (X3:extended_enat) (Y:extended_enat), (((ord_le1863327750d_enat X3) Y)->((ord_le824540014_ereal (F X3)) (F Y))))->((ord_le824540014_ereal A) (F C))))))
% 0.55/0.71 FOF formula (forall (A:extended_ereal) (F:(nat->extended_ereal)) (B:nat) (C:nat), (((ord_le824540014_ereal A) (F B))->(((ord_less_eq_nat B) C)->((forall (X3:nat) (Y:nat), (((ord_less_eq_nat X3) Y)->((ord_le824540014_ereal (F X3)) (F Y))))->((ord_le824540014_ereal A) (F C)))))) of role axiom named fact_10_order__subst1
% 0.55/0.71 A new axiom: (forall (A:extended_ereal) (F:(nat->extended_ereal)) (B:nat) (C:nat), (((ord_le824540014_ereal A) (F B))->(((ord_less_eq_nat B) C)->((forall (X3:nat) (Y:nat), (((ord_less_eq_nat X3) Y)->((ord_le824540014_ereal (F X3)) (F Y))))->((ord_le824540014_ereal A) (F C))))))
% 0.55/0.71 FOF formula (forall (A:extended_ereal) (F:(real->extended_ereal)) (B:real) (C:real), (((ord_le824540014_ereal A) (F B))->(((ord_less_eq_real B) C)->((forall (X3:real) (Y:real), (((ord_less_eq_real X3) Y)->((ord_le824540014_ereal (F X3)) (F Y))))->((ord_le824540014_ereal A) (F C)))))) of role axiom named fact_11_order__subst1
% 0.55/0.71 A new axiom: (forall (A:extended_ereal) (F:(real->extended_ereal)) (B:real) (C:real), (((ord_le824540014_ereal A) (F B))->(((ord_less_eq_real B) C)->((forall (X3:real) (Y:real), (((ord_less_eq_real X3) Y)->((ord_le824540014_ereal (F X3)) (F Y))))->((ord_le824540014_ereal A) (F C))))))
% 0.55/0.71 FOF formula (forall (A:extended_enat) (F:(extended_ereal->extended_enat)) (B:extended_ereal) (C:extended_ereal), (((ord_le1863327750d_enat A) (F B))->(((ord_le824540014_ereal B) C)->((forall (X3:extended_ereal) (Y:extended_ereal), (((ord_le824540014_ereal X3) Y)->((ord_le1863327750d_enat (F X3)) (F Y))))->((ord_le1863327750d_enat A) (F C)))))) of role axiom named fact_12_order__subst1
% 0.55/0.71 A new axiom: (forall (A:extended_enat) (F:(extended_ereal->extended_enat)) (B:extended_ereal) (C:extended_ereal), (((ord_le1863327750d_enat A) (F B))->(((ord_le824540014_ereal B) C)->((forall (X3:extended_ereal) (Y:extended_ereal), (((ord_le824540014_ereal X3) Y)->((ord_le1863327750d_enat (F X3)) (F Y))))->((ord_le1863327750d_enat A) (F C))))))
% 0.55/0.71 FOF formula (forall (A:extended_enat) (F:(extended_enat->extended_enat)) (B:extended_enat) (C:extended_enat), (((ord_le1863327750d_enat A) (F B))->(((ord_le1863327750d_enat B) C)->((forall (X3:extended_enat) (Y:extended_enat), (((ord_le1863327750d_enat X3) Y)->((ord_le1863327750d_enat (F X3)) (F Y))))->((ord_le1863327750d_enat A) (F C)))))) of role axiom named fact_13_order__subst1
% 0.55/0.71 A new axiom: (forall (A:extended_enat) (F:(extended_enat->extended_enat)) (B:extended_enat) (C:extended_enat), (((ord_le1863327750d_enat A) (F B))->(((ord_le1863327750d_enat B) C)->((forall (X3:extended_enat) (Y:extended_enat), (((ord_le1863327750d_enat X3) Y)->((ord_le1863327750d_enat (F X3)) (F Y))))->((ord_le1863327750d_enat A) (F C))))))
% 0.55/0.73 FOF formula (forall (A:extended_enat) (F:(nat->extended_enat)) (B:nat) (C:nat), (((ord_le1863327750d_enat A) (F B))->(((ord_less_eq_nat B) C)->((forall (X3:nat) (Y:nat), (((ord_less_eq_nat X3) Y)->((ord_le1863327750d_enat (F X3)) (F Y))))->((ord_le1863327750d_enat A) (F C)))))) of role axiom named fact_14_order__subst1
% 0.55/0.73 A new axiom: (forall (A:extended_enat) (F:(nat->extended_enat)) (B:nat) (C:nat), (((ord_le1863327750d_enat A) (F B))->(((ord_less_eq_nat B) C)->((forall (X3:nat) (Y:nat), (((ord_less_eq_nat X3) Y)->((ord_le1863327750d_enat (F X3)) (F Y))))->((ord_le1863327750d_enat A) (F C))))))
% 0.55/0.73 FOF formula (forall (A:extended_enat) (F:(real->extended_enat)) (B:real) (C:real), (((ord_le1863327750d_enat A) (F B))->(((ord_less_eq_real B) C)->((forall (X3:real) (Y:real), (((ord_less_eq_real X3) Y)->((ord_le1863327750d_enat (F X3)) (F Y))))->((ord_le1863327750d_enat A) (F C)))))) of role axiom named fact_15_order__subst1
% 0.55/0.73 A new axiom: (forall (A:extended_enat) (F:(real->extended_enat)) (B:real) (C:real), (((ord_le1863327750d_enat A) (F B))->(((ord_less_eq_real B) C)->((forall (X3:real) (Y:real), (((ord_less_eq_real X3) Y)->((ord_le1863327750d_enat (F X3)) (F Y))))->((ord_le1863327750d_enat A) (F C))))))
% 0.55/0.73 FOF formula (forall (A:nat) (F:(extended_ereal->nat)) (B:extended_ereal) (C:extended_ereal), (((ord_less_eq_nat A) (F B))->(((ord_le824540014_ereal B) C)->((forall (X3:extended_ereal) (Y:extended_ereal), (((ord_le824540014_ereal X3) Y)->((ord_less_eq_nat (F X3)) (F Y))))->((ord_less_eq_nat A) (F C)))))) of role axiom named fact_16_order__subst1
% 0.55/0.73 A new axiom: (forall (A:nat) (F:(extended_ereal->nat)) (B:extended_ereal) (C:extended_ereal), (((ord_less_eq_nat A) (F B))->(((ord_le824540014_ereal B) C)->((forall (X3:extended_ereal) (Y:extended_ereal), (((ord_le824540014_ereal X3) Y)->((ord_less_eq_nat (F X3)) (F Y))))->((ord_less_eq_nat A) (F C))))))
% 0.55/0.73 FOF formula (forall (A:nat) (F:(extended_enat->nat)) (B:extended_enat) (C:extended_enat), (((ord_less_eq_nat A) (F B))->(((ord_le1863327750d_enat B) C)->((forall (X3:extended_enat) (Y:extended_enat), (((ord_le1863327750d_enat X3) Y)->((ord_less_eq_nat (F X3)) (F Y))))->((ord_less_eq_nat A) (F C)))))) of role axiom named fact_17_order__subst1
% 0.55/0.73 A new axiom: (forall (A:nat) (F:(extended_enat->nat)) (B:extended_enat) (C:extended_enat), (((ord_less_eq_nat A) (F B))->(((ord_le1863327750d_enat B) C)->((forall (X3:extended_enat) (Y:extended_enat), (((ord_le1863327750d_enat X3) Y)->((ord_less_eq_nat (F X3)) (F Y))))->((ord_less_eq_nat A) (F C))))))
% 0.55/0.73 FOF formula (forall (A:extended_ereal) (B:extended_ereal) (F:(extended_ereal->extended_ereal)) (C:extended_ereal), (((ord_le824540014_ereal A) B)->(((ord_le824540014_ereal (F B)) C)->((forall (X3:extended_ereal) (Y:extended_ereal), (((ord_le824540014_ereal X3) Y)->((ord_le824540014_ereal (F X3)) (F Y))))->((ord_le824540014_ereal (F A)) C))))) of role axiom named fact_18_order__subst2
% 0.55/0.73 A new axiom: (forall (A:extended_ereal) (B:extended_ereal) (F:(extended_ereal->extended_ereal)) (C:extended_ereal), (((ord_le824540014_ereal A) B)->(((ord_le824540014_ereal (F B)) C)->((forall (X3:extended_ereal) (Y:extended_ereal), (((ord_le824540014_ereal X3) Y)->((ord_le824540014_ereal (F X3)) (F Y))))->((ord_le824540014_ereal (F A)) C)))))
% 0.55/0.73 FOF formula (forall (A:extended_ereal) (B:extended_ereal) (F:(extended_ereal->extended_enat)) (C:extended_enat), (((ord_le824540014_ereal A) B)->(((ord_le1863327750d_enat (F B)) C)->((forall (X3:extended_ereal) (Y:extended_ereal), (((ord_le824540014_ereal X3) Y)->((ord_le1863327750d_enat (F X3)) (F Y))))->((ord_le1863327750d_enat (F A)) C))))) of role axiom named fact_19_order__subst2
% 0.55/0.73 A new axiom: (forall (A:extended_ereal) (B:extended_ereal) (F:(extended_ereal->extended_enat)) (C:extended_enat), (((ord_le824540014_ereal A) B)->(((ord_le1863327750d_enat (F B)) C)->((forall (X3:extended_ereal) (Y:extended_ereal), (((ord_le824540014_ereal X3) Y)->((ord_le1863327750d_enat (F X3)) (F Y))))->((ord_le1863327750d_enat (F A)) C)))))
% 0.55/0.74 FOF formula (forall (A:extended_ereal) (B:extended_ereal) (F:(extended_ereal->nat)) (C:nat), (((ord_le824540014_ereal A) B)->(((ord_less_eq_nat (F B)) C)->((forall (X3:extended_ereal) (Y:extended_ereal), (((ord_le824540014_ereal X3) Y)->((ord_less_eq_nat (F X3)) (F Y))))->((ord_less_eq_nat (F A)) C))))) of role axiom named fact_20_order__subst2
% 0.55/0.74 A new axiom: (forall (A:extended_ereal) (B:extended_ereal) (F:(extended_ereal->nat)) (C:nat), (((ord_le824540014_ereal A) B)->(((ord_less_eq_nat (F B)) C)->((forall (X3:extended_ereal) (Y:extended_ereal), (((ord_le824540014_ereal X3) Y)->((ord_less_eq_nat (F X3)) (F Y))))->((ord_less_eq_nat (F A)) C)))))
% 0.55/0.74 FOF formula (forall (A:extended_ereal) (B:extended_ereal) (F:(extended_ereal->real)) (C:real), (((ord_le824540014_ereal A) B)->(((ord_less_eq_real (F B)) C)->((forall (X3:extended_ereal) (Y:extended_ereal), (((ord_le824540014_ereal X3) Y)->((ord_less_eq_real (F X3)) (F Y))))->((ord_less_eq_real (F A)) C))))) of role axiom named fact_21_order__subst2
% 0.55/0.74 A new axiom: (forall (A:extended_ereal) (B:extended_ereal) (F:(extended_ereal->real)) (C:real), (((ord_le824540014_ereal A) B)->(((ord_less_eq_real (F B)) C)->((forall (X3:extended_ereal) (Y:extended_ereal), (((ord_le824540014_ereal X3) Y)->((ord_less_eq_real (F X3)) (F Y))))->((ord_less_eq_real (F A)) C)))))
% 0.55/0.74 FOF formula (forall (A:extended_enat) (B:extended_enat) (F:(extended_enat->extended_ereal)) (C:extended_ereal), (((ord_le1863327750d_enat A) B)->(((ord_le824540014_ereal (F B)) C)->((forall (X3:extended_enat) (Y:extended_enat), (((ord_le1863327750d_enat X3) Y)->((ord_le824540014_ereal (F X3)) (F Y))))->((ord_le824540014_ereal (F A)) C))))) of role axiom named fact_22_order__subst2
% 0.55/0.74 A new axiom: (forall (A:extended_enat) (B:extended_enat) (F:(extended_enat->extended_ereal)) (C:extended_ereal), (((ord_le1863327750d_enat A) B)->(((ord_le824540014_ereal (F B)) C)->((forall (X3:extended_enat) (Y:extended_enat), (((ord_le1863327750d_enat X3) Y)->((ord_le824540014_ereal (F X3)) (F Y))))->((ord_le824540014_ereal (F A)) C)))))
% 0.55/0.74 FOF formula (forall (A:extended_enat) (B:extended_enat) (F:(extended_enat->extended_enat)) (C:extended_enat), (((ord_le1863327750d_enat A) B)->(((ord_le1863327750d_enat (F B)) C)->((forall (X3:extended_enat) (Y:extended_enat), (((ord_le1863327750d_enat X3) Y)->((ord_le1863327750d_enat (F X3)) (F Y))))->((ord_le1863327750d_enat (F A)) C))))) of role axiom named fact_23_order__subst2
% 0.55/0.74 A new axiom: (forall (A:extended_enat) (B:extended_enat) (F:(extended_enat->extended_enat)) (C:extended_enat), (((ord_le1863327750d_enat A) B)->(((ord_le1863327750d_enat (F B)) C)->((forall (X3:extended_enat) (Y:extended_enat), (((ord_le1863327750d_enat X3) Y)->((ord_le1863327750d_enat (F X3)) (F Y))))->((ord_le1863327750d_enat (F A)) C)))))
% 0.55/0.74 FOF formula (forall (A:extended_enat) (B:extended_enat) (F:(extended_enat->nat)) (C:nat), (((ord_le1863327750d_enat A) B)->(((ord_less_eq_nat (F B)) C)->((forall (X3:extended_enat) (Y:extended_enat), (((ord_le1863327750d_enat X3) Y)->((ord_less_eq_nat (F X3)) (F Y))))->((ord_less_eq_nat (F A)) C))))) of role axiom named fact_24_order__subst2
% 0.55/0.74 A new axiom: (forall (A:extended_enat) (B:extended_enat) (F:(extended_enat->nat)) (C:nat), (((ord_le1863327750d_enat A) B)->(((ord_less_eq_nat (F B)) C)->((forall (X3:extended_enat) (Y:extended_enat), (((ord_le1863327750d_enat X3) Y)->((ord_less_eq_nat (F X3)) (F Y))))->((ord_less_eq_nat (F A)) C)))))
% 0.55/0.74 FOF formula (forall (A:extended_enat) (B:extended_enat) (F:(extended_enat->real)) (C:real), (((ord_le1863327750d_enat A) B)->(((ord_less_eq_real (F B)) C)->((forall (X3:extended_enat) (Y:extended_enat), (((ord_le1863327750d_enat X3) Y)->((ord_less_eq_real (F X3)) (F Y))))->((ord_less_eq_real (F A)) C))))) of role axiom named fact_25_order__subst2
% 0.55/0.74 A new axiom: (forall (A:extended_enat) (B:extended_enat) (F:(extended_enat->real)) (C:real), (((ord_le1863327750d_enat A) B)->(((ord_less_eq_real (F B)) C)->((forall (X3:extended_enat) (Y:extended_enat), (((ord_le1863327750d_enat X3) Y)->((ord_less_eq_real (F X3)) (F Y))))->((ord_less_eq_real (F A)) C)))))
% 0.55/0.76 FOF formula (forall (A:nat) (B:nat) (F:(nat->extended_ereal)) (C:extended_ereal), (((ord_less_eq_nat A) B)->(((ord_le824540014_ereal (F B)) C)->((forall (X3:nat) (Y:nat), (((ord_less_eq_nat X3) Y)->((ord_le824540014_ereal (F X3)) (F Y))))->((ord_le824540014_ereal (F A)) C))))) of role axiom named fact_26_order__subst2
% 0.55/0.76 A new axiom: (forall (A:nat) (B:nat) (F:(nat->extended_ereal)) (C:extended_ereal), (((ord_less_eq_nat A) B)->(((ord_le824540014_ereal (F B)) C)->((forall (X3:nat) (Y:nat), (((ord_less_eq_nat X3) Y)->((ord_le824540014_ereal (F X3)) (F Y))))->((ord_le824540014_ereal (F A)) C)))))
% 0.55/0.76 FOF formula (forall (A:nat) (B:nat) (F:(nat->extended_enat)) (C:extended_enat), (((ord_less_eq_nat A) B)->(((ord_le1863327750d_enat (F B)) C)->((forall (X3:nat) (Y:nat), (((ord_less_eq_nat X3) Y)->((ord_le1863327750d_enat (F X3)) (F Y))))->((ord_le1863327750d_enat (F A)) C))))) of role axiom named fact_27_order__subst2
% 0.55/0.76 A new axiom: (forall (A:nat) (B:nat) (F:(nat->extended_enat)) (C:extended_enat), (((ord_less_eq_nat A) B)->(((ord_le1863327750d_enat (F B)) C)->((forall (X3:nat) (Y:nat), (((ord_less_eq_nat X3) Y)->((ord_le1863327750d_enat (F X3)) (F Y))))->((ord_le1863327750d_enat (F A)) C)))))
% 0.55/0.76 FOF formula (forall (A:extended_ereal) (B:extended_ereal), ((or ((or (((eq extended_ereal) A) B)) (((ord_le824540014_ereal A) B)->False))) (((ord_le824540014_ereal B) A)->False))) of role axiom named fact_28_verit__la__disequality
% 0.55/0.76 A new axiom: (forall (A:extended_ereal) (B:extended_ereal), ((or ((or (((eq extended_ereal) A) B)) (((ord_le824540014_ereal A) B)->False))) (((ord_le824540014_ereal B) A)->False)))
% 0.55/0.76 FOF formula (forall (A:extended_enat) (B:extended_enat), ((or ((or (((eq extended_enat) A) B)) (((ord_le1863327750d_enat A) B)->False))) (((ord_le1863327750d_enat B) A)->False))) of role axiom named fact_29_verit__la__disequality
% 0.55/0.76 A new axiom: (forall (A:extended_enat) (B:extended_enat), ((or ((or (((eq extended_enat) A) B)) (((ord_le1863327750d_enat A) B)->False))) (((ord_le1863327750d_enat B) A)->False)))
% 0.55/0.76 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_30_verit__la__disequality
% 0.55/0.76 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)))
% 0.55/0.76 FOF formula (forall (A:real) (B:real), ((or ((or (((eq real) A) B)) (((ord_less_eq_real A) B)->False))) (((ord_less_eq_real B) A)->False))) of role axiom named fact_31_verit__la__disequality
% 0.55/0.76 A new axiom: (forall (A:real) (B:real), ((or ((or (((eq real) A) B)) (((ord_less_eq_real A) B)->False))) (((ord_less_eq_real B) A)->False)))
% 0.55/0.76 FOF formula (forall (A:extended_ereal) (F:(extended_ereal->extended_ereal)) (B:extended_ereal) (C:extended_ereal), ((((eq extended_ereal) A) (F B))->(((ord_le824540014_ereal B) C)->((forall (X3:extended_ereal) (Y:extended_ereal), (((ord_le824540014_ereal X3) Y)->((ord_le824540014_ereal (F X3)) (F Y))))->((ord_le824540014_ereal A) (F C)))))) of role axiom named fact_32_ord__eq__le__subst
% 0.55/0.76 A new axiom: (forall (A:extended_ereal) (F:(extended_ereal->extended_ereal)) (B:extended_ereal) (C:extended_ereal), ((((eq extended_ereal) A) (F B))->(((ord_le824540014_ereal B) C)->((forall (X3:extended_ereal) (Y:extended_ereal), (((ord_le824540014_ereal X3) Y)->((ord_le824540014_ereal (F X3)) (F Y))))->((ord_le824540014_ereal A) (F C))))))
% 0.55/0.76 FOF formula (forall (A:extended_enat) (F:(extended_ereal->extended_enat)) (B:extended_ereal) (C:extended_ereal), ((((eq extended_enat) A) (F B))->(((ord_le824540014_ereal B) C)->((forall (X3:extended_ereal) (Y:extended_ereal), (((ord_le824540014_ereal X3) Y)->((ord_le1863327750d_enat (F X3)) (F Y))))->((ord_le1863327750d_enat A) (F C)))))) of role axiom named fact_33_ord__eq__le__subst
% 0.55/0.76 A new axiom: (forall (A:extended_enat) (F:(extended_ereal->extended_enat)) (B:extended_ereal) (C:extended_ereal), ((((eq extended_enat) A) (F B))->(((ord_le824540014_ereal B) C)->((forall (X3:extended_ereal) (Y:extended_ereal), (((ord_le824540014_ereal X3) Y)->((ord_le1863327750d_enat (F X3)) (F Y))))->((ord_le1863327750d_enat A) (F C))))))
% 0.61/0.77 FOF formula (forall (A:nat) (F:(extended_ereal->nat)) (B:extended_ereal) (C:extended_ereal), ((((eq nat) A) (F B))->(((ord_le824540014_ereal B) C)->((forall (X3:extended_ereal) (Y:extended_ereal), (((ord_le824540014_ereal X3) Y)->((ord_less_eq_nat (F X3)) (F Y))))->((ord_less_eq_nat A) (F C)))))) of role axiom named fact_34_ord__eq__le__subst
% 0.61/0.77 A new axiom: (forall (A:nat) (F:(extended_ereal->nat)) (B:extended_ereal) (C:extended_ereal), ((((eq nat) A) (F B))->(((ord_le824540014_ereal B) C)->((forall (X3:extended_ereal) (Y:extended_ereal), (((ord_le824540014_ereal X3) Y)->((ord_less_eq_nat (F X3)) (F Y))))->((ord_less_eq_nat A) (F C))))))
% 0.61/0.77 FOF formula (forall (A:real) (F:(extended_ereal->real)) (B:extended_ereal) (C:extended_ereal), ((((eq real) A) (F B))->(((ord_le824540014_ereal B) C)->((forall (X3:extended_ereal) (Y:extended_ereal), (((ord_le824540014_ereal X3) Y)->((ord_less_eq_real (F X3)) (F Y))))->((ord_less_eq_real A) (F C)))))) of role axiom named fact_35_ord__eq__le__subst
% 0.61/0.77 A new axiom: (forall (A:real) (F:(extended_ereal->real)) (B:extended_ereal) (C:extended_ereal), ((((eq real) A) (F B))->(((ord_le824540014_ereal B) C)->((forall (X3:extended_ereal) (Y:extended_ereal), (((ord_le824540014_ereal X3) Y)->((ord_less_eq_real (F X3)) (F Y))))->((ord_less_eq_real A) (F C))))))
% 0.61/0.77 FOF formula (forall (A:extended_ereal) (F:(extended_enat->extended_ereal)) (B:extended_enat) (C:extended_enat), ((((eq extended_ereal) A) (F B))->(((ord_le1863327750d_enat B) C)->((forall (X3:extended_enat) (Y:extended_enat), (((ord_le1863327750d_enat X3) Y)->((ord_le824540014_ereal (F X3)) (F Y))))->((ord_le824540014_ereal A) (F C)))))) of role axiom named fact_36_ord__eq__le__subst
% 0.61/0.77 A new axiom: (forall (A:extended_ereal) (F:(extended_enat->extended_ereal)) (B:extended_enat) (C:extended_enat), ((((eq extended_ereal) A) (F B))->(((ord_le1863327750d_enat B) C)->((forall (X3:extended_enat) (Y:extended_enat), (((ord_le1863327750d_enat X3) Y)->((ord_le824540014_ereal (F X3)) (F Y))))->((ord_le824540014_ereal A) (F C))))))
% 0.61/0.77 FOF formula (forall (A:extended_enat) (F:(extended_enat->extended_enat)) (B:extended_enat) (C:extended_enat), ((((eq extended_enat) A) (F B))->(((ord_le1863327750d_enat B) C)->((forall (X3:extended_enat) (Y:extended_enat), (((ord_le1863327750d_enat X3) Y)->((ord_le1863327750d_enat (F X3)) (F Y))))->((ord_le1863327750d_enat A) (F C)))))) of role axiom named fact_37_ord__eq__le__subst
% 0.61/0.77 A new axiom: (forall (A:extended_enat) (F:(extended_enat->extended_enat)) (B:extended_enat) (C:extended_enat), ((((eq extended_enat) A) (F B))->(((ord_le1863327750d_enat B) C)->((forall (X3:extended_enat) (Y:extended_enat), (((ord_le1863327750d_enat X3) Y)->((ord_le1863327750d_enat (F X3)) (F Y))))->((ord_le1863327750d_enat A) (F C))))))
% 0.61/0.77 FOF formula (forall (A:nat) (F:(extended_enat->nat)) (B:extended_enat) (C:extended_enat), ((((eq nat) A) (F B))->(((ord_le1863327750d_enat B) C)->((forall (X3:extended_enat) (Y:extended_enat), (((ord_le1863327750d_enat X3) Y)->((ord_less_eq_nat (F X3)) (F Y))))->((ord_less_eq_nat A) (F C)))))) of role axiom named fact_38_ord__eq__le__subst
% 0.61/0.77 A new axiom: (forall (A:nat) (F:(extended_enat->nat)) (B:extended_enat) (C:extended_enat), ((((eq nat) A) (F B))->(((ord_le1863327750d_enat B) C)->((forall (X3:extended_enat) (Y:extended_enat), (((ord_le1863327750d_enat X3) Y)->((ord_less_eq_nat (F X3)) (F Y))))->((ord_less_eq_nat A) (F C))))))
% 0.61/0.77 FOF formula (forall (A:real) (F:(extended_enat->real)) (B:extended_enat) (C:extended_enat), ((((eq real) A) (F B))->(((ord_le1863327750d_enat B) C)->((forall (X3:extended_enat) (Y:extended_enat), (((ord_le1863327750d_enat X3) Y)->((ord_less_eq_real (F X3)) (F Y))))->((ord_less_eq_real A) (F C)))))) of role axiom named fact_39_ord__eq__le__subst
% 0.61/0.77 A new axiom: (forall (A:real) (F:(extended_enat->real)) (B:extended_enat) (C:extended_enat), ((((eq real) A) (F B))->(((ord_le1863327750d_enat B) C)->((forall (X3:extended_enat) (Y:extended_enat), (((ord_le1863327750d_enat X3) Y)->((ord_less_eq_real (F X3)) (F Y))))->((ord_less_eq_real A) (F C))))))
% 0.61/0.79 FOF formula (forall (A:extended_ereal) (F:(nat->extended_ereal)) (B:nat) (C:nat), ((((eq extended_ereal) A) (F B))->(((ord_less_eq_nat B) C)->((forall (X3:nat) (Y:nat), (((ord_less_eq_nat X3) Y)->((ord_le824540014_ereal (F X3)) (F Y))))->((ord_le824540014_ereal A) (F C)))))) of role axiom named fact_40_ord__eq__le__subst
% 0.61/0.79 A new axiom: (forall (A:extended_ereal) (F:(nat->extended_ereal)) (B:nat) (C:nat), ((((eq extended_ereal) A) (F B))->(((ord_less_eq_nat B) C)->((forall (X3:nat) (Y:nat), (((ord_less_eq_nat X3) Y)->((ord_le824540014_ereal (F X3)) (F Y))))->((ord_le824540014_ereal A) (F C))))))
% 0.61/0.79 FOF formula (forall (A:extended_enat) (F:(nat->extended_enat)) (B:nat) (C:nat), ((((eq extended_enat) A) (F B))->(((ord_less_eq_nat B) C)->((forall (X3:nat) (Y:nat), (((ord_less_eq_nat X3) Y)->((ord_le1863327750d_enat (F X3)) (F Y))))->((ord_le1863327750d_enat A) (F C)))))) of role axiom named fact_41_ord__eq__le__subst
% 0.61/0.79 A new axiom: (forall (A:extended_enat) (F:(nat->extended_enat)) (B:nat) (C:nat), ((((eq extended_enat) A) (F B))->(((ord_less_eq_nat B) C)->((forall (X3:nat) (Y:nat), (((ord_less_eq_nat X3) Y)->((ord_le1863327750d_enat (F X3)) (F Y))))->((ord_le1863327750d_enat A) (F C))))))
% 0.61/0.79 FOF formula (forall (A:extended_ereal) (B:extended_ereal) (F:(extended_ereal->extended_ereal)) (C:extended_ereal), (((ord_le824540014_ereal A) B)->((((eq extended_ereal) (F B)) C)->((forall (X3:extended_ereal) (Y:extended_ereal), (((ord_le824540014_ereal X3) Y)->((ord_le824540014_ereal (F X3)) (F Y))))->((ord_le824540014_ereal (F A)) C))))) of role axiom named fact_42_ord__le__eq__subst
% 0.61/0.79 A new axiom: (forall (A:extended_ereal) (B:extended_ereal) (F:(extended_ereal->extended_ereal)) (C:extended_ereal), (((ord_le824540014_ereal A) B)->((((eq extended_ereal) (F B)) C)->((forall (X3:extended_ereal) (Y:extended_ereal), (((ord_le824540014_ereal X3) Y)->((ord_le824540014_ereal (F X3)) (F Y))))->((ord_le824540014_ereal (F A)) C)))))
% 0.61/0.79 FOF formula (forall (A:extended_ereal) (B:extended_ereal) (F:(extended_ereal->extended_enat)) (C:extended_enat), (((ord_le824540014_ereal A) B)->((((eq extended_enat) (F B)) C)->((forall (X3:extended_ereal) (Y:extended_ereal), (((ord_le824540014_ereal X3) Y)->((ord_le1863327750d_enat (F X3)) (F Y))))->((ord_le1863327750d_enat (F A)) C))))) of role axiom named fact_43_ord__le__eq__subst
% 0.61/0.79 A new axiom: (forall (A:extended_ereal) (B:extended_ereal) (F:(extended_ereal->extended_enat)) (C:extended_enat), (((ord_le824540014_ereal A) B)->((((eq extended_enat) (F B)) C)->((forall (X3:extended_ereal) (Y:extended_ereal), (((ord_le824540014_ereal X3) Y)->((ord_le1863327750d_enat (F X3)) (F Y))))->((ord_le1863327750d_enat (F A)) C)))))
% 0.61/0.79 FOF formula (forall (A:extended_ereal) (B:extended_ereal) (F:(extended_ereal->nat)) (C:nat), (((ord_le824540014_ereal A) B)->((((eq nat) (F B)) C)->((forall (X3:extended_ereal) (Y:extended_ereal), (((ord_le824540014_ereal X3) Y)->((ord_less_eq_nat (F X3)) (F Y))))->((ord_less_eq_nat (F A)) C))))) of role axiom named fact_44_ord__le__eq__subst
% 0.61/0.79 A new axiom: (forall (A:extended_ereal) (B:extended_ereal) (F:(extended_ereal->nat)) (C:nat), (((ord_le824540014_ereal A) B)->((((eq nat) (F B)) C)->((forall (X3:extended_ereal) (Y:extended_ereal), (((ord_le824540014_ereal X3) Y)->((ord_less_eq_nat (F X3)) (F Y))))->((ord_less_eq_nat (F A)) C)))))
% 0.61/0.79 FOF formula (forall (A:extended_ereal) (B:extended_ereal) (F:(extended_ereal->real)) (C:real), (((ord_le824540014_ereal A) B)->((((eq real) (F B)) C)->((forall (X3:extended_ereal) (Y:extended_ereal), (((ord_le824540014_ereal X3) Y)->((ord_less_eq_real (F X3)) (F Y))))->((ord_less_eq_real (F A)) C))))) of role axiom named fact_45_ord__le__eq__subst
% 0.61/0.79 A new axiom: (forall (A:extended_ereal) (B:extended_ereal) (F:(extended_ereal->real)) (C:real), (((ord_le824540014_ereal A) B)->((((eq real) (F B)) C)->((forall (X3:extended_ereal) (Y:extended_ereal), (((ord_le824540014_ereal X3) Y)->((ord_less_eq_real (F X3)) (F Y))))->((ord_less_eq_real (F A)) C)))))
% 0.61/0.79 FOF formula (forall (A:extended_enat) (B:extended_enat) (F:(extended_enat->extended_ereal)) (C:extended_ereal), (((ord_le1863327750d_enat A) B)->((((eq extended_ereal) (F B)) C)->((forall (X3:extended_enat) (Y:extended_enat), (((ord_le1863327750d_enat X3) Y)->((ord_le824540014_ereal (F X3)) (F Y))))->((ord_le824540014_ereal (F A)) C))))) of role axiom named fact_46_ord__le__eq__subst
% 0.61/0.80 A new axiom: (forall (A:extended_enat) (B:extended_enat) (F:(extended_enat->extended_ereal)) (C:extended_ereal), (((ord_le1863327750d_enat A) B)->((((eq extended_ereal) (F B)) C)->((forall (X3:extended_enat) (Y:extended_enat), (((ord_le1863327750d_enat X3) Y)->((ord_le824540014_ereal (F X3)) (F Y))))->((ord_le824540014_ereal (F A)) C)))))
% 0.61/0.80 FOF formula (forall (A:extended_enat) (B:extended_enat) (F:(extended_enat->extended_enat)) (C:extended_enat), (((ord_le1863327750d_enat A) B)->((((eq extended_enat) (F B)) C)->((forall (X3:extended_enat) (Y:extended_enat), (((ord_le1863327750d_enat X3) Y)->((ord_le1863327750d_enat (F X3)) (F Y))))->((ord_le1863327750d_enat (F A)) C))))) of role axiom named fact_47_ord__le__eq__subst
% 0.61/0.80 A new axiom: (forall (A:extended_enat) (B:extended_enat) (F:(extended_enat->extended_enat)) (C:extended_enat), (((ord_le1863327750d_enat A) B)->((((eq extended_enat) (F B)) C)->((forall (X3:extended_enat) (Y:extended_enat), (((ord_le1863327750d_enat X3) Y)->((ord_le1863327750d_enat (F X3)) (F Y))))->((ord_le1863327750d_enat (F A)) C)))))
% 0.61/0.80 FOF formula (forall (A:extended_enat) (B:extended_enat) (F:(extended_enat->nat)) (C:nat), (((ord_le1863327750d_enat A) B)->((((eq nat) (F B)) C)->((forall (X3:extended_enat) (Y:extended_enat), (((ord_le1863327750d_enat X3) Y)->((ord_less_eq_nat (F X3)) (F Y))))->((ord_less_eq_nat (F A)) C))))) of role axiom named fact_48_ord__le__eq__subst
% 0.61/0.80 A new axiom: (forall (A:extended_enat) (B:extended_enat) (F:(extended_enat->nat)) (C:nat), (((ord_le1863327750d_enat A) B)->((((eq nat) (F B)) C)->((forall (X3:extended_enat) (Y:extended_enat), (((ord_le1863327750d_enat X3) Y)->((ord_less_eq_nat (F X3)) (F Y))))->((ord_less_eq_nat (F A)) C)))))
% 0.61/0.80 FOF formula (forall (A:extended_enat) (B:extended_enat) (F:(extended_enat->real)) (C:real), (((ord_le1863327750d_enat A) B)->((((eq real) (F B)) C)->((forall (X3:extended_enat) (Y:extended_enat), (((ord_le1863327750d_enat X3) Y)->((ord_less_eq_real (F X3)) (F Y))))->((ord_less_eq_real (F A)) C))))) of role axiom named fact_49_ord__le__eq__subst
% 0.61/0.80 A new axiom: (forall (A:extended_enat) (B:extended_enat) (F:(extended_enat->real)) (C:real), (((ord_le1863327750d_enat A) B)->((((eq real) (F B)) C)->((forall (X3:extended_enat) (Y:extended_enat), (((ord_le1863327750d_enat X3) Y)->((ord_less_eq_real (F X3)) (F Y))))->((ord_less_eq_real (F A)) C)))))
% 0.61/0.80 FOF formula (forall (A:nat) (B:nat) (F:(nat->extended_ereal)) (C:extended_ereal), (((ord_less_eq_nat A) B)->((((eq extended_ereal) (F B)) C)->((forall (X3:nat) (Y:nat), (((ord_less_eq_nat X3) Y)->((ord_le824540014_ereal (F X3)) (F Y))))->((ord_le824540014_ereal (F A)) C))))) of role axiom named fact_50_ord__le__eq__subst
% 0.61/0.80 A new axiom: (forall (A:nat) (B:nat) (F:(nat->extended_ereal)) (C:extended_ereal), (((ord_less_eq_nat A) B)->((((eq extended_ereal) (F B)) C)->((forall (X3:nat) (Y:nat), (((ord_less_eq_nat X3) Y)->((ord_le824540014_ereal (F X3)) (F Y))))->((ord_le824540014_ereal (F A)) C)))))
% 0.61/0.80 FOF formula (forall (A:nat) (B:nat) (F:(nat->extended_enat)) (C:extended_enat), (((ord_less_eq_nat A) B)->((((eq extended_enat) (F B)) C)->((forall (X3:nat) (Y:nat), (((ord_less_eq_nat X3) Y)->((ord_le1863327750d_enat (F X3)) (F Y))))->((ord_le1863327750d_enat (F A)) C))))) of role axiom named fact_51_ord__le__eq__subst
% 0.61/0.80 A new axiom: (forall (A:nat) (B:nat) (F:(nat->extended_enat)) (C:extended_enat), (((ord_less_eq_nat A) B)->((((eq extended_enat) (F B)) C)->((forall (X3:nat) (Y:nat), (((ord_less_eq_nat X3) Y)->((ord_le1863327750d_enat (F X3)) (F Y))))->((ord_le1863327750d_enat (F A)) C)))))
% 0.61/0.80 FOF formula (forall (F:(a->extended_ereal)) (X2:a), ((ord_le824540014_ereal ((lower_881475195hull_a F) X2)) (F X2))) of role axiom named fact_52_lsc__hull__le
% 0.61/0.80 A new axiom: (forall (F:(a->extended_ereal)) (X2:a), ((ord_le824540014_ereal ((lower_881475195hull_a F) X2)) (F X2)))
% 0.61/0.82 FOF formula (forall (B:extended_ereal) (A:extended_ereal), (((ord_le824540014_ereal B) A)->(((ord_le824540014_ereal A) B)->(((eq extended_ereal) A) B)))) of role axiom named fact_53_dual__order_Oantisym
% 0.61/0.82 A new axiom: (forall (B:extended_ereal) (A:extended_ereal), (((ord_le824540014_ereal B) A)->(((ord_le824540014_ereal A) B)->(((eq extended_ereal) A) B))))
% 0.61/0.82 FOF formula (forall (B:extended_enat) (A:extended_enat), (((ord_le1863327750d_enat B) A)->(((ord_le1863327750d_enat A) B)->(((eq extended_enat) A) B)))) of role axiom named fact_54_dual__order_Oantisym
% 0.61/0.82 A new axiom: (forall (B:extended_enat) (A:extended_enat), (((ord_le1863327750d_enat B) A)->(((ord_le1863327750d_enat A) B)->(((eq extended_enat) A) B))))
% 0.61/0.82 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_55_dual__order_Oantisym
% 0.61/0.82 A new axiom: (forall (B:nat) (A:nat), (((ord_less_eq_nat B) A)->(((ord_less_eq_nat A) B)->(((eq nat) A) B))))
% 0.61/0.82 FOF formula (forall (B:real) (A:real), (((ord_less_eq_real B) A)->(((ord_less_eq_real A) B)->(((eq real) A) B)))) of role axiom named fact_56_dual__order_Oantisym
% 0.61/0.82 A new axiom: (forall (B:real) (A:real), (((ord_less_eq_real B) A)->(((ord_less_eq_real A) B)->(((eq real) A) B))))
% 0.61/0.82 FOF formula (((eq (extended_ereal->(extended_ereal->Prop))) (fun (Y2:extended_ereal) (Z2:extended_ereal)=> (((eq extended_ereal) Y2) Z2))) (fun (A2:extended_ereal) (B2:extended_ereal)=> ((and ((ord_le824540014_ereal B2) A2)) ((ord_le824540014_ereal A2) B2)))) of role axiom named fact_57_dual__order_Oeq__iff
% 0.61/0.82 A new axiom: (((eq (extended_ereal->(extended_ereal->Prop))) (fun (Y2:extended_ereal) (Z2:extended_ereal)=> (((eq extended_ereal) Y2) Z2))) (fun (A2:extended_ereal) (B2:extended_ereal)=> ((and ((ord_le824540014_ereal B2) A2)) ((ord_le824540014_ereal A2) B2))))
% 0.61/0.82 FOF formula (((eq (extended_enat->(extended_enat->Prop))) (fun (Y2:extended_enat) (Z2:extended_enat)=> (((eq extended_enat) Y2) Z2))) (fun (A2:extended_enat) (B2:extended_enat)=> ((and ((ord_le1863327750d_enat B2) A2)) ((ord_le1863327750d_enat A2) B2)))) of role axiom named fact_58_dual__order_Oeq__iff
% 0.61/0.82 A new axiom: (((eq (extended_enat->(extended_enat->Prop))) (fun (Y2:extended_enat) (Z2:extended_enat)=> (((eq extended_enat) Y2) Z2))) (fun (A2:extended_enat) (B2:extended_enat)=> ((and ((ord_le1863327750d_enat B2) A2)) ((ord_le1863327750d_enat A2) B2))))
% 0.61/0.82 FOF formula (((eq (nat->(nat->Prop))) (fun (Y2:nat) (Z2:nat)=> (((eq nat) Y2) Z2))) (fun (A2:nat) (B2:nat)=> ((and ((ord_less_eq_nat B2) A2)) ((ord_less_eq_nat A2) B2)))) of role axiom named fact_59_dual__order_Oeq__iff
% 0.61/0.82 A new axiom: (((eq (nat->(nat->Prop))) (fun (Y2:nat) (Z2:nat)=> (((eq nat) Y2) Z2))) (fun (A2:nat) (B2:nat)=> ((and ((ord_less_eq_nat B2) A2)) ((ord_less_eq_nat A2) B2))))
% 0.61/0.82 FOF formula (((eq (real->(real->Prop))) (fun (Y2:real) (Z2:real)=> (((eq real) Y2) Z2))) (fun (A2:real) (B2:real)=> ((and ((ord_less_eq_real B2) A2)) ((ord_less_eq_real A2) B2)))) of role axiom named fact_60_dual__order_Oeq__iff
% 0.61/0.82 A new axiom: (((eq (real->(real->Prop))) (fun (Y2:real) (Z2:real)=> (((eq real) Y2) Z2))) (fun (A2:real) (B2:real)=> ((and ((ord_less_eq_real B2) A2)) ((ord_less_eq_real A2) B2))))
% 0.61/0.82 FOF formula (forall (B:extended_ereal) (A:extended_ereal) (C:extended_ereal), (((ord_le824540014_ereal B) A)->(((ord_le824540014_ereal C) B)->((ord_le824540014_ereal C) A)))) of role axiom named fact_61_dual__order_Otrans
% 0.61/0.82 A new axiom: (forall (B:extended_ereal) (A:extended_ereal) (C:extended_ereal), (((ord_le824540014_ereal B) A)->(((ord_le824540014_ereal C) B)->((ord_le824540014_ereal C) A))))
% 0.61/0.82 FOF formula (forall (B:extended_enat) (A:extended_enat) (C:extended_enat), (((ord_le1863327750d_enat B) A)->(((ord_le1863327750d_enat C) B)->((ord_le1863327750d_enat C) A)))) of role axiom named fact_62_dual__order_Otrans
% 0.61/0.82 A new axiom: (forall (B:extended_enat) (A:extended_enat) (C:extended_enat), (((ord_le1863327750d_enat B) A)->(((ord_le1863327750d_enat C) B)->((ord_le1863327750d_enat C) A))))
% 0.61/0.82 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_63_dual__order_Otrans
% 0.61/0.83 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))))
% 0.61/0.83 FOF formula (forall (B:real) (A:real) (C:real), (((ord_less_eq_real B) A)->(((ord_less_eq_real C) B)->((ord_less_eq_real C) A)))) of role axiom named fact_64_dual__order_Otrans
% 0.61/0.83 A new axiom: (forall (B:real) (A:real) (C:real), (((ord_less_eq_real B) A)->(((ord_less_eq_real C) B)->((ord_less_eq_real C) A))))
% 0.61/0.83 FOF formula (forall (P:(extended_ereal->(extended_ereal->Prop))) (A:extended_ereal) (B:extended_ereal), ((forall (A3:extended_ereal) (B3:extended_ereal), (((ord_le824540014_ereal A3) B3)->((P A3) B3)))->((forall (A3:extended_ereal) (B3:extended_ereal), (((P B3) A3)->((P A3) B3)))->((P A) B)))) of role axiom named fact_65_linorder__wlog
% 0.61/0.83 A new axiom: (forall (P:(extended_ereal->(extended_ereal->Prop))) (A:extended_ereal) (B:extended_ereal), ((forall (A3:extended_ereal) (B3:extended_ereal), (((ord_le824540014_ereal A3) B3)->((P A3) B3)))->((forall (A3:extended_ereal) (B3:extended_ereal), (((P B3) A3)->((P A3) B3)))->((P A) B))))
% 0.61/0.83 FOF formula (forall (P:(extended_enat->(extended_enat->Prop))) (A:extended_enat) (B:extended_enat), ((forall (A3:extended_enat) (B3:extended_enat), (((ord_le1863327750d_enat A3) B3)->((P A3) B3)))->((forall (A3:extended_enat) (B3:extended_enat), (((P B3) A3)->((P A3) B3)))->((P A) B)))) of role axiom named fact_66_linorder__wlog
% 0.61/0.83 A new axiom: (forall (P:(extended_enat->(extended_enat->Prop))) (A:extended_enat) (B:extended_enat), ((forall (A3:extended_enat) (B3:extended_enat), (((ord_le1863327750d_enat A3) B3)->((P A3) B3)))->((forall (A3:extended_enat) (B3:extended_enat), (((P B3) A3)->((P A3) B3)))->((P A) B))))
% 0.61/0.83 FOF formula (forall (P:(nat->(nat->Prop))) (A:nat) (B:nat), ((forall (A3:nat) (B3:nat), (((ord_less_eq_nat A3) B3)->((P A3) B3)))->((forall (A3:nat) (B3:nat), (((P B3) A3)->((P A3) B3)))->((P A) B)))) of role axiom named fact_67_linorder__wlog
% 0.61/0.83 A new axiom: (forall (P:(nat->(nat->Prop))) (A:nat) (B:nat), ((forall (A3:nat) (B3:nat), (((ord_less_eq_nat A3) B3)->((P A3) B3)))->((forall (A3:nat) (B3:nat), (((P B3) A3)->((P A3) B3)))->((P A) B))))
% 0.61/0.83 FOF formula (forall (P:(real->(real->Prop))) (A:real) (B:real), ((forall (A3:real) (B3:real), (((ord_less_eq_real A3) B3)->((P A3) B3)))->((forall (A3:real) (B3:real), (((P B3) A3)->((P A3) B3)))->((P A) B)))) of role axiom named fact_68_linorder__wlog
% 0.61/0.83 A new axiom: (forall (P:(real->(real->Prop))) (A:real) (B:real), ((forall (A3:real) (B3:real), (((ord_less_eq_real A3) B3)->((P A3) B3)))->((forall (A3:real) (B3:real), (((P B3) A3)->((P A3) B3)))->((P A) B))))
% 0.61/0.83 FOF formula (forall (A:extended_ereal), ((ord_le824540014_ereal A) A)) of role axiom named fact_69_dual__order_Orefl
% 0.61/0.83 A new axiom: (forall (A:extended_ereal), ((ord_le824540014_ereal A) A))
% 0.61/0.83 FOF formula (forall (A:extended_enat), ((ord_le1863327750d_enat A) A)) of role axiom named fact_70_dual__order_Orefl
% 0.61/0.83 A new axiom: (forall (A:extended_enat), ((ord_le1863327750d_enat A) A))
% 0.61/0.83 FOF formula (forall (A:nat), ((ord_less_eq_nat A) A)) of role axiom named fact_71_dual__order_Orefl
% 0.61/0.83 A new axiom: (forall (A:nat), ((ord_less_eq_nat A) A))
% 0.61/0.83 FOF formula (forall (A:real), ((ord_less_eq_real A) A)) of role axiom named fact_72_dual__order_Orefl
% 0.61/0.83 A new axiom: (forall (A:real), ((ord_less_eq_real A) A))
% 0.61/0.83 FOF formula (forall (X2:extended_ereal) (Y3:extended_ereal) (Z3:extended_ereal), (((ord_le824540014_ereal X2) Y3)->(((ord_le824540014_ereal Y3) Z3)->((ord_le824540014_ereal X2) Z3)))) of role axiom named fact_73_order__trans
% 0.61/0.83 A new axiom: (forall (X2:extended_ereal) (Y3:extended_ereal) (Z3:extended_ereal), (((ord_le824540014_ereal X2) Y3)->(((ord_le824540014_ereal Y3) Z3)->((ord_le824540014_ereal X2) Z3))))
% 0.61/0.83 FOF formula (forall (X2:extended_enat) (Y3:extended_enat) (Z3:extended_enat), (((ord_le1863327750d_enat X2) Y3)->(((ord_le1863327750d_enat Y3) Z3)->((ord_le1863327750d_enat X2) Z3)))) of role axiom named fact_74_order__trans
% 0.61/0.83 A new axiom: (forall (X2:extended_enat) (Y3:extended_enat) (Z3:extended_enat), (((ord_le1863327750d_enat X2) Y3)->(((ord_le1863327750d_enat Y3) Z3)->((ord_le1863327750d_enat X2) Z3))))
% 0.61/0.85 FOF formula (forall (X2:nat) (Y3:nat) (Z3:nat), (((ord_less_eq_nat X2) Y3)->(((ord_less_eq_nat Y3) Z3)->((ord_less_eq_nat X2) Z3)))) of role axiom named fact_75_order__trans
% 0.61/0.85 A new axiom: (forall (X2:nat) (Y3:nat) (Z3:nat), (((ord_less_eq_nat X2) Y3)->(((ord_less_eq_nat Y3) Z3)->((ord_less_eq_nat X2) Z3))))
% 0.61/0.85 FOF formula (forall (X2:real) (Y3:real) (Z3:real), (((ord_less_eq_real X2) Y3)->(((ord_less_eq_real Y3) Z3)->((ord_less_eq_real X2) Z3)))) of role axiom named fact_76_order__trans
% 0.61/0.85 A new axiom: (forall (X2:real) (Y3:real) (Z3:real), (((ord_less_eq_real X2) Y3)->(((ord_less_eq_real Y3) Z3)->((ord_less_eq_real X2) Z3))))
% 0.61/0.85 FOF formula (forall (A:extended_ereal) (B:extended_ereal), (((ord_le824540014_ereal A) B)->(((ord_le824540014_ereal B) A)->(((eq extended_ereal) A) B)))) of role axiom named fact_77_order__class_Oorder_Oantisym
% 0.61/0.85 A new axiom: (forall (A:extended_ereal) (B:extended_ereal), (((ord_le824540014_ereal A) B)->(((ord_le824540014_ereal B) A)->(((eq extended_ereal) A) B))))
% 0.61/0.85 FOF formula (forall (A:extended_enat) (B:extended_enat), (((ord_le1863327750d_enat A) B)->(((ord_le1863327750d_enat B) A)->(((eq extended_enat) A) B)))) of role axiom named fact_78_order__class_Oorder_Oantisym
% 0.61/0.85 A new axiom: (forall (A:extended_enat) (B:extended_enat), (((ord_le1863327750d_enat A) B)->(((ord_le1863327750d_enat B) A)->(((eq extended_enat) A) B))))
% 0.61/0.85 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_79_order__class_Oorder_Oantisym
% 0.61/0.85 A new axiom: (forall (A:nat) (B:nat), (((ord_less_eq_nat A) B)->(((ord_less_eq_nat B) A)->(((eq nat) A) B))))
% 0.61/0.85 FOF formula (forall (A:real) (B:real), (((ord_less_eq_real A) B)->(((ord_less_eq_real B) A)->(((eq real) A) B)))) of role axiom named fact_80_order__class_Oorder_Oantisym
% 0.61/0.85 A new axiom: (forall (A:real) (B:real), (((ord_less_eq_real A) B)->(((ord_less_eq_real B) A)->(((eq real) A) B))))
% 0.61/0.85 FOF formula (forall (A:extended_ereal) (B:extended_ereal) (C:extended_ereal), (((ord_le824540014_ereal A) B)->((((eq extended_ereal) B) C)->((ord_le824540014_ereal A) C)))) of role axiom named fact_81_ord__le__eq__trans
% 0.61/0.85 A new axiom: (forall (A:extended_ereal) (B:extended_ereal) (C:extended_ereal), (((ord_le824540014_ereal A) B)->((((eq extended_ereal) B) C)->((ord_le824540014_ereal A) C))))
% 0.61/0.85 FOF formula (forall (A:extended_enat) (B:extended_enat) (C:extended_enat), (((ord_le1863327750d_enat A) B)->((((eq extended_enat) B) C)->((ord_le1863327750d_enat A) C)))) of role axiom named fact_82_ord__le__eq__trans
% 0.61/0.85 A new axiom: (forall (A:extended_enat) (B:extended_enat) (C:extended_enat), (((ord_le1863327750d_enat A) B)->((((eq extended_enat) B) C)->((ord_le1863327750d_enat A) C))))
% 0.61/0.85 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_83_ord__le__eq__trans
% 0.61/0.85 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))))
% 0.61/0.85 FOF formula (forall (A:real) (B:real) (C:real), (((ord_less_eq_real A) B)->((((eq real) B) C)->((ord_less_eq_real A) C)))) of role axiom named fact_84_ord__le__eq__trans
% 0.61/0.85 A new axiom: (forall (A:real) (B:real) (C:real), (((ord_less_eq_real A) B)->((((eq real) B) C)->((ord_less_eq_real A) C))))
% 0.61/0.85 FOF formula (forall (A:extended_ereal) (B:extended_ereal) (C:extended_ereal), ((((eq extended_ereal) A) B)->(((ord_le824540014_ereal B) C)->((ord_le824540014_ereal A) C)))) of role axiom named fact_85_ord__eq__le__trans
% 0.61/0.85 A new axiom: (forall (A:extended_ereal) (B:extended_ereal) (C:extended_ereal), ((((eq extended_ereal) A) B)->(((ord_le824540014_ereal B) C)->((ord_le824540014_ereal A) C))))
% 0.61/0.85 FOF formula (forall (A:extended_enat) (B:extended_enat) (C:extended_enat), ((((eq extended_enat) A) B)->(((ord_le1863327750d_enat B) C)->((ord_le1863327750d_enat A) C)))) of role axiom named fact_86_ord__eq__le__trans
% 0.61/0.85 A new axiom: (forall (A:extended_enat) (B:extended_enat) (C:extended_enat), ((((eq extended_enat) A) B)->(((ord_le1863327750d_enat B) C)->((ord_le1863327750d_enat A) C))))
% 0.61/0.86 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_87_ord__eq__le__trans
% 0.61/0.86 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))))
% 0.61/0.86 FOF formula (forall (A:real) (B:real) (C:real), ((((eq real) A) B)->(((ord_less_eq_real B) C)->((ord_less_eq_real A) C)))) of role axiom named fact_88_ord__eq__le__trans
% 0.61/0.86 A new axiom: (forall (A:real) (B:real) (C:real), ((((eq real) A) B)->(((ord_less_eq_real B) C)->((ord_less_eq_real A) C))))
% 0.61/0.86 FOF formula (((eq (extended_ereal->(extended_ereal->Prop))) (fun (Y2:extended_ereal) (Z2:extended_ereal)=> (((eq extended_ereal) Y2) Z2))) (fun (A2:extended_ereal) (B2:extended_ereal)=> ((and ((ord_le824540014_ereal A2) B2)) ((ord_le824540014_ereal B2) A2)))) of role axiom named fact_89_order__class_Oorder_Oeq__iff
% 0.61/0.86 A new axiom: (((eq (extended_ereal->(extended_ereal->Prop))) (fun (Y2:extended_ereal) (Z2:extended_ereal)=> (((eq extended_ereal) Y2) Z2))) (fun (A2:extended_ereal) (B2:extended_ereal)=> ((and ((ord_le824540014_ereal A2) B2)) ((ord_le824540014_ereal B2) A2))))
% 0.61/0.86 FOF formula (((eq (extended_enat->(extended_enat->Prop))) (fun (Y2:extended_enat) (Z2:extended_enat)=> (((eq extended_enat) Y2) Z2))) (fun (A2:extended_enat) (B2:extended_enat)=> ((and ((ord_le1863327750d_enat A2) B2)) ((ord_le1863327750d_enat B2) A2)))) of role axiom named fact_90_order__class_Oorder_Oeq__iff
% 0.61/0.86 A new axiom: (((eq (extended_enat->(extended_enat->Prop))) (fun (Y2:extended_enat) (Z2:extended_enat)=> (((eq extended_enat) Y2) Z2))) (fun (A2:extended_enat) (B2:extended_enat)=> ((and ((ord_le1863327750d_enat A2) B2)) ((ord_le1863327750d_enat B2) A2))))
% 0.61/0.86 FOF formula (((eq (nat->(nat->Prop))) (fun (Y2:nat) (Z2:nat)=> (((eq nat) Y2) Z2))) (fun (A2:nat) (B2:nat)=> ((and ((ord_less_eq_nat A2) B2)) ((ord_less_eq_nat B2) A2)))) of role axiom named fact_91_order__class_Oorder_Oeq__iff
% 0.61/0.86 A new axiom: (((eq (nat->(nat->Prop))) (fun (Y2:nat) (Z2:nat)=> (((eq nat) Y2) Z2))) (fun (A2:nat) (B2:nat)=> ((and ((ord_less_eq_nat A2) B2)) ((ord_less_eq_nat B2) A2))))
% 0.61/0.86 FOF formula (((eq (real->(real->Prop))) (fun (Y2:real) (Z2:real)=> (((eq real) Y2) Z2))) (fun (A2:real) (B2:real)=> ((and ((ord_less_eq_real A2) B2)) ((ord_less_eq_real B2) A2)))) of role axiom named fact_92_order__class_Oorder_Oeq__iff
% 0.61/0.86 A new axiom: (((eq (real->(real->Prop))) (fun (Y2:real) (Z2:real)=> (((eq real) Y2) Z2))) (fun (A2:real) (B2:real)=> ((and ((ord_less_eq_real A2) B2)) ((ord_less_eq_real B2) A2))))
% 0.61/0.86 FOF formula (forall (Y3:extended_ereal) (X2:extended_ereal), (((ord_le824540014_ereal Y3) X2)->(((eq Prop) ((ord_le824540014_ereal X2) Y3)) (((eq extended_ereal) X2) Y3)))) of role axiom named fact_93_antisym__conv
% 0.61/0.86 A new axiom: (forall (Y3:extended_ereal) (X2:extended_ereal), (((ord_le824540014_ereal Y3) X2)->(((eq Prop) ((ord_le824540014_ereal X2) Y3)) (((eq extended_ereal) X2) Y3))))
% 0.61/0.86 FOF formula (forall (Y3:extended_enat) (X2:extended_enat), (((ord_le1863327750d_enat Y3) X2)->(((eq Prop) ((ord_le1863327750d_enat X2) Y3)) (((eq extended_enat) X2) Y3)))) of role axiom named fact_94_antisym__conv
% 0.61/0.86 A new axiom: (forall (Y3:extended_enat) (X2:extended_enat), (((ord_le1863327750d_enat Y3) X2)->(((eq Prop) ((ord_le1863327750d_enat X2) Y3)) (((eq extended_enat) X2) Y3))))
% 0.61/0.86 FOF formula (forall (Y3:nat) (X2:nat), (((ord_less_eq_nat Y3) X2)->(((eq Prop) ((ord_less_eq_nat X2) Y3)) (((eq nat) X2) Y3)))) of role axiom named fact_95_antisym__conv
% 0.61/0.86 A new axiom: (forall (Y3:nat) (X2:nat), (((ord_less_eq_nat Y3) X2)->(((eq Prop) ((ord_less_eq_nat X2) Y3)) (((eq nat) X2) Y3))))
% 0.61/0.86 FOF formula (forall (Y3:real) (X2:real), (((ord_less_eq_real Y3) X2)->(((eq Prop) ((ord_less_eq_real X2) Y3)) (((eq real) X2) Y3)))) of role axiom named fact_96_antisym__conv
% 0.61/0.86 A new axiom: (forall (Y3:real) (X2:real), (((ord_less_eq_real Y3) X2)->(((eq Prop) ((ord_less_eq_real X2) Y3)) (((eq real) X2) Y3))))
% 0.61/0.86 FOF formula (forall (X2:extended_ereal) (Y3:extended_ereal) (Z3:extended_ereal), ((((ord_le824540014_ereal X2) Y3)->(((ord_le824540014_ereal Y3) Z3)->False))->((((ord_le824540014_ereal Y3) X2)->(((ord_le824540014_ereal X2) Z3)->False))->((((ord_le824540014_ereal X2) Z3)->(((ord_le824540014_ereal Z3) Y3)->False))->((((ord_le824540014_ereal Z3) Y3)->(((ord_le824540014_ereal Y3) X2)->False))->((((ord_le824540014_ereal Y3) Z3)->(((ord_le824540014_ereal Z3) X2)->False))->((((ord_le824540014_ereal Z3) X2)->(((ord_le824540014_ereal X2) Y3)->False))->False))))))) of role axiom named fact_97_le__cases3
% 0.71/0.87 A new axiom: (forall (X2:extended_ereal) (Y3:extended_ereal) (Z3:extended_ereal), ((((ord_le824540014_ereal X2) Y3)->(((ord_le824540014_ereal Y3) Z3)->False))->((((ord_le824540014_ereal Y3) X2)->(((ord_le824540014_ereal X2) Z3)->False))->((((ord_le824540014_ereal X2) Z3)->(((ord_le824540014_ereal Z3) Y3)->False))->((((ord_le824540014_ereal Z3) Y3)->(((ord_le824540014_ereal Y3) X2)->False))->((((ord_le824540014_ereal Y3) Z3)->(((ord_le824540014_ereal Z3) X2)->False))->((((ord_le824540014_ereal Z3) X2)->(((ord_le824540014_ereal X2) Y3)->False))->False)))))))
% 0.71/0.87 FOF formula (forall (X2:extended_enat) (Y3:extended_enat) (Z3:extended_enat), ((((ord_le1863327750d_enat X2) Y3)->(((ord_le1863327750d_enat Y3) Z3)->False))->((((ord_le1863327750d_enat Y3) X2)->(((ord_le1863327750d_enat X2) Z3)->False))->((((ord_le1863327750d_enat X2) Z3)->(((ord_le1863327750d_enat Z3) Y3)->False))->((((ord_le1863327750d_enat Z3) Y3)->(((ord_le1863327750d_enat Y3) X2)->False))->((((ord_le1863327750d_enat Y3) Z3)->(((ord_le1863327750d_enat Z3) X2)->False))->((((ord_le1863327750d_enat Z3) X2)->(((ord_le1863327750d_enat X2) Y3)->False))->False))))))) of role axiom named fact_98_le__cases3
% 0.71/0.87 A new axiom: (forall (X2:extended_enat) (Y3:extended_enat) (Z3:extended_enat), ((((ord_le1863327750d_enat X2) Y3)->(((ord_le1863327750d_enat Y3) Z3)->False))->((((ord_le1863327750d_enat Y3) X2)->(((ord_le1863327750d_enat X2) Z3)->False))->((((ord_le1863327750d_enat X2) Z3)->(((ord_le1863327750d_enat Z3) Y3)->False))->((((ord_le1863327750d_enat Z3) Y3)->(((ord_le1863327750d_enat Y3) X2)->False))->((((ord_le1863327750d_enat Y3) Z3)->(((ord_le1863327750d_enat Z3) X2)->False))->((((ord_le1863327750d_enat Z3) X2)->(((ord_le1863327750d_enat X2) Y3)->False))->False)))))))
% 0.71/0.87 FOF formula (forall (X2:nat) (Y3:nat) (Z3:nat), ((((ord_less_eq_nat X2) Y3)->(((ord_less_eq_nat Y3) Z3)->False))->((((ord_less_eq_nat Y3) X2)->(((ord_less_eq_nat X2) Z3)->False))->((((ord_less_eq_nat X2) Z3)->(((ord_less_eq_nat Z3) Y3)->False))->((((ord_less_eq_nat Z3) Y3)->(((ord_less_eq_nat Y3) X2)->False))->((((ord_less_eq_nat Y3) Z3)->(((ord_less_eq_nat Z3) X2)->False))->((((ord_less_eq_nat Z3) X2)->(((ord_less_eq_nat X2) Y3)->False))->False))))))) of role axiom named fact_99_le__cases3
% 0.71/0.87 A new axiom: (forall (X2:nat) (Y3:nat) (Z3:nat), ((((ord_less_eq_nat X2) Y3)->(((ord_less_eq_nat Y3) Z3)->False))->((((ord_less_eq_nat Y3) X2)->(((ord_less_eq_nat X2) Z3)->False))->((((ord_less_eq_nat X2) Z3)->(((ord_less_eq_nat Z3) Y3)->False))->((((ord_less_eq_nat Z3) Y3)->(((ord_less_eq_nat Y3) X2)->False))->((((ord_less_eq_nat Y3) Z3)->(((ord_less_eq_nat Z3) X2)->False))->((((ord_less_eq_nat Z3) X2)->(((ord_less_eq_nat X2) Y3)->False))->False)))))))
% 0.71/0.87 FOF formula (forall (X2:real) (Y3:real) (Z3:real), ((((ord_less_eq_real X2) Y3)->(((ord_less_eq_real Y3) Z3)->False))->((((ord_less_eq_real Y3) X2)->(((ord_less_eq_real X2) Z3)->False))->((((ord_less_eq_real X2) Z3)->(((ord_less_eq_real Z3) Y3)->False))->((((ord_less_eq_real Z3) Y3)->(((ord_less_eq_real Y3) X2)->False))->((((ord_less_eq_real Y3) Z3)->(((ord_less_eq_real Z3) X2)->False))->((((ord_less_eq_real Z3) X2)->(((ord_less_eq_real X2) Y3)->False))->False))))))) of role axiom named fact_100_le__cases3
% 0.71/0.87 A new axiom: (forall (X2:real) (Y3:real) (Z3:real), ((((ord_less_eq_real X2) Y3)->(((ord_less_eq_real Y3) Z3)->False))->((((ord_less_eq_real Y3) X2)->(((ord_less_eq_real X2) Z3)->False))->((((ord_less_eq_real X2) Z3)->(((ord_less_eq_real Z3) Y3)->False))->((((ord_less_eq_real Z3) Y3)->(((ord_less_eq_real Y3) X2)->False))->((((ord_less_eq_real Y3) Z3)->(((ord_less_eq_real Z3) X2)->False))->((((ord_less_eq_real Z3) X2)->(((ord_less_eq_real X2) Y3)->False))->False)))))))
% 0.71/0.88 FOF formula (forall (A:extended_ereal) (B:extended_ereal) (C:extended_ereal), (((ord_le824540014_ereal A) B)->(((ord_le824540014_ereal B) C)->((ord_le824540014_ereal A) C)))) of role axiom named fact_101_order_Otrans
% 0.71/0.88 A new axiom: (forall (A:extended_ereal) (B:extended_ereal) (C:extended_ereal), (((ord_le824540014_ereal A) B)->(((ord_le824540014_ereal B) C)->((ord_le824540014_ereal A) C))))
% 0.71/0.88 FOF formula (forall (A:extended_enat) (B:extended_enat) (C:extended_enat), (((ord_le1863327750d_enat A) B)->(((ord_le1863327750d_enat B) C)->((ord_le1863327750d_enat A) C)))) of role axiom named fact_102_order_Otrans
% 0.71/0.88 A new axiom: (forall (A:extended_enat) (B:extended_enat) (C:extended_enat), (((ord_le1863327750d_enat A) B)->(((ord_le1863327750d_enat B) C)->((ord_le1863327750d_enat A) C))))
% 0.71/0.88 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_103_order_Otrans
% 0.71/0.88 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))))
% 0.71/0.88 FOF formula (forall (A:real) (B:real) (C:real), (((ord_less_eq_real A) B)->(((ord_less_eq_real B) C)->((ord_less_eq_real A) C)))) of role axiom named fact_104_order_Otrans
% 0.71/0.88 A new axiom: (forall (A:real) (B:real) (C:real), (((ord_less_eq_real A) B)->(((ord_less_eq_real B) C)->((ord_less_eq_real A) C))))
% 0.71/0.88 FOF formula (forall (X2:extended_ereal) (Y3:extended_ereal), ((((ord_le824540014_ereal X2) Y3)->False)->((ord_le824540014_ereal Y3) X2))) of role axiom named fact_105_le__cases
% 0.71/0.88 A new axiom: (forall (X2:extended_ereal) (Y3:extended_ereal), ((((ord_le824540014_ereal X2) Y3)->False)->((ord_le824540014_ereal Y3) X2)))
% 0.71/0.88 FOF formula (forall (X2:extended_enat) (Y3:extended_enat), ((((ord_le1863327750d_enat X2) Y3)->False)->((ord_le1863327750d_enat Y3) X2))) of role axiom named fact_106_le__cases
% 0.71/0.88 A new axiom: (forall (X2:extended_enat) (Y3:extended_enat), ((((ord_le1863327750d_enat X2) Y3)->False)->((ord_le1863327750d_enat Y3) X2)))
% 0.71/0.88 FOF formula (forall (X2:nat) (Y3:nat), ((((ord_less_eq_nat X2) Y3)->False)->((ord_less_eq_nat Y3) X2))) of role axiom named fact_107_le__cases
% 0.71/0.88 A new axiom: (forall (X2:nat) (Y3:nat), ((((ord_less_eq_nat X2) Y3)->False)->((ord_less_eq_nat Y3) X2)))
% 0.71/0.88 FOF formula (forall (X2:real) (Y3:real), ((((ord_less_eq_real X2) Y3)->False)->((ord_less_eq_real Y3) X2))) of role axiom named fact_108_le__cases
% 0.71/0.88 A new axiom: (forall (X2:real) (Y3:real), ((((ord_less_eq_real X2) Y3)->False)->((ord_less_eq_real Y3) X2)))
% 0.71/0.88 FOF formula (forall (X2:extended_ereal) (Y3:extended_ereal), ((((eq extended_ereal) X2) Y3)->((ord_le824540014_ereal X2) Y3))) of role axiom named fact_109_eq__refl
% 0.71/0.88 A new axiom: (forall (X2:extended_ereal) (Y3:extended_ereal), ((((eq extended_ereal) X2) Y3)->((ord_le824540014_ereal X2) Y3)))
% 0.71/0.88 FOF formula (forall (X2:extended_enat) (Y3:extended_enat), ((((eq extended_enat) X2) Y3)->((ord_le1863327750d_enat X2) Y3))) of role axiom named fact_110_eq__refl
% 0.71/0.88 A new axiom: (forall (X2:extended_enat) (Y3:extended_enat), ((((eq extended_enat) X2) Y3)->((ord_le1863327750d_enat X2) Y3)))
% 0.71/0.88 FOF formula (forall (X2:nat) (Y3:nat), ((((eq nat) X2) Y3)->((ord_less_eq_nat X2) Y3))) of role axiom named fact_111_eq__refl
% 0.71/0.88 A new axiom: (forall (X2:nat) (Y3:nat), ((((eq nat) X2) Y3)->((ord_less_eq_nat X2) Y3)))
% 0.71/0.88 FOF formula (forall (X2:real) (Y3:real), ((((eq real) X2) Y3)->((ord_less_eq_real X2) Y3))) of role axiom named fact_112_eq__refl
% 0.71/0.88 A new axiom: (forall (X2:real) (Y3:real), ((((eq real) X2) Y3)->((ord_less_eq_real X2) Y3)))
% 0.71/0.88 FOF formula (forall (X2:extended_ereal) (Y3:extended_ereal), ((or ((ord_le824540014_ereal X2) Y3)) ((ord_le824540014_ereal Y3) X2))) of role axiom named fact_113_linear
% 0.71/0.88 A new axiom: (forall (X2:extended_ereal) (Y3:extended_ereal), ((or ((ord_le824540014_ereal X2) Y3)) ((ord_le824540014_ereal Y3) X2)))
% 0.71/0.88 FOF formula (forall (X2:extended_enat) (Y3:extended_enat), ((or ((ord_le1863327750d_enat X2) Y3)) ((ord_le1863327750d_enat Y3) X2))) of role axiom named fact_114_linear
% 0.71/0.88 A new axiom: (forall (X2:extended_enat) (Y3:extended_enat), ((or ((ord_le1863327750d_enat X2) Y3)) ((ord_le1863327750d_enat Y3) X2)))
% 0.74/0.90 FOF formula (forall (X2:nat) (Y3:nat), ((or ((ord_less_eq_nat X2) Y3)) ((ord_less_eq_nat Y3) X2))) of role axiom named fact_115_linear
% 0.74/0.90 A new axiom: (forall (X2:nat) (Y3:nat), ((or ((ord_less_eq_nat X2) Y3)) ((ord_less_eq_nat Y3) X2)))
% 0.74/0.90 FOF formula (forall (X2:real) (Y3:real), ((or ((ord_less_eq_real X2) Y3)) ((ord_less_eq_real Y3) X2))) of role axiom named fact_116_linear
% 0.74/0.90 A new axiom: (forall (X2:real) (Y3:real), ((or ((ord_less_eq_real X2) Y3)) ((ord_less_eq_real Y3) X2)))
% 0.74/0.90 FOF formula (forall (X2:extended_ereal) (Y3:extended_ereal), (((ord_le824540014_ereal X2) Y3)->(((ord_le824540014_ereal Y3) X2)->(((eq extended_ereal) X2) Y3)))) of role axiom named fact_117_antisym
% 0.74/0.90 A new axiom: (forall (X2:extended_ereal) (Y3:extended_ereal), (((ord_le824540014_ereal X2) Y3)->(((ord_le824540014_ereal Y3) X2)->(((eq extended_ereal) X2) Y3))))
% 0.74/0.90 FOF formula (forall (X2:extended_enat) (Y3:extended_enat), (((ord_le1863327750d_enat X2) Y3)->(((ord_le1863327750d_enat Y3) X2)->(((eq extended_enat) X2) Y3)))) of role axiom named fact_118_antisym
% 0.74/0.90 A new axiom: (forall (X2:extended_enat) (Y3:extended_enat), (((ord_le1863327750d_enat X2) Y3)->(((ord_le1863327750d_enat Y3) X2)->(((eq extended_enat) X2) Y3))))
% 0.74/0.90 FOF formula (forall (X2:nat) (Y3:nat), (((ord_less_eq_nat X2) Y3)->(((ord_less_eq_nat Y3) X2)->(((eq nat) X2) Y3)))) of role axiom named fact_119_antisym
% 0.74/0.90 A new axiom: (forall (X2:nat) (Y3:nat), (((ord_less_eq_nat X2) Y3)->(((ord_less_eq_nat Y3) X2)->(((eq nat) X2) Y3))))
% 0.74/0.90 FOF formula (forall (X2:real) (Y3:real), (((ord_less_eq_real X2) Y3)->(((ord_less_eq_real Y3) X2)->(((eq real) X2) Y3)))) of role axiom named fact_120_antisym
% 0.74/0.90 A new axiom: (forall (X2:real) (Y3:real), (((ord_less_eq_real X2) Y3)->(((ord_less_eq_real Y3) X2)->(((eq real) X2) Y3))))
% 0.74/0.90 FOF formula (((eq (extended_ereal->(extended_ereal->Prop))) (fun (Y2:extended_ereal) (Z2:extended_ereal)=> (((eq extended_ereal) Y2) Z2))) (fun (X4:extended_ereal) (Y4:extended_ereal)=> ((and ((ord_le824540014_ereal X4) Y4)) ((ord_le824540014_ereal Y4) X4)))) of role axiom named fact_121_eq__iff
% 0.74/0.90 A new axiom: (((eq (extended_ereal->(extended_ereal->Prop))) (fun (Y2:extended_ereal) (Z2:extended_ereal)=> (((eq extended_ereal) Y2) Z2))) (fun (X4:extended_ereal) (Y4:extended_ereal)=> ((and ((ord_le824540014_ereal X4) Y4)) ((ord_le824540014_ereal Y4) X4))))
% 0.74/0.90 FOF formula (((eq (extended_enat->(extended_enat->Prop))) (fun (Y2:extended_enat) (Z2:extended_enat)=> (((eq extended_enat) Y2) Z2))) (fun (X4:extended_enat) (Y4:extended_enat)=> ((and ((ord_le1863327750d_enat X4) Y4)) ((ord_le1863327750d_enat Y4) X4)))) of role axiom named fact_122_eq__iff
% 0.74/0.90 A new axiom: (((eq (extended_enat->(extended_enat->Prop))) (fun (Y2:extended_enat) (Z2:extended_enat)=> (((eq extended_enat) Y2) Z2))) (fun (X4:extended_enat) (Y4:extended_enat)=> ((and ((ord_le1863327750d_enat X4) Y4)) ((ord_le1863327750d_enat Y4) X4))))
% 0.74/0.90 FOF formula (((eq (nat->(nat->Prop))) (fun (Y2:nat) (Z2:nat)=> (((eq nat) Y2) Z2))) (fun (X4:nat) (Y4:nat)=> ((and ((ord_less_eq_nat X4) Y4)) ((ord_less_eq_nat Y4) X4)))) of role axiom named fact_123_eq__iff
% 0.74/0.90 A new axiom: (((eq (nat->(nat->Prop))) (fun (Y2:nat) (Z2:nat)=> (((eq nat) Y2) Z2))) (fun (X4:nat) (Y4:nat)=> ((and ((ord_less_eq_nat X4) Y4)) ((ord_less_eq_nat Y4) X4))))
% 0.74/0.90 FOF formula (((eq (real->(real->Prop))) (fun (Y2:real) (Z2:real)=> (((eq real) Y2) Z2))) (fun (X4:real) (Y4:real)=> ((and ((ord_less_eq_real X4) Y4)) ((ord_less_eq_real Y4) X4)))) of role axiom named fact_124_eq__iff
% 0.74/0.90 A new axiom: (((eq (real->(real->Prop))) (fun (Y2:real) (Z2:real)=> (((eq real) Y2) Z2))) (fun (X4:real) (Y4:real)=> ((and ((ord_less_eq_real X4) Y4)) ((ord_less_eq_real Y4) X4))))
% 0.74/0.90 FOF formula (forall (G:(a->extended_ereal)) (F:(a->extended_ereal)), (((eq Prop) (((eq (a->extended_ereal)) G) (lower_881475195hull_a F))) ((and ((and (lower_1616484581_ereal G)) (forall (X4:a), ((ord_le824540014_ereal (G X4)) (F X4))))) (forall (H:(a->extended_ereal)), (((and (lower_1616484581_ereal H)) (forall (X4:a), ((ord_le824540014_ereal (H X4)) (F X4))))->(forall (X4:a), ((ord_le824540014_ereal (H X4)) (G X4)))))))) of role axiom named fact_125_lsc__hull__iff__greatest
% 0.74/0.91 A new axiom: (forall (G:(a->extended_ereal)) (F:(a->extended_ereal)), (((eq Prop) (((eq (a->extended_ereal)) G) (lower_881475195hull_a F))) ((and ((and (lower_1616484581_ereal G)) (forall (X4:a), ((ord_le824540014_ereal (G X4)) (F X4))))) (forall (H:(a->extended_ereal)), (((and (lower_1616484581_ereal H)) (forall (X4:a), ((ord_le824540014_ereal (H X4)) (F X4))))->(forall (X4:a), ((ord_le824540014_ereal (H X4)) (G X4))))))))
% 0.74/0.91 FOF formula (forall (G:(a->extended_ereal)) (F:(a->extended_ereal)), ((lower_1616484581_ereal G)->((forall (X3:a), ((ord_le824540014_ereal (G X3)) (F X3)))->(forall (X:a), ((ord_le824540014_ereal (G X)) ((lower_881475195hull_a F) X)))))) of role axiom named fact_126_lsc__hull__greatest
% 0.74/0.91 A new axiom: (forall (G:(a->extended_ereal)) (F:(a->extended_ereal)), ((lower_1616484581_ereal G)->((forall (X3:a), ((ord_le824540014_ereal (G X3)) (F X3)))->(forall (X:a), ((ord_le824540014_ereal (G X)) ((lower_881475195hull_a F) X))))))
% 0.74/0.91 FOF formula (forall (P:(extended_ereal->Prop)) (X2:extended_ereal), ((P X2)->((forall (Y:extended_ereal), ((P Y)->((ord_le824540014_ereal Y) X2)))->(((eq extended_ereal) (order_1158471719_ereal P)) X2)))) of role axiom named fact_127_Greatest__equality
% 0.74/0.91 A new axiom: (forall (P:(extended_ereal->Prop)) (X2:extended_ereal), ((P X2)->((forall (Y:extended_ereal), ((P Y)->((ord_le824540014_ereal Y) X2)))->(((eq extended_ereal) (order_1158471719_ereal P)) X2))))
% 0.74/0.91 FOF formula (forall (P:(extended_enat->Prop)) (X2:extended_enat), ((P X2)->((forall (Y:extended_enat), ((P Y)->((ord_le1863327750d_enat Y) X2)))->(((eq extended_enat) (order_1628344639d_enat P)) X2)))) of role axiom named fact_128_Greatest__equality
% 0.74/0.91 A new axiom: (forall (P:(extended_enat->Prop)) (X2:extended_enat), ((P X2)->((forall (Y:extended_enat), ((P Y)->((ord_le1863327750d_enat Y) X2)))->(((eq extended_enat) (order_1628344639d_enat P)) X2))))
% 0.74/0.91 FOF formula (forall (P:(real->Prop)) (X2:real), ((P X2)->((forall (Y:real), ((P Y)->((ord_less_eq_real Y) X2)))->(((eq real) (order_Greatest_real P)) X2)))) of role axiom named fact_129_Greatest__equality
% 0.74/0.91 A new axiom: (forall (P:(real->Prop)) (X2:real), ((P X2)->((forall (Y:real), ((P Y)->((ord_less_eq_real Y) X2)))->(((eq real) (order_Greatest_real P)) X2))))
% 0.74/0.91 FOF formula (forall (P:(nat->Prop)) (X2:nat), ((P X2)->((forall (Y:nat), ((P Y)->((ord_less_eq_nat Y) X2)))->(((eq nat) (order_Greatest_nat P)) X2)))) of role axiom named fact_130_Greatest__equality
% 0.74/0.91 A new axiom: (forall (P:(nat->Prop)) (X2:nat), ((P X2)->((forall (Y:nat), ((P Y)->((ord_less_eq_nat Y) X2)))->(((eq nat) (order_Greatest_nat P)) X2))))
% 0.74/0.91 FOF formula (forall (P:(extended_ereal->Prop)) (X2:extended_ereal) (Q:(extended_ereal->Prop)), ((P X2)->((forall (Y:extended_ereal), ((P Y)->((ord_le824540014_ereal Y) X2)))->((forall (X3:extended_ereal), ((P X3)->((forall (Y5:extended_ereal), ((P Y5)->((ord_le824540014_ereal Y5) X3)))->(Q X3))))->(Q (order_1158471719_ereal P)))))) of role axiom named fact_131_GreatestI2__order
% 0.74/0.91 A new axiom: (forall (P:(extended_ereal->Prop)) (X2:extended_ereal) (Q:(extended_ereal->Prop)), ((P X2)->((forall (Y:extended_ereal), ((P Y)->((ord_le824540014_ereal Y) X2)))->((forall (X3:extended_ereal), ((P X3)->((forall (Y5:extended_ereal), ((P Y5)->((ord_le824540014_ereal Y5) X3)))->(Q X3))))->(Q (order_1158471719_ereal P))))))
% 0.74/0.91 FOF formula (forall (P:(extended_enat->Prop)) (X2:extended_enat) (Q:(extended_enat->Prop)), ((P X2)->((forall (Y:extended_enat), ((P Y)->((ord_le1863327750d_enat Y) X2)))->((forall (X3:extended_enat), ((P X3)->((forall (Y5:extended_enat), ((P Y5)->((ord_le1863327750d_enat Y5) X3)))->(Q X3))))->(Q (order_1628344639d_enat P)))))) of role axiom named fact_132_GreatestI2__order
% 0.74/0.91 A new axiom: (forall (P:(extended_enat->Prop)) (X2:extended_enat) (Q:(extended_enat->Prop)), ((P X2)->((forall (Y:extended_enat), ((P Y)->((ord_le1863327750d_enat Y) X2)))->((forall (X3:extended_enat), ((P X3)->((forall (Y5:extended_enat), ((P Y5)->((ord_le1863327750d_enat Y5) X3)))->(Q X3))))->(Q (order_1628344639d_enat P))))))
% 0.77/0.93 FOF formula (forall (P:(real->Prop)) (X2:real) (Q:(real->Prop)), ((P X2)->((forall (Y:real), ((P Y)->((ord_less_eq_real Y) X2)))->((forall (X3:real), ((P X3)->((forall (Y5:real), ((P Y5)->((ord_less_eq_real Y5) X3)))->(Q X3))))->(Q (order_Greatest_real P)))))) of role axiom named fact_133_GreatestI2__order
% 0.77/0.93 A new axiom: (forall (P:(real->Prop)) (X2:real) (Q:(real->Prop)), ((P X2)->((forall (Y:real), ((P Y)->((ord_less_eq_real Y) X2)))->((forall (X3:real), ((P X3)->((forall (Y5:real), ((P Y5)->((ord_less_eq_real Y5) X3)))->(Q X3))))->(Q (order_Greatest_real P))))))
% 0.77/0.93 FOF formula (forall (P:(nat->Prop)) (X2:nat) (Q:(nat->Prop)), ((P X2)->((forall (Y:nat), ((P Y)->((ord_less_eq_nat Y) X2)))->((forall (X3:nat), ((P X3)->((forall (Y5:nat), ((P Y5)->((ord_less_eq_nat Y5) X3)))->(Q X3))))->(Q (order_Greatest_nat P)))))) of role axiom named fact_134_GreatestI2__order
% 0.77/0.93 A new axiom: (forall (P:(nat->Prop)) (X2:nat) (Q:(nat->Prop)), ((P X2)->((forall (Y:nat), ((P Y)->((ord_less_eq_nat Y) X2)))->((forall (X3:nat), ((P X3)->((forall (Y5:nat), ((P Y5)->((ord_less_eq_nat Y5) X3)))->(Q X3))))->(Q (order_Greatest_nat P))))))
% 0.77/0.93 FOF formula (((eq ((Prop->extended_ereal)->((Prop->extended_ereal)->Prop))) ord_le637473275_ereal) (fun (X5:(Prop->extended_ereal)) (Y6:(Prop->extended_ereal))=> ((and ((ord_le824540014_ereal (X5 False)) (Y6 False))) ((ord_le824540014_ereal (X5 True)) (Y6 True))))) of role axiom named fact_135_le__rel__bool__arg__iff
% 0.77/0.93 A new axiom: (((eq ((Prop->extended_ereal)->((Prop->extended_ereal)->Prop))) ord_le637473275_ereal) (fun (X5:(Prop->extended_ereal)) (Y6:(Prop->extended_ereal))=> ((and ((ord_le824540014_ereal (X5 False)) (Y6 False))) ((ord_le824540014_ereal (X5 True)) (Y6 True)))))
% 0.77/0.93 FOF formula (((eq ((Prop->extended_enat)->((Prop->extended_enat)->Prop))) ord_le291126163d_enat) (fun (X5:(Prop->extended_enat)) (Y6:(Prop->extended_enat))=> ((and ((ord_le1863327750d_enat (X5 False)) (Y6 False))) ((ord_le1863327750d_enat (X5 True)) (Y6 True))))) of role axiom named fact_136_le__rel__bool__arg__iff
% 0.77/0.93 A new axiom: (((eq ((Prop->extended_enat)->((Prop->extended_enat)->Prop))) ord_le291126163d_enat) (fun (X5:(Prop->extended_enat)) (Y6:(Prop->extended_enat))=> ((and ((ord_le1863327750d_enat (X5 False)) (Y6 False))) ((ord_le1863327750d_enat (X5 True)) (Y6 True)))))
% 0.77/0.93 FOF formula (((eq ((Prop->nat)->((Prop->nat)->Prop))) ord_less_eq_o_nat) (fun (X5:(Prop->nat)) (Y6:(Prop->nat))=> ((and ((ord_less_eq_nat (X5 False)) (Y6 False))) ((ord_less_eq_nat (X5 True)) (Y6 True))))) of role axiom named fact_137_le__rel__bool__arg__iff
% 0.77/0.93 A new axiom: (((eq ((Prop->nat)->((Prop->nat)->Prop))) ord_less_eq_o_nat) (fun (X5:(Prop->nat)) (Y6:(Prop->nat))=> ((and ((ord_less_eq_nat (X5 False)) (Y6 False))) ((ord_less_eq_nat (X5 True)) (Y6 True)))))
% 0.77/0.93 FOF formula (((eq ((Prop->real)->((Prop->real)->Prop))) ord_less_eq_o_real) (fun (X5:(Prop->real)) (Y6:(Prop->real))=> ((and ((ord_less_eq_real (X5 False)) (Y6 False))) ((ord_less_eq_real (X5 True)) (Y6 True))))) of role axiom named fact_138_le__rel__bool__arg__iff
% 0.77/0.93 A new axiom: (((eq ((Prop->real)->((Prop->real)->Prop))) ord_less_eq_o_real) (fun (X5:(Prop->real)) (Y6:(Prop->real))=> ((and ((ord_less_eq_real (X5 False)) (Y6 False))) ((ord_less_eq_real (X5 True)) (Y6 True)))))
% 0.77/0.93 FOF formula (forall (F:(a->extended_ereal)), (lower_1616484581_ereal (lower_881475195hull_a F))) of role axiom named fact_139_lsc__lsc__hull
% 0.77/0.93 A new axiom: (forall (F:(a->extended_ereal)), (lower_1616484581_ereal (lower_881475195hull_a F)))
% 0.77/0.93 FOF formula (forall (M:extended_enat) (N:extended_enat), (((eq Prop) ((ord_le824540014_ereal (extend1771934483f_enat M)) (extend1771934483f_enat N))) ((ord_le1863327750d_enat M) N))) of role axiom named fact_140_ereal__of__enat__le__iff
% 0.77/0.93 A new axiom: (forall (M:extended_enat) (N:extended_enat), (((eq Prop) ((ord_le824540014_ereal (extend1771934483f_enat M)) (extend1771934483f_enat N))) ((ord_le1863327750d_enat M) N)))
% 0.77/0.93 FOF formula (((eq ((extended_ereal->extended_ereal)->Prop)) order_1408494002_ereal) (fun (F2:(extended_ereal->extended_ereal))=> (forall (X4:extended_ereal) (Y4:extended_ereal), (((ord_le824540014_ereal X4) Y4)->((ord_le824540014_ereal (F2 Y4)) (F2 X4)))))) of role axiom named fact_141_antimono__def
% 0.77/0.94 A new axiom: (((eq ((extended_ereal->extended_ereal)->Prop)) order_1408494002_ereal) (fun (F2:(extended_ereal->extended_ereal))=> (forall (X4:extended_ereal) (Y4:extended_ereal), (((ord_le824540014_ereal X4) Y4)->((ord_le824540014_ereal (F2 Y4)) (F2 X4))))))
% 0.77/0.94 FOF formula (((eq ((extended_ereal->extended_enat)->Prop)) order_680161354d_enat) (fun (F2:(extended_ereal->extended_enat))=> (forall (X4:extended_ereal) (Y4:extended_ereal), (((ord_le824540014_ereal X4) Y4)->((ord_le1863327750d_enat (F2 Y4)) (F2 X4)))))) of role axiom named fact_142_antimono__def
% 0.77/0.94 A new axiom: (((eq ((extended_ereal->extended_enat)->Prop)) order_680161354d_enat) (fun (F2:(extended_ereal->extended_enat))=> (forall (X4:extended_ereal) (Y4:extended_ereal), (((ord_le824540014_ereal X4) Y4)->((ord_le1863327750d_enat (F2 Y4)) (F2 X4))))))
% 0.77/0.94 FOF formula (((eq ((extended_ereal->nat)->Prop)) order_523806444al_nat) (fun (F2:(extended_ereal->nat))=> (forall (X4:extended_ereal) (Y4:extended_ereal), (((ord_le824540014_ereal X4) Y4)->((ord_less_eq_nat (F2 Y4)) (F2 X4)))))) of role axiom named fact_143_antimono__def
% 0.77/0.94 A new axiom: (((eq ((extended_ereal->nat)->Prop)) order_523806444al_nat) (fun (F2:(extended_ereal->nat))=> (forall (X4:extended_ereal) (Y4:extended_ereal), (((ord_le824540014_ereal X4) Y4)->((ord_less_eq_nat (F2 Y4)) (F2 X4))))))
% 0.77/0.94 FOF formula (((eq ((extended_ereal->real)->Prop)) order_1800387528l_real) (fun (F2:(extended_ereal->real))=> (forall (X4:extended_ereal) (Y4:extended_ereal), (((ord_le824540014_ereal X4) Y4)->((ord_less_eq_real (F2 Y4)) (F2 X4)))))) of role axiom named fact_144_antimono__def
% 0.77/0.94 A new axiom: (((eq ((extended_ereal->real)->Prop)) order_1800387528l_real) (fun (F2:(extended_ereal->real))=> (forall (X4:extended_ereal) (Y4:extended_ereal), (((ord_le824540014_ereal X4) Y4)->((ord_less_eq_real (F2 Y4)) (F2 X4))))))
% 0.77/0.94 FOF formula (((eq ((extended_enat->extended_ereal)->Prop)) order_1147259034_ereal) (fun (F2:(extended_enat->extended_ereal))=> (forall (X4:extended_enat) (Y4:extended_enat), (((ord_le1863327750d_enat X4) Y4)->((ord_le824540014_ereal (F2 Y4)) (F2 X4)))))) of role axiom named fact_145_antimono__def
% 0.77/0.94 A new axiom: (((eq ((extended_enat->extended_ereal)->Prop)) order_1147259034_ereal) (fun (F2:(extended_enat->extended_ereal))=> (forall (X4:extended_enat) (Y4:extended_enat), (((ord_le1863327750d_enat X4) Y4)->((ord_le824540014_ereal (F2 Y4)) (F2 X4))))))
% 0.77/0.94 FOF formula (((eq ((extended_enat->extended_enat)->Prop)) order_2047034162d_enat) (fun (F2:(extended_enat->extended_enat))=> (forall (X4:extended_enat) (Y4:extended_enat), (((ord_le1863327750d_enat X4) Y4)->((ord_le1863327750d_enat (F2 Y4)) (F2 X4)))))) of role axiom named fact_146_antimono__def
% 0.77/0.94 A new axiom: (((eq ((extended_enat->extended_enat)->Prop)) order_2047034162d_enat) (fun (F2:(extended_enat->extended_enat))=> (forall (X4:extended_enat) (Y4:extended_enat), (((ord_le1863327750d_enat X4) Y4)->((ord_le1863327750d_enat (F2 Y4)) (F2 X4))))))
% 0.77/0.94 FOF formula (((eq ((extended_enat->nat)->Prop)) order_442688004at_nat) (fun (F2:(extended_enat->nat))=> (forall (X4:extended_enat) (Y4:extended_enat), (((ord_le1863327750d_enat X4) Y4)->((ord_less_eq_nat (F2 Y4)) (F2 X4)))))) of role axiom named fact_147_antimono__def
% 0.77/0.94 A new axiom: (((eq ((extended_enat->nat)->Prop)) order_442688004at_nat) (fun (F2:(extended_enat->nat))=> (forall (X4:extended_enat) (Y4:extended_enat), (((ord_le1863327750d_enat X4) Y4)->((ord_less_eq_nat (F2 Y4)) (F2 X4))))))
% 0.77/0.94 FOF formula (((eq ((extended_enat->real)->Prop)) order_182315744t_real) (fun (F2:(extended_enat->real))=> (forall (X4:extended_enat) (Y4:extended_enat), (((ord_le1863327750d_enat X4) Y4)->((ord_less_eq_real (F2 Y4)) (F2 X4)))))) of role axiom named fact_148_antimono__def
% 0.77/0.94 A new axiom: (((eq ((extended_enat->real)->Prop)) order_182315744t_real) (fun (F2:(extended_enat->real))=> (forall (X4:extended_enat) (Y4:extended_enat), (((ord_le1863327750d_enat X4) Y4)->((ord_less_eq_real (F2 Y4)) (F2 X4))))))
% 0.77/0.94 FOF formula (((eq ((nat->extended_ereal)->Prop)) order_736687562_ereal) (fun (F2:(nat->extended_ereal))=> (forall (X4:nat) (Y4:nat), (((ord_less_eq_nat X4) Y4)->((ord_le824540014_ereal (F2 Y4)) (F2 X4)))))) of role axiom named fact_149_antimono__def
% 0.77/0.95 A new axiom: (((eq ((nat->extended_ereal)->Prop)) order_736687562_ereal) (fun (F2:(nat->extended_ereal))=> (forall (X4:nat) (Y4:nat), (((ord_less_eq_nat X4) Y4)->((ord_le824540014_ereal (F2 Y4)) (F2 X4))))))
% 0.77/0.95 FOF formula (((eq ((nat->extended_enat)->Prop)) order_1660553314d_enat) (fun (F2:(nat->extended_enat))=> (forall (X4:nat) (Y4:nat), (((ord_less_eq_nat X4) Y4)->((ord_le1863327750d_enat (F2 Y4)) (F2 X4)))))) of role axiom named fact_150_antimono__def
% 0.77/0.95 A new axiom: (((eq ((nat->extended_enat)->Prop)) order_1660553314d_enat) (fun (F2:(nat->extended_enat))=> (forall (X4:nat) (Y4:nat), (((ord_less_eq_nat X4) Y4)->((ord_le1863327750d_enat (F2 Y4)) (F2 X4))))))
% 0.77/0.95 FOF formula (forall (F:(extended_ereal->extended_ereal)), ((forall (X3:extended_ereal) (Y:extended_ereal), (((ord_le824540014_ereal X3) Y)->((ord_le824540014_ereal (F Y)) (F X3))))->(order_1408494002_ereal F))) of role axiom named fact_151_antimonoI
% 0.77/0.95 A new axiom: (forall (F:(extended_ereal->extended_ereal)), ((forall (X3:extended_ereal) (Y:extended_ereal), (((ord_le824540014_ereal X3) Y)->((ord_le824540014_ereal (F Y)) (F X3))))->(order_1408494002_ereal F)))
% 0.77/0.95 FOF formula (forall (F:(extended_ereal->extended_enat)), ((forall (X3:extended_ereal) (Y:extended_ereal), (((ord_le824540014_ereal X3) Y)->((ord_le1863327750d_enat (F Y)) (F X3))))->(order_680161354d_enat F))) of role axiom named fact_152_antimonoI
% 0.77/0.95 A new axiom: (forall (F:(extended_ereal->extended_enat)), ((forall (X3:extended_ereal) (Y:extended_ereal), (((ord_le824540014_ereal X3) Y)->((ord_le1863327750d_enat (F Y)) (F X3))))->(order_680161354d_enat F)))
% 0.77/0.95 FOF formula (forall (F:(extended_ereal->nat)), ((forall (X3:extended_ereal) (Y:extended_ereal), (((ord_le824540014_ereal X3) Y)->((ord_less_eq_nat (F Y)) (F X3))))->(order_523806444al_nat F))) of role axiom named fact_153_antimonoI
% 0.77/0.95 A new axiom: (forall (F:(extended_ereal->nat)), ((forall (X3:extended_ereal) (Y:extended_ereal), (((ord_le824540014_ereal X3) Y)->((ord_less_eq_nat (F Y)) (F X3))))->(order_523806444al_nat F)))
% 0.77/0.95 FOF formula (forall (F:(extended_ereal->real)), ((forall (X3:extended_ereal) (Y:extended_ereal), (((ord_le824540014_ereal X3) Y)->((ord_less_eq_real (F Y)) (F X3))))->(order_1800387528l_real F))) of role axiom named fact_154_antimonoI
% 0.77/0.95 A new axiom: (forall (F:(extended_ereal->real)), ((forall (X3:extended_ereal) (Y:extended_ereal), (((ord_le824540014_ereal X3) Y)->((ord_less_eq_real (F Y)) (F X3))))->(order_1800387528l_real F)))
% 0.77/0.95 FOF formula (forall (F:(extended_enat->extended_ereal)), ((forall (X3:extended_enat) (Y:extended_enat), (((ord_le1863327750d_enat X3) Y)->((ord_le824540014_ereal (F Y)) (F X3))))->(order_1147259034_ereal F))) of role axiom named fact_155_antimonoI
% 0.77/0.95 A new axiom: (forall (F:(extended_enat->extended_ereal)), ((forall (X3:extended_enat) (Y:extended_enat), (((ord_le1863327750d_enat X3) Y)->((ord_le824540014_ereal (F Y)) (F X3))))->(order_1147259034_ereal F)))
% 0.77/0.95 FOF formula (forall (F:(extended_enat->extended_enat)), ((forall (X3:extended_enat) (Y:extended_enat), (((ord_le1863327750d_enat X3) Y)->((ord_le1863327750d_enat (F Y)) (F X3))))->(order_2047034162d_enat F))) of role axiom named fact_156_antimonoI
% 0.77/0.95 A new axiom: (forall (F:(extended_enat->extended_enat)), ((forall (X3:extended_enat) (Y:extended_enat), (((ord_le1863327750d_enat X3) Y)->((ord_le1863327750d_enat (F Y)) (F X3))))->(order_2047034162d_enat F)))
% 0.77/0.95 FOF formula (forall (F:(extended_enat->nat)), ((forall (X3:extended_enat) (Y:extended_enat), (((ord_le1863327750d_enat X3) Y)->((ord_less_eq_nat (F Y)) (F X3))))->(order_442688004at_nat F))) of role axiom named fact_157_antimonoI
% 0.77/0.95 A new axiom: (forall (F:(extended_enat->nat)), ((forall (X3:extended_enat) (Y:extended_enat), (((ord_le1863327750d_enat X3) Y)->((ord_less_eq_nat (F Y)) (F X3))))->(order_442688004at_nat F)))
% 0.77/0.95 FOF formula (forall (F:(extended_enat->real)), ((forall (X3:extended_enat) (Y:extended_enat), (((ord_le1863327750d_enat X3) Y)->((ord_less_eq_real (F Y)) (F X3))))->(order_182315744t_real F))) of role axiom named fact_158_antimonoI
% 0.77/0.96 A new axiom: (forall (F:(extended_enat->real)), ((forall (X3:extended_enat) (Y:extended_enat), (((ord_le1863327750d_enat X3) Y)->((ord_less_eq_real (F Y)) (F X3))))->(order_182315744t_real F)))
% 0.77/0.96 FOF formula (forall (F:(nat->extended_ereal)), ((forall (X3:nat) (Y:nat), (((ord_less_eq_nat X3) Y)->((ord_le824540014_ereal (F Y)) (F X3))))->(order_736687562_ereal F))) of role axiom named fact_159_antimonoI
% 0.77/0.96 A new axiom: (forall (F:(nat->extended_ereal)), ((forall (X3:nat) (Y:nat), (((ord_less_eq_nat X3) Y)->((ord_le824540014_ereal (F Y)) (F X3))))->(order_736687562_ereal F)))
% 0.77/0.96 FOF formula (forall (F:(nat->extended_enat)), ((forall (X3:nat) (Y:nat), (((ord_less_eq_nat X3) Y)->((ord_le1863327750d_enat (F Y)) (F X3))))->(order_1660553314d_enat F))) of role axiom named fact_160_antimonoI
% 0.77/0.96 A new axiom: (forall (F:(nat->extended_enat)), ((forall (X3:nat) (Y:nat), (((ord_less_eq_nat X3) Y)->((ord_le1863327750d_enat (F Y)) (F X3))))->(order_1660553314d_enat F)))
% 0.77/0.96 FOF formula (forall (F:(extended_ereal->extended_ereal)) (X2:extended_ereal) (Y3:extended_ereal), ((order_1408494002_ereal F)->(((ord_le824540014_ereal X2) Y3)->((ord_le824540014_ereal (F Y3)) (F X2))))) of role axiom named fact_161_antimonoE
% 0.77/0.96 A new axiom: (forall (F:(extended_ereal->extended_ereal)) (X2:extended_ereal) (Y3:extended_ereal), ((order_1408494002_ereal F)->(((ord_le824540014_ereal X2) Y3)->((ord_le824540014_ereal (F Y3)) (F X2)))))
% 0.77/0.96 FOF formula (forall (F:(extended_ereal->extended_enat)) (X2:extended_ereal) (Y3:extended_ereal), ((order_680161354d_enat F)->(((ord_le824540014_ereal X2) Y3)->((ord_le1863327750d_enat (F Y3)) (F X2))))) of role axiom named fact_162_antimonoE
% 0.77/0.96 A new axiom: (forall (F:(extended_ereal->extended_enat)) (X2:extended_ereal) (Y3:extended_ereal), ((order_680161354d_enat F)->(((ord_le824540014_ereal X2) Y3)->((ord_le1863327750d_enat (F Y3)) (F X2)))))
% 0.77/0.96 FOF formula (forall (F:(extended_ereal->nat)) (X2:extended_ereal) (Y3:extended_ereal), ((order_523806444al_nat F)->(((ord_le824540014_ereal X2) Y3)->((ord_less_eq_nat (F Y3)) (F X2))))) of role axiom named fact_163_antimonoE
% 0.77/0.96 A new axiom: (forall (F:(extended_ereal->nat)) (X2:extended_ereal) (Y3:extended_ereal), ((order_523806444al_nat F)->(((ord_le824540014_ereal X2) Y3)->((ord_less_eq_nat (F Y3)) (F X2)))))
% 0.77/0.96 FOF formula (forall (F:(extended_ereal->real)) (X2:extended_ereal) (Y3:extended_ereal), ((order_1800387528l_real F)->(((ord_le824540014_ereal X2) Y3)->((ord_less_eq_real (F Y3)) (F X2))))) of role axiom named fact_164_antimonoE
% 0.77/0.96 A new axiom: (forall (F:(extended_ereal->real)) (X2:extended_ereal) (Y3:extended_ereal), ((order_1800387528l_real F)->(((ord_le824540014_ereal X2) Y3)->((ord_less_eq_real (F Y3)) (F X2)))))
% 0.77/0.96 FOF formula (forall (F:(extended_enat->extended_ereal)) (X2:extended_enat) (Y3:extended_enat), ((order_1147259034_ereal F)->(((ord_le1863327750d_enat X2) Y3)->((ord_le824540014_ereal (F Y3)) (F X2))))) of role axiom named fact_165_antimonoE
% 0.77/0.96 A new axiom: (forall (F:(extended_enat->extended_ereal)) (X2:extended_enat) (Y3:extended_enat), ((order_1147259034_ereal F)->(((ord_le1863327750d_enat X2) Y3)->((ord_le824540014_ereal (F Y3)) (F X2)))))
% 0.77/0.96 FOF formula (forall (F:(extended_enat->extended_enat)) (X2:extended_enat) (Y3:extended_enat), ((order_2047034162d_enat F)->(((ord_le1863327750d_enat X2) Y3)->((ord_le1863327750d_enat (F Y3)) (F X2))))) of role axiom named fact_166_antimonoE
% 0.77/0.96 A new axiom: (forall (F:(extended_enat->extended_enat)) (X2:extended_enat) (Y3:extended_enat), ((order_2047034162d_enat F)->(((ord_le1863327750d_enat X2) Y3)->((ord_le1863327750d_enat (F Y3)) (F X2)))))
% 0.77/0.96 FOF formula (forall (F:(extended_enat->nat)) (X2:extended_enat) (Y3:extended_enat), ((order_442688004at_nat F)->(((ord_le1863327750d_enat X2) Y3)->((ord_less_eq_nat (F Y3)) (F X2))))) of role axiom named fact_167_antimonoE
% 0.77/0.96 A new axiom: (forall (F:(extended_enat->nat)) (X2:extended_enat) (Y3:extended_enat), ((order_442688004at_nat F)->(((ord_le1863327750d_enat X2) Y3)->((ord_less_eq_nat (F Y3)) (F X2)))))
% 0.77/0.98 FOF formula (forall (F:(extended_enat->real)) (X2:extended_enat) (Y3:extended_enat), ((order_182315744t_real F)->(((ord_le1863327750d_enat X2) Y3)->((ord_less_eq_real (F Y3)) (F X2))))) of role axiom named fact_168_antimonoE
% 0.77/0.98 A new axiom: (forall (F:(extended_enat->real)) (X2:extended_enat) (Y3:extended_enat), ((order_182315744t_real F)->(((ord_le1863327750d_enat X2) Y3)->((ord_less_eq_real (F Y3)) (F X2)))))
% 0.77/0.98 FOF formula (forall (F:(nat->extended_ereal)) (X2:nat) (Y3:nat), ((order_736687562_ereal F)->(((ord_less_eq_nat X2) Y3)->((ord_le824540014_ereal (F Y3)) (F X2))))) of role axiom named fact_169_antimonoE
% 0.77/0.98 A new axiom: (forall (F:(nat->extended_ereal)) (X2:nat) (Y3:nat), ((order_736687562_ereal F)->(((ord_less_eq_nat X2) Y3)->((ord_le824540014_ereal (F Y3)) (F X2)))))
% 0.77/0.98 FOF formula (forall (F:(nat->extended_enat)) (X2:nat) (Y3:nat), ((order_1660553314d_enat F)->(((ord_less_eq_nat X2) Y3)->((ord_le1863327750d_enat (F Y3)) (F X2))))) of role axiom named fact_170_antimonoE
% 0.77/0.98 A new axiom: (forall (F:(nat->extended_enat)) (X2:nat) (Y3:nat), ((order_1660553314d_enat F)->(((ord_less_eq_nat X2) Y3)->((ord_le1863327750d_enat (F Y3)) (F X2)))))
% 0.77/0.98 FOF formula (forall (F:(extended_ereal->extended_ereal)) (X2:extended_ereal) (Y3:extended_ereal), ((order_1408494002_ereal F)->(((ord_le824540014_ereal X2) Y3)->((ord_le824540014_ereal (F Y3)) (F X2))))) of role axiom named fact_171_antimonoD
% 0.77/0.98 A new axiom: (forall (F:(extended_ereal->extended_ereal)) (X2:extended_ereal) (Y3:extended_ereal), ((order_1408494002_ereal F)->(((ord_le824540014_ereal X2) Y3)->((ord_le824540014_ereal (F Y3)) (F X2)))))
% 0.77/0.98 FOF formula (forall (F:(extended_ereal->extended_enat)) (X2:extended_ereal) (Y3:extended_ereal), ((order_680161354d_enat F)->(((ord_le824540014_ereal X2) Y3)->((ord_le1863327750d_enat (F Y3)) (F X2))))) of role axiom named fact_172_antimonoD
% 0.77/0.98 A new axiom: (forall (F:(extended_ereal->extended_enat)) (X2:extended_ereal) (Y3:extended_ereal), ((order_680161354d_enat F)->(((ord_le824540014_ereal X2) Y3)->((ord_le1863327750d_enat (F Y3)) (F X2)))))
% 0.77/0.98 FOF formula (forall (F:(extended_ereal->nat)) (X2:extended_ereal) (Y3:extended_ereal), ((order_523806444al_nat F)->(((ord_le824540014_ereal X2) Y3)->((ord_less_eq_nat (F Y3)) (F X2))))) of role axiom named fact_173_antimonoD
% 0.77/0.98 A new axiom: (forall (F:(extended_ereal->nat)) (X2:extended_ereal) (Y3:extended_ereal), ((order_523806444al_nat F)->(((ord_le824540014_ereal X2) Y3)->((ord_less_eq_nat (F Y3)) (F X2)))))
% 0.77/0.98 FOF formula (forall (F:(extended_ereal->real)) (X2:extended_ereal) (Y3:extended_ereal), ((order_1800387528l_real F)->(((ord_le824540014_ereal X2) Y3)->((ord_less_eq_real (F Y3)) (F X2))))) of role axiom named fact_174_antimonoD
% 0.77/0.98 A new axiom: (forall (F:(extended_ereal->real)) (X2:extended_ereal) (Y3:extended_ereal), ((order_1800387528l_real F)->(((ord_le824540014_ereal X2) Y3)->((ord_less_eq_real (F Y3)) (F X2)))))
% 0.77/0.98 FOF formula (forall (F:(extended_enat->extended_ereal)) (X2:extended_enat) (Y3:extended_enat), ((order_1147259034_ereal F)->(((ord_le1863327750d_enat X2) Y3)->((ord_le824540014_ereal (F Y3)) (F X2))))) of role axiom named fact_175_antimonoD
% 0.77/0.98 A new axiom: (forall (F:(extended_enat->extended_ereal)) (X2:extended_enat) (Y3:extended_enat), ((order_1147259034_ereal F)->(((ord_le1863327750d_enat X2) Y3)->((ord_le824540014_ereal (F Y3)) (F X2)))))
% 0.77/0.98 FOF formula (forall (F:(extended_enat->extended_enat)) (X2:extended_enat) (Y3:extended_enat), ((order_2047034162d_enat F)->(((ord_le1863327750d_enat X2) Y3)->((ord_le1863327750d_enat (F Y3)) (F X2))))) of role axiom named fact_176_antimonoD
% 0.77/0.98 A new axiom: (forall (F:(extended_enat->extended_enat)) (X2:extended_enat) (Y3:extended_enat), ((order_2047034162d_enat F)->(((ord_le1863327750d_enat X2) Y3)->((ord_le1863327750d_enat (F Y3)) (F X2)))))
% 0.77/0.98 FOF formula (forall (F:(extended_enat->nat)) (X2:extended_enat) (Y3:extended_enat), ((order_442688004at_nat F)->(((ord_le1863327750d_enat X2) Y3)->((ord_less_eq_nat (F Y3)) (F X2))))) of role axiom named fact_177_antimonoD
% 0.77/0.98 A new axiom: (forall (F:(extended_enat->nat)) (X2:extended_enat) (Y3:extended_enat), ((order_442688004at_nat F)->(((ord_le1863327750d_enat X2) Y3)->((ord_less_eq_nat (F Y3)) (F X2)))))
% 0.77/0.99 FOF formula (forall (F:(extended_enat->real)) (X2:extended_enat) (Y3:extended_enat), ((order_182315744t_real F)->(((ord_le1863327750d_enat X2) Y3)->((ord_less_eq_real (F Y3)) (F X2))))) of role axiom named fact_178_antimonoD
% 0.77/0.99 A new axiom: (forall (F:(extended_enat->real)) (X2:extended_enat) (Y3:extended_enat), ((order_182315744t_real F)->(((ord_le1863327750d_enat X2) Y3)->((ord_less_eq_real (F Y3)) (F X2)))))
% 0.77/0.99 FOF formula (forall (F:(nat->extended_ereal)) (X2:nat) (Y3:nat), ((order_736687562_ereal F)->(((ord_less_eq_nat X2) Y3)->((ord_le824540014_ereal (F Y3)) (F X2))))) of role axiom named fact_179_antimonoD
% 0.77/0.99 A new axiom: (forall (F:(nat->extended_ereal)) (X2:nat) (Y3:nat), ((order_736687562_ereal F)->(((ord_less_eq_nat X2) Y3)->((ord_le824540014_ereal (F Y3)) (F X2)))))
% 0.77/0.99 FOF formula (forall (F:(nat->extended_enat)) (X2:nat) (Y3:nat), ((order_1660553314d_enat F)->(((ord_less_eq_nat X2) Y3)->((ord_le1863327750d_enat (F Y3)) (F X2))))) of role axiom named fact_180_antimonoD
% 0.77/0.99 A new axiom: (forall (F:(nat->extended_enat)) (X2:nat) (Y3:nat), ((order_1660553314d_enat F)->(((ord_less_eq_nat X2) Y3)->((ord_le1863327750d_enat (F Y3)) (F X2)))))
% 0.77/0.99 FOF formula (forall (F:(nat->extended_ereal)) (_TPTP_I:nat) (J:nat), ((order_736687562_ereal F)->(((ord_less_eq_nat _TPTP_I) J)->((ord_le824540014_ereal (F J)) (F _TPTP_I))))) of role axiom named fact_181_decseqD
% 0.77/0.99 A new axiom: (forall (F:(nat->extended_ereal)) (_TPTP_I:nat) (J:nat), ((order_736687562_ereal F)->(((ord_less_eq_nat _TPTP_I) J)->((ord_le824540014_ereal (F J)) (F _TPTP_I)))))
% 0.77/0.99 FOF formula (forall (F:(nat->extended_enat)) (_TPTP_I:nat) (J:nat), ((order_1660553314d_enat F)->(((ord_less_eq_nat _TPTP_I) J)->((ord_le1863327750d_enat (F J)) (F _TPTP_I))))) of role axiom named fact_182_decseqD
% 0.77/0.99 A new axiom: (forall (F:(nat->extended_enat)) (_TPTP_I:nat) (J:nat), ((order_1660553314d_enat F)->(((ord_less_eq_nat _TPTP_I) J)->((ord_le1863327750d_enat (F J)) (F _TPTP_I)))))
% 0.77/0.99 FOF formula (forall (F:(nat->nat)) (_TPTP_I:nat) (J:nat), ((order_1631207636at_nat F)->(((ord_less_eq_nat _TPTP_I) J)->((ord_less_eq_nat (F J)) (F _TPTP_I))))) of role axiom named fact_183_decseqD
% 0.77/0.99 A new axiom: (forall (F:(nat->nat)) (_TPTP_I:nat) (J:nat), ((order_1631207636at_nat F)->(((ord_less_eq_nat _TPTP_I) J)->((ord_less_eq_nat (F J)) (F _TPTP_I)))))
% 0.77/0.99 FOF formula (forall (F:(nat->real)) (_TPTP_I:nat) (J:nat), ((order_106095024t_real F)->(((ord_less_eq_nat _TPTP_I) J)->((ord_less_eq_real (F J)) (F _TPTP_I))))) of role axiom named fact_184_decseqD
% 0.77/0.99 A new axiom: (forall (F:(nat->real)) (_TPTP_I:nat) (J:nat), ((order_106095024t_real F)->(((ord_less_eq_nat _TPTP_I) J)->((ord_less_eq_real (F J)) (F _TPTP_I)))))
% 0.77/0.99 FOF formula (((eq ((nat->extended_ereal)->Prop)) order_736687562_ereal) (fun (X5:(nat->extended_ereal))=> (forall (M2:nat) (N2:nat), (((ord_less_eq_nat M2) N2)->((ord_le824540014_ereal (X5 N2)) (X5 M2)))))) of role axiom named fact_185_decseq__def
% 0.77/0.99 A new axiom: (((eq ((nat->extended_ereal)->Prop)) order_736687562_ereal) (fun (X5:(nat->extended_ereal))=> (forall (M2:nat) (N2:nat), (((ord_less_eq_nat M2) N2)->((ord_le824540014_ereal (X5 N2)) (X5 M2))))))
% 0.77/0.99 FOF formula (((eq ((nat->extended_enat)->Prop)) order_1660553314d_enat) (fun (X5:(nat->extended_enat))=> (forall (M2:nat) (N2:nat), (((ord_less_eq_nat M2) N2)->((ord_le1863327750d_enat (X5 N2)) (X5 M2)))))) of role axiom named fact_186_decseq__def
% 0.77/0.99 A new axiom: (((eq ((nat->extended_enat)->Prop)) order_1660553314d_enat) (fun (X5:(nat->extended_enat))=> (forall (M2:nat) (N2:nat), (((ord_less_eq_nat M2) N2)->((ord_le1863327750d_enat (X5 N2)) (X5 M2))))))
% 0.77/0.99 FOF formula (((eq ((nat->nat)->Prop)) order_1631207636at_nat) (fun (X5:(nat->nat))=> (forall (M2:nat) (N2:nat), (((ord_less_eq_nat M2) N2)->((ord_less_eq_nat (X5 N2)) (X5 M2)))))) of role axiom named fact_187_decseq__def
% 0.77/0.99 A new axiom: (((eq ((nat->nat)->Prop)) order_1631207636at_nat) (fun (X5:(nat->nat))=> (forall (M2:nat) (N2:nat), (((ord_less_eq_nat M2) N2)->((ord_less_eq_nat (X5 N2)) (X5 M2))))))
% 0.77/0.99 FOF formula (((eq ((nat->real)->Prop)) order_106095024t_real) (fun (X5:(nat->real))=> (forall (M2:nat) (N2:nat), (((ord_less_eq_nat M2) N2)->((ord_less_eq_real (X5 N2)) (X5 M2)))))) of role axiom named fact_188_decseq__def
% 0.85/1.00 A new axiom: (((eq ((nat->real)->Prop)) order_106095024t_real) (fun (X5:(nat->real))=> (forall (M2:nat) (N2:nat), (((ord_less_eq_nat M2) N2)->((ord_less_eq_real (X5 N2)) (X5 M2))))))
% 0.85/1.00 FOF formula (forall (N:extended_enat), ((ord_le824540014_ereal zero_z163181189_ereal) (extend1771934483f_enat N))) of role axiom named fact_189_ereal__of__enat__nonneg
% 0.85/1.00 A new axiom: (forall (N:extended_enat), ((ord_le824540014_ereal zero_z163181189_ereal) (extend1771934483f_enat N)))
% 0.85/1.00 FOF formula (forall (N:extended_enat), (((eq Prop) ((ord_le824540014_ereal zero_z163181189_ereal) (extend1771934483f_enat N))) ((ord_le1863327750d_enat zero_z491942557d_enat) N))) of role axiom named fact_190_ereal__of__enat__ge__zero__cancel__iff
% 0.85/1.00 A new axiom: (forall (N:extended_enat), (((eq Prop) ((ord_le824540014_ereal zero_z163181189_ereal) (extend1771934483f_enat N))) ((ord_le1863327750d_enat zero_z491942557d_enat) N)))
% 0.85/1.00 FOF formula (forall (M:num) (N:extended_enat), (((eq Prop) ((ord_le824540014_ereal (numera1793320307_ereal M)) (extend1771934483f_enat N))) ((ord_le1863327750d_enat (numera280919179d_enat M)) N))) of role axiom named fact_191_numeral__le__ereal__of__enat__iff
% 0.85/1.00 A new axiom: (forall (M:num) (N:extended_enat), (((eq Prop) ((ord_le824540014_ereal (numera1793320307_ereal M)) (extend1771934483f_enat N))) ((ord_le1863327750d_enat (numera280919179d_enat M)) N)))
% 0.85/1.00 FOF formula (forall (X2:extended_ereal), (((eq Prop) ((ord_le824540014_ereal extend1289208545_ereal) X2)) (((eq extended_ereal) X2) extend1289208545_ereal))) of role axiom named fact_192_ereal__infty__less__eq_I1_J
% 0.85/1.00 A new axiom: (forall (X2:extended_ereal), (((eq Prop) ((ord_le824540014_ereal extend1289208545_ereal) X2)) (((eq extended_ereal) X2) extend1289208545_ereal)))
% 0.85/1.00 FOF formula (forall (F:(extended_ereal->extended_ereal)) (X2:extended_ereal) (Y3:extended_ereal), ((order_555877177_ereal F)->(((eq Prop) ((ord_le824540014_ereal (F X2)) (F Y3))) ((ord_le824540014_ereal X2) Y3)))) of role axiom named fact_193_strict__mono__less__eq
% 0.85/1.00 A new axiom: (forall (F:(extended_ereal->extended_ereal)) (X2:extended_ereal) (Y3:extended_ereal), ((order_555877177_ereal F)->(((eq Prop) ((ord_le824540014_ereal (F X2)) (F Y3))) ((ord_le824540014_ereal X2) Y3))))
% 0.85/1.00 FOF formula (forall (F:(extended_enat->extended_ereal)) (X2:extended_enat) (Y3:extended_enat), ((order_1180956065_ereal F)->(((eq Prop) ((ord_le824540014_ereal (F X2)) (F Y3))) ((ord_le1863327750d_enat X2) Y3)))) of role axiom named fact_194_strict__mono__less__eq
% 0.85/1.00 A new axiom: (forall (F:(extended_enat->extended_ereal)) (X2:extended_enat) (Y3:extended_enat), ((order_1180956065_ereal F)->(((eq Prop) ((ord_le824540014_ereal (F X2)) (F Y3))) ((ord_le1863327750d_enat X2) Y3))))
% 0.85/1.00 FOF formula (forall (F:(nat->extended_ereal)) (X2:nat) (Y3:nat), ((order_689807875_ereal F)->(((eq Prop) ((ord_le824540014_ereal (F X2)) (F Y3))) ((ord_less_eq_nat X2) Y3)))) of role axiom named fact_195_strict__mono__less__eq
% 0.85/1.00 A new axiom: (forall (F:(nat->extended_ereal)) (X2:nat) (Y3:nat), ((order_689807875_ereal F)->(((eq Prop) ((ord_le824540014_ereal (F X2)) (F Y3))) ((ord_less_eq_nat X2) Y3))))
% 0.85/1.00 FOF formula (forall (F:(real->extended_ereal)) (X2:real) (Y3:real), ((order_946214183_ereal F)->(((eq Prop) ((ord_le824540014_ereal (F X2)) (F Y3))) ((ord_less_eq_real X2) Y3)))) of role axiom named fact_196_strict__mono__less__eq
% 0.85/1.00 A new axiom: (forall (F:(real->extended_ereal)) (X2:real) (Y3:real), ((order_946214183_ereal F)->(((eq Prop) ((ord_le824540014_ereal (F X2)) (F Y3))) ((ord_less_eq_real X2) Y3))))
% 0.85/1.00 FOF formula (forall (F:(extended_ereal->extended_enat)) (X2:extended_ereal) (Y3:extended_ereal), ((order_713858385d_enat F)->(((eq Prop) ((ord_le1863327750d_enat (F X2)) (F Y3))) ((ord_le824540014_ereal X2) Y3)))) of role axiom named fact_197_strict__mono__less__eq
% 0.85/1.00 A new axiom: (forall (F:(extended_ereal->extended_enat)) (X2:extended_ereal) (Y3:extended_ereal), ((order_713858385d_enat F)->(((eq Prop) ((ord_le1863327750d_enat (F X2)) (F Y3))) ((ord_le824540014_ereal X2) Y3))))
% 0.85/1.02 FOF formula (forall (F:(extended_enat->extended_enat)) (X2:extended_enat) (Y3:extended_enat), ((order_2106278841d_enat F)->(((eq Prop) ((ord_le1863327750d_enat (F X2)) (F Y3))) ((ord_le1863327750d_enat X2) Y3)))) of role axiom named fact_198_strict__mono__less__eq
% 0.85/1.02 A new axiom: (forall (F:(extended_enat->extended_enat)) (X2:extended_enat) (Y3:extended_enat), ((order_2106278841d_enat F)->(((eq Prop) ((ord_le1863327750d_enat (F X2)) (F Y3))) ((ord_le1863327750d_enat X2) Y3))))
% 0.85/1.02 FOF formula (forall (F:(nat->extended_enat)) (X2:nat) (Y3:nat), ((order_693207323d_enat F)->(((eq Prop) ((ord_le1863327750d_enat (F X2)) (F Y3))) ((ord_less_eq_nat X2) Y3)))) of role axiom named fact_199_strict__mono__less__eq
% 0.85/1.02 A new axiom: (forall (F:(nat->extended_enat)) (X2:nat) (Y3:nat), ((order_693207323d_enat F)->(((eq Prop) ((ord_le1863327750d_enat (F X2)) (F Y3))) ((ord_less_eq_nat X2) Y3))))
% 0.85/1.02 FOF formula (forall (F:(real->extended_enat)) (X2:real) (Y3:real), ((order_1962034751d_enat F)->(((eq Prop) ((ord_le1863327750d_enat (F X2)) (F Y3))) ((ord_less_eq_real X2) Y3)))) of role axiom named fact_200_strict__mono__less__eq
% 0.85/1.02 A new axiom: (forall (F:(real->extended_enat)) (X2:real) (Y3:real), ((order_1962034751d_enat F)->(((eq Prop) ((ord_le1863327750d_enat (F X2)) (F Y3))) ((ord_less_eq_real X2) Y3))))
% 0.85/1.02 FOF formula (forall (F:(extended_ereal->nat)) (X2:extended_ereal) (Y3:extended_ereal), ((order_476926757al_nat F)->(((eq Prop) ((ord_less_eq_nat (F X2)) (F Y3))) ((ord_le824540014_ereal X2) Y3)))) of role axiom named fact_201_strict__mono__less__eq
% 0.85/1.02 A new axiom: (forall (F:(extended_ereal->nat)) (X2:extended_ereal) (Y3:extended_ereal), ((order_476926757al_nat F)->(((eq Prop) ((ord_less_eq_nat (F X2)) (F Y3))) ((ord_le824540014_ereal X2) Y3))))
% 0.85/1.02 FOF formula (forall (F:(extended_enat->nat)) (X2:extended_enat) (Y3:extended_enat), ((order_1622825661at_nat F)->(((eq Prop) ((ord_less_eq_nat (F X2)) (F Y3))) ((ord_le1863327750d_enat X2) Y3)))) of role axiom named fact_202_strict__mono__less__eq
% 0.85/1.02 A new axiom: (forall (F:(extended_enat->nat)) (X2:extended_enat) (Y3:extended_enat), ((order_1622825661at_nat F)->(((eq Prop) ((ord_less_eq_nat (F X2)) (F Y3))) ((ord_le1863327750d_enat X2) Y3))))
% 0.85/1.02 FOF formula (((eq extended_ereal) (extend1771934483f_enat zero_z491942557d_enat)) zero_z163181189_ereal) of role axiom named fact_203_ereal__of__enat__zero
% 0.85/1.02 A new axiom: (((eq extended_ereal) (extend1771934483f_enat zero_z491942557d_enat)) zero_z163181189_ereal)
% 0.85/1.02 FOF formula (forall (F:(nat->nat)) (X2:nat) (Y3:nat), ((order_769474267at_nat F)->(((eq Prop) (((eq nat) (F X2)) (F Y3))) (((eq nat) X2) Y3)))) of role axiom named fact_204_strict__mono__eq
% 0.85/1.02 A new axiom: (forall (F:(nat->nat)) (X2:nat) (Y3:nat), ((order_769474267at_nat F)->(((eq Prop) (((eq nat) (F X2)) (F Y3))) (((eq nat) X2) Y3))))
% 0.85/1.02 FOF formula (not (((eq extended_ereal) extend1289208545_ereal) zero_z163181189_ereal)) of role axiom named fact_205_Infty__neq__0_I1_J
% 0.85/1.02 A new axiom: (not (((eq extended_ereal) extend1289208545_ereal) zero_z163181189_ereal))
% 0.85/1.02 FOF formula (forall (R:(extended_ereal->extended_ereal)) (M:extended_ereal) (N:extended_ereal), ((order_555877177_ereal R)->(((ord_le824540014_ereal M) N)->((ord_le824540014_ereal (R M)) (R N))))) of role axiom named fact_206_strict__mono__leD
% 0.85/1.02 A new axiom: (forall (R:(extended_ereal->extended_ereal)) (M:extended_ereal) (N:extended_ereal), ((order_555877177_ereal R)->(((ord_le824540014_ereal M) N)->((ord_le824540014_ereal (R M)) (R N)))))
% 0.85/1.02 FOF formula (forall (R:(extended_ereal->extended_enat)) (M:extended_ereal) (N:extended_ereal), ((order_713858385d_enat R)->(((ord_le824540014_ereal M) N)->((ord_le1863327750d_enat (R M)) (R N))))) of role axiom named fact_207_strict__mono__leD
% 0.85/1.02 A new axiom: (forall (R:(extended_ereal->extended_enat)) (M:extended_ereal) (N:extended_ereal), ((order_713858385d_enat R)->(((ord_le824540014_ereal M) N)->((ord_le1863327750d_enat (R M)) (R N)))))
% 0.85/1.02 FOF formula (forall (R:(extended_ereal->nat)) (M:extended_ereal) (N:extended_ereal), ((order_476926757al_nat R)->(((ord_le824540014_ereal M) N)->((ord_less_eq_nat (R M)) (R N))))) of role axiom named fact_208_strict__mono__leD
% 0.85/1.03 A new axiom: (forall (R:(extended_ereal->nat)) (M:extended_ereal) (N:extended_ereal), ((order_476926757al_nat R)->(((ord_le824540014_ereal M) N)->((ord_less_eq_nat (R M)) (R N)))))
% 0.85/1.03 FOF formula (forall (R:(extended_ereal->real)) (M:extended_ereal) (N:extended_ereal), ((order_1560271745l_real R)->(((ord_le824540014_ereal M) N)->((ord_less_eq_real (R M)) (R N))))) of role axiom named fact_209_strict__mono__leD
% 0.85/1.03 A new axiom: (forall (R:(extended_ereal->real)) (M:extended_ereal) (N:extended_ereal), ((order_1560271745l_real R)->(((ord_le824540014_ereal M) N)->((ord_less_eq_real (R M)) (R N)))))
% 0.85/1.03 FOF formula (forall (R:(extended_enat->extended_ereal)) (M:extended_enat) (N:extended_enat), ((order_1180956065_ereal R)->(((ord_le1863327750d_enat M) N)->((ord_le824540014_ereal (R M)) (R N))))) of role axiom named fact_210_strict__mono__leD
% 0.85/1.03 A new axiom: (forall (R:(extended_enat->extended_ereal)) (M:extended_enat) (N:extended_enat), ((order_1180956065_ereal R)->(((ord_le1863327750d_enat M) N)->((ord_le824540014_ereal (R M)) (R N)))))
% 0.85/1.03 FOF formula (forall (R:(extended_enat->extended_enat)) (M:extended_enat) (N:extended_enat), ((order_2106278841d_enat R)->(((ord_le1863327750d_enat M) N)->((ord_le1863327750d_enat (R M)) (R N))))) of role axiom named fact_211_strict__mono__leD
% 0.85/1.03 A new axiom: (forall (R:(extended_enat->extended_enat)) (M:extended_enat) (N:extended_enat), ((order_2106278841d_enat R)->(((ord_le1863327750d_enat M) N)->((ord_le1863327750d_enat (R M)) (R N)))))
% 0.85/1.03 FOF formula (forall (R:(extended_enat->nat)) (M:extended_enat) (N:extended_enat), ((order_1622825661at_nat R)->(((ord_le1863327750d_enat M) N)->((ord_less_eq_nat (R M)) (R N))))) of role axiom named fact_212_strict__mono__leD
% 0.85/1.03 A new axiom: (forall (R:(extended_enat->nat)) (M:extended_enat) (N:extended_enat), ((order_1622825661at_nat R)->(((ord_le1863327750d_enat M) N)->((ord_less_eq_nat (R M)) (R N)))))
% 0.85/1.03 FOF formula (forall (R:(extended_enat->real)) (M:extended_enat) (N:extended_enat), ((order_135436057t_real R)->(((ord_le1863327750d_enat M) N)->((ord_less_eq_real (R M)) (R N))))) of role axiom named fact_213_strict__mono__leD
% 0.85/1.03 A new axiom: (forall (R:(extended_enat->real)) (M:extended_enat) (N:extended_enat), ((order_135436057t_real R)->(((ord_le1863327750d_enat M) N)->((ord_less_eq_real (R M)) (R N)))))
% 0.85/1.03 FOF formula (forall (R:(nat->extended_ereal)) (M:nat) (N:nat), ((order_689807875_ereal R)->(((ord_less_eq_nat M) N)->((ord_le824540014_ereal (R M)) (R N))))) of role axiom named fact_214_strict__mono__leD
% 0.85/1.03 A new axiom: (forall (R:(nat->extended_ereal)) (M:nat) (N:nat), ((order_689807875_ereal R)->(((ord_less_eq_nat M) N)->((ord_le824540014_ereal (R M)) (R N)))))
% 0.85/1.03 FOF formula (forall (R:(nat->extended_enat)) (M:nat) (N:nat), ((order_693207323d_enat R)->(((ord_less_eq_nat M) N)->((ord_le1863327750d_enat (R M)) (R N))))) of role axiom named fact_215_strict__mono__leD
% 0.85/1.03 A new axiom: (forall (R:(nat->extended_enat)) (M:nat) (N:nat), ((order_693207323d_enat R)->(((ord_less_eq_nat M) N)->((ord_le1863327750d_enat (R M)) (R N)))))
% 0.85/1.03 FOF formula (forall (Y3:extended_ereal) (X2:extended_ereal), ((not (((eq extended_ereal) Y3) extend1289208545_ereal))->(((ord_le824540014_ereal X2) Y3)->(not (((eq extended_ereal) X2) extend1289208545_ereal))))) of role axiom named fact_216_neq__PInf__trans
% 0.85/1.03 A new axiom: (forall (Y3:extended_ereal) (X2:extended_ereal), ((not (((eq extended_ereal) Y3) extend1289208545_ereal))->(((ord_le824540014_ereal X2) Y3)->(not (((eq extended_ereal) X2) extend1289208545_ereal)))))
% 0.85/1.03 FOF formula (forall (A:extended_ereal) (B:extended_ereal), (((ord_le824540014_ereal A) B)->((((eq extended_ereal) A) extend1289208545_ereal)->(((eq extended_ereal) B) extend1289208545_ereal)))) of role axiom named fact_217_ereal__infty__less__eq2_I1_J
% 0.85/1.03 A new axiom: (forall (A:extended_ereal) (B:extended_ereal), (((ord_le824540014_ereal A) B)->((((eq extended_ereal) A) extend1289208545_ereal)->(((eq extended_ereal) B) extend1289208545_ereal))))
% 0.85/1.03 FOF formula (forall (X2:extended_ereal), ((ord_le824540014_ereal X2) extend1289208545_ereal)) of role axiom named fact_218_ereal__less__eq_I1_J
% 0.85/1.04 A new axiom: (forall (X2:extended_ereal), ((ord_le824540014_ereal X2) extend1289208545_ereal))
% 0.85/1.04 FOF formula (forall (M:num) (N:num), (((eq Prop) ((ord_le1863327750d_enat (numera280919179d_enat M)) (numera280919179d_enat N))) ((ord_less_eq_num M) N))) of role axiom named fact_219_numeral__le__iff
% 0.85/1.04 A new axiom: (forall (M:num) (N:num), (((eq Prop) ((ord_le1863327750d_enat (numera280919179d_enat M)) (numera280919179d_enat N))) ((ord_less_eq_num M) N)))
% 0.85/1.04 FOF formula (forall (M:num) (N:num), (((eq Prop) ((ord_less_eq_nat (numeral_numeral_nat M)) (numeral_numeral_nat N))) ((ord_less_eq_num M) N))) of role axiom named fact_220_numeral__le__iff
% 0.85/1.04 A new axiom: (forall (M:num) (N:num), (((eq Prop) ((ord_less_eq_nat (numeral_numeral_nat M)) (numeral_numeral_nat N))) ((ord_less_eq_num M) N)))
% 0.85/1.04 FOF formula (forall (M:num) (N:num), (((eq Prop) ((ord_less_eq_real (numeral_numeral_real M)) (numeral_numeral_real N))) ((ord_less_eq_num M) N))) of role axiom named fact_221_numeral__le__iff
% 0.85/1.04 A new axiom: (forall (M:num) (N:num), (((eq Prop) ((ord_less_eq_real (numeral_numeral_real M)) (numeral_numeral_real N))) ((ord_less_eq_num M) N)))
% 0.85/1.04 FOF formula (forall (N:extended_enat), (((eq Prop) ((ord_le1863327750d_enat N) zero_z491942557d_enat)) (((eq extended_enat) N) zero_z491942557d_enat))) of role axiom named fact_222_le__zero__eq
% 0.85/1.04 A new axiom: (forall (N:extended_enat), (((eq Prop) ((ord_le1863327750d_enat N) zero_z491942557d_enat)) (((eq extended_enat) N) zero_z491942557d_enat)))
% 0.85/1.04 FOF formula (forall (N:nat), (((eq Prop) ((ord_less_eq_nat N) zero_zero_nat)) (((eq nat) N) zero_zero_nat))) of role axiom named fact_223_le__zero__eq
% 0.85/1.04 A new axiom: (forall (N:nat), (((eq Prop) ((ord_less_eq_nat N) zero_zero_nat)) (((eq nat) N) zero_zero_nat)))
% 0.85/1.04 FOF formula (forall (N:num), ((ord_le1863327750d_enat zero_z491942557d_enat) (numera280919179d_enat N))) of role axiom named fact_224_zero__le__numeral
% 0.85/1.04 A new axiom: (forall (N:num), ((ord_le1863327750d_enat zero_z491942557d_enat) (numera280919179d_enat N)))
% 0.85/1.04 FOF formula (forall (N:num), ((ord_less_eq_nat zero_zero_nat) (numeral_numeral_nat N))) of role axiom named fact_225_zero__le__numeral
% 0.85/1.04 A new axiom: (forall (N:num), ((ord_less_eq_nat zero_zero_nat) (numeral_numeral_nat N)))
% 0.85/1.04 FOF formula (forall (N:num), ((ord_less_eq_real zero_zero_real) (numeral_numeral_real N))) of role axiom named fact_226_zero__le__numeral
% 0.85/1.04 A new axiom: (forall (N:num), ((ord_less_eq_real zero_zero_real) (numeral_numeral_real N)))
% 0.85/1.04 FOF formula (forall (N:num), (((ord_le1863327750d_enat (numera280919179d_enat N)) zero_z491942557d_enat)->False)) of role axiom named fact_227_not__numeral__le__zero
% 0.85/1.04 A new axiom: (forall (N:num), (((ord_le1863327750d_enat (numera280919179d_enat N)) zero_z491942557d_enat)->False))
% 0.85/1.04 FOF formula (forall (N:num), (((ord_less_eq_nat (numeral_numeral_nat N)) zero_zero_nat)->False)) of role axiom named fact_228_not__numeral__le__zero
% 0.85/1.04 A new axiom: (forall (N:num), (((ord_less_eq_nat (numeral_numeral_nat N)) zero_zero_nat)->False))
% 0.85/1.04 FOF formula (forall (N:num), (((ord_less_eq_real (numeral_numeral_real N)) zero_zero_real)->False)) of role axiom named fact_229_not__numeral__le__zero
% 0.85/1.04 A new axiom: (forall (N:num), (((ord_less_eq_real (numeral_numeral_real N)) zero_zero_real)->False))
% 0.85/1.04 FOF formula (forall (M:num) (N:num), (((eq Prop) (((eq real) (numeral_numeral_real M)) (numeral_numeral_real N))) (((eq num) M) N))) of role axiom named fact_230_numeral__eq__iff
% 0.85/1.04 A new axiom: (forall (M:num) (N:num), (((eq Prop) (((eq real) (numeral_numeral_real M)) (numeral_numeral_real N))) (((eq num) M) N)))
% 0.85/1.04 FOF formula (forall (N:extended_enat), (((eq Prop) ((ord_le1863327750d_enat N) zero_z491942557d_enat)) (((eq extended_enat) N) zero_z491942557d_enat))) of role axiom named fact_231_ile0__eq
% 0.85/1.04 A new axiom: (forall (N:extended_enat), (((eq Prop) ((ord_le1863327750d_enat N) zero_z491942557d_enat)) (((eq extended_enat) N) zero_z491942557d_enat)))
% 0.85/1.04 FOF formula (forall (N:extended_enat), ((ord_le1863327750d_enat zero_z491942557d_enat) N)) of role axiom named fact_232_i0__lb
% 0.85/1.04 A new axiom: (forall (N:extended_enat), ((ord_le1863327750d_enat zero_z491942557d_enat) N))
% 0.85/1.04 FOF formula (forall (M:num) (N:num), (((eq Prop) ((ord_le1863327750d_enat (numera280919179d_enat M)) (numera280919179d_enat N))) ((ord_less_eq_nat (numeral_numeral_nat M)) (numeral_numeral_nat N)))) of role axiom named fact_233_enat__ord__number_I1_J
% 0.85/1.04 A new axiom: (forall (M:num) (N:num), (((eq Prop) ((ord_le1863327750d_enat (numera280919179d_enat M)) (numera280919179d_enat N))) ((ord_less_eq_nat (numeral_numeral_nat M)) (numeral_numeral_nat N))))
% 0.85/1.04 FOF formula (forall (A:nat), ((ord_less_eq_nat zero_zero_nat) A)) of role axiom named fact_234_bot__nat__0_Oextremum
% 0.85/1.04 A new axiom: (forall (A:nat), ((ord_less_eq_nat zero_zero_nat) A))
% 0.85/1.04 FOF formula (forall (N:nat), ((ord_less_eq_nat zero_zero_nat) N)) of role axiom named fact_235_le0
% 0.85/1.04 A new axiom: (forall (N:nat), ((ord_less_eq_nat zero_zero_nat) N))
% 0.85/1.04 FOF formula (forall (M:num) (N:nat), (((eq Prop) ((ord_le1863327750d_enat (numera280919179d_enat M)) (extended_enat2 N))) ((ord_less_eq_nat (numeral_numeral_nat M)) N))) of role axiom named fact_236_numeral__le__enat__iff
% 0.85/1.04 A new axiom: (forall (M:num) (N:nat), (((eq Prop) ((ord_le1863327750d_enat (numera280919179d_enat M)) (extended_enat2 N))) ((ord_less_eq_nat (numeral_numeral_nat M)) N)))
% 0.85/1.04 FOF formula (forall (X2:extended_ereal), (((eq Prop) ((ord_less_eq_real (extend1716541707_ereal X2)) zero_zero_real)) ((or ((ord_le824540014_ereal X2) zero_z163181189_ereal)) (((eq extended_ereal) X2) extend1289208545_ereal)))) of role axiom named fact_237_real__of__ereal__le__0
% 0.85/1.04 A new axiom: (forall (X2:extended_ereal), (((eq Prop) ((ord_less_eq_real (extend1716541707_ereal X2)) zero_zero_real)) ((or ((ord_le824540014_ereal X2) zero_z163181189_ereal)) (((eq extended_ereal) X2) extend1289208545_ereal))))
% 0.85/1.04 FOF formula (forall (A:extended_ereal), (((eq Prop) (((eq extended_ereal) (uminus1208298309_ereal A)) zero_z163181189_ereal)) (((eq extended_ereal) A) zero_z163181189_ereal))) of role axiom named fact_238_ereal__uminus__zero__iff
% 0.85/1.04 A new axiom: (forall (A:extended_ereal), (((eq Prop) (((eq extended_ereal) (uminus1208298309_ereal A)) zero_z163181189_ereal)) (((eq extended_ereal) A) zero_z163181189_ereal)))
% 0.85/1.04 FOF formula (((eq extended_ereal) (uminus1208298309_ereal zero_z163181189_ereal)) zero_z163181189_ereal) of role axiom named fact_239_ereal__uminus__zero
% 0.85/1.04 A new axiom: (((eq extended_ereal) (uminus1208298309_ereal zero_z163181189_ereal)) zero_z163181189_ereal)
% 0.85/1.04 FOF formula (forall (A:extended_ereal) (B:extended_ereal), (((eq Prop) ((ord_le824540014_ereal (uminus1208298309_ereal A)) (uminus1208298309_ereal B))) ((ord_le824540014_ereal B) A))) of role axiom named fact_240_ereal__minus__le__minus
% 0.85/1.04 A new axiom: (forall (A:extended_ereal) (B:extended_ereal), (((eq Prop) ((ord_le824540014_ereal (uminus1208298309_ereal A)) (uminus1208298309_ereal B))) ((ord_le824540014_ereal B) A)))
% 0.85/1.04 FOF formula (forall (Nat:nat) (Nat2:nat), (((eq Prop) (((eq extended_enat) (extended_enat2 Nat)) (extended_enat2 Nat2))) (((eq nat) Nat) Nat2))) of role axiom named fact_241_enat_Oinject
% 0.85/1.04 A new axiom: (forall (Nat:nat) (Nat2:nat), (((eq Prop) (((eq extended_enat) (extended_enat2 Nat)) (extended_enat2 Nat2))) (((eq nat) Nat) Nat2)))
% 0.85/1.04 FOF formula (forall (X2:extended_ereal), (((eq real) (extend1716541707_ereal (uminus1208298309_ereal X2))) (uminus_uminus_real (extend1716541707_ereal X2)))) of role axiom named fact_242_real__of__ereal
% 0.85/1.04 A new axiom: (forall (X2:extended_ereal), (((eq real) (extend1716541707_ereal (uminus1208298309_ereal X2))) (uminus_uminus_real (extend1716541707_ereal X2))))
% 0.85/1.04 FOF formula (forall (X2:extended_ereal), (((eq Prop) ((ord_le824540014_ereal X2) (uminus1208298309_ereal extend1289208545_ereal))) (((eq extended_ereal) X2) (uminus1208298309_ereal extend1289208545_ereal)))) of role axiom named fact_243_ereal__infty__less__eq_I2_J
% 0.85/1.04 A new axiom: (forall (X2:extended_ereal), (((eq Prop) ((ord_le824540014_ereal X2) (uminus1208298309_ereal extend1289208545_ereal))) (((eq extended_ereal) X2) (uminus1208298309_ereal extend1289208545_ereal))))
% 0.85/1.04 FOF formula (forall (A:extended_ereal), (((eq Prop) ((ord_le824540014_ereal (uminus1208298309_ereal A)) zero_z163181189_ereal)) ((ord_le824540014_ereal zero_z163181189_ereal) A))) of role axiom named fact_244_ereal__uminus__le__0__iff
% 0.85/1.05 A new axiom: (forall (A:extended_ereal), (((eq Prop) ((ord_le824540014_ereal (uminus1208298309_ereal A)) zero_z163181189_ereal)) ((ord_le824540014_ereal zero_z163181189_ereal) A)))
% 0.85/1.05 FOF formula (forall (A:extended_ereal), (((eq Prop) ((ord_le824540014_ereal zero_z163181189_ereal) (uminus1208298309_ereal A))) ((ord_le824540014_ereal A) zero_z163181189_ereal))) of role axiom named fact_245_ereal__0__le__uminus__iff
% 0.85/1.05 A new axiom: (forall (A:extended_ereal), (((eq Prop) ((ord_le824540014_ereal zero_z163181189_ereal) (uminus1208298309_ereal A))) ((ord_le824540014_ereal A) zero_z163181189_ereal)))
% 0.85/1.05 FOF formula (((eq real) (extend1716541707_ereal zero_z163181189_ereal)) zero_zero_real) of role axiom named fact_246_real__of__ereal__0
% 0.85/1.05 A new axiom: (((eq real) (extend1716541707_ereal zero_z163181189_ereal)) zero_zero_real)
% 0.85/1.05 FOF formula (forall (M:nat) (N:nat), (((eq Prop) ((ord_le1863327750d_enat (extended_enat2 M)) (extended_enat2 N))) ((ord_less_eq_nat M) N))) of role axiom named fact_247_enat__ord__simps_I1_J
% 0.85/1.05 A new axiom: (forall (M:nat) (N:nat), (((eq Prop) ((ord_le1863327750d_enat (extended_enat2 M)) (extended_enat2 N))) ((ord_less_eq_nat M) N)))
% 0.85/1.05 FOF formula (((eq real) (extend1716541707_ereal (uminus1208298309_ereal extend1289208545_ereal))) zero_zero_real) of role axiom named fact_248_real__of__ereal_Osimps_I3_J
% 0.85/1.05 A new axiom: (((eq real) (extend1716541707_ereal (uminus1208298309_ereal extend1289208545_ereal))) zero_zero_real)
% 0.85/1.05 FOF formula (forall (X2:extended_ereal), (((eq Prop) (((eq real) (extend1716541707_ereal X2)) zero_zero_real)) ((or ((or (((eq extended_ereal) X2) extend1289208545_ereal)) (((eq extended_ereal) X2) (uminus1208298309_ereal extend1289208545_ereal)))) (((eq extended_ereal) X2) zero_z163181189_ereal)))) of role axiom named fact_249_real__of__ereal__eq__0
% 0.85/1.05 A new axiom: (forall (X2:extended_ereal), (((eq Prop) (((eq real) (extend1716541707_ereal X2)) zero_zero_real)) ((or ((or (((eq extended_ereal) X2) extend1289208545_ereal)) (((eq extended_ereal) X2) (uminus1208298309_ereal extend1289208545_ereal)))) (((eq extended_ereal) X2) zero_z163181189_ereal))))
% 0.85/1.05 FOF formula (((eq real) (extend1716541707_ereal extend1289208545_ereal)) zero_zero_real) of role axiom named fact_250_real__of__ereal_Osimps_I2_J
% 0.85/1.05 A new axiom: (((eq real) (extend1716541707_ereal extend1289208545_ereal)) zero_zero_real)
% 0.85/1.05 FOF formula (((eq extended_enat) zero_z491942557d_enat) (extended_enat2 zero_zero_nat)) of role axiom named fact_251_zero__enat__def
% 0.85/1.05 A new axiom: (((eq extended_enat) zero_z491942557d_enat) (extended_enat2 zero_zero_nat))
% 0.85/1.05 FOF formula (forall (X2:nat), (((eq Prop) (((eq extended_enat) (extended_enat2 X2)) zero_z491942557d_enat)) (((eq nat) X2) zero_zero_nat))) of role axiom named fact_252_enat__0__iff_I1_J
% 0.85/1.05 A new axiom: (forall (X2:nat), (((eq Prop) (((eq extended_enat) (extended_enat2 X2)) zero_z491942557d_enat)) (((eq nat) X2) zero_zero_nat)))
% 0.85/1.05 FOF formula (forall (X2:nat), (((eq Prop) (((eq extended_enat) zero_z491942557d_enat) (extended_enat2 X2))) (((eq nat) X2) zero_zero_nat))) of role axiom named fact_253_enat__0__iff_I2_J
% 0.85/1.05 A new axiom: (forall (X2:nat), (((eq Prop) (((eq extended_enat) zero_z491942557d_enat) (extended_enat2 X2))) (((eq nat) X2) zero_zero_nat)))
% 0.85/1.05 FOF formula (not (((eq extended_ereal) extend1289208545_ereal) (uminus1208298309_ereal extend1289208545_ereal))) of role axiom named fact_254_MInfty__neq__PInfty_I1_J
% 0.85/1.05 A new axiom: (not (((eq extended_ereal) extend1289208545_ereal) (uminus1208298309_ereal extend1289208545_ereal)))
% 0.85/1.05 FOF formula (forall (A:extended_ereal) (B:extended_ereal), (((eq Prop) ((ord_le824540014_ereal (uminus1208298309_ereal A)) B)) ((ord_le824540014_ereal (uminus1208298309_ereal B)) A))) of role axiom named fact_255_ereal__uminus__le__reorder
% 0.85/1.05 A new axiom: (forall (A:extended_ereal) (B:extended_ereal), (((eq Prop) ((ord_le824540014_ereal (uminus1208298309_ereal A)) B)) ((ord_le824540014_ereal (uminus1208298309_ereal B)) A)))
% 0.85/1.06 FOF formula (forall (N:extended_enat) (M:nat), (((ord_le1863327750d_enat N) (extended_enat2 M))->((ex nat) (fun (K:nat)=> (((eq extended_enat) N) (extended_enat2 K)))))) of role axiom named fact_256_enat__ile
% 0.85/1.06 A new axiom: (forall (N:extended_enat) (M:nat), (((ord_le1863327750d_enat N) (extended_enat2 M))->((ex nat) (fun (K:nat)=> (((eq extended_enat) N) (extended_enat2 K))))))
% 0.85/1.06 FOF formula (((eq (num->extended_enat)) numera280919179d_enat) (fun (K2:num)=> (extended_enat2 (numeral_numeral_nat K2)))) of role axiom named fact_257_numeral__eq__enat
% 0.85/1.06 A new axiom: (((eq (num->extended_enat)) numera280919179d_enat) (fun (K2:num)=> (extended_enat2 (numeral_numeral_nat K2))))
% 0.85/1.06 FOF formula (forall (X2:extended_ereal), (((ord_le824540014_ereal zero_z163181189_ereal) X2)->((ord_less_eq_real zero_zero_real) (extend1716541707_ereal X2)))) of role axiom named fact_258_real__of__ereal__pos
% 0.85/1.06 A new axiom: (forall (X2:extended_ereal), (((ord_le824540014_ereal zero_z163181189_ereal) X2)->((ord_less_eq_real zero_zero_real) (extend1716541707_ereal X2))))
% 0.85/1.06 FOF formula (not (((eq extended_ereal) (uminus1208298309_ereal extend1289208545_ereal)) zero_z163181189_ereal)) of role axiom named fact_259_Infty__neq__0_I3_J
% 0.85/1.06 A new axiom: (not (((eq extended_ereal) (uminus1208298309_ereal extend1289208545_ereal)) zero_z163181189_ereal))
% 0.85/1.06 FOF formula (forall (A:extended_ereal) (B:extended_ereal), (((ord_le824540014_ereal A) B)->((((eq extended_ereal) B) (uminus1208298309_ereal extend1289208545_ereal))->(((eq extended_ereal) A) (uminus1208298309_ereal extend1289208545_ereal))))) of role axiom named fact_260_ereal__infty__less__eq2_I2_J
% 0.85/1.06 A new axiom: (forall (A:extended_ereal) (B:extended_ereal), (((ord_le824540014_ereal A) B)->((((eq extended_ereal) B) (uminus1208298309_ereal extend1289208545_ereal))->(((eq extended_ereal) A) (uminus1208298309_ereal extend1289208545_ereal)))))
% 0.85/1.06 FOF formula (forall (X2:extended_ereal), ((ord_le824540014_ereal (uminus1208298309_ereal extend1289208545_ereal)) X2)) of role axiom named fact_261_ereal__less__eq_I2_J
% 0.85/1.06 A new axiom: (forall (X2:extended_ereal), ((ord_le824540014_ereal (uminus1208298309_ereal extend1289208545_ereal)) X2))
% 0.85/1.06 FOF formula (forall (X2:extended_ereal) (Y3:extended_ereal), (((ord_le824540014_ereal zero_z163181189_ereal) X2)->(((ord_le824540014_ereal X2) Y3)->((not (((eq extended_ereal) Y3) extend1289208545_ereal))->((ord_less_eq_real (extend1716541707_ereal X2)) (extend1716541707_ereal Y3)))))) of role axiom named fact_262_real__of__ereal__positive__mono
% 0.85/1.06 A new axiom: (forall (X2:extended_ereal) (Y3:extended_ereal), (((ord_le824540014_ereal zero_z163181189_ereal) X2)->(((ord_le824540014_ereal X2) Y3)->((not (((eq extended_ereal) Y3) extend1289208545_ereal))->((ord_less_eq_real (extend1716541707_ereal X2)) (extend1716541707_ereal Y3))))))
% 0.85/1.06 FOF formula (forall (X2:extended_ereal), (((ord_le824540014_ereal zero_z163181189_ereal) X2)->(not (((eq extended_ereal) X2) (uminus1208298309_ereal extend1289208545_ereal))))) of role axiom named fact_263_not__MInfty__nonneg
% 0.85/1.06 A new axiom: (forall (X2:extended_ereal), (((ord_le824540014_ereal zero_z163181189_ereal) X2)->(not (((eq extended_ereal) X2) (uminus1208298309_ereal extend1289208545_ereal)))))
% 0.85/1.06 FOF formula (forall (N:nat), ((ord_less_eq_nat N) N)) of role axiom named fact_264_le__refl
% 0.85/1.06 A new axiom: (forall (N:nat), ((ord_less_eq_nat N) N))
% 0.85/1.06 FOF formula (forall (_TPTP_I:nat) (J:nat) (K3:nat), (((ord_less_eq_nat _TPTP_I) J)->(((ord_less_eq_nat J) K3)->((ord_less_eq_nat _TPTP_I) K3)))) of role axiom named fact_265_le__trans
% 0.85/1.06 A new axiom: (forall (_TPTP_I:nat) (J:nat) (K3:nat), (((ord_less_eq_nat _TPTP_I) J)->(((ord_less_eq_nat J) K3)->((ord_less_eq_nat _TPTP_I) K3))))
% 0.85/1.06 FOF formula (forall (M:nat) (N:nat), ((((eq nat) M) N)->((ord_less_eq_nat M) N))) of role axiom named fact_266_eq__imp__le
% 0.85/1.06 A new axiom: (forall (M:nat) (N:nat), ((((eq nat) M) N)->((ord_less_eq_nat M) N)))
% 0.85/1.06 FOF formula (forall (M:nat) (N:nat), (((ord_less_eq_nat M) N)->(((ord_less_eq_nat N) M)->(((eq nat) M) N)))) of role axiom named fact_267_le__antisym
% 0.85/1.06 A new axiom: (forall (M:nat) (N:nat), (((ord_less_eq_nat M) N)->(((ord_less_eq_nat N) M)->(((eq nat) M) N))))
% 0.85/1.07 FOF formula (forall (P:(nat->Prop)) (K3:nat) (B:nat), ((P K3)->((forall (Y:nat), ((P Y)->((ord_less_eq_nat Y) B)))->(P (order_Greatest_nat P))))) of role axiom named fact_268_GreatestI__nat
% 0.85/1.07 A new axiom: (forall (P:(nat->Prop)) (K3:nat) (B:nat), ((P K3)->((forall (Y:nat), ((P Y)->((ord_less_eq_nat Y) B)))->(P (order_Greatest_nat P)))))
% 0.85/1.07 FOF formula (forall (M:nat) (N:nat), ((or ((ord_less_eq_nat M) N)) ((ord_less_eq_nat N) M))) of role axiom named fact_269_nat__le__linear
% 0.85/1.07 A new axiom: (forall (M:nat) (N:nat), ((or ((ord_less_eq_nat M) N)) ((ord_less_eq_nat N) M)))
% 0.85/1.07 FOF formula (forall (P:(nat->Prop)) (K3:nat) (B:nat), ((P K3)->((forall (Y:nat), ((P Y)->((ord_less_eq_nat Y) B)))->((ord_less_eq_nat K3) (order_Greatest_nat P))))) of role axiom named fact_270_Greatest__le__nat
% 0.85/1.07 A new axiom: (forall (P:(nat->Prop)) (K3:nat) (B:nat), ((P K3)->((forall (Y:nat), ((P Y)->((ord_less_eq_nat Y) B)))->((ord_less_eq_nat K3) (order_Greatest_nat P)))))
% 0.85/1.07 FOF formula (forall (P:(nat->Prop)) (B:nat), (((ex nat) (fun (X_1:nat)=> (P X_1)))->((forall (Y:nat), ((P Y)->((ord_less_eq_nat Y) B)))->(P (order_Greatest_nat P))))) of role axiom named fact_271_GreatestI__ex__nat
% 0.85/1.07 A new axiom: (forall (P:(nat->Prop)) (B:nat), (((ex nat) (fun (X_1:nat)=> (P X_1)))->((forall (Y:nat), ((P Y)->((ord_less_eq_nat Y) B)))->(P (order_Greatest_nat P)))))
% 0.85/1.07 FOF formula (forall (P:(nat->Prop)) (K3:nat) (B:nat), ((P K3)->((forall (Y:nat), ((P Y)->((ord_less_eq_nat Y) B)))->((ex nat) (fun (X3:nat)=> ((and (P X3)) (forall (Y5:nat), ((P Y5)->((ord_less_eq_nat Y5) X3))))))))) of role axiom named fact_272_Nat_Oex__has__greatest__nat
% 0.85/1.07 A new axiom: (forall (P:(nat->Prop)) (K3:nat) (B:nat), ((P K3)->((forall (Y:nat), ((P Y)->((ord_less_eq_nat Y) B)))->((ex nat) (fun (X3:nat)=> ((and (P X3)) (forall (Y5:nat), ((P Y5)->((ord_less_eq_nat Y5) X3)))))))))
% 0.85/1.07 FOF formula (forall (F:(nat->nat)) (N:nat), ((order_769474267at_nat F)->((ord_less_eq_nat N) (F N)))) of role axiom named fact_273_strict__mono__imp__increasing
% 0.85/1.07 A new axiom: (forall (F:(nat->nat)) (N:nat), ((order_769474267at_nat F)->((ord_less_eq_nat N) (F N))))
% 0.85/1.07 FOF formula (forall (A:nat), (((ord_less_eq_nat A) zero_zero_nat)->(((eq nat) A) zero_zero_nat))) of role axiom named fact_274_bot__nat__0_Oextremum__uniqueI
% 0.85/1.07 A new axiom: (forall (A:nat), (((ord_less_eq_nat A) zero_zero_nat)->(((eq nat) A) zero_zero_nat)))
% 0.85/1.07 FOF formula (forall (A:nat), (((eq Prop) ((ord_less_eq_nat A) zero_zero_nat)) (((eq nat) A) zero_zero_nat))) of role axiom named fact_275_bot__nat__0_Oextremum__unique
% 0.85/1.07 A new axiom: (forall (A:nat), (((eq Prop) ((ord_less_eq_nat A) zero_zero_nat)) (((eq nat) A) zero_zero_nat)))
% 0.85/1.07 FOF formula (forall (N:nat), (((eq Prop) ((ord_less_eq_nat N) zero_zero_nat)) (((eq nat) N) zero_zero_nat))) of role axiom named fact_276_le__0__eq
% 0.85/1.07 A new axiom: (forall (N:nat), (((eq Prop) ((ord_less_eq_nat N) zero_zero_nat)) (((eq nat) N) zero_zero_nat)))
% 0.85/1.07 FOF formula (forall (N:nat), ((ord_less_eq_nat zero_zero_nat) N)) of role axiom named fact_277_less__eq__nat_Osimps_I1_J
% 0.85/1.07 A new axiom: (forall (N:nat), ((ord_less_eq_nat zero_zero_nat) N))
% 0.85/1.07 FOF formula (forall (N:nat), (((eq nat) (extended_the_enat (extended_enat2 N))) N)) of role axiom named fact_278_the__enat_Osimps
% 0.85/1.07 A new axiom: (forall (N:nat), (((eq nat) (extended_the_enat (extended_enat2 N))) N))
% 0.85/1.07 FOF formula (forall (A:extended_ereal), (((eq extended_ereal) (uminus1208298309_ereal (uminus1208298309_ereal A))) A)) of role axiom named fact_279_ereal__uminus__uminus
% 0.85/1.07 A new axiom: (forall (A:extended_ereal), (((eq extended_ereal) (uminus1208298309_ereal (uminus1208298309_ereal A))) A))
% 0.85/1.07 FOF formula (forall (A:extended_ereal) (B:extended_ereal), (((eq Prop) (((eq extended_ereal) (uminus1208298309_ereal A)) (uminus1208298309_ereal B))) (((eq extended_ereal) A) B))) of role axiom named fact_280_ereal__uminus__eq__iff
% 0.85/1.07 A new axiom: (forall (A:extended_ereal) (B:extended_ereal), (((eq Prop) (((eq extended_ereal) (uminus1208298309_ereal A)) (uminus1208298309_ereal B))) (((eq extended_ereal) A) B)))
% 0.85/1.07 FOF formula (forall (A:extended_ereal) (B:extended_ereal), (((eq Prop) (((eq extended_ereal) (uminus1208298309_ereal A)) B)) (((eq extended_ereal) A) (uminus1208298309_ereal B)))) of role axiom named fact_281_ereal__uminus__eq__reorder
% 0.85/1.07 A new axiom: (forall (A:extended_ereal) (B:extended_ereal), (((eq Prop) (((eq extended_ereal) (uminus1208298309_ereal A)) B)) (((eq extended_ereal) A) (uminus1208298309_ereal B))))
% 0.85/1.07 FOF formula (forall (X2:real), (((eq Prop) (((eq real) X2) zero_zero_real)) ((and ((ord_less_eq_real zero_zero_real) X2)) ((ord_less_eq_real zero_zero_real) (uminus_uminus_real X2))))) of role axiom named fact_282_real__eq__0__iff__le__ge__0
% 0.85/1.07 A new axiom: (forall (X2:real), (((eq Prop) (((eq real) X2) zero_zero_real)) ((and ((ord_less_eq_real zero_zero_real) X2)) ((ord_less_eq_real zero_zero_real) (uminus_uminus_real X2)))))
% 0.85/1.07 FOF formula (forall (R:real), (((eq Prop) ((ord_le824540014_ereal zero_z163181189_ereal) (extended_ereal2 R))) ((ord_less_eq_real zero_zero_real) R))) of role axiom named fact_283_ereal__less__eq_I5_J
% 0.85/1.07 A new axiom: (forall (R:real), (((eq Prop) ((ord_le824540014_ereal zero_z163181189_ereal) (extended_ereal2 R))) ((ord_less_eq_real zero_zero_real) R)))
% 0.85/1.07 FOF formula (forall (R:real), (((eq Prop) ((ord_le824540014_ereal (extended_ereal2 R)) zero_z163181189_ereal)) ((ord_less_eq_real R) zero_zero_real))) of role axiom named fact_284_ereal__less__eq_I4_J
% 0.85/1.07 A new axiom: (forall (R:real), (((eq Prop) ((ord_le824540014_ereal (extended_ereal2 R)) zero_z163181189_ereal)) ((ord_less_eq_real R) zero_zero_real)))
% 0.85/1.07 FOF formula (((eq extended_ereal) extended_MInfty) (uminus1208298309_ereal extend1289208545_ereal)) of role axiom named fact_285_MInfty__eq__minfinity
% 0.85/1.07 A new axiom: (((eq extended_ereal) extended_MInfty) (uminus1208298309_ereal extend1289208545_ereal))
% 0.85/1.07 FOF formula (forall (X2:real) (Y3:real), ((((eq real) X2) Y3)->(((eq extended_ereal) (extended_ereal2 X2)) (extended_ereal2 Y3)))) of role axiom named fact_286_ereal__cong
% 0.85/1.07 A new axiom: (forall (X2:real) (Y3:real), ((((eq real) X2) Y3)->(((eq extended_ereal) (extended_ereal2 X2)) (extended_ereal2 Y3))))
% 0.85/1.07 FOF formula (forall (X1:real) (Y1:real), (((eq Prop) (((eq extended_ereal) (extended_ereal2 X1)) (extended_ereal2 Y1))) (((eq real) X1) Y1))) of role axiom named fact_287_ereal_Oinject
% 0.85/1.07 A new axiom: (forall (X1:real) (Y1:real), (((eq Prop) (((eq extended_ereal) (extended_ereal2 X1)) (extended_ereal2 Y1))) (((eq real) X1) Y1)))
% 0.85/1.07 FOF formula (((eq (num->extended_ereal)) numera1793320307_ereal) (fun (W:num)=> (extended_ereal2 (numeral_numeral_real W)))) of role axiom named fact_288_numeral__eq__ereal
% 0.85/1.07 A new axiom: (((eq (num->extended_ereal)) numera1793320307_ereal) (fun (W:num)=> (extended_ereal2 (numeral_numeral_real W))))
% 0.85/1.07 FOF formula (forall (R:real), (((eq Prop) (((eq extended_ereal) (extended_ereal2 R)) zero_z163181189_ereal)) (((eq real) R) zero_zero_real))) of role axiom named fact_289_ereal__eq__0_I1_J
% 0.85/1.07 A new axiom: (forall (R:real), (((eq Prop) (((eq extended_ereal) (extended_ereal2 R)) zero_z163181189_ereal)) (((eq real) R) zero_zero_real)))
% 0.85/1.07 FOF formula (forall (R:real), (((eq Prop) (((eq extended_ereal) zero_z163181189_ereal) (extended_ereal2 R))) (((eq real) R) zero_zero_real))) of role axiom named fact_290_ereal__eq__0_I2_J
% 0.85/1.07 A new axiom: (forall (R:real), (((eq Prop) (((eq extended_ereal) zero_z163181189_ereal) (extended_ereal2 R))) (((eq real) R) zero_zero_real)))
% 0.85/1.07 FOF formula (forall (R:real) (P2:real), (((eq Prop) ((ord_le824540014_ereal (extended_ereal2 R)) (extended_ereal2 P2))) ((ord_less_eq_real R) P2))) of role axiom named fact_291_ereal__less__eq_I3_J
% 0.85/1.07 A new axiom: (forall (R:real) (P2:real), (((eq Prop) ((ord_le824540014_ereal (extended_ereal2 R)) (extended_ereal2 P2))) ((ord_less_eq_real R) P2)))
% 0.85/1.07 FOF formula (forall (X1:real), (not (((eq extended_ereal) (extended_ereal2 X1)) extended_MInfty))) of role axiom named fact_292_ereal_Odistinct_I3_J
% 0.85/1.07 A new axiom: (forall (X1:real), (not (((eq extended_ereal) (extended_ereal2 X1)) extended_MInfty)))
% 0.85/1.07 FOF formula (forall (R:real), (((eq real) (extend1716541707_ereal (extended_ereal2 R))) R)) of role axiom named fact_293_real__of__ereal_Osimps_I1_J
% 0.92/1.08 A new axiom: (forall (R:real), (((eq real) (extend1716541707_ereal (extended_ereal2 R))) R))
% 0.92/1.08 FOF formula (forall (X2:extended_ereal) (Y3:extended_ereal), ((forall (Z4:real), (((ord_le824540014_ereal X2) (extended_ereal2 Z4))->((ord_le824540014_ereal Y3) (extended_ereal2 Z4))))->((ord_le824540014_ereal Y3) X2))) of role axiom named fact_294_ereal__le__real
% 0.92/1.08 A new axiom: (forall (X2:extended_ereal) (Y3:extended_ereal), ((forall (Z4:real), (((ord_le824540014_ereal X2) (extended_ereal2 Z4))->((ord_le824540014_ereal Y3) (extended_ereal2 Z4))))->((ord_le824540014_ereal Y3) X2)))
% 0.92/1.08 FOF formula (forall (R:real), (not (((eq extended_ereal) (extended_ereal2 R)) extend1289208545_ereal))) of role axiom named fact_295_PInfty__neq__ereal_I1_J
% 0.92/1.08 A new axiom: (forall (R:real), (not (((eq extended_ereal) (extended_ereal2 R)) extend1289208545_ereal)))
% 0.92/1.08 FOF formula (((eq extended_ereal) zero_z163181189_ereal) (extended_ereal2 zero_zero_real)) of role axiom named fact_296_zero__ereal__def
% 0.92/1.08 A new axiom: (((eq extended_ereal) zero_z163181189_ereal) (extended_ereal2 zero_zero_real))
% 0.92/1.08 FOF formula (forall (A:extended_ereal) (X2:real) (Y3:real), (((ord_le824540014_ereal A) (extended_ereal2 X2))->(((ord_less_eq_real X2) Y3)->((ord_le824540014_ereal A) (extended_ereal2 Y3))))) of role axiom named fact_297_le__ereal__le
% 0.92/1.08 A new axiom: (forall (A:extended_ereal) (X2:real) (Y3:real), (((ord_le824540014_ereal A) (extended_ereal2 X2))->(((ord_less_eq_real X2) Y3)->((ord_le824540014_ereal A) (extended_ereal2 Y3)))))
% 0.92/1.08 FOF formula (forall (Y3:real) (A:extended_ereal) (X2:real), (((ord_le824540014_ereal (extended_ereal2 Y3)) A)->(((ord_less_eq_real X2) Y3)->((ord_le824540014_ereal (extended_ereal2 X2)) A)))) of role axiom named fact_298_ereal__le__le
% 0.92/1.08 A new axiom: (forall (Y3:real) (A:extended_ereal) (X2:real), (((ord_le824540014_ereal (extended_ereal2 Y3)) A)->(((ord_less_eq_real X2) Y3)->((ord_le824540014_ereal (extended_ereal2 X2)) A))))
% 0.92/1.08 FOF formula (forall (P:(extended_ereal->Prop)) (A0:extended_ereal), ((forall (R2:real), (P (extended_ereal2 R2)))->((P extend1289208545_ereal)->((P (uminus1208298309_ereal extend1289208545_ereal))->(P A0))))) of role axiom named fact_299_real__of__ereal_Oinduct
% 0.92/1.08 A new axiom: (forall (P:(extended_ereal->Prop)) (A0:extended_ereal), ((forall (R2:real), (P (extended_ereal2 R2)))->((P extend1289208545_ereal)->((P (uminus1208298309_ereal extend1289208545_ereal))->(P A0)))))
% 0.92/1.08 FOF formula (forall (X2:extended_ereal), ((forall (R2:real), (not (((eq extended_ereal) X2) (extended_ereal2 R2))))->((not (((eq extended_ereal) X2) extend1289208545_ereal))->(((eq extended_ereal) X2) (uminus1208298309_ereal extend1289208545_ereal))))) of role axiom named fact_300_real__of__ereal_Ocases
% 0.92/1.08 A new axiom: (forall (X2:extended_ereal), ((forall (R2:real), (not (((eq extended_ereal) X2) (extended_ereal2 R2))))->((not (((eq extended_ereal) X2) extend1289208545_ereal))->(((eq extended_ereal) X2) (uminus1208298309_ereal extend1289208545_ereal)))))
% 0.92/1.08 FOF formula (forall (P:(extended_ereal->(extended_ereal->Prop))) (A0:extended_ereal) (A1:extended_ereal), ((forall (R2:real) (P3:real), ((P (extended_ereal2 R2)) (extended_ereal2 P3)))->((forall (R2:real), ((P (extended_ereal2 R2)) extend1289208545_ereal))->((forall (R2:real), ((P extend1289208545_ereal) (extended_ereal2 R2)))->((forall (R2:real), ((P (extended_ereal2 R2)) (uminus1208298309_ereal extend1289208545_ereal)))->((forall (R2:real), ((P (uminus1208298309_ereal extend1289208545_ereal)) (extended_ereal2 R2)))->(((P extend1289208545_ereal) extend1289208545_ereal)->(((P (uminus1208298309_ereal extend1289208545_ereal)) extend1289208545_ereal)->(((P extend1289208545_ereal) (uminus1208298309_ereal extend1289208545_ereal))->(((P (uminus1208298309_ereal extend1289208545_ereal)) (uminus1208298309_ereal extend1289208545_ereal))->((P A0) A1))))))))))) of role axiom named fact_301_times__ereal_Oinduct
% 0.92/1.08 A new axiom: (forall (P:(extended_ereal->(extended_ereal->Prop))) (A0:extended_ereal) (A1:extended_ereal), ((forall (R2:real) (P3:real), ((P (extended_ereal2 R2)) (extended_ereal2 P3)))->((forall (R2:real), ((P (extended_ereal2 R2)) extend1289208545_ereal))->((forall (R2:real), ((P extend1289208545_ereal) (extended_ereal2 R2)))->((forall (R2:real), ((P (extended_ereal2 R2)) (uminus1208298309_ereal extend1289208545_ereal)))->((forall (R2:real), ((P (uminus1208298309_ereal extend1289208545_ereal)) (extended_ereal2 R2)))->(((P extend1289208545_ereal) extend1289208545_ereal)->(((P (uminus1208298309_ereal extend1289208545_ereal)) extend1289208545_ereal)->(((P extend1289208545_ereal) (uminus1208298309_ereal extend1289208545_ereal))->(((P (uminus1208298309_ereal extend1289208545_ereal)) (uminus1208298309_ereal extend1289208545_ereal))->((P A0) A1)))))))))))
% 0.92/1.09 FOF formula (forall (P:(extended_ereal->(extended_ereal->Prop))) (A0:extended_ereal) (A1:extended_ereal), ((forall (R2:real) (P3:real), ((P (extended_ereal2 R2)) (extended_ereal2 P3)))->((forall (X_12:extended_ereal), ((P extend1289208545_ereal) X_12))->((forall (A3:extended_ereal), ((P A3) extend1289208545_ereal))->((forall (R2:real), ((P (extended_ereal2 R2)) (uminus1208298309_ereal extend1289208545_ereal)))->((forall (P3:real), ((P (uminus1208298309_ereal extend1289208545_ereal)) (extended_ereal2 P3)))->(((P (uminus1208298309_ereal extend1289208545_ereal)) (uminus1208298309_ereal extend1289208545_ereal))->((P A0) A1)))))))) of role axiom named fact_302_plus__ereal_Oinduct
% 0.92/1.09 A new axiom: (forall (P:(extended_ereal->(extended_ereal->Prop))) (A0:extended_ereal) (A1:extended_ereal), ((forall (R2:real) (P3:real), ((P (extended_ereal2 R2)) (extended_ereal2 P3)))->((forall (X_12:extended_ereal), ((P extend1289208545_ereal) X_12))->((forall (A3:extended_ereal), ((P A3) extend1289208545_ereal))->((forall (R2:real), ((P (extended_ereal2 R2)) (uminus1208298309_ereal extend1289208545_ereal)))->((forall (P3:real), ((P (uminus1208298309_ereal extend1289208545_ereal)) (extended_ereal2 P3)))->(((P (uminus1208298309_ereal extend1289208545_ereal)) (uminus1208298309_ereal extend1289208545_ereal))->((P A0) A1))))))))
% 0.92/1.09 FOF formula (forall (P:(extended_ereal->(extended_ereal->Prop))) (A0:extended_ereal) (A1:extended_ereal), ((forall (X3:real) (Y:real), ((P (extended_ereal2 X3)) (extended_ereal2 Y)))->((forall (X_12:extended_ereal), ((P extend1289208545_ereal) X_12))->((forall (A3:extended_ereal), ((P A3) (uminus1208298309_ereal extend1289208545_ereal)))->((forall (X3:real), ((P (extended_ereal2 X3)) extend1289208545_ereal))->((forall (R2:real), ((P (uminus1208298309_ereal extend1289208545_ereal)) (extended_ereal2 R2)))->(((P (uminus1208298309_ereal extend1289208545_ereal)) extend1289208545_ereal)->((P A0) A1)))))))) of role axiom named fact_303_less__ereal_Oinduct
% 0.92/1.09 A new axiom: (forall (P:(extended_ereal->(extended_ereal->Prop))) (A0:extended_ereal) (A1:extended_ereal), ((forall (X3:real) (Y:real), ((P (extended_ereal2 X3)) (extended_ereal2 Y)))->((forall (X_12:extended_ereal), ((P extend1289208545_ereal) X_12))->((forall (A3:extended_ereal), ((P A3) (uminus1208298309_ereal extend1289208545_ereal)))->((forall (X3:real), ((P (extended_ereal2 X3)) extend1289208545_ereal))->((forall (R2:real), ((P (uminus1208298309_ereal extend1289208545_ereal)) (extended_ereal2 R2)))->(((P (uminus1208298309_ereal extend1289208545_ereal)) extend1289208545_ereal)->((P A0) A1))))))))
% 0.92/1.09 FOF formula (forall (P:(extended_ereal->Prop)) (A0:extended_ereal), ((forall (R2:real), (P (extended_ereal2 R2)))->((P (uminus1208298309_ereal extend1289208545_ereal))->((P extend1289208545_ereal)->(P A0))))) of role axiom named fact_304_abs__ereal_Oinduct
% 0.92/1.09 A new axiom: (forall (P:(extended_ereal->Prop)) (A0:extended_ereal), ((forall (R2:real), (P (extended_ereal2 R2)))->((P (uminus1208298309_ereal extend1289208545_ereal))->((P extend1289208545_ereal)->(P A0)))))
% 0.92/1.09 FOF formula (((eq ((extended_ereal->Prop)->Prop)) (fun (P4:(extended_ereal->Prop))=> (forall (X6:extended_ereal), (P4 X6)))) (fun (P5:(extended_ereal->Prop))=> ((and ((and (P5 extend1289208545_ereal)) (forall (X4:real), (P5 (extended_ereal2 X4))))) (P5 (uminus1208298309_ereal extend1289208545_ereal))))) of role axiom named fact_305_ereal__all__split
% 0.92/1.09 A new axiom: (((eq ((extended_ereal->Prop)->Prop)) (fun (P4:(extended_ereal->Prop))=> (forall (X6:extended_ereal), (P4 X6)))) (fun (P5:(extended_ereal->Prop))=> ((and ((and (P5 extend1289208545_ereal)) (forall (X4:real), (P5 (extended_ereal2 X4))))) (P5 (uminus1208298309_ereal extend1289208545_ereal)))))
% 0.92/1.11 FOF formula (forall (X2:extended_ereal), ((forall (R2:real), (not (((eq extended_ereal) X2) (extended_ereal2 R2))))->((not (((eq extended_ereal) X2) (uminus1208298309_ereal extend1289208545_ereal)))->(((eq extended_ereal) X2) extend1289208545_ereal)))) of role axiom named fact_306_abs__ereal_Ocases
% 0.92/1.11 A new axiom: (forall (X2:extended_ereal), ((forall (R2:real), (not (((eq extended_ereal) X2) (extended_ereal2 R2))))->((not (((eq extended_ereal) X2) (uminus1208298309_ereal extend1289208545_ereal)))->(((eq extended_ereal) X2) extend1289208545_ereal))))
% 0.92/1.11 FOF formula (((eq ((extended_ereal->Prop)->Prop)) (fun (P4:(extended_ereal->Prop))=> ((ex extended_ereal) (fun (X6:extended_ereal)=> (P4 X6))))) (fun (P5:(extended_ereal->Prop))=> ((or ((or (P5 extend1289208545_ereal)) ((ex real) (fun (X4:real)=> (P5 (extended_ereal2 X4)))))) (P5 (uminus1208298309_ereal extend1289208545_ereal))))) of role axiom named fact_307_ereal__ex__split
% 0.92/1.11 A new axiom: (((eq ((extended_ereal->Prop)->Prop)) (fun (P4:(extended_ereal->Prop))=> ((ex extended_ereal) (fun (X6:extended_ereal)=> (P4 X6))))) (fun (P5:(extended_ereal->Prop))=> ((or ((or (P5 extend1289208545_ereal)) ((ex real) (fun (X4:real)=> (P5 (extended_ereal2 X4)))))) (P5 (uminus1208298309_ereal extend1289208545_ereal)))))
% 0.92/1.11 FOF formula (forall (X2:extended_ereal) (Xa3:extended_ereal) (Xb:extended_ereal), ((((ex real) (fun (R2:real)=> (((eq extended_ereal) X2) (extended_ereal2 R2))))->(((ex real) (fun (Ra:real)=> (((eq extended_ereal) Xa3) (extended_ereal2 Ra))))->(forall (Rb:real), (not (((eq extended_ereal) Xb) (extended_ereal2 Rb))))))->((((ex real) (fun (R2:real)=> (((eq extended_ereal) X2) (extended_ereal2 R2))))->(((ex real) (fun (Ra:real)=> (((eq extended_ereal) Xa3) (extended_ereal2 Ra))))->(not (((eq extended_ereal) Xb) extend1289208545_ereal))))->((((ex real) (fun (R2:real)=> (((eq extended_ereal) X2) (extended_ereal2 R2))))->(((ex real) (fun (Ra:real)=> (((eq extended_ereal) Xa3) (extended_ereal2 Ra))))->(not (((eq extended_ereal) Xb) (uminus1208298309_ereal extend1289208545_ereal)))))->((((ex real) (fun (R2:real)=> (((eq extended_ereal) X2) (extended_ereal2 R2))))->((((eq extended_ereal) Xa3) extend1289208545_ereal)->(forall (Ra:real), (not (((eq extended_ereal) Xb) (extended_ereal2 Ra))))))->((((ex real) (fun (R2:real)=> (((eq extended_ereal) X2) (extended_ereal2 R2))))->((((eq extended_ereal) Xa3) extend1289208545_ereal)->(not (((eq extended_ereal) Xb) extend1289208545_ereal))))->((((ex real) (fun (R2:real)=> (((eq extended_ereal) X2) (extended_ereal2 R2))))->((((eq extended_ereal) Xa3) extend1289208545_ereal)->(not (((eq extended_ereal) Xb) (uminus1208298309_ereal extend1289208545_ereal)))))->((((ex real) (fun (R2:real)=> (((eq extended_ereal) X2) (extended_ereal2 R2))))->((((eq extended_ereal) Xa3) (uminus1208298309_ereal extend1289208545_ereal))->(forall (Ra:real), (not (((eq extended_ereal) Xb) (extended_ereal2 Ra))))))->((((ex real) (fun (R2:real)=> (((eq extended_ereal) X2) (extended_ereal2 R2))))->((((eq extended_ereal) Xa3) (uminus1208298309_ereal extend1289208545_ereal))->(not (((eq extended_ereal) Xb) extend1289208545_ereal))))->((((ex real) (fun (R2:real)=> (((eq extended_ereal) X2) (extended_ereal2 R2))))->((((eq extended_ereal) Xa3) (uminus1208298309_ereal extend1289208545_ereal))->(not (((eq extended_ereal) Xb) (uminus1208298309_ereal extend1289208545_ereal)))))->(((((eq extended_ereal) X2) extend1289208545_ereal)->(((ex real) (fun (R2:real)=> (((eq extended_ereal) Xa3) (extended_ereal2 R2))))->(forall (Ra:real), (not (((eq extended_ereal) Xb) (extended_ereal2 Ra))))))->(((((eq extended_ereal) X2) extend1289208545_ereal)->(((ex real) (fun (R2:real)=> (((eq extended_ereal) Xa3) (extended_ereal2 R2))))->(not (((eq extended_ereal) Xb) extend1289208545_ereal))))->(((((eq extended_ereal) X2) extend1289208545_ereal)->(((ex real) (fun (R2:real)=> (((eq extended_ereal) Xa3) (extended_ereal2 R2))))->(not (((eq extended_ereal) Xb) (uminus1208298309_ereal extend1289208545_ereal)))))->(((((eq extended_ereal) X2) extend1289208545_ereal)->((((eq extended_ereal) Xa3) extend1289208545_ereal)->(forall (R2:real), (not (((eq extended_ereal) Xb) (extended_ereal2 R2))))))->(((((eq extended_ereal) X2) extend1289208545_ereal)->((((eq extended_ereal) Xa3) extend1289208545_ereal)->(not (((eq extended_ereal) Xb) extend1289208545_ereal))))->(((((eq extended_ereal) X2) extend1289208545_ereal)->((((eq extended_ereal) Xa3) extend1289208545_ereal)->(not (((eq extended_ereal) Xb) (uminus1208298309_ereal extend1289208545_ereal)))))->(((((eq extended_ereal) X2) extend1289208545_ereal)->((((eq extended_ereal) Xa3) (uminus1208298309_ereal extend1289208545_ereal))->(forall (R2:real), (not (((eq extended_ereal) Xb) (extended_ereal2 R2))))))->(((((eq extended_ereal) X2) extend1289208545_ereal)->((((eq extended_ereal) Xa3) (uminus1208298309_ereal extend1289208545_ereal))->(not (((eq extended_ereal) Xb) extend1289208545_ereal))))->(((((eq extended_ereal) X2) extend1289208545_ereal)->((((eq extended_ereal) Xa3) (uminus1208298309_ereal extend1289208545_ereal))->(not (((eq extended_ereal) Xb) (uminus1208298309_ereal extend1289208545_ereal)))))->(((((eq extended_ereal) X2) (uminus1208298309_ereal extend1289208545_ereal))->(((ex real) (fun (R2:real)=> (((eq extended_ereal) Xa3) (extended_ereal2 R2))))->(forall (Ra:real), (not (((eq extended_ereal) Xb) (extended_ereal2 Ra))))))->(((((eq extended_ereal) X2) (uminus1208298309_ereal extend1289208545_ereal))->(((ex real) (fun (R2:real)=> (((eq extended_ereal) Xa3) (extended_ereal2 R2))))->(not (((eq extended_ereal) Xb) extend1289208545_ereal))))->(((((eq extended_ereal) X2) (uminus1208298309_ereal extend1289208545_ereal))->(((ex real) (fun (R2:real)=> (((eq extended_ereal) Xa3) (extended_ereal2 R2))))->(not (((eq extended_ereal) Xb) (uminus1208298309_ereal extend1289208545_ereal)))))->(((((eq extended_ereal) X2) (uminus1208298309_ereal extend1289208545_ereal))->((((eq extended_ereal) Xa3) extend1289208545_ereal)->(forall (R2:real), (not (((eq extended_ereal) Xb) (extended_ereal2 R2))))))->(((((eq extended_ereal) X2) (uminus1208298309_ereal extend1289208545_ereal))->((((eq extended_ereal) Xa3) extend1289208545_ereal)->(not (((eq extended_ereal) Xb) extend1289208545_ereal))))->(((((eq extended_ereal) X2) (uminus1208298309_ereal extend1289208545_ereal))->((((eq extended_ereal) Xa3) extend1289208545_ereal)->(not (((eq extended_ereal) Xb) (uminus1208298309_ereal extend1289208545_ereal)))))->(((((eq extended_ereal) X2) (uminus1208298309_ereal extend1289208545_ereal))->((((eq extended_ereal) Xa3) (uminus1208298309_ereal extend1289208545_ereal))->(forall (R2:real), (not (((eq extended_ereal) Xb) (extended_ereal2 R2))))))->(((((eq extended_ereal) X2) (uminus1208298309_ereal extend1289208545_ereal))->((((eq extended_ereal) Xa3) (uminus1208298309_ereal extend1289208545_ereal))->(not (((eq extended_ereal) Xb) extend1289208545_ereal))))->(((((eq extended_ereal) X2) (uminus1208298309_ereal extend1289208545_ereal))->((((eq extended_ereal) Xa3) (uminus1208298309_ereal extend1289208545_ereal))->(not (((eq extended_ereal) Xb) (uminus1208298309_ereal extend1289208545_ereal)))))->False)))))))))))))))))))))))))))) of role axiom named fact_308_ereal3__cases
% 0.92/1.11 A new axiom: (forall (X2:extended_ereal) (Xa3:extended_ereal) (Xb:extended_ereal), ((((ex real) (fun (R2:real)=> (((eq extended_ereal) X2) (extended_ereal2 R2))))->(((ex real) (fun (Ra:real)=> (((eq extended_ereal) Xa3) (extended_ereal2 Ra))))->(forall (Rb:real), (not (((eq extended_ereal) Xb) (extended_ereal2 Rb))))))->((((ex real) (fun (R2:real)=> (((eq extended_ereal) X2) (extended_ereal2 R2))))->(((ex real) (fun (Ra:real)=> (((eq extended_ereal) Xa3) (extended_ereal2 Ra))))->(not (((eq extended_ereal) Xb) extend1289208545_ereal))))->((((ex real) (fun (R2:real)=> (((eq extended_ereal) X2) (extended_ereal2 R2))))->(((ex real) (fun (Ra:real)=> (((eq extended_ereal) Xa3) (extended_ereal2 Ra))))->(not (((eq extended_ereal) Xb) (uminus1208298309_ereal extend1289208545_ereal)))))->((((ex real) (fun (R2:real)=> (((eq extended_ereal) X2) (extended_ereal2 R2))))->((((eq extended_ereal) Xa3) extend1289208545_ereal)->(forall (Ra:real), (not (((eq extended_ereal) Xb) (extended_ereal2 Ra))))))->((((ex real) (fun (R2:real)=> (((eq extended_ereal) X2) (extended_ereal2 R2))))->((((eq extended_ereal) Xa3) extend1289208545_ereal)->(not (((eq extended_ereal) Xb) extend1289208545_ereal))))->((((ex real) (fun (R2:real)=> (((eq extended_ereal) X2) (extended_ereal2 R2))))->((((eq extended_ereal) Xa3) extend1289208545_ereal)->(not (((eq extended_ereal) Xb) (uminus1208298309_ereal extend1289208545_ereal)))))->((((ex real) (fun (R2:real)=> (((eq extended_ereal) X2) (extended_ereal2 R2))))->((((eq extended_ereal) Xa3) (uminus1208298309_ereal extend1289208545_ereal))->(forall (Ra:real), (not (((eq extended_ereal) Xb) (extended_ereal2 Ra))))))->((((ex real) (fun (R2:real)=> (((eq extended_ereal) X2) (extended_ereal2 R2))))->((((eq extended_ereal) Xa3) (uminus1208298309_ereal extend1289208545_ereal))->(not (((eq extended_ereal) Xb) extend1289208545_ereal))))->((((ex real) (fun (R2:real)=> (((eq extended_ereal) X2) (extended_ereal2 R2))))->((((eq extended_ereal) Xa3) (uminus1208298309_ereal extend1289208545_ereal))->(not (((eq extended_ereal) Xb) (uminus1208298309_ereal extend1289208545_ereal)))))->(((((eq extended_ereal) X2) extend1289208545_ereal)->(((ex real) (fun (R2:real)=> (((eq extended_ereal) Xa3) (extended_ereal2 R2))))->(forall (Ra:real), (not (((eq extended_ereal) Xb) (extended_ereal2 Ra))))))->(((((eq extended_ereal) X2) extend1289208545_ereal)->(((ex real) (fun (R2:real)=> (((eq extended_ereal) Xa3) (extended_ereal2 R2))))->(not (((eq extended_ereal) Xb) extend1289208545_ereal))))->(((((eq extended_ereal) X2) extend1289208545_ereal)->(((ex real) (fun (R2:real)=> (((eq extended_ereal) Xa3) (extended_ereal2 R2))))->(not (((eq extended_ereal) Xb) (uminus1208298309_ereal extend1289208545_ereal)))))->(((((eq extended_ereal) X2) extend1289208545_ereal)->((((eq extended_ereal) Xa3) extend1289208545_ereal)->(forall (R2:real), (not (((eq extended_ereal) Xb) (extended_ereal2 R2))))))->(((((eq extended_ereal) X2) extend1289208545_ereal)->((((eq extended_ereal) Xa3) extend1289208545_ereal)->(not (((eq extended_ereal) Xb) extend1289208545_ereal))))->(((((eq extended_ereal) X2) extend1289208545_ereal)->((((eq extended_ereal) Xa3) extend1289208545_ereal)->(not (((eq extended_ereal) Xb) (uminus1208298309_ereal extend1289208545_ereal)))))->(((((eq extended_ereal) X2) extend1289208545_ereal)->((((eq extended_ereal) Xa3) (uminus1208298309_ereal extend1289208545_ereal))->(forall (R2:real), (not (((eq extended_ereal) Xb) (extended_ereal2 R2))))))->(((((eq extended_ereal) X2) extend1289208545_ereal)->((((eq extended_ereal) Xa3) (uminus1208298309_ereal extend1289208545_ereal))->(not (((eq extended_ereal) Xb) extend1289208545_ereal))))->(((((eq extended_ereal) X2) extend1289208545_ereal)->((((eq extended_ereal) Xa3) (uminus1208298309_ereal extend1289208545_ereal))->(not (((eq extended_ereal) Xb) (uminus1208298309_ereal extend1289208545_ereal)))))->(((((eq extended_ereal) X2) (uminus1208298309_ereal extend1289208545_ereal))->(((ex real) (fun (R2:real)=> (((eq extended_ereal) Xa3) (extended_ereal2 R2))))->(forall (Ra:real), (not (((eq extended_ereal) Xb) (extended_ereal2 Ra))))))->(((((eq extended_ereal) X2) (uminus1208298309_ereal extend1289208545_ereal))->(((ex real) (fun (R2:real)=> (((eq extended_ereal) Xa3) (extended_ereal2 R2))))->(not (((eq extended_ereal) Xb) extend1289208545_ereal))))->(((((eq extended_ereal) X2) (uminus1208298309_ereal extend1289208545_ereal))->(((ex real) (fun (R2:real)=> (((eq extended_ereal) Xa3) (extended_ereal2 R2))))->(not (((eq extended_ereal) Xb) (uminus1208298309_ereal extend1289208545_ereal)))))->(((((eq extended_ereal) X2) (uminus1208298309_ereal extend1289208545_ereal))->((((eq extended_ereal) Xa3) extend1289208545_ereal)->(forall (R2:real), (not (((eq extended_ereal) Xb) (extended_ereal2 R2))))))->(((((eq extended_ereal) X2) (uminus1208298309_ereal extend1289208545_ereal))->((((eq extended_ereal) Xa3) extend1289208545_ereal)->(not (((eq extended_ereal) Xb) extend1289208545_ereal))))->(((((eq extended_ereal) X2) (uminus1208298309_ereal extend1289208545_ereal))->((((eq extended_ereal) Xa3) extend1289208545_ereal)->(not (((eq extended_ereal) Xb) (uminus1208298309_ereal extend1289208545_ereal)))))->(((((eq extended_ereal) X2) (uminus1208298309_ereal extend1289208545_ereal))->((((eq extended_ereal) Xa3) (uminus1208298309_ereal extend1289208545_ereal))->(forall (R2:real), (not (((eq extended_ereal) Xb) (extended_ereal2 R2))))))->(((((eq extended_ereal) X2) (uminus1208298309_ereal extend1289208545_ereal))->((((eq extended_ereal) Xa3) (uminus1208298309_ereal extend1289208545_ereal))->(not (((eq extended_ereal) Xb) extend1289208545_ereal))))->(((((eq extended_ereal) X2) (uminus1208298309_ereal extend1289208545_ereal))->((((eq extended_ereal) Xa3) (uminus1208298309_ereal extend1289208545_ereal))->(not (((eq extended_ereal) Xb) (uminus1208298309_ereal extend1289208545_ereal)))))->False))))))))))))))))))))))))))))
% 0.92/1.12 FOF formula (forall (X2:extended_ereal) (Xa3:extended_ereal), ((((ex real) (fun (R2:real)=> (((eq extended_ereal) X2) (extended_ereal2 R2))))->(forall (Ra:real), (not (((eq extended_ereal) Xa3) (extended_ereal2 Ra)))))->((((ex real) (fun (R2:real)=> (((eq extended_ereal) X2) (extended_ereal2 R2))))->(not (((eq extended_ereal) Xa3) extend1289208545_ereal)))->((((ex real) (fun (R2:real)=> (((eq extended_ereal) X2) (extended_ereal2 R2))))->(not (((eq extended_ereal) Xa3) (uminus1208298309_ereal extend1289208545_ereal))))->(((((eq extended_ereal) X2) extend1289208545_ereal)->(forall (R2:real), (not (((eq extended_ereal) Xa3) (extended_ereal2 R2)))))->(((((eq extended_ereal) X2) extend1289208545_ereal)->(not (((eq extended_ereal) Xa3) extend1289208545_ereal)))->(((((eq extended_ereal) X2) extend1289208545_ereal)->(not (((eq extended_ereal) Xa3) (uminus1208298309_ereal extend1289208545_ereal))))->(((((eq extended_ereal) X2) (uminus1208298309_ereal extend1289208545_ereal))->(forall (R2:real), (not (((eq extended_ereal) Xa3) (extended_ereal2 R2)))))->(((((eq extended_ereal) X2) (uminus1208298309_ereal extend1289208545_ereal))->(not (((eq extended_ereal) Xa3) extend1289208545_ereal)))->(((((eq extended_ereal) X2) (uminus1208298309_ereal extend1289208545_ereal))->(not (((eq extended_ereal) Xa3) (uminus1208298309_ereal extend1289208545_ereal))))->False)))))))))) of role axiom named fact_309_ereal2__cases
% 0.92/1.12 A new axiom: (forall (X2:extended_ereal) (Xa3:extended_ereal), ((((ex real) (fun (R2:real)=> (((eq extended_ereal) X2) (extended_ereal2 R2))))->(forall (Ra:real), (not (((eq extended_ereal) Xa3) (extended_ereal2 Ra)))))->((((ex real) (fun (R2:real)=> (((eq extended_ereal) X2) (extended_ereal2 R2))))->(not (((eq extended_ereal) Xa3) extend1289208545_ereal)))->((((ex real) (fun (R2:real)=> (((eq extended_ereal) X2) (extended_ereal2 R2))))->(not (((eq extended_ereal) Xa3) (uminus1208298309_ereal extend1289208545_ereal))))->(((((eq extended_ereal) X2) extend1289208545_ereal)->(forall (R2:real), (not (((eq extended_ereal) Xa3) (extended_ereal2 R2)))))->(((((eq extended_ereal) X2) extend1289208545_ereal)->(not (((eq extended_ereal) Xa3) extend1289208545_ereal)))->(((((eq extended_ereal) X2) extend1289208545_ereal)->(not (((eq extended_ereal) Xa3) (uminus1208298309_ereal extend1289208545_ereal))))->(((((eq extended_ereal) X2) (uminus1208298309_ereal extend1289208545_ereal))->(forall (R2:real), (not (((eq extended_ereal) Xa3) (extended_ereal2 R2)))))->(((((eq extended_ereal) X2) (uminus1208298309_ereal extend1289208545_ereal))->(not (((eq extended_ereal) Xa3) extend1289208545_ereal)))->(((((eq extended_ereal) X2) (uminus1208298309_ereal extend1289208545_ereal))->(not (((eq extended_ereal) Xa3) (uminus1208298309_ereal extend1289208545_ereal))))->False))))))))))
% 0.92/1.12 FOF formula (forall (X2:extended_ereal), ((forall (R2:real), (not (((eq extended_ereal) X2) (extended_ereal2 R2))))->((not (((eq extended_ereal) X2) extend1289208545_ereal))->(((eq extended_ereal) X2) (uminus1208298309_ereal extend1289208545_ereal))))) of role axiom named fact_310_ereal__cases
% 0.92/1.12 A new axiom: (forall (X2:extended_ereal), ((forall (R2:real), (not (((eq extended_ereal) X2) (extended_ereal2 R2))))->((not (((eq extended_ereal) X2) extend1289208545_ereal))->(((eq extended_ereal) X2) (uminus1208298309_ereal extend1289208545_ereal)))))
% 0.92/1.12 FOF formula (forall (R:real), (not (((eq extended_ereal) (extended_ereal2 R)) (uminus1208298309_ereal extend1289208545_ereal)))) of role axiom named fact_311_MInfty__neq__ereal_I1_J
% 0.92/1.12 A new axiom: (forall (R:real), (not (((eq extended_ereal) (extended_ereal2 R)) (uminus1208298309_ereal extend1289208545_ereal))))
% 0.92/1.12 FOF formula (forall (X2:extended_ereal), ((forall (B4:real), ((ord_le824540014_ereal (extended_ereal2 B4)) X2))->(((eq extended_ereal) X2) extend1289208545_ereal))) of role axiom named fact_312_ereal__top
% 0.92/1.12 A new axiom: (forall (X2:extended_ereal), ((forall (B4:real), ((ord_le824540014_ereal (extended_ereal2 B4)) X2))->(((eq extended_ereal) X2) extend1289208545_ereal)))
% 0.92/1.12 FOF formula (forall (R:real), (((eq extended_ereal) (uminus1208298309_ereal (extended_ereal2 R))) (extended_ereal2 (uminus_uminus_real R)))) of role axiom named fact_313_uminus__ereal_Osimps_I1_J
% 0.92/1.12 A new axiom: (forall (R:real), (((eq extended_ereal) (uminus1208298309_ereal (extended_ereal2 R))) (extended_ereal2 (uminus_uminus_real R))))
% 0.92/1.12 FOF formula (forall (X2:extended_ereal), ((forall (B4:real), ((ord_le824540014_ereal X2) (extended_ereal2 B4)))->(((eq extended_ereal) X2) (uminus1208298309_ereal extend1289208545_ereal)))) of role axiom named fact_314_ereal__bot
% 0.92/1.12 A new axiom: (forall (X2:extended_ereal), ((forall (B4:real), ((ord_le824540014_ereal X2) (extended_ereal2 B4)))->(((eq extended_ereal) X2) (uminus1208298309_ereal extend1289208545_ereal))))
% 0.92/1.12 FOF formula (forall (X2:extended_ereal) (Y3:real), ((((eq real) (extend1716541707_ereal X2)) Y3)->((forall (R2:real), ((((eq extended_ereal) X2) (extended_ereal2 R2))->(not (((eq real) Y3) R2))))->(((((eq extended_ereal) X2) extend1289208545_ereal)->(not (((eq real) Y3) zero_zero_real)))->(((((eq extended_ereal) X2) (uminus1208298309_ereal extend1289208545_ereal))->(not (((eq real) Y3) zero_zero_real)))->False))))) of role axiom named fact_315_real__of__ereal_Oelims
% 0.92/1.12 A new axiom: (forall (X2:extended_ereal) (Y3:real), ((((eq real) (extend1716541707_ereal X2)) Y3)->((forall (R2:real), ((((eq extended_ereal) X2) (extended_ereal2 R2))->(not (((eq real) Y3) R2))))->(((((eq extended_ereal) X2) extend1289208545_ereal)->(not (((eq real) Y3) zero_zero_real)))->(((((eq extended_ereal) X2) (uminus1208298309_ereal extend1289208545_ereal))->(not (((eq real) Y3) zero_zero_real)))->False)))))
% 0.92/1.12 FOF formula (((eq nat) (extended_size_ereal extended_MInfty)) zero_zero_nat) of role axiom named fact_316_ereal_Osize__gen_I3_J
% 0.92/1.12 A new axiom: (((eq nat) (extended_size_ereal extended_MInfty)) zero_zero_nat)
% 0.92/1.12 FOF formula (forall (X1:real), (((eq nat) (extended_size_ereal (extended_ereal2 X1))) zero_zero_nat)) of role axiom named fact_317_ereal_Osize__gen_I1_J
% 0.92/1.12 A new axiom: (forall (X1:real), (((eq nat) (extended_size_ereal (extended_ereal2 X1))) zero_zero_nat))
% 0.92/1.12 FOF formula (forall (X2:extended_ereal) (Y3:extended_ereal), ((((eq extended_ereal) (uminus1208298309_ereal X2)) Y3)->((forall (R2:real), ((((eq extended_ereal) X2) (extended_ereal2 R2))->(not (((eq extended_ereal) Y3) (extended_ereal2 (uminus_uminus_real R2))))))->(((((eq extended_ereal) X2) extended_PInfty)->(not (((eq extended_ereal) Y3) extended_MInfty)))->(((((eq extended_ereal) X2) extended_MInfty)->(not (((eq extended_ereal) Y3) extended_PInfty)))->False))))) of role axiom named fact_318_uminus__ereal_Oelims
% 0.92/1.12 A new axiom: (forall (X2:extended_ereal) (Y3:extended_ereal), ((((eq extended_ereal) (uminus1208298309_ereal X2)) Y3)->((forall (R2:real), ((((eq extended_ereal) X2) (extended_ereal2 R2))->(not (((eq extended_ereal) Y3) (extended_ereal2 (uminus_uminus_real R2))))))->(((((eq extended_ereal) X2) extended_PInfty)->(not (((eq extended_ereal) Y3) extended_MInfty)))->(((((eq extended_ereal) X2) extended_MInfty)->(not (((eq extended_ereal) Y3) extended_PInfty)))->False)))))
% 0.92/1.13 FOF formula (forall (X1:real), (not (((eq extended_ereal) (extended_ereal2 X1)) extended_PInfty))) of role axiom named fact_319_ereal_Odistinct_I1_J
% 0.92/1.13 A new axiom: (forall (X1:real), (not (((eq extended_ereal) (extended_ereal2 X1)) extended_PInfty)))
% 0.92/1.13 FOF formula (((eq nat) (extended_size_ereal extended_PInfty)) zero_zero_nat) of role axiom named fact_320_ereal_Osize__gen_I2_J
% 0.92/1.13 A new axiom: (((eq nat) (extended_size_ereal extended_PInfty)) zero_zero_nat)
% 0.92/1.13 FOF formula (((eq extended_ereal) extend1289208545_ereal) extended_PInfty) of role axiom named fact_321_infinity__ereal__def
% 0.92/1.13 A new axiom: (((eq extended_ereal) extend1289208545_ereal) extended_PInfty)
% 0.92/1.13 FOF formula (not (((eq extended_ereal) extended_PInfty) extended_MInfty)) of role axiom named fact_322_ereal_Odistinct_I5_J
% 0.92/1.13 A new axiom: (not (((eq extended_ereal) extended_PInfty) extended_MInfty))
% 0.92/1.13 FOF formula (forall (P:(extended_ereal->Prop)) (A0:extended_ereal), ((forall (R2:real), (P (extended_ereal2 R2)))->((P extended_PInfty)->((P extended_MInfty)->(P A0))))) of role axiom named fact_323_uminus__ereal_Oinduct
% 0.92/1.13 A new axiom: (forall (P:(extended_ereal->Prop)) (A0:extended_ereal), ((forall (R2:real), (P (extended_ereal2 R2)))->((P extended_PInfty)->((P extended_MInfty)->(P A0)))))
% 0.92/1.13 FOF formula (forall (X2:extended_ereal), ((forall (R2:real), (not (((eq extended_ereal) X2) (extended_ereal2 R2))))->((not (((eq extended_ereal) X2) extended_PInfty))->(((eq extended_ereal) X2) extended_MInfty)))) of role axiom named fact_324_uminus__ereal_Ocases
% 0.92/1.13 A new axiom: (forall (X2:extended_ereal), ((forall (R2:real), (not (((eq extended_ereal) X2) (extended_ereal2 R2))))->((not (((eq extended_ereal) X2) extended_PInfty))->(((eq extended_ereal) X2) extended_MInfty))))
% 0.92/1.13 FOF formula (forall (Y3:extended_ereal), ((forall (X12:real), (not (((eq extended_ereal) Y3) (extended_ereal2 X12))))->((not (((eq extended_ereal) Y3) extended_PInfty))->(((eq extended_ereal) Y3) extended_MInfty)))) of role axiom named fact_325_ereal_Oexhaust
% 0.92/1.13 A new axiom: (forall (Y3:extended_ereal), ((forall (X12:real), (not (((eq extended_ereal) Y3) (extended_ereal2 X12))))->((not (((eq extended_ereal) Y3) extended_PInfty))->(((eq extended_ereal) Y3) extended_MInfty))))
% 0.92/1.13 FOF formula (forall (P:(extended_ereal->Prop)) (Ereal:extended_ereal), ((forall (X3:real), (P (extended_ereal2 X3)))->((P extended_PInfty)->((P extended_MInfty)->(P Ereal))))) of role axiom named fact_326_ereal_Oinduct
% 0.92/1.13 A new axiom: (forall (P:(extended_ereal->Prop)) (Ereal:extended_ereal), ((forall (X3:real), (P (extended_ereal2 X3)))->((P extended_PInfty)->((P extended_MInfty)->(P Ereal)))))
% 0.92/1.13 FOF formula (((eq extended_ereal) (uminus1208298309_ereal extended_PInfty)) extended_MInfty) of role axiom named fact_327_uminus__ereal_Osimps_I2_J
% 0.92/1.13 A new axiom: (((eq extended_ereal) (uminus1208298309_ereal extended_PInfty)) extended_MInfty)
% 0.92/1.13 FOF formula (((eq extended_ereal) (uminus1208298309_ereal extended_MInfty)) extended_PInfty) of role axiom named fact_328_uminus__ereal_Osimps_I3_J
% 0.92/1.13 A new axiom: (((eq extended_ereal) (uminus1208298309_ereal extended_MInfty)) extended_PInfty)
% 0.92/1.13 FOF formula (forall (R:real), ((and (((ord_less_eq_real zero_zero_real) R)->(((eq extended_ereal) ((divide595620860_ereal extend1289208545_ereal) (extended_ereal2 R))) extend1289208545_ereal))) ((((ord_less_eq_real zero_zero_real) R)->False)->(((eq extended_ereal) ((divide595620860_ereal extend1289208545_ereal) (extended_ereal2 R))) (uminus1208298309_ereal extend1289208545_ereal))))) of role axiom named fact_329_ereal__divide__ereal
% 0.92/1.13 A new axiom: (forall (R:real), ((and (((ord_less_eq_real zero_zero_real) R)->(((eq extended_ereal) ((divide595620860_ereal extend1289208545_ereal) (extended_ereal2 R))) extend1289208545_ereal))) ((((ord_less_eq_real zero_zero_real) R)->False)->(((eq extended_ereal) ((divide595620860_ereal extend1289208545_ereal) (extended_ereal2 R))) (uminus1208298309_ereal extend1289208545_ereal)))))
% 0.92/1.13 FOF formula (forall (X2:real) (Y3:extended_ereal), (((eq Prop) ((ord_less_eq_real X2) (extend1716541707_ereal Y3))) ((and ((not (((eq extended_ereal) (abs_ab1260901297_ereal Y3)) extend1289208545_ereal))->((ord_le824540014_ereal (extended_ereal2 X2)) Y3))) ((((eq extended_ereal) (abs_ab1260901297_ereal Y3)) extend1289208545_ereal)->((ord_less_eq_real X2) zero_zero_real))))) of role axiom named fact_330_ereal__le__real__iff
% 0.92/1.14 A new axiom: (forall (X2:real) (Y3:extended_ereal), (((eq Prop) ((ord_less_eq_real X2) (extend1716541707_ereal Y3))) ((and ((not (((eq extended_ereal) (abs_ab1260901297_ereal Y3)) extend1289208545_ereal))->((ord_le824540014_ereal (extended_ereal2 X2)) Y3))) ((((eq extended_ereal) (abs_ab1260901297_ereal Y3)) extend1289208545_ereal)->((ord_less_eq_real X2) zero_zero_real)))))
% 0.92/1.14 FOF formula (forall (X2:extended_ereal), (((eq extended_ereal) (abs_ab1260901297_ereal (uminus1208298309_ereal X2))) (abs_ab1260901297_ereal X2))) of role axiom named fact_331_abs__ereal__uminus
% 0.92/1.14 A new axiom: (forall (X2:extended_ereal), (((eq extended_ereal) (abs_ab1260901297_ereal (uminus1208298309_ereal X2))) (abs_ab1260901297_ereal X2)))
% 0.92/1.14 FOF formula (((eq extended_ereal) (abs_ab1260901297_ereal zero_z163181189_ereal)) zero_z163181189_ereal) of role axiom named fact_332_abs__ereal__zero
% 0.92/1.14 A new axiom: (((eq extended_ereal) (abs_ab1260901297_ereal zero_z163181189_ereal)) zero_z163181189_ereal)
% 0.92/1.14 FOF formula (forall (X2:extended_ereal) (Y3:extended_ereal), (((eq extended_ereal) ((divide595620860_ereal (uminus1208298309_ereal X2)) Y3)) (uminus1208298309_ereal ((divide595620860_ereal X2) Y3)))) of role axiom named fact_333_ereal__uminus__divide
% 0.92/1.14 A new axiom: (forall (X2:extended_ereal) (Y3:extended_ereal), (((eq extended_ereal) ((divide595620860_ereal (uminus1208298309_ereal X2)) Y3)) (uminus1208298309_ereal ((divide595620860_ereal X2) Y3))))
% 0.92/1.14 FOF formula (forall (A:extended_ereal), (((eq extended_ereal) ((divide595620860_ereal zero_z163181189_ereal) A)) zero_z163181189_ereal)) of role axiom named fact_334_ereal__divide__zero__left
% 0.92/1.14 A new axiom: (forall (A:extended_ereal), (((eq extended_ereal) ((divide595620860_ereal zero_z163181189_ereal) A)) zero_z163181189_ereal))
% 0.92/1.14 FOF formula (forall (X2:extended_ereal), (((ord_le824540014_ereal zero_z163181189_ereal) X2)->(((eq extended_ereal) (abs_ab1260901297_ereal X2)) X2))) of role axiom named fact_335_abs__ereal__ge0
% 0.92/1.14 A new axiom: (forall (X2:extended_ereal), (((ord_le824540014_ereal zero_z163181189_ereal) X2)->(((eq extended_ereal) (abs_ab1260901297_ereal X2)) X2)))
% 0.92/1.14 FOF formula (forall (X2:extended_ereal), (((eq extended_ereal) ((divide595620860_ereal X2) extend1289208545_ereal)) zero_z163181189_ereal)) of role axiom named fact_336_ereal__divide__Infty_I1_J
% 0.92/1.14 A new axiom: (forall (X2:extended_ereal), (((eq extended_ereal) ((divide595620860_ereal X2) extend1289208545_ereal)) zero_z163181189_ereal))
% 0.92/1.14 FOF formula (forall (X2:extended_ereal), (((eq extended_ereal) ((divide595620860_ereal X2) (uminus1208298309_ereal extend1289208545_ereal))) zero_z163181189_ereal)) of role axiom named fact_337_ereal__divide__Infty_I2_J
% 0.92/1.14 A new axiom: (forall (X2:extended_ereal), (((eq extended_ereal) ((divide595620860_ereal X2) (uminus1208298309_ereal extend1289208545_ereal))) zero_z163181189_ereal))
% 0.92/1.14 FOF formula (forall (X2:extended_ereal), (((eq Prop) (not (((eq extended_ereal) (abs_ab1260901297_ereal X2)) extend1289208545_ereal))) ((ex real) (fun (X7:real)=> (((eq extended_ereal) X2) (extended_ereal2 X7)))))) of role axiom named fact_338_not__infty__ereal
% 0.92/1.14 A new axiom: (forall (X2:extended_ereal), (((eq Prop) (not (((eq extended_ereal) (abs_ab1260901297_ereal X2)) extend1289208545_ereal))) ((ex real) (fun (X7:real)=> (((eq extended_ereal) X2) (extended_ereal2 X7))))))
% 0.92/1.14 <<<:
% 0.92/1.14 ( ( ( abs_ab1260901297_ereal @ X2 )
% 0.92/1.14 != extend1289208545_ereal )
% 0.92/1.14 => ~ !>>>!!!<<< [R2: real] :
% 0.92/1.14 ( X2
% 0.92/1.14 != ( extended_ereal2 @ R2 ) ) ) )).
% 0.92/1.14
% 0.92/1.14 % abs_neq_i>>>
% 0.92/1.14 statestack=[0, 1, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 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]
% 0.92/1.14 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, LexToken(THF,'thf',1,115347), LexToken(LPAR,'(',1,115350), name, LexToken(COMMA,',',1,115385), formula_role, LexToken(COMMA,',',1,115391), LexToken(LPAR,'(',1,115392), thf_quantified_formula_PRE, thf_quantifier, LexToken(LBRACKET,'[',1,115400), thf_variable_list, LexToken(RBRACKET,']',1,115419), LexToken(COLON,':',1,115421), LexToken(LPAR,'(',1,115429), thf_unitary_formula, thf_pair_connective, unary_connective]
% 0.92/1.14 Unexpected exception Syntax error at '!':BANG
% 0.92/1.14 Traceback (most recent call last):
% 0.92/1.14 File "CASC.py", line 79, in <module>
% 0.92/1.14 problem=TPTP.TPTPproblem(env=environment,debug=1,file=file)
% 0.92/1.14 File "/export/starexec/sandbox2/solver/bin/TPTP.py", line 38, in __init__
% 0.92/1.14 parser.parse(file.read(),debug=0,lexer=lexer)
% 0.92/1.14 File "/export/starexec/sandbox2/solver/bin/ply/yacc.py", line 265, in parse
% 0.92/1.14 return self.parseopt_notrack(input,lexer,debug,tracking,tokenfunc)
% 0.92/1.14 File "/export/starexec/sandbox2/solver/bin/ply/yacc.py", line 1047, in parseopt_notrack
% 0.92/1.14 tok = self.errorfunc(errtoken)
% 0.92/1.14 File "/export/starexec/sandbox2/solver/bin/TPTPparser.py", line 2099, in p_error
% 0.92/1.14 raise TPTPParsingError("Syntax error at '%s':%s" % (t.value,t.type))
% 0.92/1.14 TPTPparser.TPTPParsingError: Syntax error at '!':BANG
%------------------------------------------------------------------------------