%------------------------------------------------------------------------------ % File : cocATP---0.2.0 % Problem : SWW473^3 : TPTP v6.1.0. Released v5.3.0. % Transfm : none % Format : tptp:raw % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p % Computer : n113.star.cs.uiowa.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz % Memory : 32286.75MB % OS : Linux 2.6.32-431.20.3.el6.x86_64 % CPULimit : 300s % DateTime : Thu Jul 17 13:37:23 EDT 2014 % Result : Timeout 300.02s % Output : None % Verified : % SZS Type : None (Parsing solution fails) % Syntax : Number of formulae : 0 % Comments : %------------------------------------------------------------------------------ %----NO SOLUTION OUTPUT BY SYSTEM %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % % Problem : SWW473^3 : TPTP v6.1.0. Released v5.3.0. % % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p % % Computer : n113.star.cs.uiowa.edu % % Model : x86_64 x86_64 % % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz % % Memory : 32286.75MB % % OS : Linux 2.6.32-431.20.3.el6.x86_64 % % CPULimit : 300 % % DateTime : Thu Jul 17 09:20:46 CDT 2014 % % CPUTime : 300.02 % Python 2.7.5 % Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/'] % FOF formula (<kernel.Constant object at 0x8c3ab8>, <kernel.Type object at 0x8c3950>) of role type named ty_ty_t__a % Using role type % Declaring x_a:Type % FOF formula (<kernel.Constant object at 0xc83290>, <kernel.Type object at 0x8c3d40>) of role type named ty_ty_tc__Com__Ocom % Using role type % Declaring com:Type % FOF formula (<kernel.Constant object at 0x8c3fc8>, <kernel.Type object at 0x8c3c68>) of role type named ty_ty_tc__Com__Opname % Using role type % Declaring pname:Type % FOF formula (<kernel.Constant object at 0x8c3950>, <kernel.Type object at 0x8c3908>) of role type named ty_ty_tc__Int__Oint % Using role type % Declaring int:Type % FOF formula (<kernel.Constant object at 0x8c3d40>, <kernel.Type object at 0x8c37a0>) of role type named ty_ty_tc__Nat__Onat % Using role type % Declaring nat:Type % FOF formula (<kernel.Constant object at 0x8c3c68>, <kernel.Type object at 0x8c3b48>) of role type named ty_ty_tc__Option__Ooption_Itc__Com__Ocom_J % Using role type % Declaring option_com:Type % FOF formula (<kernel.Constant object at 0x8c3b90>, <kernel.DependentProduct object at 0x8c3368>) of role type named sy_c_Com_Obody % Using role type % Declaring body:(pname->option_com) % FOF formula (<kernel.Constant object at 0x8c35f0>, <kernel.DependentProduct object at 0x8c33b0>) of role type named sy_c_Ex % Using role type % Declaring _TPTP_ex:((int->Prop)->Prop) % FOF formula (<kernel.Constant object at 0x8c3b00>, <kernel.DependentProduct object at 0x8c3320>) of role type named sy_c_Finite__Set_Ocard_000_062_It__a_M_Eo_J % Using role type % Declaring finite_card_a_o:(((x_a->Prop)->Prop)->nat) % FOF formula (<kernel.Constant object at 0x8c3c68>, <kernel.DependentProduct object at 0x8c3440>) of role type named sy_c_Finite__Set_Ocard_000_062_Itc__Com__Opname_M_Eo_J % Using role type % Declaring finite_card_pname_o:(((pname->Prop)->Prop)->nat) % FOF formula (<kernel.Constant object at 0x8c3368>, <kernel.DependentProduct object at 0x8c3830>) of role type named sy_c_Finite__Set_Ocard_000_062_Itc__Int__Oint_M_Eo_J % Using role type % Declaring finite_card_int_o:(((int->Prop)->Prop)->nat) % FOF formula (<kernel.Constant object at 0x8c33b0>, <kernel.DependentProduct object at 0x8c37e8>) of role type named sy_c_Finite__Set_Ocard_000_062_Itc__Nat__Onat_M_Eo_J % Using role type % Declaring finite_card_nat_o:(((nat->Prop)->Prop)->nat) % FOF formula (<kernel.Constant object at 0x8c3878>, <kernel.DependentProduct object at 0x8c3560>) of role type named sy_c_Finite__Set_Ocard_000t__a % Using role type % Declaring finite_card_a:((x_a->Prop)->nat) % FOF formula (<kernel.Constant object at 0x8c3830>, <kernel.DependentProduct object at 0x8c33b0>) of role type named sy_c_Finite__Set_Ocard_000tc__Com__Opname % Using role type % Declaring finite_card_pname:((pname->Prop)->nat) % FOF formula (<kernel.Constant object at 0x8c37e8>, <kernel.DependentProduct object at 0x8c3c20>) of role type named sy_c_Finite__Set_Ocard_000tc__Int__Oint % Using role type % Declaring finite_card_int:((int->Prop)->nat) % FOF formula (<kernel.Constant object at 0x8c3b00>, <kernel.DependentProduct object at 0x8c3bd8>) of role type named sy_c_Finite__Set_Ocard_000tc__Nat__Onat % Using role type % Declaring finite_card_nat:((nat->Prop)->nat) % FOF formula (<kernel.Constant object at 0x8c3c68>, <kernel.DependentProduct object at 0x8c3440>) of role type named sy_c_Finite__Set_Ofinite_000_062_I_062_It__a_M_Eo_J_M_Eo_J % Using role type % Declaring finite_finite_a_o_o:((((x_a->Prop)->Prop)->Prop)->Prop) % FOF formula (<kernel.Constant object at 0x8c3560>, <kernel.DependentProduct object at 0x8c3440>) of role type named sy_c_Finite__Set_Ofinite_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J % Using role type % Declaring finite1066544169me_o_o:((((pname->Prop)->Prop)->Prop)->Prop) % FOF formula (<kernel.Constant object at 0x8c3bd8>, <kernel.DependentProduct object at 0xca12d8>) of role type named sy_c_Finite__Set_Ofinite_000_062_I_062_Itc__Int__Oint_M_Eo_J_M_Eo_J % Using role type % Declaring finite229719499nt_o_o:((((int->Prop)->Prop)->Prop)->Prop) % FOF formula (<kernel.Constant object at 0x8c3ef0>, <kernel.DependentProduct object at 0xca1248>) of role type named sy_c_Finite__Set_Ofinite_000_062_I_062_Itc__Nat__Onat_M_Eo_J_M_Eo_J % Using role type % Declaring finite1676163439at_o_o:((((nat->Prop)->Prop)->Prop)->Prop) % FOF formula (<kernel.Constant object at 0x8c3560>, <kernel.DependentProduct object at 0xca12d8>) of role type named sy_c_Finite__Set_Ofinite_000_062_It__a_M_Eo_J % Using role type % Declaring finite_finite_a_o:(((x_a->Prop)->Prop)->Prop) % FOF formula (<kernel.Constant object at 0x8c3bd8>, <kernel.DependentProduct object at 0xca1248>) of role type named sy_c_Finite__Set_Ofinite_000_062_Itc__Com__Opname_M_Eo_J % Using role type % Declaring finite297249702name_o:(((pname->Prop)->Prop)->Prop) % FOF formula (<kernel.Constant object at 0x8c3830>, <kernel.DependentProduct object at 0xca13b0>) of role type named sy_c_Finite__Set_Ofinite_000_062_Itc__Int__Oint_M_Eo_J % Using role type % Declaring finite_finite_int_o:(((int->Prop)->Prop)->Prop) % FOF formula (<kernel.Constant object at 0x8c3bd8>, <kernel.DependentProduct object at 0xca13b0>) of role type named sy_c_Finite__Set_Ofinite_000_062_Itc__Nat__Onat_M_Eo_J % Using role type % Declaring finite_finite_nat_o:(((nat->Prop)->Prop)->Prop) % FOF formula (<kernel.Constant object at 0x8c3bd8>, <kernel.DependentProduct object at 0xca1170>) of role type named sy_c_Finite__Set_Ofinite_000t__a % Using role type % Declaring finite_finite_a:((x_a->Prop)->Prop) % FOF formula (<kernel.Constant object at 0x8c3bd8>, <kernel.DependentProduct object at 0xca1440>) of role type named sy_c_Finite__Set_Ofinite_000tc__Com__Opname % Using role type % Declaring finite_finite_pname:((pname->Prop)->Prop) % FOF formula (<kernel.Constant object at 0xca13b0>, <kernel.DependentProduct object at 0xca1248>) of role type named sy_c_Finite__Set_Ofinite_000tc__Int__Oint % Using role type % Declaring finite_finite_int:((int->Prop)->Prop) % FOF formula (<kernel.Constant object at 0xca1320>, <kernel.DependentProduct object at 0xca1440>) of role type named sy_c_Finite__Set_Ofinite_000tc__Nat__Onat % Using role type % Declaring finite_finite_nat:((nat->Prop)->Prop) % FOF formula (<kernel.Constant object at 0xca13f8>, <kernel.DependentProduct object at 0xca13b0>) of role type named sy_c_Finite__Set_Ofolding__one_000t__a % Using role type % Declaring finite_folding_one_a:((x_a->(x_a->x_a))->(((x_a->Prop)->x_a)->Prop)) % FOF formula (<kernel.Constant object at 0xca1680>, <kernel.DependentProduct object at 0xca1320>) of role type named sy_c_Finite__Set_Ofolding__one_000tc__Com__Opname % Using role type % Declaring finite1282449217_pname:((pname->(pname->pname))->(((pname->Prop)->pname)->Prop)) % FOF formula (<kernel.Constant object at 0xca1050>, <kernel.DependentProduct object at 0xca13f8>) of role type named sy_c_Finite__Set_Ofolding__one_000tc__Int__Oint % Using role type % Declaring finite1626084323ne_int:((int->(int->int))->(((int->Prop)->int)->Prop)) % FOF formula (<kernel.Constant object at 0xca1440>, <kernel.DependentProduct object at 0xca1680>) of role type named sy_c_Finite__Set_Ofolding__one_000tc__Nat__Onat % Using role type % Declaring finite988810631ne_nat:((nat->(nat->nat))->(((nat->Prop)->nat)->Prop)) % FOF formula (<kernel.Constant object at 0xca1cf8>, <kernel.DependentProduct object at 0xca1050>) of role type named sy_c_Finite__Set_Ofolding__one__idem_000t__a % Using role type % Declaring finite1819937229idem_a:((x_a->(x_a->x_a))->(((x_a->Prop)->x_a)->Prop)) % FOF formula (<kernel.Constant object at 0xca1638>, <kernel.DependentProduct object at 0xca1440>) of role type named sy_c_Finite__Set_Ofolding__one__idem_000tc__Com__Opname % Using role type % Declaring finite89670078_pname:((pname->(pname->pname))->(((pname->Prop)->pname)->Prop)) % FOF formula (<kernel.Constant object at 0xca17a0>, <kernel.DependentProduct object at 0xca1cf8>) of role type named sy_c_Finite__Set_Ofolding__one__idem_000tc__Int__Oint % Using role type % Declaring finite1432773856em_int:((int->(int->int))->(((int->Prop)->int)->Prop)) % FOF formula (<kernel.Constant object at 0xca1680>, <kernel.DependentProduct object at 0xca1638>) of role type named sy_c_Finite__Set_Ofolding__one__idem_000tc__Nat__Onat % Using role type % Declaring finite795500164em_nat:((nat->(nat->nat))->(((nat->Prop)->nat)->Prop)) % FOF formula (<kernel.Constant object at 0xca1098>, <kernel.DependentProduct object at 0xca10e0>) of role type named sy_c_Groups_Oabs__class_Oabs_000tc__Int__Oint % Using role type % Declaring abs_abs_int:(int->int) % FOF formula (<kernel.Constant object at 0xca1cb0>, <kernel.DependentProduct object at 0xca16c8>) of role type named sy_c_Groups_Ominus__class_Ominus_000_062_It__a_M_Eo_J % Using role type % Declaring minus_minus_a_o:((x_a->Prop)->((x_a->Prop)->(x_a->Prop))) % FOF formula (<kernel.Constant object at 0xca1638>, <kernel.DependentProduct object at 0xca11b8>) of role type named sy_c_Groups_Ominus__class_Ominus_000_062_Itc__Com__Opname_M_Eo_J % Using role type % Declaring minus_minus_pname_o:((pname->Prop)->((pname->Prop)->(pname->Prop))) % FOF formula (<kernel.Constant object at 0xca15a8>, <kernel.DependentProduct object at 0xca1710>) of role type named sy_c_Groups_Ominus__class_Ominus_000_062_Itc__Int__Oint_M_Eo_J % Using role type % Declaring minus_minus_int_o:((int->Prop)->((int->Prop)->(int->Prop))) % FOF formula (<kernel.Constant object at 0xca17a0>, <kernel.DependentProduct object at 0xca1518>) of role type named sy_c_Groups_Ominus__class_Ominus_000_062_Itc__Nat__Onat_M_Eo_J % Using role type % Declaring minus_minus_nat_o:((nat->Prop)->((nat->Prop)->(nat->Prop))) % FOF formula (<kernel.Constant object at 0xca1098>, <kernel.DependentProduct object at 0xca11b8>) of role type named sy_c_Groups_Ominus__class_Ominus_000tc__Int__Oint % Using role type % Declaring minus_minus_int:(int->(int->int)) % FOF formula (<kernel.Constant object at 0xca1cb0>, <kernel.DependentProduct object at 0xca1710>) of role type named sy_c_Groups_Ominus__class_Ominus_000tc__Nat__Onat % Using role type % Declaring minus_minus_nat:(nat->(nat->nat)) % FOF formula (<kernel.Constant object at 0xca1518>, <kernel.Constant object at 0xca1710>) of role type named sy_c_Groups_Oone__class_Oone_000tc__Int__Oint % Using role type % Declaring one_one_int:int % FOF formula (<kernel.Constant object at 0xca1098>, <kernel.Constant object at 0xca1710>) of role type named sy_c_Groups_Oone__class_Oone_000tc__Nat__Onat % Using role type % Declaring one_one_nat:nat % FOF formula (<kernel.Constant object at 0xca1cb0>, <kernel.DependentProduct object at 0xca16c8>) of role type named sy_c_Groups_Oplus__class_Oplus_000tc__Int__Oint % Using role type % Declaring plus_plus_int:(int->(int->int)) % FOF formula (<kernel.Constant object at 0xca1560>, <kernel.DependentProduct object at 0xca1830>) of role type named sy_c_Groups_Oplus__class_Oplus_000tc__Nat__Onat % Using role type % Declaring plus_plus_nat:(nat->(nat->nat)) % FOF formula (<kernel.Constant object at 0xc80cb0>, <kernel.DependentProduct object at 0xca1290>) of role type named sy_c_Groups_Otimes__class_Otimes_000tc__Int__Oint % Using role type % Declaring times_times_int:(int->(int->int)) % FOF formula (<kernel.Constant object at 0xca1710>, <kernel.DependentProduct object at 0xca17a0>) of role type named sy_c_Groups_Otimes__class_Otimes_000tc__Nat__Onat % Using role type % Declaring times_times_nat:(nat->(nat->nat)) % FOF formula (<kernel.Constant object at 0xca1560>, <kernel.Constant object at 0xca17a0>) of role type named sy_c_Groups_Ozero__class_Ozero_000tc__Int__Oint % Using role type % Declaring zero_zero_int:int % FOF formula (<kernel.Constant object at 0xca18c0>, <kernel.Constant object at 0xca17a0>) of role type named sy_c_Groups_Ozero__class_Ozero_000tc__Nat__Onat % Using role type % Declaring zero_zero_nat:nat % FOF formula (<kernel.Constant object at 0xca1710>, <kernel.DependentProduct object at 0xcfddd0>) of role type named sy_c_HOL_OThe_000t__a % Using role type % Declaring the_a:((x_a->Prop)->x_a) % FOF formula (<kernel.Constant object at 0xca1cb0>, <kernel.DependentProduct object at 0xcfdcb0>) of role type named sy_c_HOL_OThe_000tc__Int__Oint % Using role type % Declaring the_int:((int->Prop)->int) % FOF formula (<kernel.Constant object at 0xca1518>, <kernel.DependentProduct object at 0xcfdb00>) of role type named sy_c_HOL_OThe_000tc__Nat__Onat % Using role type % Declaring the_nat:((nat->Prop)->nat) % FOF formula (<kernel.Constant object at 0xca1cb0>, <kernel.DependentProduct object at 0xcfd518>) of role type named sy_c_If_000tc__Nat__Onat % Using role type % Declaring if_nat:(Prop->(nat->(nat->nat))) % FOF formula (<kernel.Constant object at 0xca1710>, <kernel.DependentProduct object at 0xcfd950>) of role type named sy_c_Int_OBit1 % Using role type % Declaring bit1:(int->int) % FOF formula (<kernel.Constant object at 0xca18c0>, <kernel.Constant object at 0xcfd950>) of role type named sy_c_Int_OPls % Using role type % Declaring pls:int % FOF formula (<kernel.Constant object at 0xca1710>, <kernel.DependentProduct object at 0xcfdb00>) of role type named sy_c_Int_Onumber__class_Onumber__of_000tc__Int__Oint % Using role type % Declaring number_number_of_int:(int->int) % FOF formula (<kernel.Constant object at 0xca1710>, <kernel.DependentProduct object at 0xcfdc68>) of role type named sy_c_Int_Onumber__class_Onumber__of_000tc__Nat__Onat % Using role type % Declaring number_number_of_nat:(int->nat) % FOF formula (<kernel.Constant object at 0xcfd950>, <kernel.DependentProduct object at 0xcfd290>) of role type named sy_c_Int_Osucc % Using role type % Declaring succ:(int->int) % FOF formula (<kernel.Constant object at 0xcfdb00>, <kernel.DependentProduct object at 0xcfd5a8>) of role type named sy_c_Nat_OSuc % Using role type % Declaring suc:(nat->nat) % FOF formula (<kernel.Constant object at 0xcfd4d0>, <kernel.DependentProduct object at 0xcfd098>) of role type named sy_c_Nat_Onat_Onat__case_000_Eo % Using role type % Declaring nat_case_o:(Prop->((nat->Prop)->(nat->Prop))) % FOF formula (<kernel.Constant object at 0xcfd290>, <kernel.DependentProduct object at 0xcfdcf8>) of role type named sy_c_Nat_Onat_Onat__case_000tc__Nat__Onat % Using role type % Declaring nat_case_nat:(nat->((nat->nat)->(nat->nat))) % FOF formula (<kernel.Constant object at 0xcfd5a8>, <kernel.DependentProduct object at 0xca2878>) of role type named sy_c_Nat_Osemiring__1__class_Oof__nat_000tc__Int__Oint % Using role type % Declaring semiri1621563631at_int:(nat->int) % FOF formula (<kernel.Constant object at 0xcfd4d0>, <kernel.DependentProduct object at 0xca2878>) of role type named sy_c_Nat__Numeral_Oneg % Using role type % Declaring nat_neg:(int->Prop) % FOF formula (<kernel.Constant object at 0xcfdcb0>, <kernel.DependentProduct object at 0xcfd290>) of role type named sy_c_Nat__Transfer_Otsub % Using role type % Declaring nat_tsub:(int->(int->int)) % FOF formula (<kernel.Constant object at 0xcfdc68>, <kernel.DependentProduct object at 0xca2c20>) of role type named sy_c_Option_Othe_000tc__Com__Ocom % Using role type % Declaring the_com:(option_com->com) % FOF formula (<kernel.Constant object at 0xcfd4d0>, <kernel.DependentProduct object at 0xca2878>) of role type named sy_c_Orderings_Obot__class_Obot_000_062_It__a_M_Eo_J % Using role type % Declaring bot_bot_a_o:(x_a->Prop) % FOF formula (<kernel.Constant object at 0xcfd290>, <kernel.DependentProduct object at 0xca25a8>) of role type named sy_c_Orderings_Obot__class_Obot_000_062_Itc__Com__Opname_M_Eo_J % Using role type % Declaring bot_bot_pname_o:(pname->Prop) % FOF formula (<kernel.Constant object at 0xcfdcb0>, <kernel.DependentProduct object at 0xca2f80>) of role type named sy_c_Orderings_Obot__class_Obot_000_062_Itc__Int__Oint_M_Eo_J % Using role type % Declaring bot_bot_int_o:(int->Prop) % FOF formula (<kernel.Constant object at 0xcfd290>, <kernel.DependentProduct object at 0xca2290>) of role type named sy_c_Orderings_Obot__class_Obot_000_062_Itc__Nat__Onat_M_Eo_J % Using role type % Declaring bot_bot_nat_o:(nat->Prop) % FOF formula (<kernel.Constant object at 0xcfdcb0>, <kernel.Sort object at 0xb56cb0>) of role type named sy_c_Orderings_Obot__class_Obot_000_Eo % Using role type % Declaring bot_bot_o:Prop % FOF formula (<kernel.Constant object at 0xcfdcb0>, <kernel.Constant object at 0xca25a8>) of role type named sy_c_Orderings_Obot__class_Obot_000tc__Nat__Onat % Using role type % Declaring bot_bot_nat:nat % FOF formula (<kernel.Constant object at 0xca2f80>, <kernel.DependentProduct object at 0xca2368>) of role type named sy_c_Orderings_Oord__class_Oless_000_062_Itc__Int__Oint_M_Eo_J % Using role type % Declaring ord_less_int_o:((int->Prop)->((int->Prop)->Prop)) % FOF formula (<kernel.Constant object at 0xca27e8>, <kernel.DependentProduct object at 0xca25a8>) of role type named sy_c_Orderings_Oord__class_Oless_000_062_Itc__Nat__Onat_M_Eo_J % Using role type % Declaring ord_less_nat_o:((nat->Prop)->((nat->Prop)->Prop)) % FOF formula (<kernel.Constant object at 0xca2518>, <kernel.DependentProduct object at 0xca2368>) of role type named sy_c_Orderings_Oord__class_Oless_000tc__Int__Oint % Using role type % Declaring ord_less_int:(int->(int->Prop)) % FOF formula (<kernel.Constant object at 0xca26c8>, <kernel.DependentProduct object at 0x8a8950>) of role type named sy_c_Orderings_Oord__class_Oless_000tc__Nat__Onat % Using role type % Declaring ord_less_nat:(nat->(nat->Prop)) % FOF formula (<kernel.Constant object at 0xca25a8>, <kernel.DependentProduct object at 0x8a8908>) of role type named sy_c_Orderings_Oord__class_Oless__eq_000_062_I_062_It__a_M_Eo_J_M_Eo_J % Using role type % Declaring ord_less_eq_a_o_o:(((x_a->Prop)->Prop)->(((x_a->Prop)->Prop)->Prop)) % FOF formula (<kernel.Constant object at 0xca27e8>, <kernel.DependentProduct object at 0x8a88c0>) of role type named sy_c_Orderings_Oord__class_Oless__eq_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_ % Using role type % Declaring ord_le1205211808me_o_o:(((pname->Prop)->Prop)->(((pname->Prop)->Prop)->Prop)) % FOF formula (<kernel.Constant object at 0xca26c8>, <kernel.DependentProduct object at 0x8a87e8>) of role type named sy_c_Orderings_Oord__class_Oless__eq_000_062_I_062_Itc__Int__Oint_M_Eo_J_M_Eo_J % Using role type % Declaring ord_less_eq_int_o_o:(((int->Prop)->Prop)->(((int->Prop)->Prop)->Prop)) % FOF formula (<kernel.Constant object at 0xca25a8>, <kernel.DependentProduct object at 0x8a8830>) of role type named sy_c_Orderings_Oord__class_Oless__eq_000_062_I_062_Itc__Nat__Onat_M_Eo_J_M_Eo_J % Using role type % Declaring ord_less_eq_nat_o_o:(((nat->Prop)->Prop)->(((nat->Prop)->Prop)->Prop)) % FOF formula (<kernel.Constant object at 0xca26c8>, <kernel.DependentProduct object at 0x8a87a0>) of role type named sy_c_Orderings_Oord__class_Oless__eq_000_062_It__a_M_Eo_J % Using role type % Declaring ord_less_eq_a_o:((x_a->Prop)->((x_a->Prop)->Prop)) % FOF formula (<kernel.Constant object at 0xca25a8>, <kernel.DependentProduct object at 0x8a86c8>) of role type named sy_c_Orderings_Oord__class_Oless__eq_000_062_Itc__Com__Opname_M_Eo_J % Using role type % Declaring ord_less_eq_pname_o:((pname->Prop)->((pname->Prop)->Prop)) % FOF formula (<kernel.Constant object at 0xca27e8>, <kernel.DependentProduct object at 0x8a8710>) of role type named sy_c_Orderings_Oord__class_Oless__eq_000_062_Itc__Int__Oint_M_Eo_J % Using role type % Declaring ord_less_eq_int_o:((int->Prop)->((int->Prop)->Prop)) % FOF formula (<kernel.Constant object at 0xca27e8>, <kernel.DependentProduct object at 0x8a8638>) of role type named sy_c_Orderings_Oord__class_Oless__eq_000_062_Itc__Nat__Onat_M_Eo_J % Using role type % Declaring ord_less_eq_nat_o:((nat->Prop)->((nat->Prop)->Prop)) % FOF formula (<kernel.Constant object at 0x8a87e8>, <kernel.DependentProduct object at 0x8a8878>) of role type named sy_c_Orderings_Oord__class_Oless__eq_000_Eo % Using role type % Declaring ord_less_eq_o:(Prop->(Prop->Prop)) % FOF formula (<kernel.Constant object at 0x8a86c8>, <kernel.DependentProduct object at 0x8a8758>) of role type named sy_c_Orderings_Oord__class_Oless__eq_000tc__Int__Oint % Using role type % Declaring ord_less_eq_int:(int->(int->Prop)) % FOF formula (<kernel.Constant object at 0x8a8638>, <kernel.DependentProduct object at 0x8a8908>) of role type named sy_c_Orderings_Oord__class_Oless__eq_000tc__Nat__Onat % Using role type % Declaring ord_less_eq_nat:(nat->(nat->Prop)) % FOF formula (<kernel.Constant object at 0x8a8878>, <kernel.DependentProduct object at 0x8a8680>) of role type named sy_c_Set_OCollect_000_062_I_062_It__a_M_Eo_J_M_Eo_J % Using role type % Declaring collect_a_o_o:((((x_a->Prop)->Prop)->Prop)->(((x_a->Prop)->Prop)->Prop)) % FOF formula (<kernel.Constant object at 0x8a8758>, <kernel.DependentProduct object at 0x8a8518>) of role type named sy_c_Set_OCollect_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J % Using role type % Declaring collect_pname_o_o:((((pname->Prop)->Prop)->Prop)->(((pname->Prop)->Prop)->Prop)) % FOF formula (<kernel.Constant object at 0x8a8908>, <kernel.DependentProduct object at 0x8a8560>) of role type named sy_c_Set_OCollect_000_062_I_062_Itc__Int__Oint_M_Eo_J_M_Eo_J % Using role type % Declaring collect_int_o_o:((((int->Prop)->Prop)->Prop)->(((int->Prop)->Prop)->Prop)) % FOF formula (<kernel.Constant object at 0x8a8710>, <kernel.DependentProduct object at 0x8a8488>) of role type named sy_c_Set_OCollect_000_062_I_062_Itc__Nat__Onat_M_Eo_J_M_Eo_J % Using role type % Declaring collect_nat_o_o:((((nat->Prop)->Prop)->Prop)->(((nat->Prop)->Prop)->Prop)) % FOF formula (<kernel.Constant object at 0x8a8518>, <kernel.DependentProduct object at 0x8a83f8>) of role type named sy_c_Set_OCollect_000_062_It__a_M_Eo_J % Using role type % Declaring collect_a_o:(((x_a->Prop)->Prop)->((x_a->Prop)->Prop)) % FOF formula (<kernel.Constant object at 0x8a8560>, <kernel.DependentProduct object at 0x8a8440>) of role type named sy_c_Set_OCollect_000_062_Itc__Com__Opname_M_Eo_J % Using role type % Declaring collect_pname_o:(((pname->Prop)->Prop)->((pname->Prop)->Prop)) % FOF formula (<kernel.Constant object at 0x8a8758>, <kernel.DependentProduct object at 0x8a89e0>) of role type named sy_c_Set_OCollect_000_062_Itc__Int__Oint_M_Eo_J % Using role type % Declaring collect_int_o:(((int->Prop)->Prop)->((int->Prop)->Prop)) % FOF formula (<kernel.Constant object at 0x8a8908>, <kernel.DependentProduct object at 0x8a8a28>) of role type named sy_c_Set_OCollect_000_062_Itc__Nat__Onat_M_Eo_J % Using role type % Declaring collect_nat_o:(((nat->Prop)->Prop)->((nat->Prop)->Prop)) % FOF formula (<kernel.Constant object at 0x8a8710>, <kernel.DependentProduct object at 0x8a8680>) of role type named sy_c_Set_OCollect_000t__a % Using role type % Declaring collect_a:((x_a->Prop)->(x_a->Prop)) % FOF formula (<kernel.Constant object at 0x8a8518>, <kernel.DependentProduct object at 0x8a8a28>) of role type named sy_c_Set_OCollect_000tc__Com__Opname % Using role type % Declaring collect_pname:((pname->Prop)->(pname->Prop)) % FOF formula (<kernel.Constant object at 0x8a87a0>, <kernel.DependentProduct object at 0x8a8518>) of role type named sy_c_Set_OCollect_000tc__Int__Oint % Using role type % Declaring collect_int:((int->Prop)->(int->Prop)) % FOF formula (<kernel.Constant object at 0x8a84d0>, <kernel.DependentProduct object at 0x8a8710>) of role type named sy_c_Set_OCollect_000tc__Nat__Onat % Using role type % Declaring collect_nat:((nat->Prop)->(nat->Prop)) % FOF formula (<kernel.Constant object at 0x8a8878>, <kernel.DependentProduct object at 0x8a8680>) of role type named sy_c_Set_Oimage_000_062_It__a_M_Eo_J_000t__a % Using role type % Declaring image_a_o_a:(((x_a->Prop)->x_a)->(((x_a->Prop)->Prop)->(x_a->Prop))) % FOF formula (<kernel.Constant object at 0x8a87a0>, <kernel.DependentProduct object at 0x8a8710>) of role type named sy_c_Set_Oimage_000_062_It__a_M_Eo_J_000tc__Com__Opname % Using role type % Declaring image_a_o_pname:(((x_a->Prop)->pname)->(((x_a->Prop)->Prop)->(pname->Prop))) % FOF formula (<kernel.Constant object at 0x8a8b48>, <kernel.DependentProduct object at 0x8a8518>) of role type named sy_c_Set_Oimage_000_062_It__a_M_Eo_J_000tc__Int__Oint % Using role type % Declaring image_a_o_int:(((x_a->Prop)->int)->(((x_a->Prop)->Prop)->(int->Prop))) % FOF formula (<kernel.Constant object at 0x8a8a28>, <kernel.DependentProduct object at 0x8a8878>) of role type named sy_c_Set_Oimage_000_062_It__a_M_Eo_J_000tc__Nat__Onat % Using role type % Declaring image_a_o_nat:(((x_a->Prop)->nat)->(((x_a->Prop)->Prop)->(nat->Prop))) % FOF formula (<kernel.Constant object at 0x8a8c20>, <kernel.DependentProduct object at 0x8a87a0>) of role type named sy_c_Set_Oimage_000_062_Itc__Com__Opname_M_Eo_J_000t__a % Using role type % Declaring image_pname_o_a:(((pname->Prop)->x_a)->(((pname->Prop)->Prop)->(x_a->Prop))) % FOF formula (<kernel.Constant object at 0x8a8c68>, <kernel.DependentProduct object at 0x8a8b48>) of role type named sy_c_Set_Oimage_000_062_Itc__Com__Opname_M_Eo_J_000tc__Com__Opname % Using role type % Declaring image_pname_o_pname:(((pname->Prop)->pname)->(((pname->Prop)->Prop)->(pname->Prop))) % FOF formula (<kernel.Constant object at 0x8a8710>, <kernel.DependentProduct object at 0x8a8a28>) of role type named sy_c_Set_Oimage_000_062_Itc__Com__Opname_M_Eo_J_000tc__Int__Oint % Using role type % Declaring image_pname_o_int:(((pname->Prop)->int)->(((pname->Prop)->Prop)->(int->Prop))) % FOF formula (<kernel.Constant object at 0x8a8518>, <kernel.DependentProduct object at 0x8a8c20>) of role type named sy_c_Set_Oimage_000_062_Itc__Com__Opname_M_Eo_J_000tc__Nat__Onat % Using role type % Declaring image_pname_o_nat:(((pname->Prop)->nat)->(((pname->Prop)->Prop)->(nat->Prop))) % FOF formula (<kernel.Constant object at 0x8a8878>, <kernel.DependentProduct object at 0x8a8c68>) of role type named sy_c_Set_Oimage_000_062_Itc__Int__Oint_M_Eo_J_000t__a % Using role type % Declaring image_int_o_a:(((int->Prop)->x_a)->(((int->Prop)->Prop)->(x_a->Prop))) % FOF formula (<kernel.Constant object at 0x8a87a0>, <kernel.DependentProduct object at 0x8a8710>) of role type named sy_c_Set_Oimage_000_062_Itc__Int__Oint_M_Eo_J_000tc__Com__Opname % Using role type % Declaring image_int_o_pname:(((int->Prop)->pname)->(((int->Prop)->Prop)->(pname->Prop))) % FOF formula (<kernel.Constant object at 0x8a8dd0>, <kernel.DependentProduct object at 0x8a8518>) of role type named sy_c_Set_Oimage_000_062_Itc__Int__Oint_M_Eo_J_000tc__Int__Oint % Using role type % Declaring image_int_o_int:(((int->Prop)->int)->(((int->Prop)->Prop)->(int->Prop))) % FOF formula (<kernel.Constant object at 0x8a8a28>, <kernel.DependentProduct object at 0x8a8878>) of role type named sy_c_Set_Oimage_000_062_Itc__Int__Oint_M_Eo_J_000tc__Nat__Onat % Using role type % Declaring image_int_o_nat:(((int->Prop)->nat)->(((int->Prop)->Prop)->(nat->Prop))) % FOF formula (<kernel.Constant object at 0x8a8e60>, <kernel.DependentProduct object at 0x8a87a0>) of role type named sy_c_Set_Oimage_000_062_Itc__Nat__Onat_M_Eo_J_000t__a % Using role type % Declaring image_nat_o_a:(((nat->Prop)->x_a)->(((nat->Prop)->Prop)->(x_a->Prop))) % FOF formula (<kernel.Constant object at 0x8a8ea8>, <kernel.DependentProduct object at 0x8a8dd0>) of role type named sy_c_Set_Oimage_000_062_Itc__Nat__Onat_M_Eo_J_000tc__Com__Opname % Using role type % Declaring image_nat_o_pname:(((nat->Prop)->pname)->(((nat->Prop)->Prop)->(pname->Prop))) % FOF formula (<kernel.Constant object at 0x8a8ef0>, <kernel.DependentProduct object at 0x8a8a28>) of role type named sy_c_Set_Oimage_000_062_Itc__Nat__Onat_M_Eo_J_000tc__Int__Oint % Using role type % Declaring image_nat_o_int:(((nat->Prop)->int)->(((nat->Prop)->Prop)->(int->Prop))) % FOF formula (<kernel.Constant object at 0x8a8518>, <kernel.DependentProduct object at 0x8a8e60>) of role type named sy_c_Set_Oimage_000_062_Itc__Nat__Onat_M_Eo_J_000tc__Nat__Onat % Using role type % Declaring image_nat_o_nat:(((nat->Prop)->nat)->(((nat->Prop)->Prop)->(nat->Prop))) % FOF formula (<kernel.Constant object at 0x8a8f80>, <kernel.DependentProduct object at 0x8a8e60>) of role type named sy_c_Set_Oimage_000t__a_000_062_It__a_M_Eo_J % Using role type % Declaring image_a_a_o:((x_a->(x_a->Prop))->((x_a->Prop)->((x_a->Prop)->Prop))) % FOF formula (<kernel.Constant object at 0x8a8fc8>, <kernel.DependentProduct object at 0x8a8e60>) of role type named sy_c_Set_Oimage_000t__a_000_062_Itc__Com__Opname_M_Eo_J % Using role type % Declaring image_a_pname_o:((x_a->(pname->Prop))->((x_a->Prop)->((pname->Prop)->Prop))) % FOF formula (<kernel.Constant object at 0x8a8ef0>, <kernel.DependentProduct object at 0x8a8e60>) of role type named sy_c_Set_Oimage_000t__a_000_062_Itc__Int__Oint_M_Eo_J % Using role type % Declaring image_a_int_o:((x_a->(int->Prop))->((x_a->Prop)->((int->Prop)->Prop))) % FOF formula (<kernel.Constant object at 0x8a8dd0>, <kernel.DependentProduct object at 0x8a8fc8>) of role type named sy_c_Set_Oimage_000t__a_000_062_Itc__Nat__Onat_M_Eo_J % Using role type % Declaring image_a_nat_o:((x_a->(nat->Prop))->((x_a->Prop)->((nat->Prop)->Prop))) % FOF formula (<kernel.Constant object at 0x8a8908>, <kernel.DependentProduct object at 0xc95050>) of role type named sy_c_Set_Oimage_000t__a_000t__a % Using role type % Declaring image_a_a:((x_a->x_a)->((x_a->Prop)->(x_a->Prop))) % FOF formula (<kernel.Constant object at 0x8a8ef0>, <kernel.DependentProduct object at 0xc95170>) of role type named sy_c_Set_Oimage_000t__a_000tc__Com__Opname % Using role type % Declaring image_a_pname:((x_a->pname)->((x_a->Prop)->(pname->Prop))) % FOF formula (<kernel.Constant object at 0x8a8fc8>, <kernel.DependentProduct object at 0xc95200>) of role type named sy_c_Set_Oimage_000t__a_000tc__Int__Oint % Using role type % Declaring image_a_int:((x_a->int)->((x_a->Prop)->(int->Prop))) % FOF formula (<kernel.Constant object at 0x8a8ef0>, <kernel.DependentProduct object at 0xc95290>) of role type named sy_c_Set_Oimage_000t__a_000tc__Nat__Onat % Using role type % Declaring image_a_nat:((x_a->nat)->((x_a->Prop)->(nat->Prop))) % FOF formula (<kernel.Constant object at 0x8a8908>, <kernel.DependentProduct object at 0xc95098>) of role type named sy_c_Set_Oimage_000tc__Com__Opname_000_062_It__a_M_Eo_J % Using role type % Declaring image_pname_a_o:((pname->(x_a->Prop))->((pname->Prop)->((x_a->Prop)->Prop))) % FOF formula (<kernel.Constant object at 0x8a8ef0>, <kernel.DependentProduct object at 0xc95290>) of role type named sy_c_Set_Oimage_000tc__Com__Opname_000_062_Itc__Com__Opname_M_Eo_J % Using role type % Declaring image_pname_pname_o:((pname->(pname->Prop))->((pname->Prop)->((pname->Prop)->Prop))) % FOF formula (<kernel.Constant object at 0x8a8ef0>, <kernel.DependentProduct object at 0xc95098>) of role type named sy_c_Set_Oimage_000tc__Com__Opname_000_062_Itc__Int__Oint_M_Eo_J % Using role type % Declaring image_pname_int_o:((pname->(int->Prop))->((pname->Prop)->((int->Prop)->Prop))) % FOF formula (<kernel.Constant object at 0xc95128>, <kernel.DependentProduct object at 0xc95290>) of role type named sy_c_Set_Oimage_000tc__Com__Opname_000_062_Itc__Nat__Onat_M_Eo_J % Using role type % Declaring image_pname_nat_o:((pname->(nat->Prop))->((pname->Prop)->((nat->Prop)->Prop))) % FOF formula (<kernel.Constant object at 0xc951b8>, <kernel.DependentProduct object at 0xc95368>) of role type named sy_c_Set_Oimage_000tc__Com__Opname_000t__a % Using role type % Declaring image_pname_a:((pname->x_a)->((pname->Prop)->(x_a->Prop))) % FOF formula (<kernel.Constant object at 0xc950e0>, <kernel.DependentProduct object at 0xc95440>) of role type named sy_c_Set_Oimage_000tc__Com__Opname_000tc__Com__Opname % Using role type % Declaring image_pname_pname:((pname->pname)->((pname->Prop)->(pname->Prop))) % FOF formula (<kernel.Constant object at 0xc953f8>, <kernel.DependentProduct object at 0xc95488>) of role type named sy_c_Set_Oimage_000tc__Com__Opname_000tc__Int__Oint % Using role type % Declaring image_pname_int:((pname->int)->((pname->Prop)->(int->Prop))) % FOF formula (<kernel.Constant object at 0xc95200>, <kernel.DependentProduct object at 0xc954d0>) of role type named sy_c_Set_Oimage_000tc__Com__Opname_000tc__Nat__Onat % Using role type % Declaring image_pname_nat:((pname->nat)->((pname->Prop)->(nat->Prop))) % FOF formula (<kernel.Constant object at 0xc95170>, <kernel.DependentProduct object at 0xc95488>) of role type named sy_c_Set_Oimage_000tc__Int__Oint_000_062_It__a_M_Eo_J % Using role type % Declaring image_int_a_o:((int->(x_a->Prop))->((int->Prop)->((x_a->Prop)->Prop))) % FOF formula (<kernel.Constant object at 0xc95128>, <kernel.DependentProduct object at 0xc954d0>) of role type named sy_c_Set_Oimage_000tc__Int__Oint_000_062_Itc__Com__Opname_M_Eo_J % Using role type % Declaring image_int_pname_o:((int->(pname->Prop))->((int->Prop)->((pname->Prop)->Prop))) % FOF formula (<kernel.Constant object at 0xc953f8>, <kernel.DependentProduct object at 0xc95488>) of role type named sy_c_Set_Oimage_000tc__Int__Oint_000_062_Itc__Int__Oint_M_Eo_J % Using role type % Declaring image_int_int_o:((int->(int->Prop))->((int->Prop)->((int->Prop)->Prop))) % FOF formula (<kernel.Constant object at 0xc95518>, <kernel.DependentProduct object at 0xc954d0>) of role type named sy_c_Set_Oimage_000tc__Int__Oint_000_062_Itc__Nat__Onat_M_Eo_J % Using role type % Declaring image_int_nat_o:((int->(nat->Prop))->((int->Prop)->((nat->Prop)->Prop))) % FOF formula (<kernel.Constant object at 0xc95170>, <kernel.DependentProduct object at 0xc955a8>) of role type named sy_c_Set_Oimage_000tc__Int__Oint_000t__a % Using role type % Declaring image_int_a:((int->x_a)->((int->Prop)->(x_a->Prop))) % FOF formula (<kernel.Constant object at 0xc95128>, <kernel.DependentProduct object at 0xc95680>) of role type named sy_c_Set_Oimage_000tc__Int__Oint_000tc__Com__Opname % Using role type % Declaring image_int_pname:((int->pname)->((int->Prop)->(pname->Prop))) % FOF formula (<kernel.Constant object at 0xc95488>, <kernel.DependentProduct object at 0xc955a8>) of role type named sy_c_Set_Oimage_000tc__Nat__Onat_000_062_It__a_M_Eo_J % Using role type % Declaring image_nat_a_o:((nat->(x_a->Prop))->((nat->Prop)->((x_a->Prop)->Prop))) % FOF formula (<kernel.Constant object at 0xc950e0>, <kernel.DependentProduct object at 0xc95680>) of role type named sy_c_Set_Oimage_000tc__Nat__Onat_000_062_Itc__Com__Opname_M_Eo_J % Using role type % Declaring image_nat_pname_o:((nat->(pname->Prop))->((nat->Prop)->((pname->Prop)->Prop))) % FOF formula (<kernel.Constant object at 0xc95170>, <kernel.DependentProduct object at 0xc955a8>) of role type named sy_c_Set_Oimage_000tc__Nat__Onat_000_062_Itc__Int__Oint_M_Eo_J % Using role type % Declaring image_nat_int_o:((nat->(int->Prop))->((nat->Prop)->((int->Prop)->Prop))) % FOF formula (<kernel.Constant object at 0xc956c8>, <kernel.DependentProduct object at 0xc95680>) of role type named sy_c_Set_Oimage_000tc__Nat__Onat_000_062_Itc__Nat__Onat_M_Eo_J % Using role type % Declaring image_nat_nat_o:((nat->(nat->Prop))->((nat->Prop)->((nat->Prop)->Prop))) % FOF formula (<kernel.Constant object at 0xc95488>, <kernel.DependentProduct object at 0xc95758>) of role type named sy_c_Set_Oimage_000tc__Nat__Onat_000t__a % Using role type % Declaring image_nat_a:((nat->x_a)->((nat->Prop)->(x_a->Prop))) % FOF formula (<kernel.Constant object at 0xc950e0>, <kernel.DependentProduct object at 0xc95830>) of role type named sy_c_Set_Oimage_000tc__Nat__Onat_000tc__Com__Opname % Using role type % Declaring image_nat_pname:((nat->pname)->((nat->Prop)->(pname->Prop))) % FOF formula (<kernel.Constant object at 0xc955a8>, <kernel.DependentProduct object at 0xc95878>) of role type named sy_c_Set_Oimage_000tc__Nat__Onat_000tc__Int__Oint % Using role type % Declaring image_nat_int:((nat->int)->((nat->Prop)->(int->Prop))) % FOF formula (<kernel.Constant object at 0xc95518>, <kernel.DependentProduct object at 0xc95830>) of role type named sy_c_Set_Oinsert_000_062_It__a_M_Eo_J % Using role type % Declaring insert_a_o:((x_a->Prop)->(((x_a->Prop)->Prop)->((x_a->Prop)->Prop))) % FOF formula (<kernel.Constant object at 0xc95758>, <kernel.DependentProduct object at 0xc95878>) of role type named sy_c_Set_Oinsert_000_062_Itc__Com__Opname_M_Eo_J % Using role type % Declaring insert_pname_o:((pname->Prop)->(((pname->Prop)->Prop)->((pname->Prop)->Prop))) % FOF formula (<kernel.Constant object at 0xc956c8>, <kernel.DependentProduct object at 0xc95830>) of role type named sy_c_Set_Oinsert_000_062_Itc__Int__Oint_M_Eo_J % Using role type % Declaring insert_int_o:((int->Prop)->(((int->Prop)->Prop)->((int->Prop)->Prop))) % FOF formula (<kernel.Constant object at 0xc95908>, <kernel.DependentProduct object at 0xc95878>) of role type named sy_c_Set_Oinsert_000_062_Itc__Nat__Onat_M_Eo_J % Using role type % Declaring insert_nat_o:((nat->Prop)->(((nat->Prop)->Prop)->((nat->Prop)->Prop))) % FOF formula (<kernel.Constant object at 0xc95950>, <kernel.DependentProduct object at 0xc95518>) of role type named sy_c_Set_Oinsert_000t__a % Using role type % Declaring insert_a:(x_a->((x_a->Prop)->(x_a->Prop))) % FOF formula (<kernel.Constant object at 0xc95050>, <kernel.DependentProduct object at 0xc95758>) of role type named sy_c_Set_Oinsert_000tc__Com__Opname % Using role type % Declaring insert_pname:(pname->((pname->Prop)->(pname->Prop))) % FOF formula (<kernel.Constant object at 0xc95998>, <kernel.DependentProduct object at 0xc95ab8>) of role type named sy_c_Set_Oinsert_000tc__Int__Oint % Using role type % Declaring insert_int:(int->((int->Prop)->(int->Prop))) % FOF formula (<kernel.Constant object at 0xc95710>, <kernel.DependentProduct object at 0xc95b00>) of role type named sy_c_Set_Oinsert_000tc__Nat__Onat % Using role type % Declaring insert_nat:(nat->((nat->Prop)->(nat->Prop))) % FOF formula (<kernel.Constant object at 0xc95758>, <kernel.DependentProduct object at 0xc95050>) of role type named sy_c_Set_Othe__elem_000t__a % Using role type % Declaring the_elem_a:((x_a->Prop)->x_a) % FOF formula (<kernel.Constant object at 0xc95998>, <kernel.DependentProduct object at 0xc95a28>) of role type named sy_c_Set_Othe__elem_000tc__Int__Oint % Using role type % Declaring the_elem_int:((int->Prop)->int) % FOF formula (<kernel.Constant object at 0xc956c8>, <kernel.DependentProduct object at 0xc95b48>) of role type named sy_c_Set_Othe__elem_000tc__Nat__Onat % Using role type % Declaring the_elem_nat:((nat->Prop)->nat) % FOF formula (<kernel.Constant object at 0xc95830>, <kernel.DependentProduct object at 0xc95758>) of role type named sy_c_fequal_000t__a % Using role type % Declaring fequal_a:(x_a->(x_a->Prop)) % FOF formula (<kernel.Constant object at 0xc955a8>, <kernel.DependentProduct object at 0xc95830>) of role type named sy_c_fequal_000tc__Int__Oint % Using role type % Declaring fequal_int:(int->(int->Prop)) % FOF formula (<kernel.Constant object at 0xc95b00>, <kernel.DependentProduct object at 0xc95b90>) of role type named sy_c_fequal_000tc__Nat__Onat % Using role type % Declaring fequal_nat:(nat->(nat->Prop)) % FOF formula (<kernel.Constant object at 0xc95998>, <kernel.DependentProduct object at 0xc95bd8>) of role type named sy_c_member_000_062_It__a_M_Eo_J % Using role type % Declaring member_a_o:((x_a->Prop)->(((x_a->Prop)->Prop)->Prop)) % FOF formula (<kernel.Constant object at 0xc95830>, <kernel.DependentProduct object at 0xc95b48>) of role type named sy_c_member_000_062_Itc__Com__Opname_M_Eo_J % Using role type % Declaring member_pname_o:((pname->Prop)->(((pname->Prop)->Prop)->Prop)) % FOF formula (<kernel.Constant object at 0xc95b00>, <kernel.DependentProduct object at 0xc95cb0>) of role type named sy_c_member_000_062_Itc__Int__Oint_M_Eo_J % Using role type % Declaring member_int_o:((int->Prop)->(((int->Prop)->Prop)->Prop)) % FOF formula (<kernel.Constant object at 0xc95c68>, <kernel.DependentProduct object at 0xc95cf8>) of role type named sy_c_member_000_062_Itc__Nat__Onat_M_Eo_J % Using role type % Declaring member_nat_o:((nat->Prop)->(((nat->Prop)->Prop)->Prop)) % FOF formula (<kernel.Constant object at 0xc95ab8>, <kernel.DependentProduct object at 0xc95d88>) of role type named sy_c_member_000t__a % Using role type % Declaring member_a:(x_a->((x_a->Prop)->Prop)) % FOF formula (<kernel.Constant object at 0xc956c8>, <kernel.DependentProduct object at 0xc95e18>) of role type named sy_c_member_000tc__Com__Opname % Using role type % Declaring member_pname:(pname->((pname->Prop)->Prop)) % FOF formula (<kernel.Constant object at 0xc95998>, <kernel.DependentProduct object at 0xc95e60>) of role type named sy_c_member_000tc__Int__Oint % Using role type % Declaring member_int:(int->((int->Prop)->Prop)) % FOF formula (<kernel.Constant object at 0xc95b00>, <kernel.DependentProduct object at 0xc95ea8>) of role type named sy_c_member_000tc__Nat__Onat % Using role type % Declaring member_nat:(nat->((nat->Prop)->Prop)) % FOF formula (<kernel.Constant object at 0xc95e18>, <kernel.DependentProduct object at 0xc956c8>) of role type named sy_v_G % Using role type % Declaring g:(x_a->Prop) % FOF formula (<kernel.Constant object at 0xc95998>, <kernel.DependentProduct object at 0xc95ef0>) of role type named sy_v_P % Using role type % Declaring p:((x_a->Prop)->((x_a->Prop)->Prop)) % FOF formula (<kernel.Constant object at 0xc95b00>, <kernel.DependentProduct object at 0xc95cf8>) of role type named sy_v_U % Using role type % Declaring u:(pname->Prop) % FOF formula (<kernel.Constant object at 0xc95d40>, <kernel.DependentProduct object at 0xc95f38>) of role type named sy_v_mgt % Using role type % Declaring mgt:(com->x_a) % FOF formula (<kernel.Constant object at 0xc95ef0>, <kernel.DependentProduct object at 0xc95f80>) of role type named sy_v_mgt__call % Using role type % Declaring mgt_call:(pname->x_a) % FOF formula (<kernel.Constant object at 0xc95cf8>, <kernel.Constant object at 0xc95f80>) of role type named sy_v_na % Using role type % Declaring na:nat % FOF formula (<kernel.Constant object at 0xc95d40>, <kernel.Constant object at 0xc95f80>) of role type named sy_v_pn % Using role type % Declaring pn:pname % FOF formula (<kernel.Constant object at 0xc95ef0>, <kernel.DependentProduct object at 0xc9d050>) of role type named sy_v_wt % Using role type % Declaring wt:(com->Prop) % FOF formula (forall (Ts:(x_a->Prop)) (G:(x_a->Prop)), (((ord_less_eq_a_o Ts) G)->((p G) Ts))) of role axiom named fact_0_assms_I1_J % A new axiom: (forall (Ts:(x_a->Prop)) (G:(x_a->Prop)), (((ord_less_eq_a_o Ts) G)->((p G) Ts))) % FOF formula (forall (A_161:((int->Prop)->Prop)), ((finite_finite_int_o A_161)->(finite229719499nt_o_o (collect_int_o_o (fun (B_26:((int->Prop)->Prop))=> ((ord_less_eq_int_o_o B_26) A_161)))))) of role axiom named fact_1_finite__Collect__subsets % A new axiom: (forall (A_161:((int->Prop)->Prop)), ((finite_finite_int_o A_161)->(finite229719499nt_o_o (collect_int_o_o (fun (B_26:((int->Prop)->Prop))=> ((ord_less_eq_int_o_o B_26) A_161)))))) % FOF formula (forall (A_161:((nat->Prop)->Prop)), ((finite_finite_nat_o A_161)->(finite1676163439at_o_o (collect_nat_o_o (fun (B_26:((nat->Prop)->Prop))=> ((ord_less_eq_nat_o_o B_26) A_161)))))) of role axiom named fact_2_finite__Collect__subsets % A new axiom: (forall (A_161:((nat->Prop)->Prop)), ((finite_finite_nat_o A_161)->(finite1676163439at_o_o (collect_nat_o_o (fun (B_26:((nat->Prop)->Prop))=> ((ord_less_eq_nat_o_o B_26) A_161)))))) % FOF formula (forall (A_161:((pname->Prop)->Prop)), ((finite297249702name_o A_161)->(finite1066544169me_o_o (collect_pname_o_o (fun (B_26:((pname->Prop)->Prop))=> ((ord_le1205211808me_o_o B_26) A_161)))))) of role axiom named fact_3_finite__Collect__subsets % A new axiom: (forall (A_161:((pname->Prop)->Prop)), ((finite297249702name_o A_161)->(finite1066544169me_o_o (collect_pname_o_o (fun (B_26:((pname->Prop)->Prop))=> ((ord_le1205211808me_o_o B_26) A_161)))))) % FOF formula (forall (A_161:((x_a->Prop)->Prop)), ((finite_finite_a_o A_161)->(finite_finite_a_o_o (collect_a_o_o (fun (B_26:((x_a->Prop)->Prop))=> ((ord_less_eq_a_o_o B_26) A_161)))))) of role axiom named fact_4_finite__Collect__subsets % A new axiom: (forall (A_161:((x_a->Prop)->Prop)), ((finite_finite_a_o A_161)->(finite_finite_a_o_o (collect_a_o_o (fun (B_26:((x_a->Prop)->Prop))=> ((ord_less_eq_a_o_o B_26) A_161)))))) % FOF formula (forall (A_161:(x_a->Prop)), ((finite_finite_a A_161)->(finite_finite_a_o (collect_a_o (fun (B_26:(x_a->Prop))=> ((ord_less_eq_a_o B_26) A_161)))))) of role axiom named fact_5_finite__Collect__subsets % A new axiom: (forall (A_161:(x_a->Prop)), ((finite_finite_a A_161)->(finite_finite_a_o (collect_a_o (fun (B_26:(x_a->Prop))=> ((ord_less_eq_a_o B_26) A_161)))))) % FOF formula (forall (A_161:(pname->Prop)), ((finite_finite_pname A_161)->(finite297249702name_o (collect_pname_o (fun (B_26:(pname->Prop))=> ((ord_less_eq_pname_o B_26) A_161)))))) of role axiom named fact_6_finite__Collect__subsets % A new axiom: (forall (A_161:(pname->Prop)), ((finite_finite_pname A_161)->(finite297249702name_o (collect_pname_o (fun (B_26:(pname->Prop))=> ((ord_less_eq_pname_o B_26) A_161)))))) % FOF formula (forall (A_161:(nat->Prop)), ((finite_finite_nat A_161)->(finite_finite_nat_o (collect_nat_o (fun (B_26:(nat->Prop))=> ((ord_less_eq_nat_o B_26) A_161)))))) of role axiom named fact_7_finite__Collect__subsets % A new axiom: (forall (A_161:(nat->Prop)), ((finite_finite_nat A_161)->(finite_finite_nat_o (collect_nat_o (fun (B_26:(nat->Prop))=> ((ord_less_eq_nat_o B_26) A_161)))))) % FOF formula (forall (A_161:(int->Prop)), ((finite_finite_int A_161)->(finite_finite_int_o (collect_int_o (fun (B_26:(int->Prop))=> ((ord_less_eq_int_o B_26) A_161)))))) of role axiom named fact_8_finite__Collect__subsets % A new axiom: (forall (A_161:(int->Prop)), ((finite_finite_int A_161)->(finite_finite_int_o (collect_int_o (fun (B_26:(int->Prop))=> ((ord_less_eq_int_o B_26) A_161)))))) % FOF formula (forall (H:(pname->(int->Prop))) (F_42:(pname->Prop)), ((finite_finite_pname F_42)->(finite_finite_int_o ((image_pname_int_o H) F_42)))) of role axiom named fact_9_finite__imageI % A new axiom: (forall (H:(pname->(int->Prop))) (F_42:(pname->Prop)), ((finite_finite_pname F_42)->(finite_finite_int_o ((image_pname_int_o H) F_42)))) % FOF formula (forall (H:(pname->(nat->Prop))) (F_42:(pname->Prop)), ((finite_finite_pname F_42)->(finite_finite_nat_o ((image_pname_nat_o H) F_42)))) of role axiom named fact_10_finite__imageI % A new axiom: (forall (H:(pname->(nat->Prop))) (F_42:(pname->Prop)), ((finite_finite_pname F_42)->(finite_finite_nat_o ((image_pname_nat_o H) F_42)))) % FOF formula (forall (H:(pname->(pname->Prop))) (F_42:(pname->Prop)), ((finite_finite_pname F_42)->(finite297249702name_o ((image_pname_pname_o H) F_42)))) of role axiom named fact_11_finite__imageI % A new axiom: (forall (H:(pname->(pname->Prop))) (F_42:(pname->Prop)), ((finite_finite_pname F_42)->(finite297249702name_o ((image_pname_pname_o H) F_42)))) % FOF formula (forall (H:(pname->(x_a->Prop))) (F_42:(pname->Prop)), ((finite_finite_pname F_42)->(finite_finite_a_o ((image_pname_a_o H) F_42)))) of role axiom named fact_12_finite__imageI % A new axiom: (forall (H:(pname->(x_a->Prop))) (F_42:(pname->Prop)), ((finite_finite_pname F_42)->(finite_finite_a_o ((image_pname_a_o H) F_42)))) % FOF formula (forall (H:(nat->x_a)) (F_42:(nat->Prop)), ((finite_finite_nat F_42)->(finite_finite_a ((image_nat_a H) F_42)))) of role axiom named fact_13_finite__imageI % A new axiom: (forall (H:(nat->x_a)) (F_42:(nat->Prop)), ((finite_finite_nat F_42)->(finite_finite_a ((image_nat_a H) F_42)))) % FOF formula (forall (H:(nat->(int->Prop))) (F_42:(nat->Prop)), ((finite_finite_nat F_42)->(finite_finite_int_o ((image_nat_int_o H) F_42)))) of role axiom named fact_14_finite__imageI % A new axiom: (forall (H:(nat->(int->Prop))) (F_42:(nat->Prop)), ((finite_finite_nat F_42)->(finite_finite_int_o ((image_nat_int_o H) F_42)))) % FOF formula (forall (H:(nat->(nat->Prop))) (F_42:(nat->Prop)), ((finite_finite_nat F_42)->(finite_finite_nat_o ((image_nat_nat_o H) F_42)))) of role axiom named fact_15_finite__imageI % A new axiom: (forall (H:(nat->(nat->Prop))) (F_42:(nat->Prop)), ((finite_finite_nat F_42)->(finite_finite_nat_o ((image_nat_nat_o H) F_42)))) % FOF formula (forall (H:(nat->(pname->Prop))) (F_42:(nat->Prop)), ((finite_finite_nat F_42)->(finite297249702name_o ((image_nat_pname_o H) F_42)))) of role axiom named fact_16_finite__imageI % A new axiom: (forall (H:(nat->(pname->Prop))) (F_42:(nat->Prop)), ((finite_finite_nat F_42)->(finite297249702name_o ((image_nat_pname_o H) F_42)))) % FOF formula (forall (H:(nat->(x_a->Prop))) (F_42:(nat->Prop)), ((finite_finite_nat F_42)->(finite_finite_a_o ((image_nat_a_o H) F_42)))) of role axiom named fact_17_finite__imageI % A new axiom: (forall (H:(nat->(x_a->Prop))) (F_42:(nat->Prop)), ((finite_finite_nat F_42)->(finite_finite_a_o ((image_nat_a_o H) F_42)))) % FOF formula (forall (H:(int->x_a)) (F_42:(int->Prop)), ((finite_finite_int F_42)->(finite_finite_a ((image_int_a H) F_42)))) of role axiom named fact_18_finite__imageI % A new axiom: (forall (H:(int->x_a)) (F_42:(int->Prop)), ((finite_finite_int F_42)->(finite_finite_a ((image_int_a H) F_42)))) % FOF formula (forall (H:(int->(int->Prop))) (F_42:(int->Prop)), ((finite_finite_int F_42)->(finite_finite_int_o ((image_int_int_o H) F_42)))) of role axiom named fact_19_finite__imageI % A new axiom: (forall (H:(int->(int->Prop))) (F_42:(int->Prop)), ((finite_finite_int F_42)->(finite_finite_int_o ((image_int_int_o H) F_42)))) % FOF formula (forall (H:(int->(nat->Prop))) (F_42:(int->Prop)), ((finite_finite_int F_42)->(finite_finite_nat_o ((image_int_nat_o H) F_42)))) of role axiom named fact_20_finite__imageI % A new axiom: (forall (H:(int->(nat->Prop))) (F_42:(int->Prop)), ((finite_finite_int F_42)->(finite_finite_nat_o ((image_int_nat_o H) F_42)))) % FOF formula (forall (H:(int->(pname->Prop))) (F_42:(int->Prop)), ((finite_finite_int F_42)->(finite297249702name_o ((image_int_pname_o H) F_42)))) of role axiom named fact_21_finite__imageI % A new axiom: (forall (H:(int->(pname->Prop))) (F_42:(int->Prop)), ((finite_finite_int F_42)->(finite297249702name_o ((image_int_pname_o H) F_42)))) % FOF formula (forall (H:(int->(x_a->Prop))) (F_42:(int->Prop)), ((finite_finite_int F_42)->(finite_finite_a_o ((image_int_a_o H) F_42)))) of role axiom named fact_22_finite__imageI % A new axiom: (forall (H:(int->(x_a->Prop))) (F_42:(int->Prop)), ((finite_finite_int F_42)->(finite_finite_a_o ((image_int_a_o H) F_42)))) % FOF formula (forall (H:(x_a->pname)) (F_42:(x_a->Prop)), ((finite_finite_a F_42)->(finite_finite_pname ((image_a_pname H) F_42)))) of role axiom named fact_23_finite__imageI % A new axiom: (forall (H:(x_a->pname)) (F_42:(x_a->Prop)), ((finite_finite_a F_42)->(finite_finite_pname ((image_a_pname H) F_42)))) % FOF formula (forall (H:((int->Prop)->pname)) (F_42:((int->Prop)->Prop)), ((finite_finite_int_o F_42)->(finite_finite_pname ((image_int_o_pname H) F_42)))) of role axiom named fact_24_finite__imageI % A new axiom: (forall (H:((int->Prop)->pname)) (F_42:((int->Prop)->Prop)), ((finite_finite_int_o F_42)->(finite_finite_pname ((image_int_o_pname H) F_42)))) % FOF formula (forall (H:((nat->Prop)->pname)) (F_42:((nat->Prop)->Prop)), ((finite_finite_nat_o F_42)->(finite_finite_pname ((image_nat_o_pname H) F_42)))) of role axiom named fact_25_finite__imageI % A new axiom: (forall (H:((nat->Prop)->pname)) (F_42:((nat->Prop)->Prop)), ((finite_finite_nat_o F_42)->(finite_finite_pname ((image_nat_o_pname H) F_42)))) % FOF formula (forall (H:((pname->Prop)->pname)) (F_42:((pname->Prop)->Prop)), ((finite297249702name_o F_42)->(finite_finite_pname ((image_pname_o_pname H) F_42)))) of role axiom named fact_26_finite__imageI % A new axiom: (forall (H:((pname->Prop)->pname)) (F_42:((pname->Prop)->Prop)), ((finite297249702name_o F_42)->(finite_finite_pname ((image_pname_o_pname H) F_42)))) % FOF formula (forall (H:((x_a->Prop)->pname)) (F_42:((x_a->Prop)->Prop)), ((finite_finite_a_o F_42)->(finite_finite_pname ((image_a_o_pname H) F_42)))) of role axiom named fact_27_finite__imageI % A new axiom: (forall (H:((x_a->Prop)->pname)) (F_42:((x_a->Prop)->Prop)), ((finite_finite_a_o F_42)->(finite_finite_pname ((image_a_o_pname H) F_42)))) % FOF formula (forall (H:(x_a->nat)) (F_42:(x_a->Prop)), ((finite_finite_a F_42)->(finite_finite_nat ((image_a_nat H) F_42)))) of role axiom named fact_28_finite__imageI % A new axiom: (forall (H:(x_a->nat)) (F_42:(x_a->Prop)), ((finite_finite_a F_42)->(finite_finite_nat ((image_a_nat H) F_42)))) % FOF formula (forall (H:((int->Prop)->nat)) (F_42:((int->Prop)->Prop)), ((finite_finite_int_o F_42)->(finite_finite_nat ((image_int_o_nat H) F_42)))) of role axiom named fact_29_finite__imageI % A new axiom: (forall (H:((int->Prop)->nat)) (F_42:((int->Prop)->Prop)), ((finite_finite_int_o F_42)->(finite_finite_nat ((image_int_o_nat H) F_42)))) % FOF formula (forall (H:((nat->Prop)->nat)) (F_42:((nat->Prop)->Prop)), ((finite_finite_nat_o F_42)->(finite_finite_nat ((image_nat_o_nat H) F_42)))) of role axiom named fact_30_finite__imageI % A new axiom: (forall (H:((nat->Prop)->nat)) (F_42:((nat->Prop)->Prop)), ((finite_finite_nat_o F_42)->(finite_finite_nat ((image_nat_o_nat H) F_42)))) % FOF formula (forall (H:((pname->Prop)->nat)) (F_42:((pname->Prop)->Prop)), ((finite297249702name_o F_42)->(finite_finite_nat ((image_pname_o_nat H) F_42)))) of role axiom named fact_31_finite__imageI % A new axiom: (forall (H:((pname->Prop)->nat)) (F_42:((pname->Prop)->Prop)), ((finite297249702name_o F_42)->(finite_finite_nat ((image_pname_o_nat H) F_42)))) % FOF formula (forall (H:((x_a->Prop)->nat)) (F_42:((x_a->Prop)->Prop)), ((finite_finite_a_o F_42)->(finite_finite_nat ((image_a_o_nat H) F_42)))) of role axiom named fact_32_finite__imageI % A new axiom: (forall (H:((x_a->Prop)->nat)) (F_42:((x_a->Prop)->Prop)), ((finite_finite_a_o F_42)->(finite_finite_nat ((image_a_o_nat H) F_42)))) % FOF formula (forall (H:(x_a->int)) (F_42:(x_a->Prop)), ((finite_finite_a F_42)->(finite_finite_int ((image_a_int H) F_42)))) of role axiom named fact_33_finite__imageI % A new axiom: (forall (H:(x_a->int)) (F_42:(x_a->Prop)), ((finite_finite_a F_42)->(finite_finite_int ((image_a_int H) F_42)))) % FOF formula (forall (H:((int->Prop)->int)) (F_42:((int->Prop)->Prop)), ((finite_finite_int_o F_42)->(finite_finite_int ((image_int_o_int H) F_42)))) of role axiom named fact_34_finite__imageI % A new axiom: (forall (H:((int->Prop)->int)) (F_42:((int->Prop)->Prop)), ((finite_finite_int_o F_42)->(finite_finite_int ((image_int_o_int H) F_42)))) % FOF formula (forall (H:((nat->Prop)->int)) (F_42:((nat->Prop)->Prop)), ((finite_finite_nat_o F_42)->(finite_finite_int ((image_nat_o_int H) F_42)))) of role axiom named fact_35_finite__imageI % A new axiom: (forall (H:((nat->Prop)->int)) (F_42:((nat->Prop)->Prop)), ((finite_finite_nat_o F_42)->(finite_finite_int ((image_nat_o_int H) F_42)))) % FOF formula (forall (H:((pname->Prop)->int)) (F_42:((pname->Prop)->Prop)), ((finite297249702name_o F_42)->(finite_finite_int ((image_pname_o_int H) F_42)))) of role axiom named fact_36_finite__imageI % A new axiom: (forall (H:((pname->Prop)->int)) (F_42:((pname->Prop)->Prop)), ((finite297249702name_o F_42)->(finite_finite_int ((image_pname_o_int H) F_42)))) % FOF formula (forall (H:((x_a->Prop)->int)) (F_42:((x_a->Prop)->Prop)), ((finite_finite_a_o F_42)->(finite_finite_int ((image_a_o_int H) F_42)))) of role axiom named fact_37_finite__imageI % A new axiom: (forall (H:((x_a->Prop)->int)) (F_42:((x_a->Prop)->Prop)), ((finite_finite_a_o F_42)->(finite_finite_int ((image_a_o_int H) F_42)))) % FOF formula (forall (H:(pname->x_a)) (F_42:(pname->Prop)), ((finite_finite_pname F_42)->(finite_finite_a ((image_pname_a H) F_42)))) of role axiom named fact_38_finite__imageI % A new axiom: (forall (H:(pname->x_a)) (F_42:(pname->Prop)), ((finite_finite_pname F_42)->(finite_finite_a ((image_pname_a H) F_42)))) % FOF formula (forall (H:(nat->int)) (F_42:(nat->Prop)), ((finite_finite_nat F_42)->(finite_finite_int ((image_nat_int H) F_42)))) of role axiom named fact_39_finite__imageI % A new axiom: (forall (H:(nat->int)) (F_42:(nat->Prop)), ((finite_finite_nat F_42)->(finite_finite_int ((image_nat_int H) F_42)))) % FOF formula (forall (A_160:(int->Prop)) (A_159:((int->Prop)->Prop)), ((finite_finite_int_o A_159)->(finite_finite_int_o ((insert_int_o A_160) A_159)))) of role axiom named fact_40_finite_OinsertI % A new axiom: (forall (A_160:(int->Prop)) (A_159:((int->Prop)->Prop)), ((finite_finite_int_o A_159)->(finite_finite_int_o ((insert_int_o A_160) A_159)))) % FOF formula (forall (A_160:(nat->Prop)) (A_159:((nat->Prop)->Prop)), ((finite_finite_nat_o A_159)->(finite_finite_nat_o ((insert_nat_o A_160) A_159)))) of role axiom named fact_41_finite_OinsertI % A new axiom: (forall (A_160:(nat->Prop)) (A_159:((nat->Prop)->Prop)), ((finite_finite_nat_o A_159)->(finite_finite_nat_o ((insert_nat_o A_160) A_159)))) % FOF formula (forall (A_160:(pname->Prop)) (A_159:((pname->Prop)->Prop)), ((finite297249702name_o A_159)->(finite297249702name_o ((insert_pname_o A_160) A_159)))) of role axiom named fact_42_finite_OinsertI % A new axiom: (forall (A_160:(pname->Prop)) (A_159:((pname->Prop)->Prop)), ((finite297249702name_o A_159)->(finite297249702name_o ((insert_pname_o A_160) A_159)))) % FOF formula (forall (A_160:(x_a->Prop)) (A_159:((x_a->Prop)->Prop)), ((finite_finite_a_o A_159)->(finite_finite_a_o ((insert_a_o A_160) A_159)))) of role axiom named fact_43_finite_OinsertI % A new axiom: (forall (A_160:(x_a->Prop)) (A_159:((x_a->Prop)->Prop)), ((finite_finite_a_o A_159)->(finite_finite_a_o ((insert_a_o A_160) A_159)))) % FOF formula (forall (A_160:pname) (A_159:(pname->Prop)), ((finite_finite_pname A_159)->(finite_finite_pname ((insert_pname A_160) A_159)))) of role axiom named fact_44_finite_OinsertI % A new axiom: (forall (A_160:pname) (A_159:(pname->Prop)), ((finite_finite_pname A_159)->(finite_finite_pname ((insert_pname A_160) A_159)))) % FOF formula (forall (A_160:nat) (A_159:(nat->Prop)), ((finite_finite_nat A_159)->(finite_finite_nat ((insert_nat A_160) A_159)))) of role axiom named fact_45_finite_OinsertI % A new axiom: (forall (A_160:nat) (A_159:(nat->Prop)), ((finite_finite_nat A_159)->(finite_finite_nat ((insert_nat A_160) A_159)))) % FOF formula (forall (A_160:int) (A_159:(int->Prop)), ((finite_finite_int A_159)->(finite_finite_int ((insert_int A_160) A_159)))) of role axiom named fact_46_finite_OinsertI % A new axiom: (forall (A_160:int) (A_159:(int->Prop)), ((finite_finite_int A_159)->(finite_finite_int ((insert_int A_160) A_159)))) % FOF formula (forall (A_160:x_a) (A_159:(x_a->Prop)), ((finite_finite_a A_159)->(finite_finite_a ((insert_a A_160) A_159)))) of role axiom named fact_47_finite_OinsertI % A new axiom: (forall (A_160:x_a) (A_159:(x_a->Prop)), ((finite_finite_a A_159)->(finite_finite_a ((insert_a A_160) A_159)))) % FOF formula (forall (F_41:(pname->pname)) (A_158:(pname->Prop)), ((finite_finite_pname A_158)->((ord_less_eq_nat (finite_card_pname ((image_pname_pname F_41) A_158))) (finite_card_pname A_158)))) of role axiom named fact_48_card__image__le % A new axiom: (forall (F_41:(pname->pname)) (A_158:(pname->Prop)), ((finite_finite_pname A_158)->((ord_less_eq_nat (finite_card_pname ((image_pname_pname F_41) A_158))) (finite_card_pname A_158)))) % FOF formula (forall (F_41:(x_a->x_a)) (A_158:(x_a->Prop)), ((finite_finite_a A_158)->((ord_less_eq_nat (finite_card_a ((image_a_a F_41) A_158))) (finite_card_a A_158)))) of role axiom named fact_49_card__image__le % A new axiom: (forall (F_41:(x_a->x_a)) (A_158:(x_a->Prop)), ((finite_finite_a A_158)->((ord_less_eq_nat (finite_card_a ((image_a_a F_41) A_158))) (finite_card_a A_158)))) % FOF formula (forall (F_41:((int->Prop)->x_a)) (A_158:((int->Prop)->Prop)), ((finite_finite_int_o A_158)->((ord_less_eq_nat (finite_card_a ((image_int_o_a F_41) A_158))) (finite_card_int_o A_158)))) of role axiom named fact_50_card__image__le % A new axiom: (forall (F_41:((int->Prop)->x_a)) (A_158:((int->Prop)->Prop)), ((finite_finite_int_o A_158)->((ord_less_eq_nat (finite_card_a ((image_int_o_a F_41) A_158))) (finite_card_int_o A_158)))) % FOF formula (forall (F_41:((nat->Prop)->x_a)) (A_158:((nat->Prop)->Prop)), ((finite_finite_nat_o A_158)->((ord_less_eq_nat (finite_card_a ((image_nat_o_a F_41) A_158))) (finite_card_nat_o A_158)))) of role axiom named fact_51_card__image__le % A new axiom: (forall (F_41:((nat->Prop)->x_a)) (A_158:((nat->Prop)->Prop)), ((finite_finite_nat_o A_158)->((ord_less_eq_nat (finite_card_a ((image_nat_o_a F_41) A_158))) (finite_card_nat_o A_158)))) % FOF formula (forall (F_41:((pname->Prop)->x_a)) (A_158:((pname->Prop)->Prop)), ((finite297249702name_o A_158)->((ord_less_eq_nat (finite_card_a ((image_pname_o_a F_41) A_158))) (finite_card_pname_o A_158)))) of role axiom named fact_52_card__image__le % A new axiom: (forall (F_41:((pname->Prop)->x_a)) (A_158:((pname->Prop)->Prop)), ((finite297249702name_o A_158)->((ord_less_eq_nat (finite_card_a ((image_pname_o_a F_41) A_158))) (finite_card_pname_o A_158)))) % FOF formula (forall (F_41:((x_a->Prop)->x_a)) (A_158:((x_a->Prop)->Prop)), ((finite_finite_a_o A_158)->((ord_less_eq_nat (finite_card_a ((image_a_o_a F_41) A_158))) (finite_card_a_o A_158)))) of role axiom named fact_53_card__image__le % A new axiom: (forall (F_41:((x_a->Prop)->x_a)) (A_158:((x_a->Prop)->Prop)), ((finite_finite_a_o A_158)->((ord_less_eq_nat (finite_card_a ((image_a_o_a F_41) A_158))) (finite_card_a_o A_158)))) % FOF formula (forall (F_41:(pname->nat)) (A_158:(pname->Prop)), ((finite_finite_pname A_158)->((ord_less_eq_nat (finite_card_nat ((image_pname_nat F_41) A_158))) (finite_card_pname A_158)))) of role axiom named fact_54_card__image__le % A new axiom: (forall (F_41:(pname->nat)) (A_158:(pname->Prop)), ((finite_finite_pname A_158)->((ord_less_eq_nat (finite_card_nat ((image_pname_nat F_41) A_158))) (finite_card_pname A_158)))) % FOF formula (forall (F_41:(x_a->nat)) (A_158:(x_a->Prop)), ((finite_finite_a A_158)->((ord_less_eq_nat (finite_card_nat ((image_a_nat F_41) A_158))) (finite_card_a A_158)))) of role axiom named fact_55_card__image__le % A new axiom: (forall (F_41:(x_a->nat)) (A_158:(x_a->Prop)), ((finite_finite_a A_158)->((ord_less_eq_nat (finite_card_nat ((image_a_nat F_41) A_158))) (finite_card_a A_158)))) % FOF formula (forall (F_41:((int->Prop)->nat)) (A_158:((int->Prop)->Prop)), ((finite_finite_int_o A_158)->((ord_less_eq_nat (finite_card_nat ((image_int_o_nat F_41) A_158))) (finite_card_int_o A_158)))) of role axiom named fact_56_card__image__le % A new axiom: (forall (F_41:((int->Prop)->nat)) (A_158:((int->Prop)->Prop)), ((finite_finite_int_o A_158)->((ord_less_eq_nat (finite_card_nat ((image_int_o_nat F_41) A_158))) (finite_card_int_o A_158)))) % FOF formula (forall (F_41:((nat->Prop)->nat)) (A_158:((nat->Prop)->Prop)), ((finite_finite_nat_o A_158)->((ord_less_eq_nat (finite_card_nat ((image_nat_o_nat F_41) A_158))) (finite_card_nat_o A_158)))) of role axiom named fact_57_card__image__le % A new axiom: (forall (F_41:((nat->Prop)->nat)) (A_158:((nat->Prop)->Prop)), ((finite_finite_nat_o A_158)->((ord_less_eq_nat (finite_card_nat ((image_nat_o_nat F_41) A_158))) (finite_card_nat_o A_158)))) % FOF formula (forall (F_41:((pname->Prop)->nat)) (A_158:((pname->Prop)->Prop)), ((finite297249702name_o A_158)->((ord_less_eq_nat (finite_card_nat ((image_pname_o_nat F_41) A_158))) (finite_card_pname_o A_158)))) of role axiom named fact_58_card__image__le % A new axiom: (forall (F_41:((pname->Prop)->nat)) (A_158:((pname->Prop)->Prop)), ((finite297249702name_o A_158)->((ord_less_eq_nat (finite_card_nat ((image_pname_o_nat F_41) A_158))) (finite_card_pname_o A_158)))) % FOF formula (forall (F_41:((x_a->Prop)->nat)) (A_158:((x_a->Prop)->Prop)), ((finite_finite_a_o A_158)->((ord_less_eq_nat (finite_card_nat ((image_a_o_nat F_41) A_158))) (finite_card_a_o A_158)))) of role axiom named fact_59_card__image__le % A new axiom: (forall (F_41:((x_a->Prop)->nat)) (A_158:((x_a->Prop)->Prop)), ((finite_finite_a_o A_158)->((ord_less_eq_nat (finite_card_nat ((image_a_o_nat F_41) A_158))) (finite_card_a_o A_158)))) % FOF formula (forall (F_41:(pname->int)) (A_158:(pname->Prop)), ((finite_finite_pname A_158)->((ord_less_eq_nat (finite_card_int ((image_pname_int F_41) A_158))) (finite_card_pname A_158)))) of role axiom named fact_60_card__image__le % A new axiom: (forall (F_41:(pname->int)) (A_158:(pname->Prop)), ((finite_finite_pname A_158)->((ord_less_eq_nat (finite_card_int ((image_pname_int F_41) A_158))) (finite_card_pname A_158)))) % FOF formula (forall (F_41:(x_a->int)) (A_158:(x_a->Prop)), ((finite_finite_a A_158)->((ord_less_eq_nat (finite_card_int ((image_a_int F_41) A_158))) (finite_card_a A_158)))) of role axiom named fact_61_card__image__le % A new axiom: (forall (F_41:(x_a->int)) (A_158:(x_a->Prop)), ((finite_finite_a A_158)->((ord_less_eq_nat (finite_card_int ((image_a_int F_41) A_158))) (finite_card_a A_158)))) % FOF formula (forall (F_41:((int->Prop)->int)) (A_158:((int->Prop)->Prop)), ((finite_finite_int_o A_158)->((ord_less_eq_nat (finite_card_int ((image_int_o_int F_41) A_158))) (finite_card_int_o A_158)))) of role axiom named fact_62_card__image__le % A new axiom: (forall (F_41:((int->Prop)->int)) (A_158:((int->Prop)->Prop)), ((finite_finite_int_o A_158)->((ord_less_eq_nat (finite_card_int ((image_int_o_int F_41) A_158))) (finite_card_int_o A_158)))) % FOF formula (forall (F_41:((nat->Prop)->int)) (A_158:((nat->Prop)->Prop)), ((finite_finite_nat_o A_158)->((ord_less_eq_nat (finite_card_int ((image_nat_o_int F_41) A_158))) (finite_card_nat_o A_158)))) of role axiom named fact_63_card__image__le % A new axiom: (forall (F_41:((nat->Prop)->int)) (A_158:((nat->Prop)->Prop)), ((finite_finite_nat_o A_158)->((ord_less_eq_nat (finite_card_int ((image_nat_o_int F_41) A_158))) (finite_card_nat_o A_158)))) % FOF formula (forall (F_41:((pname->Prop)->int)) (A_158:((pname->Prop)->Prop)), ((finite297249702name_o A_158)->((ord_less_eq_nat (finite_card_int ((image_pname_o_int F_41) A_158))) (finite_card_pname_o A_158)))) of role axiom named fact_64_card__image__le % A new axiom: (forall (F_41:((pname->Prop)->int)) (A_158:((pname->Prop)->Prop)), ((finite297249702name_o A_158)->((ord_less_eq_nat (finite_card_int ((image_pname_o_int F_41) A_158))) (finite_card_pname_o A_158)))) % FOF formula (forall (F_41:((x_a->Prop)->int)) (A_158:((x_a->Prop)->Prop)), ((finite_finite_a_o A_158)->((ord_less_eq_nat (finite_card_int ((image_a_o_int F_41) A_158))) (finite_card_a_o A_158)))) of role axiom named fact_65_card__image__le % A new axiom: (forall (F_41:((x_a->Prop)->int)) (A_158:((x_a->Prop)->Prop)), ((finite_finite_a_o A_158)->((ord_less_eq_nat (finite_card_int ((image_a_o_int F_41) A_158))) (finite_card_a_o A_158)))) % FOF formula (forall (F_41:(x_a->pname)) (A_158:(x_a->Prop)), ((finite_finite_a A_158)->((ord_less_eq_nat (finite_card_pname ((image_a_pname F_41) A_158))) (finite_card_a A_158)))) of role axiom named fact_66_card__image__le % A new axiom: (forall (F_41:(x_a->pname)) (A_158:(x_a->Prop)), ((finite_finite_a A_158)->((ord_less_eq_nat (finite_card_pname ((image_a_pname F_41) A_158))) (finite_card_a A_158)))) % FOF formula (forall (F_41:(nat->pname)) (A_158:(nat->Prop)), ((finite_finite_nat A_158)->((ord_less_eq_nat (finite_card_pname ((image_nat_pname F_41) A_158))) (finite_card_nat A_158)))) of role axiom named fact_67_card__image__le % A new axiom: (forall (F_41:(nat->pname)) (A_158:(nat->Prop)), ((finite_finite_nat A_158)->((ord_less_eq_nat (finite_card_pname ((image_nat_pname F_41) A_158))) (finite_card_nat A_158)))) % FOF formula (forall (F_41:(int->pname)) (A_158:(int->Prop)), ((finite_finite_int A_158)->((ord_less_eq_nat (finite_card_pname ((image_int_pname F_41) A_158))) (finite_card_int A_158)))) of role axiom named fact_68_card__image__le % A new axiom: (forall (F_41:(int->pname)) (A_158:(int->Prop)), ((finite_finite_int A_158)->((ord_less_eq_nat (finite_card_pname ((image_int_pname F_41) A_158))) (finite_card_int A_158)))) % FOF formula (forall (F_41:(pname->x_a)) (A_158:(pname->Prop)), ((finite_finite_pname A_158)->((ord_less_eq_nat (finite_card_a ((image_pname_a F_41) A_158))) (finite_card_pname A_158)))) of role axiom named fact_69_card__image__le % A new axiom: (forall (F_41:(pname->x_a)) (A_158:(pname->Prop)), ((finite_finite_pname A_158)->((ord_less_eq_nat (finite_card_a ((image_pname_a F_41) A_158))) (finite_card_pname A_158)))) % FOF formula (forall (F_41:(nat->int)) (A_158:(nat->Prop)), ((finite_finite_nat A_158)->((ord_less_eq_nat (finite_card_int ((image_nat_int F_41) A_158))) (finite_card_nat A_158)))) of role axiom named fact_70_card__image__le % A new axiom: (forall (F_41:(nat->int)) (A_158:(nat->Prop)), ((finite_finite_nat A_158)->((ord_less_eq_nat (finite_card_int ((image_nat_int F_41) A_158))) (finite_card_nat A_158)))) % FOF formula (forall (A_157:((int->Prop)->Prop)) (B_89:((int->Prop)->Prop)), ((finite_finite_int_o B_89)->(((ord_less_eq_int_o_o A_157) B_89)->((ord_less_eq_nat (finite_card_int_o A_157)) (finite_card_int_o B_89))))) of role axiom named fact_71_card__mono % A new axiom: (forall (A_157:((int->Prop)->Prop)) (B_89:((int->Prop)->Prop)), ((finite_finite_int_o B_89)->(((ord_less_eq_int_o_o A_157) B_89)->((ord_less_eq_nat (finite_card_int_o A_157)) (finite_card_int_o B_89))))) % FOF formula (forall (A_157:((nat->Prop)->Prop)) (B_89:((nat->Prop)->Prop)), ((finite_finite_nat_o B_89)->(((ord_less_eq_nat_o_o A_157) B_89)->((ord_less_eq_nat (finite_card_nat_o A_157)) (finite_card_nat_o B_89))))) of role axiom named fact_72_card__mono % A new axiom: (forall (A_157:((nat->Prop)->Prop)) (B_89:((nat->Prop)->Prop)), ((finite_finite_nat_o B_89)->(((ord_less_eq_nat_o_o A_157) B_89)->((ord_less_eq_nat (finite_card_nat_o A_157)) (finite_card_nat_o B_89))))) % FOF formula (forall (A_157:((pname->Prop)->Prop)) (B_89:((pname->Prop)->Prop)), ((finite297249702name_o B_89)->(((ord_le1205211808me_o_o A_157) B_89)->((ord_less_eq_nat (finite_card_pname_o A_157)) (finite_card_pname_o B_89))))) of role axiom named fact_73_card__mono % A new axiom: (forall (A_157:((pname->Prop)->Prop)) (B_89:((pname->Prop)->Prop)), ((finite297249702name_o B_89)->(((ord_le1205211808me_o_o A_157) B_89)->((ord_less_eq_nat (finite_card_pname_o A_157)) (finite_card_pname_o B_89))))) % FOF formula (forall (A_157:((x_a->Prop)->Prop)) (B_89:((x_a->Prop)->Prop)), ((finite_finite_a_o B_89)->(((ord_less_eq_a_o_o A_157) B_89)->((ord_less_eq_nat (finite_card_a_o A_157)) (finite_card_a_o B_89))))) of role axiom named fact_74_card__mono % A new axiom: (forall (A_157:((x_a->Prop)->Prop)) (B_89:((x_a->Prop)->Prop)), ((finite_finite_a_o B_89)->(((ord_less_eq_a_o_o A_157) B_89)->((ord_less_eq_nat (finite_card_a_o A_157)) (finite_card_a_o B_89))))) % FOF formula (forall (A_157:(pname->Prop)) (B_89:(pname->Prop)), ((finite_finite_pname B_89)->(((ord_less_eq_pname_o A_157) B_89)->((ord_less_eq_nat (finite_card_pname A_157)) (finite_card_pname B_89))))) of role axiom named fact_75_card__mono % A new axiom: (forall (A_157:(pname->Prop)) (B_89:(pname->Prop)), ((finite_finite_pname B_89)->(((ord_less_eq_pname_o A_157) B_89)->((ord_less_eq_nat (finite_card_pname A_157)) (finite_card_pname B_89))))) % FOF formula (forall (A_157:(x_a->Prop)) (B_89:(x_a->Prop)), ((finite_finite_a B_89)->(((ord_less_eq_a_o A_157) B_89)->((ord_less_eq_nat (finite_card_a A_157)) (finite_card_a B_89))))) of role axiom named fact_76_card__mono % A new axiom: (forall (A_157:(x_a->Prop)) (B_89:(x_a->Prop)), ((finite_finite_a B_89)->(((ord_less_eq_a_o A_157) B_89)->((ord_less_eq_nat (finite_card_a A_157)) (finite_card_a B_89))))) % FOF formula (forall (A_157:(nat->Prop)) (B_89:(nat->Prop)), ((finite_finite_nat B_89)->(((ord_less_eq_nat_o A_157) B_89)->((ord_less_eq_nat (finite_card_nat A_157)) (finite_card_nat B_89))))) of role axiom named fact_77_card__mono % A new axiom: (forall (A_157:(nat->Prop)) (B_89:(nat->Prop)), ((finite_finite_nat B_89)->(((ord_less_eq_nat_o A_157) B_89)->((ord_less_eq_nat (finite_card_nat A_157)) (finite_card_nat B_89))))) % FOF formula (forall (A_157:(int->Prop)) (B_89:(int->Prop)), ((finite_finite_int B_89)->(((ord_less_eq_int_o A_157) B_89)->((ord_less_eq_nat (finite_card_int A_157)) (finite_card_int B_89))))) of role axiom named fact_78_card__mono % A new axiom: (forall (A_157:(int->Prop)) (B_89:(int->Prop)), ((finite_finite_int B_89)->(((ord_less_eq_int_o A_157) B_89)->((ord_less_eq_nat (finite_card_int A_157)) (finite_card_int B_89))))) % FOF formula (forall (A_156:((int->Prop)->Prop)) (B_88:((int->Prop)->Prop)), ((finite_finite_int_o B_88)->(((ord_less_eq_int_o_o A_156) B_88)->(((ord_less_eq_nat (finite_card_int_o B_88)) (finite_card_int_o A_156))->(((eq ((int->Prop)->Prop)) A_156) B_88))))) of role axiom named fact_79_card__seteq % A new axiom: (forall (A_156:((int->Prop)->Prop)) (B_88:((int->Prop)->Prop)), ((finite_finite_int_o B_88)->(((ord_less_eq_int_o_o A_156) B_88)->(((ord_less_eq_nat (finite_card_int_o B_88)) (finite_card_int_o A_156))->(((eq ((int->Prop)->Prop)) A_156) B_88))))) % FOF formula (forall (A_156:((nat->Prop)->Prop)) (B_88:((nat->Prop)->Prop)), ((finite_finite_nat_o B_88)->(((ord_less_eq_nat_o_o A_156) B_88)->(((ord_less_eq_nat (finite_card_nat_o B_88)) (finite_card_nat_o A_156))->(((eq ((nat->Prop)->Prop)) A_156) B_88))))) of role axiom named fact_80_card__seteq % A new axiom: (forall (A_156:((nat->Prop)->Prop)) (B_88:((nat->Prop)->Prop)), ((finite_finite_nat_o B_88)->(((ord_less_eq_nat_o_o A_156) B_88)->(((ord_less_eq_nat (finite_card_nat_o B_88)) (finite_card_nat_o A_156))->(((eq ((nat->Prop)->Prop)) A_156) B_88))))) % FOF formula (forall (A_156:((pname->Prop)->Prop)) (B_88:((pname->Prop)->Prop)), ((finite297249702name_o B_88)->(((ord_le1205211808me_o_o A_156) B_88)->(((ord_less_eq_nat (finite_card_pname_o B_88)) (finite_card_pname_o A_156))->(((eq ((pname->Prop)->Prop)) A_156) B_88))))) of role axiom named fact_81_card__seteq % A new axiom: (forall (A_156:((pname->Prop)->Prop)) (B_88:((pname->Prop)->Prop)), ((finite297249702name_o B_88)->(((ord_le1205211808me_o_o A_156) B_88)->(((ord_less_eq_nat (finite_card_pname_o B_88)) (finite_card_pname_o A_156))->(((eq ((pname->Prop)->Prop)) A_156) B_88))))) % FOF formula (forall (A_156:((x_a->Prop)->Prop)) (B_88:((x_a->Prop)->Prop)), ((finite_finite_a_o B_88)->(((ord_less_eq_a_o_o A_156) B_88)->(((ord_less_eq_nat (finite_card_a_o B_88)) (finite_card_a_o A_156))->(((eq ((x_a->Prop)->Prop)) A_156) B_88))))) of role axiom named fact_82_card__seteq % A new axiom: (forall (A_156:((x_a->Prop)->Prop)) (B_88:((x_a->Prop)->Prop)), ((finite_finite_a_o B_88)->(((ord_less_eq_a_o_o A_156) B_88)->(((ord_less_eq_nat (finite_card_a_o B_88)) (finite_card_a_o A_156))->(((eq ((x_a->Prop)->Prop)) A_156) B_88))))) % FOF formula (forall (A_156:(pname->Prop)) (B_88:(pname->Prop)), ((finite_finite_pname B_88)->(((ord_less_eq_pname_o A_156) B_88)->(((ord_less_eq_nat (finite_card_pname B_88)) (finite_card_pname A_156))->(((eq (pname->Prop)) A_156) B_88))))) of role axiom named fact_83_card__seteq % A new axiom: (forall (A_156:(pname->Prop)) (B_88:(pname->Prop)), ((finite_finite_pname B_88)->(((ord_less_eq_pname_o A_156) B_88)->(((ord_less_eq_nat (finite_card_pname B_88)) (finite_card_pname A_156))->(((eq (pname->Prop)) A_156) B_88))))) % FOF formula (forall (A_156:(x_a->Prop)) (B_88:(x_a->Prop)), ((finite_finite_a B_88)->(((ord_less_eq_a_o A_156) B_88)->(((ord_less_eq_nat (finite_card_a B_88)) (finite_card_a A_156))->(((eq (x_a->Prop)) A_156) B_88))))) of role axiom named fact_84_card__seteq % A new axiom: (forall (A_156:(x_a->Prop)) (B_88:(x_a->Prop)), ((finite_finite_a B_88)->(((ord_less_eq_a_o A_156) B_88)->(((ord_less_eq_nat (finite_card_a B_88)) (finite_card_a A_156))->(((eq (x_a->Prop)) A_156) B_88))))) % FOF formula (forall (A_156:(nat->Prop)) (B_88:(nat->Prop)), ((finite_finite_nat B_88)->(((ord_less_eq_nat_o A_156) B_88)->(((ord_less_eq_nat (finite_card_nat B_88)) (finite_card_nat A_156))->(((eq (nat->Prop)) A_156) B_88))))) of role axiom named fact_85_card__seteq % A new axiom: (forall (A_156:(nat->Prop)) (B_88:(nat->Prop)), ((finite_finite_nat B_88)->(((ord_less_eq_nat_o A_156) B_88)->(((ord_less_eq_nat (finite_card_nat B_88)) (finite_card_nat A_156))->(((eq (nat->Prop)) A_156) B_88))))) % FOF formula (forall (A_156:(int->Prop)) (B_88:(int->Prop)), ((finite_finite_int B_88)->(((ord_less_eq_int_o A_156) B_88)->(((ord_less_eq_nat (finite_card_int B_88)) (finite_card_int A_156))->(((eq (int->Prop)) A_156) B_88))))) of role axiom named fact_86_card__seteq % A new axiom: (forall (A_156:(int->Prop)) (B_88:(int->Prop)), ((finite_finite_int B_88)->(((ord_less_eq_int_o A_156) B_88)->(((ord_less_eq_nat (finite_card_int B_88)) (finite_card_int A_156))->(((eq (int->Prop)) A_156) B_88))))) % FOF formula (forall (X_53:(int->Prop)) (A_155:((int->Prop)->Prop)), ((finite_finite_int_o A_155)->((ord_less_eq_nat (finite_card_int_o A_155)) (finite_card_int_o ((insert_int_o X_53) A_155))))) of role axiom named fact_87_card__insert__le % A new axiom: (forall (X_53:(int->Prop)) (A_155:((int->Prop)->Prop)), ((finite_finite_int_o A_155)->((ord_less_eq_nat (finite_card_int_o A_155)) (finite_card_int_o ((insert_int_o X_53) A_155))))) % FOF formula (forall (X_53:(nat->Prop)) (A_155:((nat->Prop)->Prop)), ((finite_finite_nat_o A_155)->((ord_less_eq_nat (finite_card_nat_o A_155)) (finite_card_nat_o ((insert_nat_o X_53) A_155))))) of role axiom named fact_88_card__insert__le % A new axiom: (forall (X_53:(nat->Prop)) (A_155:((nat->Prop)->Prop)), ((finite_finite_nat_o A_155)->((ord_less_eq_nat (finite_card_nat_o A_155)) (finite_card_nat_o ((insert_nat_o X_53) A_155))))) % FOF formula (forall (X_53:(pname->Prop)) (A_155:((pname->Prop)->Prop)), ((finite297249702name_o A_155)->((ord_less_eq_nat (finite_card_pname_o A_155)) (finite_card_pname_o ((insert_pname_o X_53) A_155))))) of role axiom named fact_89_card__insert__le % A new axiom: (forall (X_53:(pname->Prop)) (A_155:((pname->Prop)->Prop)), ((finite297249702name_o A_155)->((ord_less_eq_nat (finite_card_pname_o A_155)) (finite_card_pname_o ((insert_pname_o X_53) A_155))))) % FOF formula (forall (X_53:(x_a->Prop)) (A_155:((x_a->Prop)->Prop)), ((finite_finite_a_o A_155)->((ord_less_eq_nat (finite_card_a_o A_155)) (finite_card_a_o ((insert_a_o X_53) A_155))))) of role axiom named fact_90_card__insert__le % A new axiom: (forall (X_53:(x_a->Prop)) (A_155:((x_a->Prop)->Prop)), ((finite_finite_a_o A_155)->((ord_less_eq_nat (finite_card_a_o A_155)) (finite_card_a_o ((insert_a_o X_53) A_155))))) % FOF formula (forall (X_53:pname) (A_155:(pname->Prop)), ((finite_finite_pname A_155)->((ord_less_eq_nat (finite_card_pname A_155)) (finite_card_pname ((insert_pname X_53) A_155))))) of role axiom named fact_91_card__insert__le % A new axiom: (forall (X_53:pname) (A_155:(pname->Prop)), ((finite_finite_pname A_155)->((ord_less_eq_nat (finite_card_pname A_155)) (finite_card_pname ((insert_pname X_53) A_155))))) % FOF formula (forall (X_53:nat) (A_155:(nat->Prop)), ((finite_finite_nat A_155)->((ord_less_eq_nat (finite_card_nat A_155)) (finite_card_nat ((insert_nat X_53) A_155))))) of role axiom named fact_92_card__insert__le % A new axiom: (forall (X_53:nat) (A_155:(nat->Prop)), ((finite_finite_nat A_155)->((ord_less_eq_nat (finite_card_nat A_155)) (finite_card_nat ((insert_nat X_53) A_155))))) % FOF formula (forall (X_53:int) (A_155:(int->Prop)), ((finite_finite_int A_155)->((ord_less_eq_nat (finite_card_int A_155)) (finite_card_int ((insert_int X_53) A_155))))) of role axiom named fact_93_card__insert__le % A new axiom: (forall (X_53:int) (A_155:(int->Prop)), ((finite_finite_int A_155)->((ord_less_eq_nat (finite_card_int A_155)) (finite_card_int ((insert_int X_53) A_155))))) % FOF formula (forall (X_53:x_a) (A_155:(x_a->Prop)), ((finite_finite_a A_155)->((ord_less_eq_nat (finite_card_a A_155)) (finite_card_a ((insert_a X_53) A_155))))) of role axiom named fact_94_card__insert__le % A new axiom: (forall (X_53:x_a) (A_155:(x_a->Prop)), ((finite_finite_a A_155)->((ord_less_eq_nat (finite_card_a A_155)) (finite_card_a ((insert_a X_53) A_155))))) % FOF formula (forall (X_52:(int->Prop)) (A_154:((int->Prop)->Prop)), ((finite_finite_int_o A_154)->((and (((member_int_o X_52) A_154)->(((eq nat) (finite_card_int_o ((insert_int_o X_52) A_154))) (finite_card_int_o A_154)))) ((((member_int_o X_52) A_154)->False)->(((eq nat) (finite_card_int_o ((insert_int_o X_52) A_154))) (suc (finite_card_int_o A_154))))))) of role axiom named fact_95_card__insert__if % A new axiom: (forall (X_52:(int->Prop)) (A_154:((int->Prop)->Prop)), ((finite_finite_int_o A_154)->((and (((member_int_o X_52) A_154)->(((eq nat) (finite_card_int_o ((insert_int_o X_52) A_154))) (finite_card_int_o A_154)))) ((((member_int_o X_52) A_154)->False)->(((eq nat) (finite_card_int_o ((insert_int_o X_52) A_154))) (suc (finite_card_int_o A_154))))))) % FOF formula (forall (X_52:(nat->Prop)) (A_154:((nat->Prop)->Prop)), ((finite_finite_nat_o A_154)->((and (((member_nat_o X_52) A_154)->(((eq nat) (finite_card_nat_o ((insert_nat_o X_52) A_154))) (finite_card_nat_o A_154)))) ((((member_nat_o X_52) A_154)->False)->(((eq nat) (finite_card_nat_o ((insert_nat_o X_52) A_154))) (suc (finite_card_nat_o A_154))))))) of role axiom named fact_96_card__insert__if % A new axiom: (forall (X_52:(nat->Prop)) (A_154:((nat->Prop)->Prop)), ((finite_finite_nat_o A_154)->((and (((member_nat_o X_52) A_154)->(((eq nat) (finite_card_nat_o ((insert_nat_o X_52) A_154))) (finite_card_nat_o A_154)))) ((((member_nat_o X_52) A_154)->False)->(((eq nat) (finite_card_nat_o ((insert_nat_o X_52) A_154))) (suc (finite_card_nat_o A_154))))))) % FOF formula (forall (X_52:(pname->Prop)) (A_154:((pname->Prop)->Prop)), ((finite297249702name_o A_154)->((and (((member_pname_o X_52) A_154)->(((eq nat) (finite_card_pname_o ((insert_pname_o X_52) A_154))) (finite_card_pname_o A_154)))) ((((member_pname_o X_52) A_154)->False)->(((eq nat) (finite_card_pname_o ((insert_pname_o X_52) A_154))) (suc (finite_card_pname_o A_154))))))) of role axiom named fact_97_card__insert__if % A new axiom: (forall (X_52:(pname->Prop)) (A_154:((pname->Prop)->Prop)), ((finite297249702name_o A_154)->((and (((member_pname_o X_52) A_154)->(((eq nat) (finite_card_pname_o ((insert_pname_o X_52) A_154))) (finite_card_pname_o A_154)))) ((((member_pname_o X_52) A_154)->False)->(((eq nat) (finite_card_pname_o ((insert_pname_o X_52) A_154))) (suc (finite_card_pname_o A_154))))))) % FOF formula (forall (X_52:(x_a->Prop)) (A_154:((x_a->Prop)->Prop)), ((finite_finite_a_o A_154)->((and (((member_a_o X_52) A_154)->(((eq nat) (finite_card_a_o ((insert_a_o X_52) A_154))) (finite_card_a_o A_154)))) ((((member_a_o X_52) A_154)->False)->(((eq nat) (finite_card_a_o ((insert_a_o X_52) A_154))) (suc (finite_card_a_o A_154))))))) of role axiom named fact_98_card__insert__if % A new axiom: (forall (X_52:(x_a->Prop)) (A_154:((x_a->Prop)->Prop)), ((finite_finite_a_o A_154)->((and (((member_a_o X_52) A_154)->(((eq nat) (finite_card_a_o ((insert_a_o X_52) A_154))) (finite_card_a_o A_154)))) ((((member_a_o X_52) A_154)->False)->(((eq nat) (finite_card_a_o ((insert_a_o X_52) A_154))) (suc (finite_card_a_o A_154))))))) % FOF formula (forall (X_52:pname) (A_154:(pname->Prop)), ((finite_finite_pname A_154)->((and (((member_pname X_52) A_154)->(((eq nat) (finite_card_pname ((insert_pname X_52) A_154))) (finite_card_pname A_154)))) ((((member_pname X_52) A_154)->False)->(((eq nat) (finite_card_pname ((insert_pname X_52) A_154))) (suc (finite_card_pname A_154))))))) of role axiom named fact_99_card__insert__if % A new axiom: (forall (X_52:pname) (A_154:(pname->Prop)), ((finite_finite_pname A_154)->((and (((member_pname X_52) A_154)->(((eq nat) (finite_card_pname ((insert_pname X_52) A_154))) (finite_card_pname A_154)))) ((((member_pname X_52) A_154)->False)->(((eq nat) (finite_card_pname ((insert_pname X_52) A_154))) (suc (finite_card_pname A_154))))))) % FOF formula (forall (X_52:nat) (A_154:(nat->Prop)), ((finite_finite_nat A_154)->((and (((member_nat X_52) A_154)->(((eq nat) (finite_card_nat ((insert_nat X_52) A_154))) (finite_card_nat A_154)))) ((((member_nat X_52) A_154)->False)->(((eq nat) (finite_card_nat ((insert_nat X_52) A_154))) (suc (finite_card_nat A_154))))))) of role axiom named fact_100_card__insert__if % A new axiom: (forall (X_52:nat) (A_154:(nat->Prop)), ((finite_finite_nat A_154)->((and (((member_nat X_52) A_154)->(((eq nat) (finite_card_nat ((insert_nat X_52) A_154))) (finite_card_nat A_154)))) ((((member_nat X_52) A_154)->False)->(((eq nat) (finite_card_nat ((insert_nat X_52) A_154))) (suc (finite_card_nat A_154))))))) % FOF formula (forall (X_52:int) (A_154:(int->Prop)), ((finite_finite_int A_154)->((and (((member_int X_52) A_154)->(((eq nat) (finite_card_int ((insert_int X_52) A_154))) (finite_card_int A_154)))) ((((member_int X_52) A_154)->False)->(((eq nat) (finite_card_int ((insert_int X_52) A_154))) (suc (finite_card_int A_154))))))) of role axiom named fact_101_card__insert__if % A new axiom: (forall (X_52:int) (A_154:(int->Prop)), ((finite_finite_int A_154)->((and (((member_int X_52) A_154)->(((eq nat) (finite_card_int ((insert_int X_52) A_154))) (finite_card_int A_154)))) ((((member_int X_52) A_154)->False)->(((eq nat) (finite_card_int ((insert_int X_52) A_154))) (suc (finite_card_int A_154))))))) % FOF formula (forall (X_52:x_a) (A_154:(x_a->Prop)), ((finite_finite_a A_154)->((and (((member_a X_52) A_154)->(((eq nat) (finite_card_a ((insert_a X_52) A_154))) (finite_card_a A_154)))) ((((member_a X_52) A_154)->False)->(((eq nat) (finite_card_a ((insert_a X_52) A_154))) (suc (finite_card_a A_154))))))) of role axiom named fact_102_card__insert__if % A new axiom: (forall (X_52:x_a) (A_154:(x_a->Prop)), ((finite_finite_a A_154)->((and (((member_a X_52) A_154)->(((eq nat) (finite_card_a ((insert_a X_52) A_154))) (finite_card_a A_154)))) ((((member_a X_52) A_154)->False)->(((eq nat) (finite_card_a ((insert_a X_52) A_154))) (suc (finite_card_a A_154))))))) % FOF formula (forall (X_51:(int->Prop)) (A_153:((int->Prop)->Prop)), ((finite_finite_int_o A_153)->((((member_int_o X_51) A_153)->False)->(((eq nat) (finite_card_int_o ((insert_int_o X_51) A_153))) (suc (finite_card_int_o A_153)))))) of role axiom named fact_103_card__insert__disjoint % A new axiom: (forall (X_51:(int->Prop)) (A_153:((int->Prop)->Prop)), ((finite_finite_int_o A_153)->((((member_int_o X_51) A_153)->False)->(((eq nat) (finite_card_int_o ((insert_int_o X_51) A_153))) (suc (finite_card_int_o A_153)))))) % FOF formula (forall (X_51:(nat->Prop)) (A_153:((nat->Prop)->Prop)), ((finite_finite_nat_o A_153)->((((member_nat_o X_51) A_153)->False)->(((eq nat) (finite_card_nat_o ((insert_nat_o X_51) A_153))) (suc (finite_card_nat_o A_153)))))) of role axiom named fact_104_card__insert__disjoint % A new axiom: (forall (X_51:(nat->Prop)) (A_153:((nat->Prop)->Prop)), ((finite_finite_nat_o A_153)->((((member_nat_o X_51) A_153)->False)->(((eq nat) (finite_card_nat_o ((insert_nat_o X_51) A_153))) (suc (finite_card_nat_o A_153)))))) % FOF formula (forall (X_51:(pname->Prop)) (A_153:((pname->Prop)->Prop)), ((finite297249702name_o A_153)->((((member_pname_o X_51) A_153)->False)->(((eq nat) (finite_card_pname_o ((insert_pname_o X_51) A_153))) (suc (finite_card_pname_o A_153)))))) of role axiom named fact_105_card__insert__disjoint % A new axiom: (forall (X_51:(pname->Prop)) (A_153:((pname->Prop)->Prop)), ((finite297249702name_o A_153)->((((member_pname_o X_51) A_153)->False)->(((eq nat) (finite_card_pname_o ((insert_pname_o X_51) A_153))) (suc (finite_card_pname_o A_153)))))) % FOF formula (forall (X_51:(x_a->Prop)) (A_153:((x_a->Prop)->Prop)), ((finite_finite_a_o A_153)->((((member_a_o X_51) A_153)->False)->(((eq nat) (finite_card_a_o ((insert_a_o X_51) A_153))) (suc (finite_card_a_o A_153)))))) of role axiom named fact_106_card__insert__disjoint % A new axiom: (forall (X_51:(x_a->Prop)) (A_153:((x_a->Prop)->Prop)), ((finite_finite_a_o A_153)->((((member_a_o X_51) A_153)->False)->(((eq nat) (finite_card_a_o ((insert_a_o X_51) A_153))) (suc (finite_card_a_o A_153)))))) % FOF formula (forall (X_51:pname) (A_153:(pname->Prop)), ((finite_finite_pname A_153)->((((member_pname X_51) A_153)->False)->(((eq nat) (finite_card_pname ((insert_pname X_51) A_153))) (suc (finite_card_pname A_153)))))) of role axiom named fact_107_card__insert__disjoint % A new axiom: (forall (X_51:pname) (A_153:(pname->Prop)), ((finite_finite_pname A_153)->((((member_pname X_51) A_153)->False)->(((eq nat) (finite_card_pname ((insert_pname X_51) A_153))) (suc (finite_card_pname A_153)))))) % FOF formula (forall (X_51:nat) (A_153:(nat->Prop)), ((finite_finite_nat A_153)->((((member_nat X_51) A_153)->False)->(((eq nat) (finite_card_nat ((insert_nat X_51) A_153))) (suc (finite_card_nat A_153)))))) of role axiom named fact_108_card__insert__disjoint % A new axiom: (forall (X_51:nat) (A_153:(nat->Prop)), ((finite_finite_nat A_153)->((((member_nat X_51) A_153)->False)->(((eq nat) (finite_card_nat ((insert_nat X_51) A_153))) (suc (finite_card_nat A_153)))))) % FOF formula (forall (X_51:int) (A_153:(int->Prop)), ((finite_finite_int A_153)->((((member_int X_51) A_153)->False)->(((eq nat) (finite_card_int ((insert_int X_51) A_153))) (suc (finite_card_int A_153)))))) of role axiom named fact_109_card__insert__disjoint % A new axiom: (forall (X_51:int) (A_153:(int->Prop)), ((finite_finite_int A_153)->((((member_int X_51) A_153)->False)->(((eq nat) (finite_card_int ((insert_int X_51) A_153))) (suc (finite_card_int A_153)))))) % FOF formula (forall (X_51:x_a) (A_153:(x_a->Prop)), ((finite_finite_a A_153)->((((member_a X_51) A_153)->False)->(((eq nat) (finite_card_a ((insert_a X_51) A_153))) (suc (finite_card_a A_153)))))) of role axiom named fact_110_card__insert__disjoint % A new axiom: (forall (X_51:x_a) (A_153:(x_a->Prop)), ((finite_finite_a A_153)->((((member_a X_51) A_153)->False)->(((eq nat) (finite_card_a ((insert_a X_51) A_153))) (suc (finite_card_a A_153)))))) % FOF formula (forall (Q_3:(x_a->Prop)) (P_13:(x_a->Prop)), (((or (finite_finite_a (collect_a P_13))) (finite_finite_a (collect_a Q_3)))->(finite_finite_a (collect_a (fun (X_1:x_a)=> ((and (P_13 X_1)) (Q_3 X_1))))))) of role axiom named fact_111_finite__Collect__conjI % A new axiom: (forall (Q_3:(x_a->Prop)) (P_13:(x_a->Prop)), (((or (finite_finite_a (collect_a P_13))) (finite_finite_a (collect_a Q_3)))->(finite_finite_a (collect_a (fun (X_1:x_a)=> ((and (P_13 X_1)) (Q_3 X_1))))))) % FOF formula (forall (Q_3:((int->Prop)->Prop)) (P_13:((int->Prop)->Prop)), (((or (finite_finite_int_o (collect_int_o P_13))) (finite_finite_int_o (collect_int_o Q_3)))->(finite_finite_int_o (collect_int_o (fun (X_1:(int->Prop))=> ((and (P_13 X_1)) (Q_3 X_1))))))) of role axiom named fact_112_finite__Collect__conjI % A new axiom: (forall (Q_3:((int->Prop)->Prop)) (P_13:((int->Prop)->Prop)), (((or (finite_finite_int_o (collect_int_o P_13))) (finite_finite_int_o (collect_int_o Q_3)))->(finite_finite_int_o (collect_int_o (fun (X_1:(int->Prop))=> ((and (P_13 X_1)) (Q_3 X_1))))))) % FOF formula (forall (Q_3:((nat->Prop)->Prop)) (P_13:((nat->Prop)->Prop)), (((or (finite_finite_nat_o (collect_nat_o P_13))) (finite_finite_nat_o (collect_nat_o Q_3)))->(finite_finite_nat_o (collect_nat_o (fun (X_1:(nat->Prop))=> ((and (P_13 X_1)) (Q_3 X_1))))))) of role axiom named fact_113_finite__Collect__conjI % A new axiom: (forall (Q_3:((nat->Prop)->Prop)) (P_13:((nat->Prop)->Prop)), (((or (finite_finite_nat_o (collect_nat_o P_13))) (finite_finite_nat_o (collect_nat_o Q_3)))->(finite_finite_nat_o (collect_nat_o (fun (X_1:(nat->Prop))=> ((and (P_13 X_1)) (Q_3 X_1))))))) % FOF formula (forall (Q_3:((pname->Prop)->Prop)) (P_13:((pname->Prop)->Prop)), (((or (finite297249702name_o (collect_pname_o P_13))) (finite297249702name_o (collect_pname_o Q_3)))->(finite297249702name_o (collect_pname_o (fun (X_1:(pname->Prop))=> ((and (P_13 X_1)) (Q_3 X_1))))))) of role axiom named fact_114_finite__Collect__conjI % A new axiom: (forall (Q_3:((pname->Prop)->Prop)) (P_13:((pname->Prop)->Prop)), (((or (finite297249702name_o (collect_pname_o P_13))) (finite297249702name_o (collect_pname_o Q_3)))->(finite297249702name_o (collect_pname_o (fun (X_1:(pname->Prop))=> ((and (P_13 X_1)) (Q_3 X_1))))))) % FOF formula (forall (Q_3:((x_a->Prop)->Prop)) (P_13:((x_a->Prop)->Prop)), (((or (finite_finite_a_o (collect_a_o P_13))) (finite_finite_a_o (collect_a_o Q_3)))->(finite_finite_a_o (collect_a_o (fun (X_1:(x_a->Prop))=> ((and (P_13 X_1)) (Q_3 X_1))))))) of role axiom named fact_115_finite__Collect__conjI % A new axiom: (forall (Q_3:((x_a->Prop)->Prop)) (P_13:((x_a->Prop)->Prop)), (((or (finite_finite_a_o (collect_a_o P_13))) (finite_finite_a_o (collect_a_o Q_3)))->(finite_finite_a_o (collect_a_o (fun (X_1:(x_a->Prop))=> ((and (P_13 X_1)) (Q_3 X_1))))))) % FOF formula (forall (Q_3:(pname->Prop)) (P_13:(pname->Prop)), (((or (finite_finite_pname (collect_pname P_13))) (finite_finite_pname (collect_pname Q_3)))->(finite_finite_pname (collect_pname (fun (X_1:pname)=> ((and (P_13 X_1)) (Q_3 X_1))))))) of role axiom named fact_116_finite__Collect__conjI % A new axiom: (forall (Q_3:(pname->Prop)) (P_13:(pname->Prop)), (((or (finite_finite_pname (collect_pname P_13))) (finite_finite_pname (collect_pname Q_3)))->(finite_finite_pname (collect_pname (fun (X_1:pname)=> ((and (P_13 X_1)) (Q_3 X_1))))))) % FOF formula (forall (Q_3:(nat->Prop)) (P_13:(nat->Prop)), (((or (finite_finite_nat (collect_nat P_13))) (finite_finite_nat (collect_nat Q_3)))->(finite_finite_nat (collect_nat (fun (X_1:nat)=> ((and (P_13 X_1)) (Q_3 X_1))))))) of role axiom named fact_117_finite__Collect__conjI % A new axiom: (forall (Q_3:(nat->Prop)) (P_13:(nat->Prop)), (((or (finite_finite_nat (collect_nat P_13))) (finite_finite_nat (collect_nat Q_3)))->(finite_finite_nat (collect_nat (fun (X_1:nat)=> ((and (P_13 X_1)) (Q_3 X_1))))))) % FOF formula (forall (Q_3:(int->Prop)) (P_13:(int->Prop)), (((or (finite_finite_int (collect_int P_13))) (finite_finite_int (collect_int Q_3)))->(finite_finite_int (collect_int (fun (X_1:int)=> ((and (P_13 X_1)) (Q_3 X_1))))))) of role axiom named fact_118_finite__Collect__conjI % A new axiom: (forall (Q_3:(int->Prop)) (P_13:(int->Prop)), (((or (finite_finite_int (collect_int P_13))) (finite_finite_int (collect_int Q_3)))->(finite_finite_int (collect_int (fun (X_1:int)=> ((and (P_13 X_1)) (Q_3 X_1))))))) % FOF formula (forall (N:nat) (M:nat), (((ord_less_eq_nat N) M)->(((eq nat) ((minus_minus_nat (suc M)) N)) (suc ((minus_minus_nat M) N))))) of role axiom named fact_119_Suc__diff__le % A new axiom: (forall (N:nat) (M:nat), (((ord_less_eq_nat N) M)->(((eq nat) ((minus_minus_nat (suc M)) N)) (suc ((minus_minus_nat M) N))))) % FOF formula (forall (K:nat), (finite_finite_nat (collect_nat (fun (N_1:nat)=> ((ord_less_eq_nat N_1) K))))) of role axiom named fact_120_finite__Collect__le__nat % A new axiom: (forall (K:nat), (finite_finite_nat (collect_nat (fun (N_1:nat)=> ((ord_less_eq_nat N_1) K))))) % FOF formula (forall (N:nat), (((eq nat) (finite_card_nat (collect_nat (fun (_TPTP_I:nat)=> ((ord_less_eq_nat _TPTP_I) N))))) (suc N))) of role axiom named fact_121_card__Collect__le__nat % A new axiom: (forall (N:nat), (((eq nat) (finite_card_nat (collect_nat (fun (_TPTP_I:nat)=> ((ord_less_eq_nat _TPTP_I) N))))) (suc N))) % FOF formula (forall (X:nat) (Y:nat), ((((eq nat) (suc X)) (suc Y))->(((eq nat) X) Y))) of role axiom named fact_122_Suc__inject % A new axiom: (forall (X:nat) (Y:nat), ((((eq nat) (suc X)) (suc Y))->(((eq nat) X) Y))) % FOF formula (forall (Nat_4:nat) (Nat_1:nat), ((iff (((eq nat) (suc Nat_4)) (suc Nat_1))) (((eq nat) Nat_4) Nat_1))) of role axiom named fact_123_nat_Oinject % A new axiom: (forall (Nat_4:nat) (Nat_1:nat), ((iff (((eq nat) (suc Nat_4)) (suc Nat_1))) (((eq nat) Nat_4) Nat_1))) % FOF formula (forall (N:nat), (not (((eq nat) (suc N)) N))) of role axiom named fact_124_Suc__n__not__n % A new axiom: (forall (N:nat), (not (((eq nat) (suc N)) N))) % FOF formula (forall (N:nat), (not (((eq nat) N) (suc N)))) of role axiom named fact_125_n__not__Suc__n % A new axiom: (forall (N:nat), (not (((eq nat) N) (suc N)))) % 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_126_le__antisym % A new axiom: (forall (M:nat) (N:nat), (((ord_less_eq_nat M) N)->(((ord_less_eq_nat N) M)->(((eq nat) M) N)))) % FOF formula (forall (K:nat) (I_1:nat) (J:nat), (((ord_less_eq_nat I_1) J)->(((ord_less_eq_nat J) K)->((ord_less_eq_nat I_1) K)))) of role axiom named fact_127_le__trans % A new axiom: (forall (K:nat) (I_1:nat) (J:nat), (((ord_less_eq_nat I_1) J)->(((ord_less_eq_nat J) K)->((ord_less_eq_nat I_1) K)))) % FOF formula (forall (M:nat) (N:nat), ((((eq nat) M) N)->((ord_less_eq_nat M) N))) of role axiom named fact_128_eq__imp__le % A new axiom: (forall (M:nat) (N:nat), ((((eq nat) M) N)->((ord_less_eq_nat M) N))) % 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_129_nat__le__linear % A new axiom: (forall (M:nat) (N:nat), ((or ((ord_less_eq_nat M) N)) ((ord_less_eq_nat N) M))) % FOF formula (forall (N:nat), ((ord_less_eq_nat N) N)) of role axiom named fact_130_le__refl % A new axiom: (forall (N:nat), ((ord_less_eq_nat N) N)) % FOF formula (forall (I_1:nat) (J:nat) (K:nat), (((eq nat) ((minus_minus_nat ((minus_minus_nat I_1) J)) K)) ((minus_minus_nat ((minus_minus_nat I_1) K)) J))) of role axiom named fact_131_diff__commute % A new axiom: (forall (I_1:nat) (J:nat) (K:nat), (((eq nat) ((minus_minus_nat ((minus_minus_nat I_1) J)) K)) ((minus_minus_nat ((minus_minus_nat I_1) K)) J))) % FOF formula (forall (P_12:(x_a->Prop)) (Q_2:(x_a->Prop)), ((iff (finite_finite_a (collect_a (fun (X_1:x_a)=> ((or (P_12 X_1)) (Q_2 X_1)))))) ((and (finite_finite_a (collect_a P_12))) (finite_finite_a (collect_a Q_2))))) of role axiom named fact_132_finite__Collect__disjI % A new axiom: (forall (P_12:(x_a->Prop)) (Q_2:(x_a->Prop)), ((iff (finite_finite_a (collect_a (fun (X_1:x_a)=> ((or (P_12 X_1)) (Q_2 X_1)))))) ((and (finite_finite_a (collect_a P_12))) (finite_finite_a (collect_a Q_2))))) % FOF formula (forall (P_12:((int->Prop)->Prop)) (Q_2:((int->Prop)->Prop)), ((iff (finite_finite_int_o (collect_int_o (fun (X_1:(int->Prop))=> ((or (P_12 X_1)) (Q_2 X_1)))))) ((and (finite_finite_int_o (collect_int_o P_12))) (finite_finite_int_o (collect_int_o Q_2))))) of role axiom named fact_133_finite__Collect__disjI % A new axiom: (forall (P_12:((int->Prop)->Prop)) (Q_2:((int->Prop)->Prop)), ((iff (finite_finite_int_o (collect_int_o (fun (X_1:(int->Prop))=> ((or (P_12 X_1)) (Q_2 X_1)))))) ((and (finite_finite_int_o (collect_int_o P_12))) (finite_finite_int_o (collect_int_o Q_2))))) % FOF formula (forall (P_12:((nat->Prop)->Prop)) (Q_2:((nat->Prop)->Prop)), ((iff (finite_finite_nat_o (collect_nat_o (fun (X_1:(nat->Prop))=> ((or (P_12 X_1)) (Q_2 X_1)))))) ((and (finite_finite_nat_o (collect_nat_o P_12))) (finite_finite_nat_o (collect_nat_o Q_2))))) of role axiom named fact_134_finite__Collect__disjI % A new axiom: (forall (P_12:((nat->Prop)->Prop)) (Q_2:((nat->Prop)->Prop)), ((iff (finite_finite_nat_o (collect_nat_o (fun (X_1:(nat->Prop))=> ((or (P_12 X_1)) (Q_2 X_1)))))) ((and (finite_finite_nat_o (collect_nat_o P_12))) (finite_finite_nat_o (collect_nat_o Q_2))))) % FOF formula (forall (P_12:((pname->Prop)->Prop)) (Q_2:((pname->Prop)->Prop)), ((iff (finite297249702name_o (collect_pname_o (fun (X_1:(pname->Prop))=> ((or (P_12 X_1)) (Q_2 X_1)))))) ((and (finite297249702name_o (collect_pname_o P_12))) (finite297249702name_o (collect_pname_o Q_2))))) of role axiom named fact_135_finite__Collect__disjI % A new axiom: (forall (P_12:((pname->Prop)->Prop)) (Q_2:((pname->Prop)->Prop)), ((iff (finite297249702name_o (collect_pname_o (fun (X_1:(pname->Prop))=> ((or (P_12 X_1)) (Q_2 X_1)))))) ((and (finite297249702name_o (collect_pname_o P_12))) (finite297249702name_o (collect_pname_o Q_2))))) % FOF formula (forall (P_12:((x_a->Prop)->Prop)) (Q_2:((x_a->Prop)->Prop)), ((iff (finite_finite_a_o (collect_a_o (fun (X_1:(x_a->Prop))=> ((or (P_12 X_1)) (Q_2 X_1)))))) ((and (finite_finite_a_o (collect_a_o P_12))) (finite_finite_a_o (collect_a_o Q_2))))) of role axiom named fact_136_finite__Collect__disjI % A new axiom: (forall (P_12:((x_a->Prop)->Prop)) (Q_2:((x_a->Prop)->Prop)), ((iff (finite_finite_a_o (collect_a_o (fun (X_1:(x_a->Prop))=> ((or (P_12 X_1)) (Q_2 X_1)))))) ((and (finite_finite_a_o (collect_a_o P_12))) (finite_finite_a_o (collect_a_o Q_2))))) % FOF formula (forall (P_12:(pname->Prop)) (Q_2:(pname->Prop)), ((iff (finite_finite_pname (collect_pname (fun (X_1:pname)=> ((or (P_12 X_1)) (Q_2 X_1)))))) ((and (finite_finite_pname (collect_pname P_12))) (finite_finite_pname (collect_pname Q_2))))) of role axiom named fact_137_finite__Collect__disjI % A new axiom: (forall (P_12:(pname->Prop)) (Q_2:(pname->Prop)), ((iff (finite_finite_pname (collect_pname (fun (X_1:pname)=> ((or (P_12 X_1)) (Q_2 X_1)))))) ((and (finite_finite_pname (collect_pname P_12))) (finite_finite_pname (collect_pname Q_2))))) % FOF formula (forall (P_12:(nat->Prop)) (Q_2:(nat->Prop)), ((iff (finite_finite_nat (collect_nat (fun (X_1:nat)=> ((or (P_12 X_1)) (Q_2 X_1)))))) ((and (finite_finite_nat (collect_nat P_12))) (finite_finite_nat (collect_nat Q_2))))) of role axiom named fact_138_finite__Collect__disjI % A new axiom: (forall (P_12:(nat->Prop)) (Q_2:(nat->Prop)), ((iff (finite_finite_nat (collect_nat (fun (X_1:nat)=> ((or (P_12 X_1)) (Q_2 X_1)))))) ((and (finite_finite_nat (collect_nat P_12))) (finite_finite_nat (collect_nat Q_2))))) % FOF formula (forall (P_12:(int->Prop)) (Q_2:(int->Prop)), ((iff (finite_finite_int (collect_int (fun (X_1:int)=> ((or (P_12 X_1)) (Q_2 X_1)))))) ((and (finite_finite_int (collect_int P_12))) (finite_finite_int (collect_int Q_2))))) of role axiom named fact_139_finite__Collect__disjI % A new axiom: (forall (P_12:(int->Prop)) (Q_2:(int->Prop)), ((iff (finite_finite_int (collect_int (fun (X_1:int)=> ((or (P_12 X_1)) (Q_2 X_1)))))) ((and (finite_finite_int (collect_int P_12))) (finite_finite_int (collect_int Q_2))))) % FOF formula (forall (A_152:(int->Prop)) (A_151:((int->Prop)->Prop)), ((iff (finite_finite_int_o ((insert_int_o A_152) A_151))) (finite_finite_int_o A_151))) of role axiom named fact_140_finite__insert % A new axiom: (forall (A_152:(int->Prop)) (A_151:((int->Prop)->Prop)), ((iff (finite_finite_int_o ((insert_int_o A_152) A_151))) (finite_finite_int_o A_151))) % FOF formula (forall (A_152:(nat->Prop)) (A_151:((nat->Prop)->Prop)), ((iff (finite_finite_nat_o ((insert_nat_o A_152) A_151))) (finite_finite_nat_o A_151))) of role axiom named fact_141_finite__insert % A new axiom: (forall (A_152:(nat->Prop)) (A_151:((nat->Prop)->Prop)), ((iff (finite_finite_nat_o ((insert_nat_o A_152) A_151))) (finite_finite_nat_o A_151))) % FOF formula (forall (A_152:(pname->Prop)) (A_151:((pname->Prop)->Prop)), ((iff (finite297249702name_o ((insert_pname_o A_152) A_151))) (finite297249702name_o A_151))) of role axiom named fact_142_finite__insert % A new axiom: (forall (A_152:(pname->Prop)) (A_151:((pname->Prop)->Prop)), ((iff (finite297249702name_o ((insert_pname_o A_152) A_151))) (finite297249702name_o A_151))) % FOF formula (forall (A_152:(x_a->Prop)) (A_151:((x_a->Prop)->Prop)), ((iff (finite_finite_a_o ((insert_a_o A_152) A_151))) (finite_finite_a_o A_151))) of role axiom named fact_143_finite__insert % A new axiom: (forall (A_152:(x_a->Prop)) (A_151:((x_a->Prop)->Prop)), ((iff (finite_finite_a_o ((insert_a_o A_152) A_151))) (finite_finite_a_o A_151))) % FOF formula (forall (A_152:pname) (A_151:(pname->Prop)), ((iff (finite_finite_pname ((insert_pname A_152) A_151))) (finite_finite_pname A_151))) of role axiom named fact_144_finite__insert % A new axiom: (forall (A_152:pname) (A_151:(pname->Prop)), ((iff (finite_finite_pname ((insert_pname A_152) A_151))) (finite_finite_pname A_151))) % FOF formula (forall (A_152:nat) (A_151:(nat->Prop)), ((iff (finite_finite_nat ((insert_nat A_152) A_151))) (finite_finite_nat A_151))) of role axiom named fact_145_finite__insert % A new axiom: (forall (A_152:nat) (A_151:(nat->Prop)), ((iff (finite_finite_nat ((insert_nat A_152) A_151))) (finite_finite_nat A_151))) % FOF formula (forall (A_152:int) (A_151:(int->Prop)), ((iff (finite_finite_int ((insert_int A_152) A_151))) (finite_finite_int A_151))) of role axiom named fact_146_finite__insert % A new axiom: (forall (A_152:int) (A_151:(int->Prop)), ((iff (finite_finite_int ((insert_int A_152) A_151))) (finite_finite_int A_151))) % FOF formula (forall (A_152:x_a) (A_151:(x_a->Prop)), ((iff (finite_finite_a ((insert_a A_152) A_151))) (finite_finite_a A_151))) of role axiom named fact_147_finite__insert % A new axiom: (forall (A_152:x_a) (A_151:(x_a->Prop)), ((iff (finite_finite_a ((insert_a A_152) A_151))) (finite_finite_a A_151))) % FOF formula (forall (A_150:((int->Prop)->Prop)) (B_87:((int->Prop)->Prop)), (((ord_less_eq_int_o_o A_150) B_87)->((finite_finite_int_o B_87)->(finite_finite_int_o A_150)))) of role axiom named fact_148_finite__subset % A new axiom: (forall (A_150:((int->Prop)->Prop)) (B_87:((int->Prop)->Prop)), (((ord_less_eq_int_o_o A_150) B_87)->((finite_finite_int_o B_87)->(finite_finite_int_o A_150)))) % FOF formula (forall (A_150:((nat->Prop)->Prop)) (B_87:((nat->Prop)->Prop)), (((ord_less_eq_nat_o_o A_150) B_87)->((finite_finite_nat_o B_87)->(finite_finite_nat_o A_150)))) of role axiom named fact_149_finite__subset % A new axiom: (forall (A_150:((nat->Prop)->Prop)) (B_87:((nat->Prop)->Prop)), (((ord_less_eq_nat_o_o A_150) B_87)->((finite_finite_nat_o B_87)->(finite_finite_nat_o A_150)))) % FOF formula (forall (A_150:((pname->Prop)->Prop)) (B_87:((pname->Prop)->Prop)), (((ord_le1205211808me_o_o A_150) B_87)->((finite297249702name_o B_87)->(finite297249702name_o A_150)))) of role axiom named fact_150_finite__subset % A new axiom: (forall (A_150:((pname->Prop)->Prop)) (B_87:((pname->Prop)->Prop)), (((ord_le1205211808me_o_o A_150) B_87)->((finite297249702name_o B_87)->(finite297249702name_o A_150)))) % FOF formula (forall (A_150:((x_a->Prop)->Prop)) (B_87:((x_a->Prop)->Prop)), (((ord_less_eq_a_o_o A_150) B_87)->((finite_finite_a_o B_87)->(finite_finite_a_o A_150)))) of role axiom named fact_151_finite__subset % A new axiom: (forall (A_150:((x_a->Prop)->Prop)) (B_87:((x_a->Prop)->Prop)), (((ord_less_eq_a_o_o A_150) B_87)->((finite_finite_a_o B_87)->(finite_finite_a_o A_150)))) % FOF formula (forall (A_150:(x_a->Prop)) (B_87:(x_a->Prop)), (((ord_less_eq_a_o A_150) B_87)->((finite_finite_a B_87)->(finite_finite_a A_150)))) of role axiom named fact_152_finite__subset % A new axiom: (forall (A_150:(x_a->Prop)) (B_87:(x_a->Prop)), (((ord_less_eq_a_o A_150) B_87)->((finite_finite_a B_87)->(finite_finite_a A_150)))) % FOF formula (forall (A_150:(pname->Prop)) (B_87:(pname->Prop)), (((ord_less_eq_pname_o A_150) B_87)->((finite_finite_pname B_87)->(finite_finite_pname A_150)))) of role axiom named fact_153_finite__subset % A new axiom: (forall (A_150:(pname->Prop)) (B_87:(pname->Prop)), (((ord_less_eq_pname_o A_150) B_87)->((finite_finite_pname B_87)->(finite_finite_pname A_150)))) % FOF formula (forall (A_150:(nat->Prop)) (B_87:(nat->Prop)), (((ord_less_eq_nat_o A_150) B_87)->((finite_finite_nat B_87)->(finite_finite_nat A_150)))) of role axiom named fact_154_finite__subset % A new axiom: (forall (A_150:(nat->Prop)) (B_87:(nat->Prop)), (((ord_less_eq_nat_o A_150) B_87)->((finite_finite_nat B_87)->(finite_finite_nat A_150)))) % FOF formula (forall (A_150:(int->Prop)) (B_87:(int->Prop)), (((ord_less_eq_int_o A_150) B_87)->((finite_finite_int B_87)->(finite_finite_int A_150)))) of role axiom named fact_155_finite__subset % A new axiom: (forall (A_150:(int->Prop)) (B_87:(int->Prop)), (((ord_less_eq_int_o A_150) B_87)->((finite_finite_int B_87)->(finite_finite_int A_150)))) % FOF formula (forall (A_149:((int->Prop)->Prop)) (B_86:((int->Prop)->Prop)), ((finite_finite_int_o B_86)->(((ord_less_eq_int_o_o A_149) B_86)->(finite_finite_int_o A_149)))) of role axiom named fact_156_rev__finite__subset % A new axiom: (forall (A_149:((int->Prop)->Prop)) (B_86:((int->Prop)->Prop)), ((finite_finite_int_o B_86)->(((ord_less_eq_int_o_o A_149) B_86)->(finite_finite_int_o A_149)))) % FOF formula (forall (A_149:((nat->Prop)->Prop)) (B_86:((nat->Prop)->Prop)), ((finite_finite_nat_o B_86)->(((ord_less_eq_nat_o_o A_149) B_86)->(finite_finite_nat_o A_149)))) of role axiom named fact_157_rev__finite__subset % A new axiom: (forall (A_149:((nat->Prop)->Prop)) (B_86:((nat->Prop)->Prop)), ((finite_finite_nat_o B_86)->(((ord_less_eq_nat_o_o A_149) B_86)->(finite_finite_nat_o A_149)))) % FOF formula (forall (A_149:((pname->Prop)->Prop)) (B_86:((pname->Prop)->Prop)), ((finite297249702name_o B_86)->(((ord_le1205211808me_o_o A_149) B_86)->(finite297249702name_o A_149)))) of role axiom named fact_158_rev__finite__subset % A new axiom: (forall (A_149:((pname->Prop)->Prop)) (B_86:((pname->Prop)->Prop)), ((finite297249702name_o B_86)->(((ord_le1205211808me_o_o A_149) B_86)->(finite297249702name_o A_149)))) % FOF formula (forall (A_149:((x_a->Prop)->Prop)) (B_86:((x_a->Prop)->Prop)), ((finite_finite_a_o B_86)->(((ord_less_eq_a_o_o A_149) B_86)->(finite_finite_a_o A_149)))) of role axiom named fact_159_rev__finite__subset % A new axiom: (forall (A_149:((x_a->Prop)->Prop)) (B_86:((x_a->Prop)->Prop)), ((finite_finite_a_o B_86)->(((ord_less_eq_a_o_o A_149) B_86)->(finite_finite_a_o A_149)))) % FOF formula (forall (A_149:(x_a->Prop)) (B_86:(x_a->Prop)), ((finite_finite_a B_86)->(((ord_less_eq_a_o A_149) B_86)->(finite_finite_a A_149)))) of role axiom named fact_160_rev__finite__subset % A new axiom: (forall (A_149:(x_a->Prop)) (B_86:(x_a->Prop)), ((finite_finite_a B_86)->(((ord_less_eq_a_o A_149) B_86)->(finite_finite_a A_149)))) % FOF formula (forall (A_149:(pname->Prop)) (B_86:(pname->Prop)), ((finite_finite_pname B_86)->(((ord_less_eq_pname_o A_149) B_86)->(finite_finite_pname A_149)))) of role axiom named fact_161_rev__finite__subset % A new axiom: (forall (A_149:(pname->Prop)) (B_86:(pname->Prop)), ((finite_finite_pname B_86)->(((ord_less_eq_pname_o A_149) B_86)->(finite_finite_pname A_149)))) % FOF formula (forall (A_149:(nat->Prop)) (B_86:(nat->Prop)), ((finite_finite_nat B_86)->(((ord_less_eq_nat_o A_149) B_86)->(finite_finite_nat A_149)))) of role axiom named fact_162_rev__finite__subset % A new axiom: (forall (A_149:(nat->Prop)) (B_86:(nat->Prop)), ((finite_finite_nat B_86)->(((ord_less_eq_nat_o A_149) B_86)->(finite_finite_nat A_149)))) % FOF formula (forall (A_149:(int->Prop)) (B_86:(int->Prop)), ((finite_finite_int B_86)->(((ord_less_eq_int_o A_149) B_86)->(finite_finite_int A_149)))) of role axiom named fact_163_rev__finite__subset % A new axiom: (forall (A_149:(int->Prop)) (B_86:(int->Prop)), ((finite_finite_int B_86)->(((ord_less_eq_int_o A_149) B_86)->(finite_finite_int A_149)))) % FOF formula (forall (M:nat) (N:nat), (((ord_less_eq_nat (suc M)) N)->((ord_less_eq_nat M) N))) of role axiom named fact_164_Suc__leD % A new axiom: (forall (M:nat) (N:nat), (((ord_less_eq_nat (suc M)) N)->((ord_less_eq_nat M) N))) % FOF formula (forall (M:nat) (N:nat), (((ord_less_eq_nat M) (suc N))->((((ord_less_eq_nat M) N)->False)->(((eq nat) M) (suc N))))) of role axiom named fact_165_le__SucE % A new axiom: (forall (M:nat) (N:nat), (((ord_less_eq_nat M) (suc N))->((((ord_less_eq_nat M) N)->False)->(((eq nat) M) (suc N))))) % FOF formula (forall (M:nat) (N:nat), (((ord_less_eq_nat M) N)->((ord_less_eq_nat M) (suc N)))) of role axiom named fact_166_le__SucI % A new axiom: (forall (M:nat) (N:nat), (((ord_less_eq_nat M) N)->((ord_less_eq_nat M) (suc N)))) % FOF formula (forall (N:nat) (M:nat), ((iff ((ord_less_eq_nat (suc N)) (suc M))) ((ord_less_eq_nat N) M))) of role axiom named fact_167_Suc__le__mono % A new axiom: (forall (N:nat) (M:nat), ((iff ((ord_less_eq_nat (suc N)) (suc M))) ((ord_less_eq_nat N) M))) % FOF formula (forall (M:nat) (N:nat), ((iff ((ord_less_eq_nat M) (suc N))) ((or ((ord_less_eq_nat M) N)) (((eq nat) M) (suc N))))) of role axiom named fact_168_le__Suc__eq % A new axiom: (forall (M:nat) (N:nat), ((iff ((ord_less_eq_nat M) (suc N))) ((or ((ord_less_eq_nat M) N)) (((eq nat) M) (suc N))))) % FOF formula (forall (M:nat) (N:nat), ((iff (((ord_less_eq_nat M) N)->False)) ((ord_less_eq_nat (suc N)) M))) of role axiom named fact_169_not__less__eq__eq % A new axiom: (forall (M:nat) (N:nat), ((iff (((ord_less_eq_nat M) N)->False)) ((ord_less_eq_nat (suc N)) M))) % FOF formula (forall (N:nat), (((ord_less_eq_nat (suc N)) N)->False)) of role axiom named fact_170_Suc__n__not__le__n % A new axiom: (forall (N:nat), (((ord_less_eq_nat (suc N)) N)->False)) % FOF formula (forall (M:nat) (N:nat) (K:nat), (((eq nat) ((minus_minus_nat ((minus_minus_nat (suc M)) N)) (suc K))) ((minus_minus_nat ((minus_minus_nat M) N)) K))) of role axiom named fact_171_Suc__diff__diff % A new axiom: (forall (M:nat) (N:nat) (K:nat), (((eq nat) ((minus_minus_nat ((minus_minus_nat (suc M)) N)) (suc K))) ((minus_minus_nat ((minus_minus_nat M) N)) K))) % FOF formula (forall (M:nat) (N:nat), (((eq nat) ((minus_minus_nat (suc M)) (suc N))) ((minus_minus_nat M) N))) of role axiom named fact_172_diff__Suc__Suc % A new axiom: (forall (M:nat) (N:nat), (((eq nat) ((minus_minus_nat (suc M)) (suc N))) ((minus_minus_nat M) N))) % FOF formula (forall (N:nat) (K:nat) (M:nat), (((ord_less_eq_nat K) M)->(((ord_less_eq_nat K) N)->((iff ((ord_less_eq_nat ((minus_minus_nat M) K)) ((minus_minus_nat N) K))) ((ord_less_eq_nat M) N))))) of role axiom named fact_173_le__diff__iff % A new axiom: (forall (N:nat) (K:nat) (M:nat), (((ord_less_eq_nat K) M)->(((ord_less_eq_nat K) N)->((iff ((ord_less_eq_nat ((minus_minus_nat M) K)) ((minus_minus_nat N) K))) ((ord_less_eq_nat M) N))))) % FOF formula (forall (N:nat) (K:nat) (M:nat), (((ord_less_eq_nat K) M)->(((ord_less_eq_nat K) N)->(((eq nat) ((minus_minus_nat ((minus_minus_nat M) K)) ((minus_minus_nat N) K))) ((minus_minus_nat M) N))))) of role axiom named fact_174_Nat_Odiff__diff__eq % A new axiom: (forall (N:nat) (K:nat) (M:nat), (((ord_less_eq_nat K) M)->(((ord_less_eq_nat K) N)->(((eq nat) ((minus_minus_nat ((minus_minus_nat M) K)) ((minus_minus_nat N) K))) ((minus_minus_nat M) N))))) % FOF formula (forall (N:nat) (K:nat) (M:nat), (((ord_less_eq_nat K) M)->(((ord_less_eq_nat K) N)->((iff (((eq nat) ((minus_minus_nat M) K)) ((minus_minus_nat N) K))) (((eq nat) M) N))))) of role axiom named fact_175_eq__diff__iff % A new axiom: (forall (N:nat) (K:nat) (M:nat), (((ord_less_eq_nat K) M)->(((ord_less_eq_nat K) N)->((iff (((eq nat) ((minus_minus_nat M) K)) ((minus_minus_nat N) K))) (((eq nat) M) N))))) % FOF formula (forall (I_1:nat) (N:nat), (((ord_less_eq_nat I_1) N)->(((eq nat) ((minus_minus_nat N) ((minus_minus_nat N) I_1))) I_1))) of role axiom named fact_176_diff__diff__cancel % A new axiom: (forall (I_1:nat) (N:nat), (((ord_less_eq_nat I_1) N)->(((eq nat) ((minus_minus_nat N) ((minus_minus_nat N) I_1))) I_1))) % FOF formula (forall (L:nat) (M:nat) (N:nat), (((ord_less_eq_nat M) N)->((ord_less_eq_nat ((minus_minus_nat M) L)) ((minus_minus_nat N) L)))) of role axiom named fact_177_diff__le__mono % A new axiom: (forall (L:nat) (M:nat) (N:nat), (((ord_less_eq_nat M) N)->((ord_less_eq_nat ((minus_minus_nat M) L)) ((minus_minus_nat N) L)))) % FOF formula (forall (L:nat) (M:nat) (N:nat), (((ord_less_eq_nat M) N)->((ord_less_eq_nat ((minus_minus_nat L) N)) ((minus_minus_nat L) M)))) of role axiom named fact_178_diff__le__mono2 % A new axiom: (forall (L:nat) (M:nat) (N:nat), (((ord_less_eq_nat M) N)->((ord_less_eq_nat ((minus_minus_nat L) N)) ((minus_minus_nat L) M)))) % FOF formula (forall (M:nat) (N:nat), ((ord_less_eq_nat ((minus_minus_nat M) N)) M)) of role axiom named fact_179_diff__le__self % A new axiom: (forall (M:nat) (N:nat), ((ord_less_eq_nat ((minus_minus_nat M) N)) M)) % FOF formula (forall (B_85:(x_a->Prop)) (F_40:(x_a->x_a)) (A_148:(x_a->Prop)), ((finite_finite_a A_148)->(((ord_less_eq_a_o B_85) ((image_a_a F_40) A_148))->(finite_finite_a B_85)))) of role axiom named fact_180_finite__surj % A new axiom: (forall (B_85:(x_a->Prop)) (F_40:(x_a->x_a)) (A_148:(x_a->Prop)), ((finite_finite_a A_148)->(((ord_less_eq_a_o B_85) ((image_a_a F_40) A_148))->(finite_finite_a B_85)))) % FOF formula (forall (B_85:(x_a->Prop)) (F_40:((int->Prop)->x_a)) (A_148:((int->Prop)->Prop)), ((finite_finite_int_o A_148)->(((ord_less_eq_a_o B_85) ((image_int_o_a F_40) A_148))->(finite_finite_a B_85)))) of role axiom named fact_181_finite__surj % A new axiom: (forall (B_85:(x_a->Prop)) (F_40:((int->Prop)->x_a)) (A_148:((int->Prop)->Prop)), ((finite_finite_int_o A_148)->(((ord_less_eq_a_o B_85) ((image_int_o_a F_40) A_148))->(finite_finite_a B_85)))) % FOF formula (forall (B_85:(x_a->Prop)) (F_40:((nat->Prop)->x_a)) (A_148:((nat->Prop)->Prop)), ((finite_finite_nat_o A_148)->(((ord_less_eq_a_o B_85) ((image_nat_o_a F_40) A_148))->(finite_finite_a B_85)))) of role axiom named fact_182_finite__surj % A new axiom: (forall (B_85:(x_a->Prop)) (F_40:((nat->Prop)->x_a)) (A_148:((nat->Prop)->Prop)), ((finite_finite_nat_o A_148)->(((ord_less_eq_a_o B_85) ((image_nat_o_a F_40) A_148))->(finite_finite_a B_85)))) % FOF formula (forall (B_85:(x_a->Prop)) (F_40:((pname->Prop)->x_a)) (A_148:((pname->Prop)->Prop)), ((finite297249702name_o A_148)->(((ord_less_eq_a_o B_85) ((image_pname_o_a F_40) A_148))->(finite_finite_a B_85)))) of role axiom named fact_183_finite__surj % A new axiom: (forall (B_85:(x_a->Prop)) (F_40:((pname->Prop)->x_a)) (A_148:((pname->Prop)->Prop)), ((finite297249702name_o A_148)->(((ord_less_eq_a_o B_85) ((image_pname_o_a F_40) A_148))->(finite_finite_a B_85)))) % FOF formula (forall (B_85:(x_a->Prop)) (F_40:((x_a->Prop)->x_a)) (A_148:((x_a->Prop)->Prop)), ((finite_finite_a_o A_148)->(((ord_less_eq_a_o B_85) ((image_a_o_a F_40) A_148))->(finite_finite_a B_85)))) of role axiom named fact_184_finite__surj % A new axiom: (forall (B_85:(x_a->Prop)) (F_40:((x_a->Prop)->x_a)) (A_148:((x_a->Prop)->Prop)), ((finite_finite_a_o A_148)->(((ord_less_eq_a_o B_85) ((image_a_o_a F_40) A_148))->(finite_finite_a B_85)))) % FOF formula (forall (B_85:((int->Prop)->Prop)) (F_40:(pname->(int->Prop))) (A_148:(pname->Prop)), ((finite_finite_pname A_148)->(((ord_less_eq_int_o_o B_85) ((image_pname_int_o F_40) A_148))->(finite_finite_int_o B_85)))) of role axiom named fact_185_finite__surj % A new axiom: (forall (B_85:((int->Prop)->Prop)) (F_40:(pname->(int->Prop))) (A_148:(pname->Prop)), ((finite_finite_pname A_148)->(((ord_less_eq_int_o_o B_85) ((image_pname_int_o F_40) A_148))->(finite_finite_int_o B_85)))) % FOF formula (forall (B_85:((nat->Prop)->Prop)) (F_40:(pname->(nat->Prop))) (A_148:(pname->Prop)), ((finite_finite_pname A_148)->(((ord_less_eq_nat_o_o B_85) ((image_pname_nat_o F_40) A_148))->(finite_finite_nat_o B_85)))) of role axiom named fact_186_finite__surj % A new axiom: (forall (B_85:((nat->Prop)->Prop)) (F_40:(pname->(nat->Prop))) (A_148:(pname->Prop)), ((finite_finite_pname A_148)->(((ord_less_eq_nat_o_o B_85) ((image_pname_nat_o F_40) A_148))->(finite_finite_nat_o B_85)))) % FOF formula (forall (B_85:((pname->Prop)->Prop)) (F_40:(pname->(pname->Prop))) (A_148:(pname->Prop)), ((finite_finite_pname A_148)->(((ord_le1205211808me_o_o B_85) ((image_pname_pname_o F_40) A_148))->(finite297249702name_o B_85)))) of role axiom named fact_187_finite__surj % A new axiom: (forall (B_85:((pname->Prop)->Prop)) (F_40:(pname->(pname->Prop))) (A_148:(pname->Prop)), ((finite_finite_pname A_148)->(((ord_le1205211808me_o_o B_85) ((image_pname_pname_o F_40) A_148))->(finite297249702name_o B_85)))) % FOF formula (forall (B_85:((x_a->Prop)->Prop)) (F_40:(pname->(x_a->Prop))) (A_148:(pname->Prop)), ((finite_finite_pname A_148)->(((ord_less_eq_a_o_o B_85) ((image_pname_a_o F_40) A_148))->(finite_finite_a_o B_85)))) of role axiom named fact_188_finite__surj % A new axiom: (forall (B_85:((x_a->Prop)->Prop)) (F_40:(pname->(x_a->Prop))) (A_148:(pname->Prop)), ((finite_finite_pname A_148)->(((ord_less_eq_a_o_o B_85) ((image_pname_a_o F_40) A_148))->(finite_finite_a_o B_85)))) % FOF formula (forall (B_85:(pname->Prop)) (F_40:(pname->pname)) (A_148:(pname->Prop)), ((finite_finite_pname A_148)->(((ord_less_eq_pname_o B_85) ((image_pname_pname F_40) A_148))->(finite_finite_pname B_85)))) of role axiom named fact_189_finite__surj % A new axiom: (forall (B_85:(pname->Prop)) (F_40:(pname->pname)) (A_148:(pname->Prop)), ((finite_finite_pname A_148)->(((ord_less_eq_pname_o B_85) ((image_pname_pname F_40) A_148))->(finite_finite_pname B_85)))) % FOF formula (forall (B_85:(x_a->Prop)) (F_40:(nat->x_a)) (A_148:(nat->Prop)), ((finite_finite_nat A_148)->(((ord_less_eq_a_o B_85) ((image_nat_a F_40) A_148))->(finite_finite_a B_85)))) of role axiom named fact_190_finite__surj % A new axiom: (forall (B_85:(x_a->Prop)) (F_40:(nat->x_a)) (A_148:(nat->Prop)), ((finite_finite_nat A_148)->(((ord_less_eq_a_o B_85) ((image_nat_a F_40) A_148))->(finite_finite_a B_85)))) % FOF formula (forall (B_85:((int->Prop)->Prop)) (F_40:(nat->(int->Prop))) (A_148:(nat->Prop)), ((finite_finite_nat A_148)->(((ord_less_eq_int_o_o B_85) ((image_nat_int_o F_40) A_148))->(finite_finite_int_o B_85)))) of role axiom named fact_191_finite__surj % A new axiom: (forall (B_85:((int->Prop)->Prop)) (F_40:(nat->(int->Prop))) (A_148:(nat->Prop)), ((finite_finite_nat A_148)->(((ord_less_eq_int_o_o B_85) ((image_nat_int_o F_40) A_148))->(finite_finite_int_o B_85)))) % FOF formula (forall (B_85:((nat->Prop)->Prop)) (F_40:(nat->(nat->Prop))) (A_148:(nat->Prop)), ((finite_finite_nat A_148)->(((ord_less_eq_nat_o_o B_85) ((image_nat_nat_o F_40) A_148))->(finite_finite_nat_o B_85)))) of role axiom named fact_192_finite__surj % A new axiom: (forall (B_85:((nat->Prop)->Prop)) (F_40:(nat->(nat->Prop))) (A_148:(nat->Prop)), ((finite_finite_nat A_148)->(((ord_less_eq_nat_o_o B_85) ((image_nat_nat_o F_40) A_148))->(finite_finite_nat_o B_85)))) % FOF formula (forall (B_85:((pname->Prop)->Prop)) (F_40:(nat->(pname->Prop))) (A_148:(nat->Prop)), ((finite_finite_nat A_148)->(((ord_le1205211808me_o_o B_85) ((image_nat_pname_o F_40) A_148))->(finite297249702name_o B_85)))) of role axiom named fact_193_finite__surj % A new axiom: (forall (B_85:((pname->Prop)->Prop)) (F_40:(nat->(pname->Prop))) (A_148:(nat->Prop)), ((finite_finite_nat A_148)->(((ord_le1205211808me_o_o B_85) ((image_nat_pname_o F_40) A_148))->(finite297249702name_o B_85)))) % FOF formula (forall (B_85:((x_a->Prop)->Prop)) (F_40:(nat->(x_a->Prop))) (A_148:(nat->Prop)), ((finite_finite_nat A_148)->(((ord_less_eq_a_o_o B_85) ((image_nat_a_o F_40) A_148))->(finite_finite_a_o B_85)))) of role axiom named fact_194_finite__surj % A new axiom: (forall (B_85:((x_a->Prop)->Prop)) (F_40:(nat->(x_a->Prop))) (A_148:(nat->Prop)), ((finite_finite_nat A_148)->(((ord_less_eq_a_o_o B_85) ((image_nat_a_o F_40) A_148))->(finite_finite_a_o B_85)))) % FOF formula (forall (B_85:(pname->Prop)) (F_40:(nat->pname)) (A_148:(nat->Prop)), ((finite_finite_nat A_148)->(((ord_less_eq_pname_o B_85) ((image_nat_pname F_40) A_148))->(finite_finite_pname B_85)))) of role axiom named fact_195_finite__surj % A new axiom: (forall (B_85:(pname->Prop)) (F_40:(nat->pname)) (A_148:(nat->Prop)), ((finite_finite_nat A_148)->(((ord_less_eq_pname_o B_85) ((image_nat_pname F_40) A_148))->(finite_finite_pname B_85)))) % FOF formula (forall (B_85:(x_a->Prop)) (F_40:(int->x_a)) (A_148:(int->Prop)), ((finite_finite_int A_148)->(((ord_less_eq_a_o B_85) ((image_int_a F_40) A_148))->(finite_finite_a B_85)))) of role axiom named fact_196_finite__surj % A new axiom: (forall (B_85:(x_a->Prop)) (F_40:(int->x_a)) (A_148:(int->Prop)), ((finite_finite_int A_148)->(((ord_less_eq_a_o B_85) ((image_int_a F_40) A_148))->(finite_finite_a B_85)))) % FOF formula (forall (B_85:((int->Prop)->Prop)) (F_40:(int->(int->Prop))) (A_148:(int->Prop)), ((finite_finite_int A_148)->(((ord_less_eq_int_o_o B_85) ((image_int_int_o F_40) A_148))->(finite_finite_int_o B_85)))) of role axiom named fact_197_finite__surj % A new axiom: (forall (B_85:((int->Prop)->Prop)) (F_40:(int->(int->Prop))) (A_148:(int->Prop)), ((finite_finite_int A_148)->(((ord_less_eq_int_o_o B_85) ((image_int_int_o F_40) A_148))->(finite_finite_int_o B_85)))) % FOF formula (forall (B_85:((nat->Prop)->Prop)) (F_40:(int->(nat->Prop))) (A_148:(int->Prop)), ((finite_finite_int A_148)->(((ord_less_eq_nat_o_o B_85) ((image_int_nat_o F_40) A_148))->(finite_finite_nat_o B_85)))) of role axiom named fact_198_finite__surj % A new axiom: (forall (B_85:((nat->Prop)->Prop)) (F_40:(int->(nat->Prop))) (A_148:(int->Prop)), ((finite_finite_int A_148)->(((ord_less_eq_nat_o_o B_85) ((image_int_nat_o F_40) A_148))->(finite_finite_nat_o B_85)))) % FOF formula (forall (B_85:((pname->Prop)->Prop)) (F_40:(int->(pname->Prop))) (A_148:(int->Prop)), ((finite_finite_int A_148)->(((ord_le1205211808me_o_o B_85) ((image_int_pname_o F_40) A_148))->(finite297249702name_o B_85)))) of role axiom named fact_199_finite__surj % A new axiom: (forall (B_85:((pname->Prop)->Prop)) (F_40:(int->(pname->Prop))) (A_148:(int->Prop)), ((finite_finite_int A_148)->(((ord_le1205211808me_o_o B_85) ((image_int_pname_o F_40) A_148))->(finite297249702name_o B_85)))) % FOF formula (forall (B_85:((x_a->Prop)->Prop)) (F_40:(int->(x_a->Prop))) (A_148:(int->Prop)), ((finite_finite_int A_148)->(((ord_less_eq_a_o_o B_85) ((image_int_a_o F_40) A_148))->(finite_finite_a_o B_85)))) of role axiom named fact_200_finite__surj % A new axiom: (forall (B_85:((x_a->Prop)->Prop)) (F_40:(int->(x_a->Prop))) (A_148:(int->Prop)), ((finite_finite_int A_148)->(((ord_less_eq_a_o_o B_85) ((image_int_a_o F_40) A_148))->(finite_finite_a_o B_85)))) % FOF formula (forall (B_85:(pname->Prop)) (F_40:(int->pname)) (A_148:(int->Prop)), ((finite_finite_int A_148)->(((ord_less_eq_pname_o B_85) ((image_int_pname F_40) A_148))->(finite_finite_pname B_85)))) of role axiom named fact_201_finite__surj % A new axiom: (forall (B_85:(pname->Prop)) (F_40:(int->pname)) (A_148:(int->Prop)), ((finite_finite_int A_148)->(((ord_less_eq_pname_o B_85) ((image_int_pname F_40) A_148))->(finite_finite_pname B_85)))) % FOF formula (forall (B_85:(pname->Prop)) (F_40:(x_a->pname)) (A_148:(x_a->Prop)), ((finite_finite_a A_148)->(((ord_less_eq_pname_o B_85) ((image_a_pname F_40) A_148))->(finite_finite_pname B_85)))) of role axiom named fact_202_finite__surj % A new axiom: (forall (B_85:(pname->Prop)) (F_40:(x_a->pname)) (A_148:(x_a->Prop)), ((finite_finite_a A_148)->(((ord_less_eq_pname_o B_85) ((image_a_pname F_40) A_148))->(finite_finite_pname B_85)))) % FOF formula (forall (B_85:(pname->Prop)) (F_40:((int->Prop)->pname)) (A_148:((int->Prop)->Prop)), ((finite_finite_int_o A_148)->(((ord_less_eq_pname_o B_85) ((image_int_o_pname F_40) A_148))->(finite_finite_pname B_85)))) of role axiom named fact_203_finite__surj % A new axiom: (forall (B_85:(pname->Prop)) (F_40:((int->Prop)->pname)) (A_148:((int->Prop)->Prop)), ((finite_finite_int_o A_148)->(((ord_less_eq_pname_o B_85) ((image_int_o_pname F_40) A_148))->(finite_finite_pname B_85)))) % FOF formula (forall (B_85:(pname->Prop)) (F_40:((nat->Prop)->pname)) (A_148:((nat->Prop)->Prop)), ((finite_finite_nat_o A_148)->(((ord_less_eq_pname_o B_85) ((image_nat_o_pname F_40) A_148))->(finite_finite_pname B_85)))) of role axiom named fact_204_finite__surj % A new axiom: (forall (B_85:(pname->Prop)) (F_40:((nat->Prop)->pname)) (A_148:((nat->Prop)->Prop)), ((finite_finite_nat_o A_148)->(((ord_less_eq_pname_o B_85) ((image_nat_o_pname F_40) A_148))->(finite_finite_pname B_85)))) % FOF formula (forall (B_85:(pname->Prop)) (F_40:((pname->Prop)->pname)) (A_148:((pname->Prop)->Prop)), ((finite297249702name_o A_148)->(((ord_less_eq_pname_o B_85) ((image_pname_o_pname F_40) A_148))->(finite_finite_pname B_85)))) of role axiom named fact_205_finite__surj % A new axiom: (forall (B_85:(pname->Prop)) (F_40:((pname->Prop)->pname)) (A_148:((pname->Prop)->Prop)), ((finite297249702name_o A_148)->(((ord_less_eq_pname_o B_85) ((image_pname_o_pname F_40) A_148))->(finite_finite_pname B_85)))) % FOF formula (forall (B_85:(pname->Prop)) (F_40:((x_a->Prop)->pname)) (A_148:((x_a->Prop)->Prop)), ((finite_finite_a_o A_148)->(((ord_less_eq_pname_o B_85) ((image_a_o_pname F_40) A_148))->(finite_finite_pname B_85)))) of role axiom named fact_206_finite__surj % A new axiom: (forall (B_85:(pname->Prop)) (F_40:((x_a->Prop)->pname)) (A_148:((x_a->Prop)->Prop)), ((finite_finite_a_o A_148)->(((ord_less_eq_pname_o B_85) ((image_a_o_pname F_40) A_148))->(finite_finite_pname B_85)))) % FOF formula (forall (B_85:(nat->Prop)) (F_40:(x_a->nat)) (A_148:(x_a->Prop)), ((finite_finite_a A_148)->(((ord_less_eq_nat_o B_85) ((image_a_nat F_40) A_148))->(finite_finite_nat B_85)))) of role axiom named fact_207_finite__surj % A new axiom: (forall (B_85:(nat->Prop)) (F_40:(x_a->nat)) (A_148:(x_a->Prop)), ((finite_finite_a A_148)->(((ord_less_eq_nat_o B_85) ((image_a_nat F_40) A_148))->(finite_finite_nat B_85)))) % FOF formula (forall (B_85:(nat->Prop)) (F_40:((int->Prop)->nat)) (A_148:((int->Prop)->Prop)), ((finite_finite_int_o A_148)->(((ord_less_eq_nat_o B_85) ((image_int_o_nat F_40) A_148))->(finite_finite_nat B_85)))) of role axiom named fact_208_finite__surj % A new axiom: (forall (B_85:(nat->Prop)) (F_40:((int->Prop)->nat)) (A_148:((int->Prop)->Prop)), ((finite_finite_int_o A_148)->(((ord_less_eq_nat_o B_85) ((image_int_o_nat F_40) A_148))->(finite_finite_nat B_85)))) % FOF formula (forall (B_85:(nat->Prop)) (F_40:((nat->Prop)->nat)) (A_148:((nat->Prop)->Prop)), ((finite_finite_nat_o A_148)->(((ord_less_eq_nat_o B_85) ((image_nat_o_nat F_40) A_148))->(finite_finite_nat B_85)))) of role axiom named fact_209_finite__surj % A new axiom: (forall (B_85:(nat->Prop)) (F_40:((nat->Prop)->nat)) (A_148:((nat->Prop)->Prop)), ((finite_finite_nat_o A_148)->(((ord_less_eq_nat_o B_85) ((image_nat_o_nat F_40) A_148))->(finite_finite_nat B_85)))) % FOF formula (forall (B_85:(nat->Prop)) (F_40:((pname->Prop)->nat)) (A_148:((pname->Prop)->Prop)), ((finite297249702name_o A_148)->(((ord_less_eq_nat_o B_85) ((image_pname_o_nat F_40) A_148))->(finite_finite_nat B_85)))) of role axiom named fact_210_finite__surj % A new axiom: (forall (B_85:(nat->Prop)) (F_40:((pname->Prop)->nat)) (A_148:((pname->Prop)->Prop)), ((finite297249702name_o A_148)->(((ord_less_eq_nat_o B_85) ((image_pname_o_nat F_40) A_148))->(finite_finite_nat B_85)))) % FOF formula (forall (B_85:(nat->Prop)) (F_40:((x_a->Prop)->nat)) (A_148:((x_a->Prop)->Prop)), ((finite_finite_a_o A_148)->(((ord_less_eq_nat_o B_85) ((image_a_o_nat F_40) A_148))->(finite_finite_nat B_85)))) of role axiom named fact_211_finite__surj % A new axiom: (forall (B_85:(nat->Prop)) (F_40:((x_a->Prop)->nat)) (A_148:((x_a->Prop)->Prop)), ((finite_finite_a_o A_148)->(((ord_less_eq_nat_o B_85) ((image_a_o_nat F_40) A_148))->(finite_finite_nat B_85)))) % FOF formula (forall (B_85:(int->Prop)) (F_40:(x_a->int)) (A_148:(x_a->Prop)), ((finite_finite_a A_148)->(((ord_less_eq_int_o B_85) ((image_a_int F_40) A_148))->(finite_finite_int B_85)))) of role axiom named fact_212_finite__surj % A new axiom: (forall (B_85:(int->Prop)) (F_40:(x_a->int)) (A_148:(x_a->Prop)), ((finite_finite_a A_148)->(((ord_less_eq_int_o B_85) ((image_a_int F_40) A_148))->(finite_finite_int B_85)))) % FOF formula (forall (B_85:(int->Prop)) (F_40:((int->Prop)->int)) (A_148:((int->Prop)->Prop)), ((finite_finite_int_o A_148)->(((ord_less_eq_int_o B_85) ((image_int_o_int F_40) A_148))->(finite_finite_int B_85)))) of role axiom named fact_213_finite__surj % A new axiom: (forall (B_85:(int->Prop)) (F_40:((int->Prop)->int)) (A_148:((int->Prop)->Prop)), ((finite_finite_int_o A_148)->(((ord_less_eq_int_o B_85) ((image_int_o_int F_40) A_148))->(finite_finite_int B_85)))) % FOF formula (forall (B_85:(int->Prop)) (F_40:((nat->Prop)->int)) (A_148:((nat->Prop)->Prop)), ((finite_finite_nat_o A_148)->(((ord_less_eq_int_o B_85) ((image_nat_o_int F_40) A_148))->(finite_finite_int B_85)))) of role axiom named fact_214_finite__surj % A new axiom: (forall (B_85:(int->Prop)) (F_40:((nat->Prop)->int)) (A_148:((nat->Prop)->Prop)), ((finite_finite_nat_o A_148)->(((ord_less_eq_int_o B_85) ((image_nat_o_int F_40) A_148))->(finite_finite_int B_85)))) % FOF formula (forall (B_85:(int->Prop)) (F_40:((pname->Prop)->int)) (A_148:((pname->Prop)->Prop)), ((finite297249702name_o A_148)->(((ord_less_eq_int_o B_85) ((image_pname_o_int F_40) A_148))->(finite_finite_int B_85)))) of role axiom named fact_215_finite__surj % A new axiom: (forall (B_85:(int->Prop)) (F_40:((pname->Prop)->int)) (A_148:((pname->Prop)->Prop)), ((finite297249702name_o A_148)->(((ord_less_eq_int_o B_85) ((image_pname_o_int F_40) A_148))->(finite_finite_int B_85)))) % FOF formula (forall (B_85:(int->Prop)) (F_40:((x_a->Prop)->int)) (A_148:((x_a->Prop)->Prop)), ((finite_finite_a_o A_148)->(((ord_less_eq_int_o B_85) ((image_a_o_int F_40) A_148))->(finite_finite_int B_85)))) of role axiom named fact_216_finite__surj % A new axiom: (forall (B_85:(int->Prop)) (F_40:((x_a->Prop)->int)) (A_148:((x_a->Prop)->Prop)), ((finite_finite_a_o A_148)->(((ord_less_eq_int_o B_85) ((image_a_o_int F_40) A_148))->(finite_finite_int B_85)))) % FOF formula (forall (B_85:(x_a->Prop)) (F_40:(pname->x_a)) (A_148:(pname->Prop)), ((finite_finite_pname A_148)->(((ord_less_eq_a_o B_85) ((image_pname_a F_40) A_148))->(finite_finite_a B_85)))) of role axiom named fact_217_finite__surj % A new axiom: (forall (B_85:(x_a->Prop)) (F_40:(pname->x_a)) (A_148:(pname->Prop)), ((finite_finite_pname A_148)->(((ord_less_eq_a_o B_85) ((image_pname_a F_40) A_148))->(finite_finite_a B_85)))) % FOF formula (forall (B_85:(int->Prop)) (F_40:(nat->int)) (A_148:(nat->Prop)), ((finite_finite_nat A_148)->(((ord_less_eq_int_o B_85) ((image_nat_int F_40) A_148))->(finite_finite_int B_85)))) of role axiom named fact_218_finite__surj % A new axiom: (forall (B_85:(int->Prop)) (F_40:(nat->int)) (A_148:(nat->Prop)), ((finite_finite_nat A_148)->(((ord_less_eq_int_o B_85) ((image_nat_int F_40) A_148))->(finite_finite_int B_85)))) % FOF formula (forall (F_39:((int->Prop)->x_a)) (A_147:((int->Prop)->Prop)) (B_84:(x_a->Prop)), ((finite_finite_a B_84)->(((ord_less_eq_a_o B_84) ((image_int_o_a F_39) A_147))->((ex ((int->Prop)->Prop)) (fun (C_34:((int->Prop)->Prop))=> ((and ((and ((ord_less_eq_int_o_o C_34) A_147)) (finite_finite_int_o C_34))) (((eq (x_a->Prop)) B_84) ((image_int_o_a F_39) C_34)))))))) of role axiom named fact_219_finite__subset__image % A new axiom: (forall (F_39:((int->Prop)->x_a)) (A_147:((int->Prop)->Prop)) (B_84:(x_a->Prop)), ((finite_finite_a B_84)->(((ord_less_eq_a_o B_84) ((image_int_o_a F_39) A_147))->((ex ((int->Prop)->Prop)) (fun (C_34:((int->Prop)->Prop))=> ((and ((and ((ord_less_eq_int_o_o C_34) A_147)) (finite_finite_int_o C_34))) (((eq (x_a->Prop)) B_84) ((image_int_o_a F_39) C_34)))))))) % FOF formula (forall (F_39:((nat->Prop)->x_a)) (A_147:((nat->Prop)->Prop)) (B_84:(x_a->Prop)), ((finite_finite_a B_84)->(((ord_less_eq_a_o B_84) ((image_nat_o_a F_39) A_147))->((ex ((nat->Prop)->Prop)) (fun (C_34:((nat->Prop)->Prop))=> ((and ((and ((ord_less_eq_nat_o_o C_34) A_147)) (finite_finite_nat_o C_34))) (((eq (x_a->Prop)) B_84) ((image_nat_o_a F_39) C_34)))))))) of role axiom named fact_220_finite__subset__image % A new axiom: (forall (F_39:((nat->Prop)->x_a)) (A_147:((nat->Prop)->Prop)) (B_84:(x_a->Prop)), ((finite_finite_a B_84)->(((ord_less_eq_a_o B_84) ((image_nat_o_a F_39) A_147))->((ex ((nat->Prop)->Prop)) (fun (C_34:((nat->Prop)->Prop))=> ((and ((and ((ord_less_eq_nat_o_o C_34) A_147)) (finite_finite_nat_o C_34))) (((eq (x_a->Prop)) B_84) ((image_nat_o_a F_39) C_34)))))))) % FOF formula (forall (F_39:((pname->Prop)->x_a)) (A_147:((pname->Prop)->Prop)) (B_84:(x_a->Prop)), ((finite_finite_a B_84)->(((ord_less_eq_a_o B_84) ((image_pname_o_a F_39) A_147))->((ex ((pname->Prop)->Prop)) (fun (C_34:((pname->Prop)->Prop))=> ((and ((and ((ord_le1205211808me_o_o C_34) A_147)) (finite297249702name_o C_34))) (((eq (x_a->Prop)) B_84) ((image_pname_o_a F_39) C_34)))))))) of role axiom named fact_221_finite__subset__image % A new axiom: (forall (F_39:((pname->Prop)->x_a)) (A_147:((pname->Prop)->Prop)) (B_84:(x_a->Prop)), ((finite_finite_a B_84)->(((ord_less_eq_a_o B_84) ((image_pname_o_a F_39) A_147))->((ex ((pname->Prop)->Prop)) (fun (C_34:((pname->Prop)->Prop))=> ((and ((and ((ord_le1205211808me_o_o C_34) A_147)) (finite297249702name_o C_34))) (((eq (x_a->Prop)) B_84) ((image_pname_o_a F_39) C_34)))))))) % FOF formula (forall (F_39:((x_a->Prop)->x_a)) (A_147:((x_a->Prop)->Prop)) (B_84:(x_a->Prop)), ((finite_finite_a B_84)->(((ord_less_eq_a_o B_84) ((image_a_o_a F_39) A_147))->((ex ((x_a->Prop)->Prop)) (fun (C_34:((x_a->Prop)->Prop))=> ((and ((and ((ord_less_eq_a_o_o C_34) A_147)) (finite_finite_a_o C_34))) (((eq (x_a->Prop)) B_84) ((image_a_o_a F_39) C_34)))))))) of role axiom named fact_222_finite__subset__image % A new axiom: (forall (F_39:((x_a->Prop)->x_a)) (A_147:((x_a->Prop)->Prop)) (B_84:(x_a->Prop)), ((finite_finite_a B_84)->(((ord_less_eq_a_o B_84) ((image_a_o_a F_39) A_147))->((ex ((x_a->Prop)->Prop)) (fun (C_34:((x_a->Prop)->Prop))=> ((and ((and ((ord_less_eq_a_o_o C_34) A_147)) (finite_finite_a_o C_34))) (((eq (x_a->Prop)) B_84) ((image_a_o_a F_39) C_34)))))))) % FOF formula (forall (F_39:(x_a->x_a)) (A_147:(x_a->Prop)) (B_84:(x_a->Prop)), ((finite_finite_a B_84)->(((ord_less_eq_a_o B_84) ((image_a_a F_39) A_147))->((ex (x_a->Prop)) (fun (C_34:(x_a->Prop))=> ((and ((and ((ord_less_eq_a_o C_34) A_147)) (finite_finite_a C_34))) (((eq (x_a->Prop)) B_84) ((image_a_a F_39) C_34)))))))) of role axiom named fact_223_finite__subset__image % A new axiom: (forall (F_39:(x_a->x_a)) (A_147:(x_a->Prop)) (B_84:(x_a->Prop)), ((finite_finite_a B_84)->(((ord_less_eq_a_o B_84) ((image_a_a F_39) A_147))->((ex (x_a->Prop)) (fun (C_34:(x_a->Prop))=> ((and ((and ((ord_less_eq_a_o C_34) A_147)) (finite_finite_a C_34))) (((eq (x_a->Prop)) B_84) ((image_a_a F_39) C_34)))))))) % FOF formula (forall (F_39:(x_a->(int->Prop))) (A_147:(x_a->Prop)) (B_84:((int->Prop)->Prop)), ((finite_finite_int_o B_84)->(((ord_less_eq_int_o_o B_84) ((image_a_int_o F_39) A_147))->((ex (x_a->Prop)) (fun (C_34:(x_a->Prop))=> ((and ((and ((ord_less_eq_a_o C_34) A_147)) (finite_finite_a C_34))) (((eq ((int->Prop)->Prop)) B_84) ((image_a_int_o F_39) C_34)))))))) of role axiom named fact_224_finite__subset__image % A new axiom: (forall (F_39:(x_a->(int->Prop))) (A_147:(x_a->Prop)) (B_84:((int->Prop)->Prop)), ((finite_finite_int_o B_84)->(((ord_less_eq_int_o_o B_84) ((image_a_int_o F_39) A_147))->((ex (x_a->Prop)) (fun (C_34:(x_a->Prop))=> ((and ((and ((ord_less_eq_a_o C_34) A_147)) (finite_finite_a C_34))) (((eq ((int->Prop)->Prop)) B_84) ((image_a_int_o F_39) C_34)))))))) % FOF formula (forall (F_39:(x_a->(nat->Prop))) (A_147:(x_a->Prop)) (B_84:((nat->Prop)->Prop)), ((finite_finite_nat_o B_84)->(((ord_less_eq_nat_o_o B_84) ((image_a_nat_o F_39) A_147))->((ex (x_a->Prop)) (fun (C_34:(x_a->Prop))=> ((and ((and ((ord_less_eq_a_o C_34) A_147)) (finite_finite_a C_34))) (((eq ((nat->Prop)->Prop)) B_84) ((image_a_nat_o F_39) C_34)))))))) of role axiom named fact_225_finite__subset__image % A new axiom: (forall (F_39:(x_a->(nat->Prop))) (A_147:(x_a->Prop)) (B_84:((nat->Prop)->Prop)), ((finite_finite_nat_o B_84)->(((ord_less_eq_nat_o_o B_84) ((image_a_nat_o F_39) A_147))->((ex (x_a->Prop)) (fun (C_34:(x_a->Prop))=> ((and ((and ((ord_less_eq_a_o C_34) A_147)) (finite_finite_a C_34))) (((eq ((nat->Prop)->Prop)) B_84) ((image_a_nat_o F_39) C_34)))))))) % FOF formula (forall (F_39:(x_a->(pname->Prop))) (A_147:(x_a->Prop)) (B_84:((pname->Prop)->Prop)), ((finite297249702name_o B_84)->(((ord_le1205211808me_o_o B_84) ((image_a_pname_o F_39) A_147))->((ex (x_a->Prop)) (fun (C_34:(x_a->Prop))=> ((and ((and ((ord_less_eq_a_o C_34) A_147)) (finite_finite_a C_34))) (((eq ((pname->Prop)->Prop)) B_84) ((image_a_pname_o F_39) C_34)))))))) of role axiom named fact_226_finite__subset__image % A new axiom: (forall (F_39:(x_a->(pname->Prop))) (A_147:(x_a->Prop)) (B_84:((pname->Prop)->Prop)), ((finite297249702name_o B_84)->(((ord_le1205211808me_o_o B_84) ((image_a_pname_o F_39) A_147))->((ex (x_a->Prop)) (fun (C_34:(x_a->Prop))=> ((and ((and ((ord_less_eq_a_o C_34) A_147)) (finite_finite_a C_34))) (((eq ((pname->Prop)->Prop)) B_84) ((image_a_pname_o F_39) C_34)))))))) % FOF formula (forall (F_39:(x_a->(x_a->Prop))) (A_147:(x_a->Prop)) (B_84:((x_a->Prop)->Prop)), ((finite_finite_a_o B_84)->(((ord_less_eq_a_o_o B_84) ((image_a_a_o F_39) A_147))->((ex (x_a->Prop)) (fun (C_34:(x_a->Prop))=> ((and ((and ((ord_less_eq_a_o C_34) A_147)) (finite_finite_a C_34))) (((eq ((x_a->Prop)->Prop)) B_84) ((image_a_a_o F_39) C_34)))))))) of role axiom named fact_227_finite__subset__image % A new axiom: (forall (F_39:(x_a->(x_a->Prop))) (A_147:(x_a->Prop)) (B_84:((x_a->Prop)->Prop)), ((finite_finite_a_o B_84)->(((ord_less_eq_a_o_o B_84) ((image_a_a_o F_39) A_147))->((ex (x_a->Prop)) (fun (C_34:(x_a->Prop))=> ((and ((and ((ord_less_eq_a_o C_34) A_147)) (finite_finite_a C_34))) (((eq ((x_a->Prop)->Prop)) B_84) ((image_a_a_o F_39) C_34)))))))) % FOF formula (forall (F_39:(x_a->pname)) (A_147:(x_a->Prop)) (B_84:(pname->Prop)), ((finite_finite_pname B_84)->(((ord_less_eq_pname_o B_84) ((image_a_pname F_39) A_147))->((ex (x_a->Prop)) (fun (C_34:(x_a->Prop))=> ((and ((and ((ord_less_eq_a_o C_34) A_147)) (finite_finite_a C_34))) (((eq (pname->Prop)) B_84) ((image_a_pname F_39) C_34)))))))) of role axiom named fact_228_finite__subset__image % A new axiom: (forall (F_39:(x_a->pname)) (A_147:(x_a->Prop)) (B_84:(pname->Prop)), ((finite_finite_pname B_84)->(((ord_less_eq_pname_o B_84) ((image_a_pname F_39) A_147))->((ex (x_a->Prop)) (fun (C_34:(x_a->Prop))=> ((and ((and ((ord_less_eq_a_o C_34) A_147)) (finite_finite_a C_34))) (((eq (pname->Prop)) B_84) ((image_a_pname F_39) C_34)))))))) % FOF formula (forall (F_39:((int->Prop)->pname)) (A_147:((int->Prop)->Prop)) (B_84:(pname->Prop)), ((finite_finite_pname B_84)->(((ord_less_eq_pname_o B_84) ((image_int_o_pname F_39) A_147))->((ex ((int->Prop)->Prop)) (fun (C_34:((int->Prop)->Prop))=> ((and ((and ((ord_less_eq_int_o_o C_34) A_147)) (finite_finite_int_o C_34))) (((eq (pname->Prop)) B_84) ((image_int_o_pname F_39) C_34)))))))) of role axiom named fact_229_finite__subset__image % A new axiom: (forall (F_39:((int->Prop)->pname)) (A_147:((int->Prop)->Prop)) (B_84:(pname->Prop)), ((finite_finite_pname B_84)->(((ord_less_eq_pname_o B_84) ((image_int_o_pname F_39) A_147))->((ex ((int->Prop)->Prop)) (fun (C_34:((int->Prop)->Prop))=> ((and ((and ((ord_less_eq_int_o_o C_34) A_147)) (finite_finite_int_o C_34))) (((eq (pname->Prop)) B_84) ((image_int_o_pname F_39) C_34)))))))) % FOF formula (forall (F_39:((nat->Prop)->pname)) (A_147:((nat->Prop)->Prop)) (B_84:(pname->Prop)), ((finite_finite_pname B_84)->(((ord_less_eq_pname_o B_84) ((image_nat_o_pname F_39) A_147))->((ex ((nat->Prop)->Prop)) (fun (C_34:((nat->Prop)->Prop))=> ((and ((and ((ord_less_eq_nat_o_o C_34) A_147)) (finite_finite_nat_o C_34))) (((eq (pname->Prop)) B_84) ((image_nat_o_pname F_39) C_34)))))))) of role axiom named fact_230_finite__subset__image % A new axiom: (forall (F_39:((nat->Prop)->pname)) (A_147:((nat->Prop)->Prop)) (B_84:(pname->Prop)), ((finite_finite_pname B_84)->(((ord_less_eq_pname_o B_84) ((image_nat_o_pname F_39) A_147))->((ex ((nat->Prop)->Prop)) (fun (C_34:((nat->Prop)->Prop))=> ((and ((and ((ord_less_eq_nat_o_o C_34) A_147)) (finite_finite_nat_o C_34))) (((eq (pname->Prop)) B_84) ((image_nat_o_pname F_39) C_34)))))))) % FOF formula (forall (F_39:((pname->Prop)->pname)) (A_147:((pname->Prop)->Prop)) (B_84:(pname->Prop)), ((finite_finite_pname B_84)->(((ord_less_eq_pname_o B_84) ((image_pname_o_pname F_39) A_147))->((ex ((pname->Prop)->Prop)) (fun (C_34:((pname->Prop)->Prop))=> ((and ((and ((ord_le1205211808me_o_o C_34) A_147)) (finite297249702name_o C_34))) (((eq (pname->Prop)) B_84) ((image_pname_o_pname F_39) C_34)))))))) of role axiom named fact_231_finite__subset__image % A new axiom: (forall (F_39:((pname->Prop)->pname)) (A_147:((pname->Prop)->Prop)) (B_84:(pname->Prop)), ((finite_finite_pname B_84)->(((ord_less_eq_pname_o B_84) ((image_pname_o_pname F_39) A_147))->((ex ((pname->Prop)->Prop)) (fun (C_34:((pname->Prop)->Prop))=> ((and ((and ((ord_le1205211808me_o_o C_34) A_147)) (finite297249702name_o C_34))) (((eq (pname->Prop)) B_84) ((image_pname_o_pname F_39) C_34)))))))) % FOF formula (forall (F_39:((x_a->Prop)->pname)) (A_147:((x_a->Prop)->Prop)) (B_84:(pname->Prop)), ((finite_finite_pname B_84)->(((ord_less_eq_pname_o B_84) ((image_a_o_pname F_39) A_147))->((ex ((x_a->Prop)->Prop)) (fun (C_34:((x_a->Prop)->Prop))=> ((and ((and ((ord_less_eq_a_o_o C_34) A_147)) (finite_finite_a_o C_34))) (((eq (pname->Prop)) B_84) ((image_a_o_pname F_39) C_34)))))))) of role axiom named fact_232_finite__subset__image % A new axiom: (forall (F_39:((x_a->Prop)->pname)) (A_147:((x_a->Prop)->Prop)) (B_84:(pname->Prop)), ((finite_finite_pname B_84)->(((ord_less_eq_pname_o B_84) ((image_a_o_pname F_39) A_147))->((ex ((x_a->Prop)->Prop)) (fun (C_34:((x_a->Prop)->Prop))=> ((and ((and ((ord_less_eq_a_o_o C_34) A_147)) (finite_finite_a_o C_34))) (((eq (pname->Prop)) B_84) ((image_a_o_pname F_39) C_34)))))))) % FOF formula (forall (F_39:(x_a->nat)) (A_147:(x_a->Prop)) (B_84:(nat->Prop)), ((finite_finite_nat B_84)->(((ord_less_eq_nat_o B_84) ((image_a_nat F_39) A_147))->((ex (x_a->Prop)) (fun (C_34:(x_a->Prop))=> ((and ((and ((ord_less_eq_a_o C_34) A_147)) (finite_finite_a C_34))) (((eq (nat->Prop)) B_84) ((image_a_nat F_39) C_34)))))))) of role axiom named fact_233_finite__subset__image % A new axiom: (forall (F_39:(x_a->nat)) (A_147:(x_a->Prop)) (B_84:(nat->Prop)), ((finite_finite_nat B_84)->(((ord_less_eq_nat_o B_84) ((image_a_nat F_39) A_147))->((ex (x_a->Prop)) (fun (C_34:(x_a->Prop))=> ((and ((and ((ord_less_eq_a_o C_34) A_147)) (finite_finite_a C_34))) (((eq (nat->Prop)) B_84) ((image_a_nat F_39) C_34)))))))) % FOF formula (forall (F_39:((int->Prop)->nat)) (A_147:((int->Prop)->Prop)) (B_84:(nat->Prop)), ((finite_finite_nat B_84)->(((ord_less_eq_nat_o B_84) ((image_int_o_nat F_39) A_147))->((ex ((int->Prop)->Prop)) (fun (C_34:((int->Prop)->Prop))=> ((and ((and ((ord_less_eq_int_o_o C_34) A_147)) (finite_finite_int_o C_34))) (((eq (nat->Prop)) B_84) ((image_int_o_nat F_39) C_34)))))))) of role axiom named fact_234_finite__subset__image % A new axiom: (forall (F_39:((int->Prop)->nat)) (A_147:((int->Prop)->Prop)) (B_84:(nat->Prop)), ((finite_finite_nat B_84)->(((ord_less_eq_nat_o B_84) ((image_int_o_nat F_39) A_147))->((ex ((int->Prop)->Prop)) (fun (C_34:((int->Prop)->Prop))=> ((and ((and ((ord_less_eq_int_o_o C_34) A_147)) (finite_finite_int_o C_34))) (((eq (nat->Prop)) B_84) ((image_int_o_nat F_39) C_34)))))))) % FOF formula (forall (F_39:((nat->Prop)->nat)) (A_147:((nat->Prop)->Prop)) (B_84:(nat->Prop)), ((finite_finite_nat B_84)->(((ord_less_eq_nat_o B_84) ((image_nat_o_nat F_39) A_147))->((ex ((nat->Prop)->Prop)) (fun (C_34:((nat->Prop)->Prop))=> ((and ((and ((ord_less_eq_nat_o_o C_34) A_147)) (finite_finite_nat_o C_34))) (((eq (nat->Prop)) B_84) ((image_nat_o_nat F_39) C_34)))))))) of role axiom named fact_235_finite__subset__image % A new axiom: (forall (F_39:((nat->Prop)->nat)) (A_147:((nat->Prop)->Prop)) (B_84:(nat->Prop)), ((finite_finite_nat B_84)->(((ord_less_eq_nat_o B_84) ((image_nat_o_nat F_39) A_147))->((ex ((nat->Prop)->Prop)) (fun (C_34:((nat->Prop)->Prop))=> ((and ((and ((ord_less_eq_nat_o_o C_34) A_147)) (finite_finite_nat_o C_34))) (((eq (nat->Prop)) B_84) ((image_nat_o_nat F_39) C_34)))))))) % FOF formula (forall (F_39:((pname->Prop)->nat)) (A_147:((pname->Prop)->Prop)) (B_84:(nat->Prop)), ((finite_finite_nat B_84)->(((ord_less_eq_nat_o B_84) ((image_pname_o_nat F_39) A_147))->((ex ((pname->Prop)->Prop)) (fun (C_34:((pname->Prop)->Prop))=> ((and ((and ((ord_le1205211808me_o_o C_34) A_147)) (finite297249702name_o C_34))) (((eq (nat->Prop)) B_84) ((image_pname_o_nat F_39) C_34)))))))) of role axiom named fact_236_finite__subset__image % A new axiom: (forall (F_39:((pname->Prop)->nat)) (A_147:((pname->Prop)->Prop)) (B_84:(nat->Prop)), ((finite_finite_nat B_84)->(((ord_less_eq_nat_o B_84) ((image_pname_o_nat F_39) A_147))->((ex ((pname->Prop)->Prop)) (fun (C_34:((pname->Prop)->Prop))=> ((and ((and ((ord_le1205211808me_o_o C_34) A_147)) (finite297249702name_o C_34))) (((eq (nat->Prop)) B_84) ((image_pname_o_nat F_39) C_34)))))))) % FOF formula (forall (F_39:((x_a->Prop)->nat)) (A_147:((x_a->Prop)->Prop)) (B_84:(nat->Prop)), ((finite_finite_nat B_84)->(((ord_less_eq_nat_o B_84) ((image_a_o_nat F_39) A_147))->((ex ((x_a->Prop)->Prop)) (fun (C_34:((x_a->Prop)->Prop))=> ((and ((and ((ord_less_eq_a_o_o C_34) A_147)) (finite_finite_a_o C_34))) (((eq (nat->Prop)) B_84) ((image_a_o_nat F_39) C_34)))))))) of role axiom named fact_237_finite__subset__image % A new axiom: (forall (F_39:((x_a->Prop)->nat)) (A_147:((x_a->Prop)->Prop)) (B_84:(nat->Prop)), ((finite_finite_nat B_84)->(((ord_less_eq_nat_o B_84) ((image_a_o_nat F_39) A_147))->((ex ((x_a->Prop)->Prop)) (fun (C_34:((x_a->Prop)->Prop))=> ((and ((and ((ord_less_eq_a_o_o C_34) A_147)) (finite_finite_a_o C_34))) (((eq (nat->Prop)) B_84) ((image_a_o_nat F_39) C_34)))))))) % FOF formula (forall (F_39:(pname->nat)) (A_147:(pname->Prop)) (B_84:(nat->Prop)), ((finite_finite_nat B_84)->(((ord_less_eq_nat_o B_84) ((image_pname_nat F_39) A_147))->((ex (pname->Prop)) (fun (C_34:(pname->Prop))=> ((and ((and ((ord_less_eq_pname_o C_34) A_147)) (finite_finite_pname C_34))) (((eq (nat->Prop)) B_84) ((image_pname_nat F_39) C_34)))))))) of role axiom named fact_238_finite__subset__image % A new axiom: (forall (F_39:(pname->nat)) (A_147:(pname->Prop)) (B_84:(nat->Prop)), ((finite_finite_nat B_84)->(((ord_less_eq_nat_o B_84) ((image_pname_nat F_39) A_147))->((ex (pname->Prop)) (fun (C_34:(pname->Prop))=> ((and ((and ((ord_less_eq_pname_o C_34) A_147)) (finite_finite_pname C_34))) (((eq (nat->Prop)) B_84) ((image_pname_nat F_39) C_34)))))))) % FOF formula (forall (F_39:(x_a->int)) (A_147:(x_a->Prop)) (B_84:(int->Prop)), ((finite_finite_int B_84)->(((ord_less_eq_int_o B_84) ((image_a_int F_39) A_147))->((ex (x_a->Prop)) (fun (C_34:(x_a->Prop))=> ((and ((and ((ord_less_eq_a_o C_34) A_147)) (finite_finite_a C_34))) (((eq (int->Prop)) B_84) ((image_a_int F_39) C_34)))))))) of role axiom named fact_239_finite__subset__image % A new axiom: (forall (F_39:(x_a->int)) (A_147:(x_a->Prop)) (B_84:(int->Prop)), ((finite_finite_int B_84)->(((ord_less_eq_int_o B_84) ((image_a_int F_39) A_147))->((ex (x_a->Prop)) (fun (C_34:(x_a->Prop))=> ((and ((and ((ord_less_eq_a_o C_34) A_147)) (finite_finite_a C_34))) (((eq (int->Prop)) B_84) ((image_a_int F_39) C_34)))))))) % FOF formula (forall (F_39:((int->Prop)->int)) (A_147:((int->Prop)->Prop)) (B_84:(int->Prop)), ((finite_finite_int B_84)->(((ord_less_eq_int_o B_84) ((image_int_o_int F_39) A_147))->((ex ((int->Prop)->Prop)) (fun (C_34:((int->Prop)->Prop))=> ((and ((and ((ord_less_eq_int_o_o C_34) A_147)) (finite_finite_int_o C_34))) (((eq (int->Prop)) B_84) ((image_int_o_int F_39) C_34)))))))) of role axiom named fact_240_finite__subset__image % A new axiom: (forall (F_39:((int->Prop)->int)) (A_147:((int->Prop)->Prop)) (B_84:(int->Prop)), ((finite_finite_int B_84)->(((ord_less_eq_int_o B_84) ((image_int_o_int F_39) A_147))->((ex ((int->Prop)->Prop)) (fun (C_34:((int->Prop)->Prop))=> ((and ((and ((ord_less_eq_int_o_o C_34) A_147)) (finite_finite_int_o C_34))) (((eq (int->Prop)) B_84) ((image_int_o_int F_39) C_34)))))))) % FOF formula (forall (F_39:((nat->Prop)->int)) (A_147:((nat->Prop)->Prop)) (B_84:(int->Prop)), ((finite_finite_int B_84)->(((ord_less_eq_int_o B_84) ((image_nat_o_int F_39) A_147))->((ex ((nat->Prop)->Prop)) (fun (C_34:((nat->Prop)->Prop))=> ((and ((and ((ord_less_eq_nat_o_o C_34) A_147)) (finite_finite_nat_o C_34))) (((eq (int->Prop)) B_84) ((image_nat_o_int F_39) C_34)))))))) of role axiom named fact_241_finite__subset__image % A new axiom: (forall (F_39:((nat->Prop)->int)) (A_147:((nat->Prop)->Prop)) (B_84:(int->Prop)), ((finite_finite_int B_84)->(((ord_less_eq_int_o B_84) ((image_nat_o_int F_39) A_147))->((ex ((nat->Prop)->Prop)) (fun (C_34:((nat->Prop)->Prop))=> ((and ((and ((ord_less_eq_nat_o_o C_34) A_147)) (finite_finite_nat_o C_34))) (((eq (int->Prop)) B_84) ((image_nat_o_int F_39) C_34)))))))) % FOF formula (forall (F_39:((pname->Prop)->int)) (A_147:((pname->Prop)->Prop)) (B_84:(int->Prop)), ((finite_finite_int B_84)->(((ord_less_eq_int_o B_84) ((image_pname_o_int F_39) A_147))->((ex ((pname->Prop)->Prop)) (fun (C_34:((pname->Prop)->Prop))=> ((and ((and ((ord_le1205211808me_o_o C_34) A_147)) (finite297249702name_o C_34))) (((eq (int->Prop)) B_84) ((image_pname_o_int F_39) C_34)))))))) of role axiom named fact_242_finite__subset__image % A new axiom: (forall (F_39:((pname->Prop)->int)) (A_147:((pname->Prop)->Prop)) (B_84:(int->Prop)), ((finite_finite_int B_84)->(((ord_less_eq_int_o B_84) ((image_pname_o_int F_39) A_147))->((ex ((pname->Prop)->Prop)) (fun (C_34:((pname->Prop)->Prop))=> ((and ((and ((ord_le1205211808me_o_o C_34) A_147)) (finite297249702name_o C_34))) (((eq (int->Prop)) B_84) ((image_pname_o_int F_39) C_34)))))))) % FOF formula (forall (F_39:((x_a->Prop)->int)) (A_147:((x_a->Prop)->Prop)) (B_84:(int->Prop)), ((finite_finite_int B_84)->(((ord_less_eq_int_o B_84) ((image_a_o_int F_39) A_147))->((ex ((x_a->Prop)->Prop)) (fun (C_34:((x_a->Prop)->Prop))=> ((and ((and ((ord_less_eq_a_o_o C_34) A_147)) (finite_finite_a_o C_34))) (((eq (int->Prop)) B_84) ((image_a_o_int F_39) C_34)))))))) of role axiom named fact_243_finite__subset__image % A new axiom: (forall (F_39:((x_a->Prop)->int)) (A_147:((x_a->Prop)->Prop)) (B_84:(int->Prop)), ((finite_finite_int B_84)->(((ord_less_eq_int_o B_84) ((image_a_o_int F_39) A_147))->((ex ((x_a->Prop)->Prop)) (fun (C_34:((x_a->Prop)->Prop))=> ((and ((and ((ord_less_eq_a_o_o C_34) A_147)) (finite_finite_a_o C_34))) (((eq (int->Prop)) B_84) ((image_a_o_int F_39) C_34)))))))) % FOF formula (forall (F_39:(pname->int)) (A_147:(pname->Prop)) (B_84:(int->Prop)), ((finite_finite_int B_84)->(((ord_less_eq_int_o B_84) ((image_pname_int F_39) A_147))->((ex (pname->Prop)) (fun (C_34:(pname->Prop))=> ((and ((and ((ord_less_eq_pname_o C_34) A_147)) (finite_finite_pname C_34))) (((eq (int->Prop)) B_84) ((image_pname_int F_39) C_34)))))))) of role axiom named fact_244_finite__subset__image % A new axiom: (forall (F_39:(pname->int)) (A_147:(pname->Prop)) (B_84:(int->Prop)), ((finite_finite_int B_84)->(((ord_less_eq_int_o B_84) ((image_pname_int F_39) A_147))->((ex (pname->Prop)) (fun (C_34:(pname->Prop))=> ((and ((and ((ord_less_eq_pname_o C_34) A_147)) (finite_finite_pname C_34))) (((eq (int->Prop)) B_84) ((image_pname_int F_39) C_34)))))))) % FOF formula (forall (F_39:(pname->(int->Prop))) (A_147:(pname->Prop)) (B_84:((int->Prop)->Prop)), ((finite_finite_int_o B_84)->(((ord_less_eq_int_o_o B_84) ((image_pname_int_o F_39) A_147))->((ex (pname->Prop)) (fun (C_34:(pname->Prop))=> ((and ((and ((ord_less_eq_pname_o C_34) A_147)) (finite_finite_pname C_34))) (((eq ((int->Prop)->Prop)) B_84) ((image_pname_int_o F_39) C_34)))))))) of role axiom named fact_245_finite__subset__image % A new axiom: (forall (F_39:(pname->(int->Prop))) (A_147:(pname->Prop)) (B_84:((int->Prop)->Prop)), ((finite_finite_int_o B_84)->(((ord_less_eq_int_o_o B_84) ((image_pname_int_o F_39) A_147))->((ex (pname->Prop)) (fun (C_34:(pname->Prop))=> ((and ((and ((ord_less_eq_pname_o C_34) A_147)) (finite_finite_pname C_34))) (((eq ((int->Prop)->Prop)) B_84) ((image_pname_int_o F_39) C_34)))))))) % FOF formula (forall (F_39:(pname->(nat->Prop))) (A_147:(pname->Prop)) (B_84:((nat->Prop)->Prop)), ((finite_finite_nat_o B_84)->(((ord_less_eq_nat_o_o B_84) ((image_pname_nat_o F_39) A_147))->((ex (pname->Prop)) (fun (C_34:(pname->Prop))=> ((and ((and ((ord_less_eq_pname_o C_34) A_147)) (finite_finite_pname C_34))) (((eq ((nat->Prop)->Prop)) B_84) ((image_pname_nat_o F_39) C_34)))))))) of role axiom named fact_246_finite__subset__image % A new axiom: (forall (F_39:(pname->(nat->Prop))) (A_147:(pname->Prop)) (B_84:((nat->Prop)->Prop)), ((finite_finite_nat_o B_84)->(((ord_less_eq_nat_o_o B_84) ((image_pname_nat_o F_39) A_147))->((ex (pname->Prop)) (fun (C_34:(pname->Prop))=> ((and ((and ((ord_less_eq_pname_o C_34) A_147)) (finite_finite_pname C_34))) (((eq ((nat->Prop)->Prop)) B_84) ((image_pname_nat_o F_39) C_34)))))))) % FOF formula (forall (F_39:(pname->(pname->Prop))) (A_147:(pname->Prop)) (B_84:((pname->Prop)->Prop)), ((finite297249702name_o B_84)->(((ord_le1205211808me_o_o B_84) ((image_pname_pname_o F_39) A_147))->((ex (pname->Prop)) (fun (C_34:(pname->Prop))=> ((and ((and ((ord_less_eq_pname_o C_34) A_147)) (finite_finite_pname C_34))) (((eq ((pname->Prop)->Prop)) B_84) ((image_pname_pname_o F_39) C_34)))))))) of role axiom named fact_247_finite__subset__image % A new axiom: (forall (F_39:(pname->(pname->Prop))) (A_147:(pname->Prop)) (B_84:((pname->Prop)->Prop)), ((finite297249702name_o B_84)->(((ord_le1205211808me_o_o B_84) ((image_pname_pname_o F_39) A_147))->((ex (pname->Prop)) (fun (C_34:(pname->Prop))=> ((and ((and ((ord_less_eq_pname_o C_34) A_147)) (finite_finite_pname C_34))) (((eq ((pname->Prop)->Prop)) B_84) ((image_pname_pname_o F_39) C_34)))))))) % FOF formula (forall (F_39:(pname->(x_a->Prop))) (A_147:(pname->Prop)) (B_84:((x_a->Prop)->Prop)), ((finite_finite_a_o B_84)->(((ord_less_eq_a_o_o B_84) ((image_pname_a_o F_39) A_147))->((ex (pname->Prop)) (fun (C_34:(pname->Prop))=> ((and ((and ((ord_less_eq_pname_o C_34) A_147)) (finite_finite_pname C_34))) (((eq ((x_a->Prop)->Prop)) B_84) ((image_pname_a_o F_39) C_34)))))))) of role axiom named fact_248_finite__subset__image % A new axiom: (forall (F_39:(pname->(x_a->Prop))) (A_147:(pname->Prop)) (B_84:((x_a->Prop)->Prop)), ((finite_finite_a_o B_84)->(((ord_less_eq_a_o_o B_84) ((image_pname_a_o F_39) A_147))->((ex (pname->Prop)) (fun (C_34:(pname->Prop))=> ((and ((and ((ord_less_eq_pname_o C_34) A_147)) (finite_finite_pname C_34))) (((eq ((x_a->Prop)->Prop)) B_84) ((image_pname_a_o F_39) C_34)))))))) % FOF formula (forall (F_39:(pname->pname)) (A_147:(pname->Prop)) (B_84:(pname->Prop)), ((finite_finite_pname B_84)->(((ord_less_eq_pname_o B_84) ((image_pname_pname F_39) A_147))->((ex (pname->Prop)) (fun (C_34:(pname->Prop))=> ((and ((and ((ord_less_eq_pname_o C_34) A_147)) (finite_finite_pname C_34))) (((eq (pname->Prop)) B_84) ((image_pname_pname F_39) C_34)))))))) of role axiom named fact_249_finite__subset__image % A new axiom: (forall (F_39:(pname->pname)) (A_147:(pname->Prop)) (B_84:(pname->Prop)), ((finite_finite_pname B_84)->(((ord_less_eq_pname_o B_84) ((image_pname_pname F_39) A_147))->((ex (pname->Prop)) (fun (C_34:(pname->Prop))=> ((and ((and ((ord_less_eq_pname_o C_34) A_147)) (finite_finite_pname C_34))) (((eq (pname->Prop)) B_84) ((image_pname_pname F_39) C_34)))))))) % FOF formula (forall (F_39:(nat->x_a)) (A_147:(nat->Prop)) (B_84:(x_a->Prop)), ((finite_finite_a B_84)->(((ord_less_eq_a_o B_84) ((image_nat_a F_39) A_147))->((ex (nat->Prop)) (fun (C_34:(nat->Prop))=> ((and ((and ((ord_less_eq_nat_o C_34) A_147)) (finite_finite_nat C_34))) (((eq (x_a->Prop)) B_84) ((image_nat_a F_39) C_34)))))))) of role axiom named fact_250_finite__subset__image % A new axiom: (forall (F_39:(nat->x_a)) (A_147:(nat->Prop)) (B_84:(x_a->Prop)), ((finite_finite_a B_84)->(((ord_less_eq_a_o B_84) ((image_nat_a F_39) A_147))->((ex (nat->Prop)) (fun (C_34:(nat->Prop))=> ((and ((and ((ord_less_eq_nat_o C_34) A_147)) (finite_finite_nat C_34))) (((eq (x_a->Prop)) B_84) ((image_nat_a F_39) C_34)))))))) % FOF formula (forall (F_39:(nat->(int->Prop))) (A_147:(nat->Prop)) (B_84:((int->Prop)->Prop)), ((finite_finite_int_o B_84)->(((ord_less_eq_int_o_o B_84) ((image_nat_int_o F_39) A_147))->((ex (nat->Prop)) (fun (C_34:(nat->Prop))=> ((and ((and ((ord_less_eq_nat_o C_34) A_147)) (finite_finite_nat C_34))) (((eq ((int->Prop)->Prop)) B_84) ((image_nat_int_o F_39) C_34)))))))) of role axiom named fact_251_finite__subset__image % A new axiom: (forall (F_39:(nat->(int->Prop))) (A_147:(nat->Prop)) (B_84:((int->Prop)->Prop)), ((finite_finite_int_o B_84)->(((ord_less_eq_int_o_o B_84) ((image_nat_int_o F_39) A_147))->((ex (nat->Prop)) (fun (C_34:(nat->Prop))=> ((and ((and ((ord_less_eq_nat_o C_34) A_147)) (finite_finite_nat C_34))) (((eq ((int->Prop)->Prop)) B_84) ((image_nat_int_o F_39) C_34)))))))) % FOF formula (forall (F_39:(nat->(nat->Prop))) (A_147:(nat->Prop)) (B_84:((nat->Prop)->Prop)), ((finite_finite_nat_o B_84)->(((ord_less_eq_nat_o_o B_84) ((image_nat_nat_o F_39) A_147))->((ex (nat->Prop)) (fun (C_34:(nat->Prop))=> ((and ((and ((ord_less_eq_nat_o C_34) A_147)) (finite_finite_nat C_34))) (((eq ((nat->Prop)->Prop)) B_84) ((image_nat_nat_o F_39) C_34)))))))) of role axiom named fact_252_finite__subset__image % A new axiom: (forall (F_39:(nat->(nat->Prop))) (A_147:(nat->Prop)) (B_84:((nat->Prop)->Prop)), ((finite_finite_nat_o B_84)->(((ord_less_eq_nat_o_o B_84) ((image_nat_nat_o F_39) A_147))->((ex (nat->Prop)) (fun (C_34:(nat->Prop))=> ((and ((and ((ord_less_eq_nat_o C_34) A_147)) (finite_finite_nat C_34))) (((eq ((nat->Prop)->Prop)) B_84) ((image_nat_nat_o F_39) C_34)))))))) % FOF formula (forall (F_39:(nat->(pname->Prop))) (A_147:(nat->Prop)) (B_84:((pname->Prop)->Prop)), ((finite297249702name_o B_84)->(((ord_le1205211808me_o_o B_84) ((image_nat_pname_o F_39) A_147))->((ex (nat->Prop)) (fun (C_34:(nat->Prop))=> ((and ((and ((ord_less_eq_nat_o C_34) A_147)) (finite_finite_nat C_34))) (((eq ((pname->Prop)->Prop)) B_84) ((image_nat_pname_o F_39) C_34)))))))) of role axiom named fact_253_finite__subset__image % A new axiom: (forall (F_39:(nat->(pname->Prop))) (A_147:(nat->Prop)) (B_84:((pname->Prop)->Prop)), ((finite297249702name_o B_84)->(((ord_le1205211808me_o_o B_84) ((image_nat_pname_o F_39) A_147))->((ex (nat->Prop)) (fun (C_34:(nat->Prop))=> ((and ((and ((ord_less_eq_nat_o C_34) A_147)) (finite_finite_nat C_34))) (((eq ((pname->Prop)->Prop)) B_84) ((image_nat_pname_o F_39) C_34)))))))) % FOF formula (forall (F_39:(nat->(x_a->Prop))) (A_147:(nat->Prop)) (B_84:((x_a->Prop)->Prop)), ((finite_finite_a_o B_84)->(((ord_less_eq_a_o_o B_84) ((image_nat_a_o F_39) A_147))->((ex (nat->Prop)) (fun (C_34:(nat->Prop))=> ((and ((and ((ord_less_eq_nat_o C_34) A_147)) (finite_finite_nat C_34))) (((eq ((x_a->Prop)->Prop)) B_84) ((image_nat_a_o F_39) C_34)))))))) of role axiom named fact_254_finite__subset__image % A new axiom: (forall (F_39:(nat->(x_a->Prop))) (A_147:(nat->Prop)) (B_84:((x_a->Prop)->Prop)), ((finite_finite_a_o B_84)->(((ord_less_eq_a_o_o B_84) ((image_nat_a_o F_39) A_147))->((ex (nat->Prop)) (fun (C_34:(nat->Prop))=> ((and ((and ((ord_less_eq_nat_o C_34) A_147)) (finite_finite_nat C_34))) (((eq ((x_a->Prop)->Prop)) B_84) ((image_nat_a_o F_39) C_34)))))))) % FOF formula (forall (F_39:(nat->pname)) (A_147:(nat->Prop)) (B_84:(pname->Prop)), ((finite_finite_pname B_84)->(((ord_less_eq_pname_o B_84) ((image_nat_pname F_39) A_147))->((ex (nat->Prop)) (fun (C_34:(nat->Prop))=> ((and ((and ((ord_less_eq_nat_o C_34) A_147)) (finite_finite_nat C_34))) (((eq (pname->Prop)) B_84) ((image_nat_pname F_39) C_34)))))))) of role axiom named fact_255_finite__subset__image % A new axiom: (forall (F_39:(nat->pname)) (A_147:(nat->Prop)) (B_84:(pname->Prop)), ((finite_finite_pname B_84)->(((ord_less_eq_pname_o B_84) ((image_nat_pname F_39) A_147))->((ex (nat->Prop)) (fun (C_34:(nat->Prop))=> ((and ((and ((ord_less_eq_nat_o C_34) A_147)) (finite_finite_nat C_34))) (((eq (pname->Prop)) B_84) ((image_nat_pname F_39) C_34)))))))) % FOF formula (forall (F_39:(int->x_a)) (A_147:(int->Prop)) (B_84:(x_a->Prop)), ((finite_finite_a B_84)->(((ord_less_eq_a_o B_84) ((image_int_a F_39) A_147))->((ex (int->Prop)) (fun (C_34:(int->Prop))=> ((and ((and ((ord_less_eq_int_o C_34) A_147)) (finite_finite_int C_34))) (((eq (x_a->Prop)) B_84) ((image_int_a F_39) C_34)))))))) of role axiom named fact_256_finite__subset__image % A new axiom: (forall (F_39:(int->x_a)) (A_147:(int->Prop)) (B_84:(x_a->Prop)), ((finite_finite_a B_84)->(((ord_less_eq_a_o B_84) ((image_int_a F_39) A_147))->((ex (int->Prop)) (fun (C_34:(int->Prop))=> ((and ((and ((ord_less_eq_int_o C_34) A_147)) (finite_finite_int C_34))) (((eq (x_a->Prop)) B_84) ((image_int_a F_39) C_34)))))))) % FOF formula (forall (F_39:(int->(int->Prop))) (A_147:(int->Prop)) (B_84:((int->Prop)->Prop)), ((finite_finite_int_o B_84)->(((ord_less_eq_int_o_o B_84) ((image_int_int_o F_39) A_147))->((ex (int->Prop)) (fun (C_34:(int->Prop))=> ((and ((and ((ord_less_eq_int_o C_34) A_147)) (finite_finite_int C_34))) (((eq ((int->Prop)->Prop)) B_84) ((image_int_int_o F_39) C_34)))))))) of role axiom named fact_257_finite__subset__image % A new axiom: (forall (F_39:(int->(int->Prop))) (A_147:(int->Prop)) (B_84:((int->Prop)->Prop)), ((finite_finite_int_o B_84)->(((ord_less_eq_int_o_o B_84) ((image_int_int_o F_39) A_147))->((ex (int->Prop)) (fun (C_34:(int->Prop))=> ((and ((and ((ord_less_eq_int_o C_34) A_147)) (finite_finite_int C_34))) (((eq ((int->Prop)->Prop)) B_84) ((image_int_int_o F_39) C_34)))))))) % FOF formula (forall (F_39:(int->(nat->Prop))) (A_147:(int->Prop)) (B_84:((nat->Prop)->Prop)), ((finite_finite_nat_o B_84)->(((ord_less_eq_nat_o_o B_84) ((image_int_nat_o F_39) A_147))->((ex (int->Prop)) (fun (C_34:(int->Prop))=> ((and ((and ((ord_less_eq_int_o C_34) A_147)) (finite_finite_int C_34))) (((eq ((nat->Prop)->Prop)) B_84) ((image_int_nat_o F_39) C_34)))))))) of role axiom named fact_258_finite__subset__image % A new axiom: (forall (F_39:(int->(nat->Prop))) (A_147:(int->Prop)) (B_84:((nat->Prop)->Prop)), ((finite_finite_nat_o B_84)->(((ord_less_eq_nat_o_o B_84) ((image_int_nat_o F_39) A_147))->((ex (int->Prop)) (fun (C_34:(int->Prop))=> ((and ((and ((ord_less_eq_int_o C_34) A_147)) (finite_finite_int C_34))) (((eq ((nat->Prop)->Prop)) B_84) ((image_int_nat_o F_39) C_34)))))))) % FOF formula (forall (F_39:(int->(pname->Prop))) (A_147:(int->Prop)) (B_84:((pname->Prop)->Prop)), ((finite297249702name_o B_84)->(((ord_le1205211808me_o_o B_84) ((image_int_pname_o F_39) A_147))->((ex (int->Prop)) (fun (C_34:(int->Prop))=> ((and ((and ((ord_less_eq_int_o C_34) A_147)) (finite_finite_int C_34))) (((eq ((pname->Prop)->Prop)) B_84) ((image_int_pname_o F_39) C_34)))))))) of role axiom named fact_259_finite__subset__image % A new axiom: (forall (F_39:(int->(pname->Prop))) (A_147:(int->Prop)) (B_84:((pname->Prop)->Prop)), ((finite297249702name_o B_84)->(((ord_le1205211808me_o_o B_84) ((image_int_pname_o F_39) A_147))->((ex (int->Prop)) (fun (C_34:(int->Prop))=> ((and ((and ((ord_less_eq_int_o C_34) A_147)) (finite_finite_int C_34))) (((eq ((pname->Prop)->Prop)) B_84) ((image_int_pname_o F_39) C_34)))))))) % FOF formula (forall (F_39:(int->(x_a->Prop))) (A_147:(int->Prop)) (B_84:((x_a->Prop)->Prop)), ((finite_finite_a_o B_84)->(((ord_less_eq_a_o_o B_84) ((image_int_a_o F_39) A_147))->((ex (int->Prop)) (fun (C_34:(int->Prop))=> ((and ((and ((ord_less_eq_int_o C_34) A_147)) (finite_finite_int C_34))) (((eq ((x_a->Prop)->Prop)) B_84) ((image_int_a_o F_39) C_34)))))))) of role axiom named fact_260_finite__subset__image % A new axiom: (forall (F_39:(int->(x_a->Prop))) (A_147:(int->Prop)) (B_84:((x_a->Prop)->Prop)), ((finite_finite_a_o B_84)->(((ord_less_eq_a_o_o B_84) ((image_int_a_o F_39) A_147))->((ex (int->Prop)) (fun (C_34:(int->Prop))=> ((and ((and ((ord_less_eq_int_o C_34) A_147)) (finite_finite_int C_34))) (((eq ((x_a->Prop)->Prop)) B_84) ((image_int_a_o F_39) C_34)))))))) % FOF formula (forall (F_39:(int->pname)) (A_147:(int->Prop)) (B_84:(pname->Prop)), ((finite_finite_pname B_84)->(((ord_less_eq_pname_o B_84) ((image_int_pname F_39) A_147))->((ex (int->Prop)) (fun (C_34:(int->Prop))=> ((and ((and ((ord_less_eq_int_o C_34) A_147)) (finite_finite_int C_34))) (((eq (pname->Prop)) B_84) ((image_int_pname F_39) C_34)))))))) of role axiom named fact_261_finite__subset__image % A new axiom: (forall (F_39:(int->pname)) (A_147:(int->Prop)) (B_84:(pname->Prop)), ((finite_finite_pname B_84)->(((ord_less_eq_pname_o B_84) ((image_int_pname F_39) A_147))->((ex (int->Prop)) (fun (C_34:(int->Prop))=> ((and ((and ((ord_less_eq_int_o C_34) A_147)) (finite_finite_int C_34))) (((eq (pname->Prop)) B_84) ((image_int_pname F_39) C_34)))))))) % FOF formula (forall (F_39:(pname->x_a)) (A_147:(pname->Prop)) (B_84:(x_a->Prop)), ((finite_finite_a B_84)->(((ord_less_eq_a_o B_84) ((image_pname_a F_39) A_147))->((ex (pname->Prop)) (fun (C_34:(pname->Prop))=> ((and ((and ((ord_less_eq_pname_o C_34) A_147)) (finite_finite_pname C_34))) (((eq (x_a->Prop)) B_84) ((image_pname_a F_39) C_34)))))))) of role axiom named fact_262_finite__subset__image % A new axiom: (forall (F_39:(pname->x_a)) (A_147:(pname->Prop)) (B_84:(x_a->Prop)), ((finite_finite_a B_84)->(((ord_less_eq_a_o B_84) ((image_pname_a F_39) A_147))->((ex (pname->Prop)) (fun (C_34:(pname->Prop))=> ((and ((and ((ord_less_eq_pname_o C_34) A_147)) (finite_finite_pname C_34))) (((eq (x_a->Prop)) B_84) ((image_pname_a F_39) C_34)))))))) % FOF formula (forall (F_39:(nat->int)) (A_147:(nat->Prop)) (B_84:(int->Prop)), ((finite_finite_int B_84)->(((ord_less_eq_int_o B_84) ((image_nat_int F_39) A_147))->((ex (nat->Prop)) (fun (C_34:(nat->Prop))=> ((and ((and ((ord_less_eq_nat_o C_34) A_147)) (finite_finite_nat C_34))) (((eq (int->Prop)) B_84) ((image_nat_int F_39) C_34)))))))) of role axiom named fact_263_finite__subset__image % A new axiom: (forall (F_39:(nat->int)) (A_147:(nat->Prop)) (B_84:(int->Prop)), ((finite_finite_int B_84)->(((ord_less_eq_int_o B_84) ((image_nat_int F_39) A_147))->((ex (nat->Prop)) (fun (C_34:(nat->Prop))=> ((and ((and ((ord_less_eq_nat_o C_34) A_147)) (finite_finite_nat C_34))) (((eq (int->Prop)) B_84) ((image_nat_int F_39) C_34)))))))) % FOF formula (forall (N_4:nat) (N_3:nat) (F_38:(nat->(pname->Prop))), ((forall (N_1:nat), ((ord_less_eq_pname_o (F_38 N_1)) (F_38 (suc N_1))))->(((ord_less_eq_nat N_4) N_3)->((ord_less_eq_pname_o (F_38 N_4)) (F_38 N_3))))) of role axiom named fact_264_lift__Suc__mono__le % A new axiom: (forall (N_4:nat) (N_3:nat) (F_38:(nat->(pname->Prop))), ((forall (N_1:nat), ((ord_less_eq_pname_o (F_38 N_1)) (F_38 (suc N_1))))->(((ord_less_eq_nat N_4) N_3)->((ord_less_eq_pname_o (F_38 N_4)) (F_38 N_3))))) % FOF formula (forall (N_4:nat) (N_3:nat) (F_38:(nat->Prop)), ((forall (N_1:nat), ((ord_less_eq_o (F_38 N_1)) (F_38 (suc N_1))))->(((ord_less_eq_nat N_4) N_3)->((ord_less_eq_o (F_38 N_4)) (F_38 N_3))))) of role axiom named fact_265_lift__Suc__mono__le % A new axiom: (forall (N_4:nat) (N_3:nat) (F_38:(nat->Prop)), ((forall (N_1:nat), ((ord_less_eq_o (F_38 N_1)) (F_38 (suc N_1))))->(((ord_less_eq_nat N_4) N_3)->((ord_less_eq_o (F_38 N_4)) (F_38 N_3))))) % FOF formula (forall (N_4:nat) (N_3:nat) (F_38:(nat->(x_a->Prop))), ((forall (N_1:nat), ((ord_less_eq_a_o (F_38 N_1)) (F_38 (suc N_1))))->(((ord_less_eq_nat N_4) N_3)->((ord_less_eq_a_o (F_38 N_4)) (F_38 N_3))))) of role axiom named fact_266_lift__Suc__mono__le % A new axiom: (forall (N_4:nat) (N_3:nat) (F_38:(nat->(x_a->Prop))), ((forall (N_1:nat), ((ord_less_eq_a_o (F_38 N_1)) (F_38 (suc N_1))))->(((ord_less_eq_nat N_4) N_3)->((ord_less_eq_a_o (F_38 N_4)) (F_38 N_3))))) % FOF formula (forall (N_4:nat) (N_3:nat) (F_38:(nat->nat)), ((forall (N_1:nat), ((ord_less_eq_nat (F_38 N_1)) (F_38 (suc N_1))))->(((ord_less_eq_nat N_4) N_3)->((ord_less_eq_nat (F_38 N_4)) (F_38 N_3))))) of role axiom named fact_267_lift__Suc__mono__le % A new axiom: (forall (N_4:nat) (N_3:nat) (F_38:(nat->nat)), ((forall (N_1:nat), ((ord_less_eq_nat (F_38 N_1)) (F_38 (suc N_1))))->(((ord_less_eq_nat N_4) N_3)->((ord_less_eq_nat (F_38 N_4)) (F_38 N_3))))) % FOF formula (forall (N_4:nat) (N_3:nat) (F_38:(nat->int)), ((forall (N_1:nat), ((ord_less_eq_int (F_38 N_1)) (F_38 (suc N_1))))->(((ord_less_eq_nat N_4) N_3)->((ord_less_eq_int (F_38 N_4)) (F_38 N_3))))) of role axiom named fact_268_lift__Suc__mono__le % A new axiom: (forall (N_4:nat) (N_3:nat) (F_38:(nat->int)), ((forall (N_1:nat), ((ord_less_eq_int (F_38 N_1)) (F_38 (suc N_1))))->(((ord_less_eq_nat N_4) N_3)->((ord_less_eq_int (F_38 N_4)) (F_38 N_3))))) % FOF formula (forall (N_4:nat) (N_3:nat) (F_38:(nat->(nat->Prop))), ((forall (N_1:nat), ((ord_less_eq_nat_o (F_38 N_1)) (F_38 (suc N_1))))->(((ord_less_eq_nat N_4) N_3)->((ord_less_eq_nat_o (F_38 N_4)) (F_38 N_3))))) of role axiom named fact_269_lift__Suc__mono__le % A new axiom: (forall (N_4:nat) (N_3:nat) (F_38:(nat->(nat->Prop))), ((forall (N_1:nat), ((ord_less_eq_nat_o (F_38 N_1)) (F_38 (suc N_1))))->(((ord_less_eq_nat N_4) N_3)->((ord_less_eq_nat_o (F_38 N_4)) (F_38 N_3))))) % FOF formula (forall (N_4:nat) (N_3:nat) (F_38:(nat->(int->Prop))), ((forall (N_1:nat), ((ord_less_eq_int_o (F_38 N_1)) (F_38 (suc N_1))))->(((ord_less_eq_nat N_4) N_3)->((ord_less_eq_int_o (F_38 N_4)) (F_38 N_3))))) of role axiom named fact_270_lift__Suc__mono__le % A new axiom: (forall (N_4:nat) (N_3:nat) (F_38:(nat->(int->Prop))), ((forall (N_1:nat), ((ord_less_eq_int_o (F_38 N_1)) (F_38 (suc N_1))))->(((ord_less_eq_nat N_4) N_3)->((ord_less_eq_int_o (F_38 N_4)) (F_38 N_3))))) % FOF formula (forall (F_37:(nat->(int->Prop))) (A_146:(nat->Prop)), (((finite_finite_nat A_146)->False)->((finite_finite_int_o ((image_nat_int_o F_37) A_146))->((ex nat) (fun (X_1:nat)=> ((and ((member_nat X_1) A_146)) ((finite_finite_nat (collect_nat (fun (A_37:nat)=> ((and ((member_nat A_37) A_146)) (((eq (int->Prop)) (F_37 A_37)) (F_37 X_1))))))->False))))))) of role axiom named fact_271_pigeonhole__infinite % A new axiom: (forall (F_37:(nat->(int->Prop))) (A_146:(nat->Prop)), (((finite_finite_nat A_146)->False)->((finite_finite_int_o ((image_nat_int_o F_37) A_146))->((ex nat) (fun (X_1:nat)=> ((and ((member_nat X_1) A_146)) ((finite_finite_nat (collect_nat (fun (A_37:nat)=> ((and ((member_nat A_37) A_146)) (((eq (int->Prop)) (F_37 A_37)) (F_37 X_1))))))->False))))))) % FOF formula (forall (F_37:(nat->(nat->Prop))) (A_146:(nat->Prop)), (((finite_finite_nat A_146)->False)->((finite_finite_nat_o ((image_nat_nat_o F_37) A_146))->((ex nat) (fun (X_1:nat)=> ((and ((member_nat X_1) A_146)) ((finite_finite_nat (collect_nat (fun (A_37:nat)=> ((and ((member_nat A_37) A_146)) (((eq (nat->Prop)) (F_37 A_37)) (F_37 X_1))))))->False))))))) of role axiom named fact_272_pigeonhole__infinite % A new axiom: (forall (F_37:(nat->(nat->Prop))) (A_146:(nat->Prop)), (((finite_finite_nat A_146)->False)->((finite_finite_nat_o ((image_nat_nat_o F_37) A_146))->((ex nat) (fun (X_1:nat)=> ((and ((member_nat X_1) A_146)) ((finite_finite_nat (collect_nat (fun (A_37:nat)=> ((and ((member_nat A_37) A_146)) (((eq (nat->Prop)) (F_37 A_37)) (F_37 X_1))))))->False))))))) % FOF formula (forall (F_37:(nat->(pname->Prop))) (A_146:(nat->Prop)), (((finite_finite_nat A_146)->False)->((finite297249702name_o ((image_nat_pname_o F_37) A_146))->((ex nat) (fun (X_1:nat)=> ((and ((member_nat X_1) A_146)) ((finite_finite_nat (collect_nat (fun (A_37:nat)=> ((and ((member_nat A_37) A_146)) (((eq (pname->Prop)) (F_37 A_37)) (F_37 X_1))))))->False))))))) of role axiom named fact_273_pigeonhole__infinite % A new axiom: (forall (F_37:(nat->(pname->Prop))) (A_146:(nat->Prop)), (((finite_finite_nat A_146)->False)->((finite297249702name_o ((image_nat_pname_o F_37) A_146))->((ex nat) (fun (X_1:nat)=> ((and ((member_nat X_1) A_146)) ((finite_finite_nat (collect_nat (fun (A_37:nat)=> ((and ((member_nat A_37) A_146)) (((eq (pname->Prop)) (F_37 A_37)) (F_37 X_1))))))->False))))))) % FOF formula (forall (F_37:(nat->(x_a->Prop))) (A_146:(nat->Prop)), (((finite_finite_nat A_146)->False)->((finite_finite_a_o ((image_nat_a_o F_37) A_146))->((ex nat) (fun (X_1:nat)=> ((and ((member_nat X_1) A_146)) ((finite_finite_nat (collect_nat (fun (A_37:nat)=> ((and ((member_nat A_37) A_146)) (((eq (x_a->Prop)) (F_37 A_37)) (F_37 X_1))))))->False))))))) of role axiom named fact_274_pigeonhole__infinite % A new axiom: (forall (F_37:(nat->(x_a->Prop))) (A_146:(nat->Prop)), (((finite_finite_nat A_146)->False)->((finite_finite_a_o ((image_nat_a_o F_37) A_146))->((ex nat) (fun (X_1:nat)=> ((and ((member_nat X_1) A_146)) ((finite_finite_nat (collect_nat (fun (A_37:nat)=> ((and ((member_nat A_37) A_146)) (((eq (x_a->Prop)) (F_37 A_37)) (F_37 X_1))))))->False))))))) % FOF formula (forall (F_37:(int->x_a)) (A_146:(int->Prop)), (((finite_finite_int A_146)->False)->((finite_finite_a ((image_int_a F_37) A_146))->((ex int) (fun (X_1:int)=> ((and ((member_int X_1) A_146)) ((finite_finite_int (collect_int (fun (A_37:int)=> ((and ((member_int A_37) A_146)) (((eq x_a) (F_37 A_37)) (F_37 X_1))))))->False))))))) of role axiom named fact_275_pigeonhole__infinite % A new axiom: (forall (F_37:(int->x_a)) (A_146:(int->Prop)), (((finite_finite_int A_146)->False)->((finite_finite_a ((image_int_a F_37) A_146))->((ex int) (fun (X_1:int)=> ((and ((member_int X_1) A_146)) ((finite_finite_int (collect_int (fun (A_37:int)=> ((and ((member_int A_37) A_146)) (((eq x_a) (F_37 A_37)) (F_37 X_1))))))->False))))))) % FOF formula (forall (F_37:(int->(int->Prop))) (A_146:(int->Prop)), (((finite_finite_int A_146)->False)->((finite_finite_int_o ((image_int_int_o F_37) A_146))->((ex int) (fun (X_1:int)=> ((and ((member_int X_1) A_146)) ((finite_finite_int (collect_int (fun (A_37:int)=> ((and ((member_int A_37) A_146)) (((eq (int->Prop)) (F_37 A_37)) (F_37 X_1))))))->False))))))) of role axiom named fact_276_pigeonhole__infinite % A new axiom: (forall (F_37:(int->(int->Prop))) (A_146:(int->Prop)), (((finite_finite_int A_146)->False)->((finite_finite_int_o ((image_int_int_o F_37) A_146))->((ex int) (fun (X_1:int)=> ((and ((member_int X_1) A_146)) ((finite_finite_int (collect_int (fun (A_37:int)=> ((and ((member_int A_37) A_146)) (((eq (int->Prop)) (F_37 A_37)) (F_37 X_1))))))->False))))))) % FOF formula (forall (F_37:(int->(nat->Prop))) (A_146:(int->Prop)), (((finite_finite_int A_146)->False)->((finite_finite_nat_o ((image_int_nat_o F_37) A_146))->((ex int) (fun (X_1:int)=> ((and ((member_int X_1) A_146)) ((finite_finite_int (collect_int (fun (A_37:int)=> ((and ((member_int A_37) A_146)) (((eq (nat->Prop)) (F_37 A_37)) (F_37 X_1))))))->False))))))) of role axiom named fact_277_pigeonhole__infinite % A new axiom: (forall (F_37:(int->(nat->Prop))) (A_146:(int->Prop)), (((finite_finite_int A_146)->False)->((finite_finite_nat_o ((image_int_nat_o F_37) A_146))->((ex int) (fun (X_1:int)=> ((and ((member_int X_1) A_146)) ((finite_finite_int (collect_int (fun (A_37:int)=> ((and ((member_int A_37) A_146)) (((eq (nat->Prop)) (F_37 A_37)) (F_37 X_1))))))->False))))))) % FOF formula (forall (F_37:(int->(pname->Prop))) (A_146:(int->Prop)), (((finite_finite_int A_146)->False)->((finite297249702name_o ((image_int_pname_o F_37) A_146))->((ex int) (fun (X_1:int)=> ((and ((member_int X_1) A_146)) ((finite_finite_int (collect_int (fun (A_37:int)=> ((and ((member_int A_37) A_146)) (((eq (pname->Prop)) (F_37 A_37)) (F_37 X_1))))))->False))))))) of role axiom named fact_278_pigeonhole__infinite % A new axiom: (forall (F_37:(int->(pname->Prop))) (A_146:(int->Prop)), (((finite_finite_int A_146)->False)->((finite297249702name_o ((image_int_pname_o F_37) A_146))->((ex int) (fun (X_1:int)=> ((and ((member_int X_1) A_146)) ((finite_finite_int (collect_int (fun (A_37:int)=> ((and ((member_int A_37) A_146)) (((eq (pname->Prop)) (F_37 A_37)) (F_37 X_1))))))->False))))))) % FOF formula (forall (F_37:(int->(x_a->Prop))) (A_146:(int->Prop)), (((finite_finite_int A_146)->False)->((finite_finite_a_o ((image_int_a_o F_37) A_146))->((ex int) (fun (X_1:int)=> ((and ((member_int X_1) A_146)) ((finite_finite_int (collect_int (fun (A_37:int)=> ((and ((member_int A_37) A_146)) (((eq (x_a->Prop)) (F_37 A_37)) (F_37 X_1))))))->False))))))) of role axiom named fact_279_pigeonhole__infinite % A new axiom: (forall (F_37:(int->(x_a->Prop))) (A_146:(int->Prop)), (((finite_finite_int A_146)->False)->((finite_finite_a_o ((image_int_a_o F_37) A_146))->((ex int) (fun (X_1:int)=> ((and ((member_int X_1) A_146)) ((finite_finite_int (collect_int (fun (A_37:int)=> ((and ((member_int A_37) A_146)) (((eq (x_a->Prop)) (F_37 A_37)) (F_37 X_1))))))->False))))))) % FOF formula (forall (F_37:(pname->x_a)) (A_146:(pname->Prop)), (((finite_finite_pname A_146)->False)->((finite_finite_a ((image_pname_a F_37) A_146))->((ex pname) (fun (X_1:pname)=> ((and ((member_pname X_1) A_146)) ((finite_finite_pname (collect_pname (fun (A_37:pname)=> ((and ((member_pname A_37) A_146)) (((eq x_a) (F_37 A_37)) (F_37 X_1))))))->False))))))) of role axiom named fact_280_pigeonhole__infinite % A new axiom: (forall (F_37:(pname->x_a)) (A_146:(pname->Prop)), (((finite_finite_pname A_146)->False)->((finite_finite_a ((image_pname_a F_37) A_146))->((ex pname) (fun (X_1:pname)=> ((and ((member_pname X_1) A_146)) ((finite_finite_pname (collect_pname (fun (A_37:pname)=> ((and ((member_pname A_37) A_146)) (((eq x_a) (F_37 A_37)) (F_37 X_1))))))->False))))))) % FOF formula (forall (F_37:(nat->int)) (A_146:(nat->Prop)), (((finite_finite_nat A_146)->False)->((finite_finite_int ((image_nat_int F_37) A_146))->((ex nat) (fun (X_1:nat)=> ((and ((member_nat X_1) A_146)) ((finite_finite_nat (collect_nat (fun (A_37:nat)=> ((and ((member_nat A_37) A_146)) (((eq int) (F_37 A_37)) (F_37 X_1))))))->False))))))) of role axiom named fact_281_pigeonhole__infinite % A new axiom: (forall (F_37:(nat->int)) (A_146:(nat->Prop)), (((finite_finite_nat A_146)->False)->((finite_finite_int ((image_nat_int F_37) A_146))->((ex nat) (fun (X_1:nat)=> ((and ((member_nat X_1) A_146)) ((finite_finite_nat (collect_nat (fun (A_37:nat)=> ((and ((member_nat A_37) A_146)) (((eq int) (F_37 A_37)) (F_37 X_1))))))->False))))))) % FOF formula (forall (A_145:(nat->Prop)) (B_83:int) (F_36:(nat->int)) (X_50:nat), ((((eq int) B_83) (F_36 X_50))->(((member_nat X_50) A_145)->((member_int B_83) ((image_nat_int F_36) A_145))))) of role axiom named fact_282_image__eqI % A new axiom: (forall (A_145:(nat->Prop)) (B_83:int) (F_36:(nat->int)) (X_50:nat), ((((eq int) B_83) (F_36 X_50))->(((member_nat X_50) A_145)->((member_int B_83) ((image_nat_int F_36) A_145))))) % FOF formula (forall (A_145:(pname->Prop)) (B_83:x_a) (F_36:(pname->x_a)) (X_50:pname), ((((eq x_a) B_83) (F_36 X_50))->(((member_pname X_50) A_145)->((member_a B_83) ((image_pname_a F_36) A_145))))) of role axiom named fact_283_image__eqI % A new axiom: (forall (A_145:(pname->Prop)) (B_83:x_a) (F_36:(pname->x_a)) (X_50:pname), ((((eq x_a) B_83) (F_36 X_50))->(((member_pname X_50) A_145)->((member_a B_83) ((image_pname_a F_36) A_145))))) % FOF formula (forall (A_144:(int->Prop)) (B_82:(int->Prop)), (((ord_less_eq_int_o A_144) B_82)->(((ord_less_eq_int_o B_82) A_144)->(((eq (int->Prop)) A_144) B_82)))) of role axiom named fact_284_equalityI % A new axiom: (forall (A_144:(int->Prop)) (B_82:(int->Prop)), (((ord_less_eq_int_o A_144) B_82)->(((ord_less_eq_int_o B_82) A_144)->(((eq (int->Prop)) A_144) B_82)))) % FOF formula (forall (A_144:(nat->Prop)) (B_82:(nat->Prop)), (((ord_less_eq_nat_o A_144) B_82)->(((ord_less_eq_nat_o B_82) A_144)->(((eq (nat->Prop)) A_144) B_82)))) of role axiom named fact_285_equalityI % A new axiom: (forall (A_144:(nat->Prop)) (B_82:(nat->Prop)), (((ord_less_eq_nat_o A_144) B_82)->(((ord_less_eq_nat_o B_82) A_144)->(((eq (nat->Prop)) A_144) B_82)))) % FOF formula (forall (A_144:(x_a->Prop)) (B_82:(x_a->Prop)), (((ord_less_eq_a_o A_144) B_82)->(((ord_less_eq_a_o B_82) A_144)->(((eq (x_a->Prop)) A_144) B_82)))) of role axiom named fact_286_equalityI % A new axiom: (forall (A_144:(x_a->Prop)) (B_82:(x_a->Prop)), (((ord_less_eq_a_o A_144) B_82)->(((ord_less_eq_a_o B_82) A_144)->(((eq (x_a->Prop)) A_144) B_82)))) % FOF formula (forall (C_33:int) (A_143:(int->Prop)) (B_81:(int->Prop)), (((ord_less_eq_int_o A_143) B_81)->(((member_int C_33) A_143)->((member_int C_33) B_81)))) of role axiom named fact_287_subsetD % A new axiom: (forall (C_33:int) (A_143:(int->Prop)) (B_81:(int->Prop)), (((ord_less_eq_int_o A_143) B_81)->(((member_int C_33) A_143)->((member_int C_33) B_81)))) % FOF formula (forall (C_33:nat) (A_143:(nat->Prop)) (B_81:(nat->Prop)), (((ord_less_eq_nat_o A_143) B_81)->(((member_nat C_33) A_143)->((member_nat C_33) B_81)))) of role axiom named fact_288_subsetD % A new axiom: (forall (C_33:nat) (A_143:(nat->Prop)) (B_81:(nat->Prop)), (((ord_less_eq_nat_o A_143) B_81)->(((member_nat C_33) A_143)->((member_nat C_33) B_81)))) % FOF formula (forall (C_33:x_a) (A_143:(x_a->Prop)) (B_81:(x_a->Prop)), (((ord_less_eq_a_o A_143) B_81)->(((member_a C_33) A_143)->((member_a C_33) B_81)))) of role axiom named fact_289_subsetD % A new axiom: (forall (C_33:x_a) (A_143:(x_a->Prop)) (B_81:(x_a->Prop)), (((ord_less_eq_a_o A_143) B_81)->(((member_a C_33) A_143)->((member_a C_33) B_81)))) % FOF formula (forall (C_33:pname) (A_143:(pname->Prop)) (B_81:(pname->Prop)), (((ord_less_eq_pname_o A_143) B_81)->(((member_pname C_33) A_143)->((member_pname C_33) B_81)))) of role axiom named fact_290_subsetD % A new axiom: (forall (C_33:pname) (A_143:(pname->Prop)) (B_81:(pname->Prop)), (((ord_less_eq_pname_o A_143) B_81)->(((member_pname C_33) A_143)->((member_pname C_33) B_81)))) % FOF formula (forall (B_80:x_a) (A_142:x_a) (B_79:(x_a->Prop)), (((((member_a A_142) B_79)->False)->(((eq x_a) A_142) B_80))->((member_a A_142) ((insert_a B_80) B_79)))) of role axiom named fact_291_insertCI % A new axiom: (forall (B_80:x_a) (A_142:x_a) (B_79:(x_a->Prop)), (((((member_a A_142) B_79)->False)->(((eq x_a) A_142) B_80))->((member_a A_142) ((insert_a B_80) B_79)))) % FOF formula (forall (B_80:int) (A_142:int) (B_79:(int->Prop)), (((((member_int A_142) B_79)->False)->(((eq int) A_142) B_80))->((member_int A_142) ((insert_int B_80) B_79)))) of role axiom named fact_292_insertCI % A new axiom: (forall (B_80:int) (A_142:int) (B_79:(int->Prop)), (((((member_int A_142) B_79)->False)->(((eq int) A_142) B_80))->((member_int A_142) ((insert_int B_80) B_79)))) % FOF formula (forall (B_80:nat) (A_142:nat) (B_79:(nat->Prop)), (((((member_nat A_142) B_79)->False)->(((eq nat) A_142) B_80))->((member_nat A_142) ((insert_nat B_80) B_79)))) of role axiom named fact_293_insertCI % A new axiom: (forall (B_80:nat) (A_142:nat) (B_79:(nat->Prop)), (((((member_nat A_142) B_79)->False)->(((eq nat) A_142) B_80))->((member_nat A_142) ((insert_nat B_80) B_79)))) % FOF formula (forall (B_80:pname) (A_142:pname) (B_79:(pname->Prop)), (((((member_pname A_142) B_79)->False)->(((eq pname) A_142) B_80))->((member_pname A_142) ((insert_pname B_80) B_79)))) of role axiom named fact_294_insertCI % A new axiom: (forall (B_80:pname) (A_142:pname) (B_79:(pname->Prop)), (((((member_pname A_142) B_79)->False)->(((eq pname) A_142) B_80))->((member_pname A_142) ((insert_pname B_80) B_79)))) % FOF formula (forall (A_141:x_a) (B_78:x_a) (A_140:(x_a->Prop)), (((member_a A_141) ((insert_a B_78) A_140))->((not (((eq x_a) A_141) B_78))->((member_a A_141) A_140)))) of role axiom named fact_295_insertE % A new axiom: (forall (A_141:x_a) (B_78:x_a) (A_140:(x_a->Prop)), (((member_a A_141) ((insert_a B_78) A_140))->((not (((eq x_a) A_141) B_78))->((member_a A_141) A_140)))) % FOF formula (forall (A_141:int) (B_78:int) (A_140:(int->Prop)), (((member_int A_141) ((insert_int B_78) A_140))->((not (((eq int) A_141) B_78))->((member_int A_141) A_140)))) of role axiom named fact_296_insertE % A new axiom: (forall (A_141:int) (B_78:int) (A_140:(int->Prop)), (((member_int A_141) ((insert_int B_78) A_140))->((not (((eq int) A_141) B_78))->((member_int A_141) A_140)))) % FOF formula (forall (A_141:nat) (B_78:nat) (A_140:(nat->Prop)), (((member_nat A_141) ((insert_nat B_78) A_140))->((not (((eq nat) A_141) B_78))->((member_nat A_141) A_140)))) of role axiom named fact_297_insertE % A new axiom: (forall (A_141:nat) (B_78:nat) (A_140:(nat->Prop)), (((member_nat A_141) ((insert_nat B_78) A_140))->((not (((eq nat) A_141) B_78))->((member_nat A_141) A_140)))) % FOF formula (forall (A_141:pname) (B_78:pname) (A_140:(pname->Prop)), (((member_pname A_141) ((insert_pname B_78) A_140))->((not (((eq pname) A_141) B_78))->((member_pname A_141) A_140)))) of role axiom named fact_298_insertE % A new axiom: (forall (A_141:pname) (B_78:pname) (A_140:(pname->Prop)), (((member_pname A_141) ((insert_pname B_78) A_140))->((not (((eq pname) A_141) B_78))->((member_pname A_141) A_140)))) % FOF formula (forall (I_1:nat) (P:(nat->Prop)) (K:nat), ((P K)->((forall (N_1:nat), ((P (suc N_1))->(P N_1)))->(P ((minus_minus_nat K) I_1))))) of role axiom named fact_299_zero__induct__lemma % A new axiom: (forall (I_1:nat) (P:(nat->Prop)) (K:nat), ((P K)->((forall (N_1:nat), ((P (suc N_1))->(P N_1)))->(P ((minus_minus_nat K) I_1))))) % FOF formula (forall (N:nat) (M_3:nat), (((ord_less_eq_nat (suc N)) M_3)->((ex nat) (fun (M_1:nat)=> (((eq nat) M_3) (suc M_1)))))) of role axiom named fact_300_Suc__le__D % A new axiom: (forall (N:nat) (M_3:nat), (((ord_less_eq_nat (suc N)) M_3)->((ex nat) (fun (M_1:nat)=> (((eq nat) M_3) (suc M_1)))))) % FOF formula (forall (X_49:(int->Prop)), ((ord_less_eq_int_o X_49) X_49)) of role axiom named fact_301_order__refl % A new axiom: (forall (X_49:(int->Prop)), ((ord_less_eq_int_o X_49) X_49)) % FOF formula (forall (X_49:(nat->Prop)), ((ord_less_eq_nat_o X_49) X_49)) of role axiom named fact_302_order__refl % A new axiom: (forall (X_49:(nat->Prop)), ((ord_less_eq_nat_o X_49) X_49)) % FOF formula (forall (X_49:int), ((ord_less_eq_int X_49) X_49)) of role axiom named fact_303_order__refl % A new axiom: (forall (X_49:int), ((ord_less_eq_int X_49) X_49)) % FOF formula (forall (X_49:nat), ((ord_less_eq_nat X_49) X_49)) of role axiom named fact_304_order__refl % A new axiom: (forall (X_49:nat), ((ord_less_eq_nat X_49) X_49)) % FOF formula (forall (X_49:(x_a->Prop)), ((ord_less_eq_a_o X_49) X_49)) of role axiom named fact_305_order__refl % A new axiom: (forall (X_49:(x_a->Prop)), ((ord_less_eq_a_o X_49) X_49)) % FOF formula (forall (X_48:int) (Y_12:int), ((or ((ord_less_eq_int X_48) Y_12)) ((ord_less_eq_int Y_12) X_48))) of role axiom named fact_306_linorder__linear % A new axiom: (forall (X_48:int) (Y_12:int), ((or ((ord_less_eq_int X_48) Y_12)) ((ord_less_eq_int Y_12) X_48))) % FOF formula (forall (X_48:nat) (Y_12:nat), ((or ((ord_less_eq_nat X_48) Y_12)) ((ord_less_eq_nat Y_12) X_48))) of role axiom named fact_307_linorder__linear % A new axiom: (forall (X_48:nat) (Y_12:nat), ((or ((ord_less_eq_nat X_48) Y_12)) ((ord_less_eq_nat Y_12) X_48))) % FOF formula (forall (X_47:(int->Prop)) (Y_11:(int->Prop)), ((iff (((eq (int->Prop)) X_47) Y_11)) ((and ((ord_less_eq_int_o X_47) Y_11)) ((ord_less_eq_int_o Y_11) X_47)))) of role axiom named fact_308_order__eq__iff % A new axiom: (forall (X_47:(int->Prop)) (Y_11:(int->Prop)), ((iff (((eq (int->Prop)) X_47) Y_11)) ((and ((ord_less_eq_int_o X_47) Y_11)) ((ord_less_eq_int_o Y_11) X_47)))) % FOF formula (forall (X_47:(nat->Prop)) (Y_11:(nat->Prop)), ((iff (((eq (nat->Prop)) X_47) Y_11)) ((and ((ord_less_eq_nat_o X_47) Y_11)) ((ord_less_eq_nat_o Y_11) X_47)))) of role axiom named fact_309_order__eq__iff % A new axiom: (forall (X_47:(nat->Prop)) (Y_11:(nat->Prop)), ((iff (((eq (nat->Prop)) X_47) Y_11)) ((and ((ord_less_eq_nat_o X_47) Y_11)) ((ord_less_eq_nat_o Y_11) X_47)))) % FOF formula (forall (X_47:int) (Y_11:int), ((iff (((eq int) X_47) Y_11)) ((and ((ord_less_eq_int X_47) Y_11)) ((ord_less_eq_int Y_11) X_47)))) of role axiom named fact_310_order__eq__iff % A new axiom: (forall (X_47:int) (Y_11:int), ((iff (((eq int) X_47) Y_11)) ((and ((ord_less_eq_int X_47) Y_11)) ((ord_less_eq_int Y_11) X_47)))) % FOF formula (forall (X_47:nat) (Y_11:nat), ((iff (((eq nat) X_47) Y_11)) ((and ((ord_less_eq_nat X_47) Y_11)) ((ord_less_eq_nat Y_11) X_47)))) of role axiom named fact_311_order__eq__iff % A new axiom: (forall (X_47:nat) (Y_11:nat), ((iff (((eq nat) X_47) Y_11)) ((and ((ord_less_eq_nat X_47) Y_11)) ((ord_less_eq_nat Y_11) X_47)))) % FOF formula (forall (X_47:(x_a->Prop)) (Y_11:(x_a->Prop)), ((iff (((eq (x_a->Prop)) X_47) Y_11)) ((and ((ord_less_eq_a_o X_47) Y_11)) ((ord_less_eq_a_o Y_11) X_47)))) of role axiom named fact_312_order__eq__iff % A new axiom: (forall (X_47:(x_a->Prop)) (Y_11:(x_a->Prop)), ((iff (((eq (x_a->Prop)) X_47) Y_11)) ((and ((ord_less_eq_a_o X_47) Y_11)) ((ord_less_eq_a_o Y_11) X_47)))) % FOF formula (forall (X_46:(int->Prop)) (Y_10:(int->Prop)), ((((eq (int->Prop)) X_46) Y_10)->((ord_less_eq_int_o X_46) Y_10))) of role axiom named fact_313_order__eq__refl % A new axiom: (forall (X_46:(int->Prop)) (Y_10:(int->Prop)), ((((eq (int->Prop)) X_46) Y_10)->((ord_less_eq_int_o X_46) Y_10))) % FOF formula (forall (X_46:(nat->Prop)) (Y_10:(nat->Prop)), ((((eq (nat->Prop)) X_46) Y_10)->((ord_less_eq_nat_o X_46) Y_10))) of role axiom named fact_314_order__eq__refl % A new axiom: (forall (X_46:(nat->Prop)) (Y_10:(nat->Prop)), ((((eq (nat->Prop)) X_46) Y_10)->((ord_less_eq_nat_o X_46) Y_10))) % FOF formula (forall (X_46:int) (Y_10:int), ((((eq int) X_46) Y_10)->((ord_less_eq_int X_46) Y_10))) of role axiom named fact_315_order__eq__refl % A new axiom: (forall (X_46:int) (Y_10:int), ((((eq int) X_46) Y_10)->((ord_less_eq_int X_46) Y_10))) % FOF formula (forall (X_46:nat) (Y_10:nat), ((((eq nat) X_46) Y_10)->((ord_less_eq_nat X_46) Y_10))) of role axiom named fact_316_order__eq__refl % A new axiom: (forall (X_46:nat) (Y_10:nat), ((((eq nat) X_46) Y_10)->((ord_less_eq_nat X_46) Y_10))) % FOF formula (forall (X_46:(x_a->Prop)) (Y_10:(x_a->Prop)), ((((eq (x_a->Prop)) X_46) Y_10)->((ord_less_eq_a_o X_46) Y_10))) of role axiom named fact_317_order__eq__refl % A new axiom: (forall (X_46:(x_a->Prop)) (Y_10:(x_a->Prop)), ((((eq (x_a->Prop)) X_46) Y_10)->((ord_less_eq_a_o X_46) Y_10))) % FOF formula (forall (Y_9:(int->Prop)) (X_45:(int->Prop)), (((ord_less_eq_int_o Y_9) X_45)->((iff ((ord_less_eq_int_o X_45) Y_9)) (((eq (int->Prop)) X_45) Y_9)))) of role axiom named fact_318_order__antisym__conv % A new axiom: (forall (Y_9:(int->Prop)) (X_45:(int->Prop)), (((ord_less_eq_int_o Y_9) X_45)->((iff ((ord_less_eq_int_o X_45) Y_9)) (((eq (int->Prop)) X_45) Y_9)))) % FOF formula (forall (Y_9:(nat->Prop)) (X_45:(nat->Prop)), (((ord_less_eq_nat_o Y_9) X_45)->((iff ((ord_less_eq_nat_o X_45) Y_9)) (((eq (nat->Prop)) X_45) Y_9)))) of role axiom named fact_319_order__antisym__conv % A new axiom: (forall (Y_9:(nat->Prop)) (X_45:(nat->Prop)), (((ord_less_eq_nat_o Y_9) X_45)->((iff ((ord_less_eq_nat_o X_45) Y_9)) (((eq (nat->Prop)) X_45) Y_9)))) % FOF formula (forall (Y_9:int) (X_45:int), (((ord_less_eq_int Y_9) X_45)->((iff ((ord_less_eq_int X_45) Y_9)) (((eq int) X_45) Y_9)))) of role axiom named fact_320_order__antisym__conv % A new axiom: (forall (Y_9:int) (X_45:int), (((ord_less_eq_int Y_9) X_45)->((iff ((ord_less_eq_int X_45) Y_9)) (((eq int) X_45) Y_9)))) % FOF formula (forall (Y_9:nat) (X_45:nat), (((ord_less_eq_nat Y_9) X_45)->((iff ((ord_less_eq_nat X_45) Y_9)) (((eq nat) X_45) Y_9)))) of role axiom named fact_321_order__antisym__conv % A new axiom: (forall (Y_9:nat) (X_45:nat), (((ord_less_eq_nat Y_9) X_45)->((iff ((ord_less_eq_nat X_45) Y_9)) (((eq nat) X_45) Y_9)))) % FOF formula (forall (Y_9:(x_a->Prop)) (X_45:(x_a->Prop)), (((ord_less_eq_a_o Y_9) X_45)->((iff ((ord_less_eq_a_o X_45) Y_9)) (((eq (x_a->Prop)) X_45) Y_9)))) of role axiom named fact_322_order__antisym__conv % A new axiom: (forall (Y_9:(x_a->Prop)) (X_45:(x_a->Prop)), (((ord_less_eq_a_o Y_9) X_45)->((iff ((ord_less_eq_a_o X_45) Y_9)) (((eq (x_a->Prop)) X_45) Y_9)))) % FOF formula (forall (C_32:(int->Prop)) (A_139:(int->Prop)) (B_77:(int->Prop)), ((((eq (int->Prop)) A_139) B_77)->(((ord_less_eq_int_o B_77) C_32)->((ord_less_eq_int_o A_139) C_32)))) of role axiom named fact_323_ord__eq__le__trans % A new axiom: (forall (C_32:(int->Prop)) (A_139:(int->Prop)) (B_77:(int->Prop)), ((((eq (int->Prop)) A_139) B_77)->(((ord_less_eq_int_o B_77) C_32)->((ord_less_eq_int_o A_139) C_32)))) % FOF formula (forall (C_32:(nat->Prop)) (A_139:(nat->Prop)) (B_77:(nat->Prop)), ((((eq (nat->Prop)) A_139) B_77)->(((ord_less_eq_nat_o B_77) C_32)->((ord_less_eq_nat_o A_139) C_32)))) of role axiom named fact_324_ord__eq__le__trans % A new axiom: (forall (C_32:(nat->Prop)) (A_139:(nat->Prop)) (B_77:(nat->Prop)), ((((eq (nat->Prop)) A_139) B_77)->(((ord_less_eq_nat_o B_77) C_32)->((ord_less_eq_nat_o A_139) C_32)))) % FOF formula (forall (C_32:int) (A_139:int) (B_77:int), ((((eq int) A_139) B_77)->(((ord_less_eq_int B_77) C_32)->((ord_less_eq_int A_139) C_32)))) of role axiom named fact_325_ord__eq__le__trans % A new axiom: (forall (C_32:int) (A_139:int) (B_77:int), ((((eq int) A_139) B_77)->(((ord_less_eq_int B_77) C_32)->((ord_less_eq_int A_139) C_32)))) % FOF formula (forall (C_32:nat) (A_139:nat) (B_77:nat), ((((eq nat) A_139) B_77)->(((ord_less_eq_nat B_77) C_32)->((ord_less_eq_nat A_139) C_32)))) of role axiom named fact_326_ord__eq__le__trans % A new axiom: (forall (C_32:nat) (A_139:nat) (B_77:nat), ((((eq nat) A_139) B_77)->(((ord_less_eq_nat B_77) C_32)->((ord_less_eq_nat A_139) C_32)))) % FOF formula (forall (C_32:(x_a->Prop)) (A_139:(x_a->Prop)) (B_77:(x_a->Prop)), ((((eq (x_a->Prop)) A_139) B_77)->(((ord_less_eq_a_o B_77) C_32)->((ord_less_eq_a_o A_139) C_32)))) of role axiom named fact_327_ord__eq__le__trans % A new axiom: (forall (C_32:(x_a->Prop)) (A_139:(x_a->Prop)) (B_77:(x_a->Prop)), ((((eq (x_a->Prop)) A_139) B_77)->(((ord_less_eq_a_o B_77) C_32)->((ord_less_eq_a_o A_139) C_32)))) % FOF formula (forall (C_31:(int->Prop)) (A_138:(int->Prop)) (B_76:(int->Prop)), ((((eq (int->Prop)) A_138) B_76)->(((ord_less_eq_int_o C_31) B_76)->((ord_less_eq_int_o C_31) A_138)))) of role axiom named fact_328_xt1_I3_J % A new axiom: (forall (C_31:(int->Prop)) (A_138:(int->Prop)) (B_76:(int->Prop)), ((((eq (int->Prop)) A_138) B_76)->(((ord_less_eq_int_o C_31) B_76)->((ord_less_eq_int_o C_31) A_138)))) % FOF formula (forall (C_31:(nat->Prop)) (A_138:(nat->Prop)) (B_76:(nat->Prop)), ((((eq (nat->Prop)) A_138) B_76)->(((ord_less_eq_nat_o C_31) B_76)->((ord_less_eq_nat_o C_31) A_138)))) of role axiom named fact_329_xt1_I3_J % A new axiom: (forall (C_31:(nat->Prop)) (A_138:(nat->Prop)) (B_76:(nat->Prop)), ((((eq (nat->Prop)) A_138) B_76)->(((ord_less_eq_nat_o C_31) B_76)->((ord_less_eq_nat_o C_31) A_138)))) % FOF formula (forall (C_31:int) (A_138:int) (B_76:int), ((((eq int) A_138) B_76)->(((ord_less_eq_int C_31) B_76)->((ord_less_eq_int C_31) A_138)))) of role axiom named fact_330_xt1_I3_J % A new axiom: (forall (C_31:int) (A_138:int) (B_76:int), ((((eq int) A_138) B_76)->(((ord_less_eq_int C_31) B_76)->((ord_less_eq_int C_31) A_138)))) % FOF formula (forall (C_31:nat) (A_138:nat) (B_76:nat), ((((eq nat) A_138) B_76)->(((ord_less_eq_nat C_31) B_76)->((ord_less_eq_nat C_31) A_138)))) of role axiom named fact_331_xt1_I3_J % A new axiom: (forall (C_31:nat) (A_138:nat) (B_76:nat), ((((eq nat) A_138) B_76)->(((ord_less_eq_nat C_31) B_76)->((ord_less_eq_nat C_31) A_138)))) % FOF formula (forall (C_31:(x_a->Prop)) (A_138:(x_a->Prop)) (B_76:(x_a->Prop)), ((((eq (x_a->Prop)) A_138) B_76)->(((ord_less_eq_a_o C_31) B_76)->((ord_less_eq_a_o C_31) A_138)))) of role axiom named fact_332_xt1_I3_J % A new axiom: (forall (C_31:(x_a->Prop)) (A_138:(x_a->Prop)) (B_76:(x_a->Prop)), ((((eq (x_a->Prop)) A_138) B_76)->(((ord_less_eq_a_o C_31) B_76)->((ord_less_eq_a_o C_31) A_138)))) % FOF formula (forall (C_30:(int->Prop)) (A_137:(int->Prop)) (B_75:(int->Prop)), (((ord_less_eq_int_o A_137) B_75)->((((eq (int->Prop)) B_75) C_30)->((ord_less_eq_int_o A_137) C_30)))) of role axiom named fact_333_ord__le__eq__trans % A new axiom: (forall (C_30:(int->Prop)) (A_137:(int->Prop)) (B_75:(int->Prop)), (((ord_less_eq_int_o A_137) B_75)->((((eq (int->Prop)) B_75) C_30)->((ord_less_eq_int_o A_137) C_30)))) % FOF formula (forall (C_30:(nat->Prop)) (A_137:(nat->Prop)) (B_75:(nat->Prop)), (((ord_less_eq_nat_o A_137) B_75)->((((eq (nat->Prop)) B_75) C_30)->((ord_less_eq_nat_o A_137) C_30)))) of role axiom named fact_334_ord__le__eq__trans % A new axiom: (forall (C_30:(nat->Prop)) (A_137:(nat->Prop)) (B_75:(nat->Prop)), (((ord_less_eq_nat_o A_137) B_75)->((((eq (nat->Prop)) B_75) C_30)->((ord_less_eq_nat_o A_137) C_30)))) % FOF formula (forall (C_30:int) (A_137:int) (B_75:int), (((ord_less_eq_int A_137) B_75)->((((eq int) B_75) C_30)->((ord_less_eq_int A_137) C_30)))) of role axiom named fact_335_ord__le__eq__trans % A new axiom: (forall (C_30:int) (A_137:int) (B_75:int), (((ord_less_eq_int A_137) B_75)->((((eq int) B_75) C_30)->((ord_less_eq_int A_137) C_30)))) % FOF formula (forall (C_30:nat) (A_137:nat) (B_75:nat), (((ord_less_eq_nat A_137) B_75)->((((eq nat) B_75) C_30)->((ord_less_eq_nat A_137) C_30)))) of role axiom named fact_336_ord__le__eq__trans % A new axiom: (forall (C_30:nat) (A_137:nat) (B_75:nat), (((ord_less_eq_nat A_137) B_75)->((((eq nat) B_75) C_30)->((ord_less_eq_nat A_137) C_30)))) % FOF formula (forall (C_30:(x_a->Prop)) (A_137:(x_a->Prop)) (B_75:(x_a->Prop)), (((ord_less_eq_a_o A_137) B_75)->((((eq (x_a->Prop)) B_75) C_30)->((ord_less_eq_a_o A_137) C_30)))) of role axiom named fact_337_ord__le__eq__trans % A new axiom: (forall (C_30:(x_a->Prop)) (A_137:(x_a->Prop)) (B_75:(x_a->Prop)), (((ord_less_eq_a_o A_137) B_75)->((((eq (x_a->Prop)) B_75) C_30)->((ord_less_eq_a_o A_137) C_30)))) % FOF formula (forall (C_29:(int->Prop)) (B_74:(int->Prop)) (A_136:(int->Prop)), (((ord_less_eq_int_o B_74) A_136)->((((eq (int->Prop)) B_74) C_29)->((ord_less_eq_int_o C_29) A_136)))) of role axiom named fact_338_xt1_I4_J % A new axiom: (forall (C_29:(int->Prop)) (B_74:(int->Prop)) (A_136:(int->Prop)), (((ord_less_eq_int_o B_74) A_136)->((((eq (int->Prop)) B_74) C_29)->((ord_less_eq_int_o C_29) A_136)))) % FOF formula (forall (C_29:(nat->Prop)) (B_74:(nat->Prop)) (A_136:(nat->Prop)), (((ord_less_eq_nat_o B_74) A_136)->((((eq (nat->Prop)) B_74) C_29)->((ord_less_eq_nat_o C_29) A_136)))) of role axiom named fact_339_xt1_I4_J % A new axiom: (forall (C_29:(nat->Prop)) (B_74:(nat->Prop)) (A_136:(nat->Prop)), (((ord_less_eq_nat_o B_74) A_136)->((((eq (nat->Prop)) B_74) C_29)->((ord_less_eq_nat_o C_29) A_136)))) % FOF formula (forall (C_29:int) (B_74:int) (A_136:int), (((ord_less_eq_int B_74) A_136)->((((eq int) B_74) C_29)->((ord_less_eq_int C_29) A_136)))) of role axiom named fact_340_xt1_I4_J % A new axiom: (forall (C_29:int) (B_74:int) (A_136:int), (((ord_less_eq_int B_74) A_136)->((((eq int) B_74) C_29)->((ord_less_eq_int C_29) A_136)))) % FOF formula (forall (C_29:nat) (B_74:nat) (A_136:nat), (((ord_less_eq_nat B_74) A_136)->((((eq nat) B_74) C_29)->((ord_less_eq_nat C_29) A_136)))) of role axiom named fact_341_xt1_I4_J % A new axiom: (forall (C_29:nat) (B_74:nat) (A_136:nat), (((ord_less_eq_nat B_74) A_136)->((((eq nat) B_74) C_29)->((ord_less_eq_nat C_29) A_136)))) % FOF formula (forall (C_29:(x_a->Prop)) (B_74:(x_a->Prop)) (A_136:(x_a->Prop)), (((ord_less_eq_a_o B_74) A_136)->((((eq (x_a->Prop)) B_74) C_29)->((ord_less_eq_a_o C_29) A_136)))) of role axiom named fact_342_xt1_I4_J % A new axiom: (forall (C_29:(x_a->Prop)) (B_74:(x_a->Prop)) (A_136:(x_a->Prop)), (((ord_less_eq_a_o B_74) A_136)->((((eq (x_a->Prop)) B_74) C_29)->((ord_less_eq_a_o C_29) A_136)))) % FOF formula (forall (X_44:(int->Prop)) (Y_8:(int->Prop)), (((ord_less_eq_int_o X_44) Y_8)->(((ord_less_eq_int_o Y_8) X_44)->(((eq (int->Prop)) X_44) Y_8)))) of role axiom named fact_343_order__antisym % A new axiom: (forall (X_44:(int->Prop)) (Y_8:(int->Prop)), (((ord_less_eq_int_o X_44) Y_8)->(((ord_less_eq_int_o Y_8) X_44)->(((eq (int->Prop)) X_44) Y_8)))) % FOF formula (forall (X_44:(nat->Prop)) (Y_8:(nat->Prop)), (((ord_less_eq_nat_o X_44) Y_8)->(((ord_less_eq_nat_o Y_8) X_44)->(((eq (nat->Prop)) X_44) Y_8)))) of role axiom named fact_344_order__antisym % A new axiom: (forall (X_44:(nat->Prop)) (Y_8:(nat->Prop)), (((ord_less_eq_nat_o X_44) Y_8)->(((ord_less_eq_nat_o Y_8) X_44)->(((eq (nat->Prop)) X_44) Y_8)))) % FOF formula (forall (X_44:int) (Y_8:int), (((ord_less_eq_int X_44) Y_8)->(((ord_less_eq_int Y_8) X_44)->(((eq int) X_44) Y_8)))) of role axiom named fact_345_order__antisym % A new axiom: (forall (X_44:int) (Y_8:int), (((ord_less_eq_int X_44) Y_8)->(((ord_less_eq_int Y_8) X_44)->(((eq int) X_44) Y_8)))) % FOF formula (forall (X_44:nat) (Y_8:nat), (((ord_less_eq_nat X_44) Y_8)->(((ord_less_eq_nat Y_8) X_44)->(((eq nat) X_44) Y_8)))) of role axiom named fact_346_order__antisym % A new axiom: (forall (X_44:nat) (Y_8:nat), (((ord_less_eq_nat X_44) Y_8)->(((ord_less_eq_nat Y_8) X_44)->(((eq nat) X_44) Y_8)))) % FOF formula (forall (X_44:(x_a->Prop)) (Y_8:(x_a->Prop)), (((ord_less_eq_a_o X_44) Y_8)->(((ord_less_eq_a_o Y_8) X_44)->(((eq (x_a->Prop)) X_44) Y_8)))) of role axiom named fact_347_order__antisym % A new axiom: (forall (X_44:(x_a->Prop)) (Y_8:(x_a->Prop)), (((ord_less_eq_a_o X_44) Y_8)->(((ord_less_eq_a_o Y_8) X_44)->(((eq (x_a->Prop)) X_44) Y_8)))) % FOF formula (forall (Z_6:(int->Prop)) (X_43:(int->Prop)) (Y_7:(int->Prop)), (((ord_less_eq_int_o X_43) Y_7)->(((ord_less_eq_int_o Y_7) Z_6)->((ord_less_eq_int_o X_43) Z_6)))) of role axiom named fact_348_order__trans % A new axiom: (forall (Z_6:(int->Prop)) (X_43:(int->Prop)) (Y_7:(int->Prop)), (((ord_less_eq_int_o X_43) Y_7)->(((ord_less_eq_int_o Y_7) Z_6)->((ord_less_eq_int_o X_43) Z_6)))) % FOF formula (forall (Z_6:(nat->Prop)) (X_43:(nat->Prop)) (Y_7:(nat->Prop)), (((ord_less_eq_nat_o X_43) Y_7)->(((ord_less_eq_nat_o Y_7) Z_6)->((ord_less_eq_nat_o X_43) Z_6)))) of role axiom named fact_349_order__trans % A new axiom: (forall (Z_6:(nat->Prop)) (X_43:(nat->Prop)) (Y_7:(nat->Prop)), (((ord_less_eq_nat_o X_43) Y_7)->(((ord_less_eq_nat_o Y_7) Z_6)->((ord_less_eq_nat_o X_43) Z_6)))) % FOF formula (forall (Z_6:int) (X_43:int) (Y_7:int), (((ord_less_eq_int X_43) Y_7)->(((ord_less_eq_int Y_7) Z_6)->((ord_less_eq_int X_43) Z_6)))) of role axiom named fact_350_order__trans % A new axiom: (forall (Z_6:int) (X_43:int) (Y_7:int), (((ord_less_eq_int X_43) Y_7)->(((ord_less_eq_int Y_7) Z_6)->((ord_less_eq_int X_43) Z_6)))) % FOF formula (forall (Z_6:nat) (X_43:nat) (Y_7:nat), (((ord_less_eq_nat X_43) Y_7)->(((ord_less_eq_nat Y_7) Z_6)->((ord_less_eq_nat X_43) Z_6)))) of role axiom named fact_351_order__trans % A new axiom: (forall (Z_6:nat) (X_43:nat) (Y_7:nat), (((ord_less_eq_nat X_43) Y_7)->(((ord_less_eq_nat Y_7) Z_6)->((ord_less_eq_nat X_43) Z_6)))) % FOF formula (forall (Z_6:(x_a->Prop)) (X_43:(x_a->Prop)) (Y_7:(x_a->Prop)), (((ord_less_eq_a_o X_43) Y_7)->(((ord_less_eq_a_o Y_7) Z_6)->((ord_less_eq_a_o X_43) Z_6)))) of role axiom named fact_352_order__trans % A new axiom: (forall (Z_6:(x_a->Prop)) (X_43:(x_a->Prop)) (Y_7:(x_a->Prop)), (((ord_less_eq_a_o X_43) Y_7)->(((ord_less_eq_a_o Y_7) Z_6)->((ord_less_eq_a_o X_43) Z_6)))) % FOF formula (forall (Y_6:(int->Prop)) (X_42:(int->Prop)), (((ord_less_eq_int_o Y_6) X_42)->(((ord_less_eq_int_o X_42) Y_6)->(((eq (int->Prop)) X_42) Y_6)))) of role axiom named fact_353_xt1_I5_J % A new axiom: (forall (Y_6:(int->Prop)) (X_42:(int->Prop)), (((ord_less_eq_int_o Y_6) X_42)->(((ord_less_eq_int_o X_42) Y_6)->(((eq (int->Prop)) X_42) Y_6)))) % FOF formula (forall (Y_6:(nat->Prop)) (X_42:(nat->Prop)), (((ord_less_eq_nat_o Y_6) X_42)->(((ord_less_eq_nat_o X_42) Y_6)->(((eq (nat->Prop)) X_42) Y_6)))) of role axiom named fact_354_xt1_I5_J % A new axiom: (forall (Y_6:(nat->Prop)) (X_42:(nat->Prop)), (((ord_less_eq_nat_o Y_6) X_42)->(((ord_less_eq_nat_o X_42) Y_6)->(((eq (nat->Prop)) X_42) Y_6)))) % FOF formula (forall (Y_6:int) (X_42:int), (((ord_less_eq_int Y_6) X_42)->(((ord_less_eq_int X_42) Y_6)->(((eq int) X_42) Y_6)))) of role axiom named fact_355_xt1_I5_J % A new axiom: (forall (Y_6:int) (X_42:int), (((ord_less_eq_int Y_6) X_42)->(((ord_less_eq_int X_42) Y_6)->(((eq int) X_42) Y_6)))) % FOF formula (forall (Y_6:nat) (X_42:nat), (((ord_less_eq_nat Y_6) X_42)->(((ord_less_eq_nat X_42) Y_6)->(((eq nat) X_42) Y_6)))) of role axiom named fact_356_xt1_I5_J % A new axiom: (forall (Y_6:nat) (X_42:nat), (((ord_less_eq_nat Y_6) X_42)->(((ord_less_eq_nat X_42) Y_6)->(((eq nat) X_42) Y_6)))) % FOF formula (forall (Y_6:(x_a->Prop)) (X_42:(x_a->Prop)), (((ord_less_eq_a_o Y_6) X_42)->(((ord_less_eq_a_o X_42) Y_6)->(((eq (x_a->Prop)) X_42) Y_6)))) of role axiom named fact_357_xt1_I5_J % A new axiom: (forall (Y_6:(x_a->Prop)) (X_42:(x_a->Prop)), (((ord_less_eq_a_o Y_6) X_42)->(((ord_less_eq_a_o X_42) Y_6)->(((eq (x_a->Prop)) X_42) Y_6)))) % FOF formula (forall (Z_5:(int->Prop)) (Y_5:(int->Prop)) (X_41:(int->Prop)), (((ord_less_eq_int_o Y_5) X_41)->(((ord_less_eq_int_o Z_5) Y_5)->((ord_less_eq_int_o Z_5) X_41)))) of role axiom named fact_358_xt1_I6_J % A new axiom: (forall (Z_5:(int->Prop)) (Y_5:(int->Prop)) (X_41:(int->Prop)), (((ord_less_eq_int_o Y_5) X_41)->(((ord_less_eq_int_o Z_5) Y_5)->((ord_less_eq_int_o Z_5) X_41)))) % FOF formula (forall (Z_5:(nat->Prop)) (Y_5:(nat->Prop)) (X_41:(nat->Prop)), (((ord_less_eq_nat_o Y_5) X_41)->(((ord_less_eq_nat_o Z_5) Y_5)->((ord_less_eq_nat_o Z_5) X_41)))) of role axiom named fact_359_xt1_I6_J % A new axiom: (forall (Z_5:(nat->Prop)) (Y_5:(nat->Prop)) (X_41:(nat->Prop)), (((ord_less_eq_nat_o Y_5) X_41)->(((ord_less_eq_nat_o Z_5) Y_5)->((ord_less_eq_nat_o Z_5) X_41)))) % FOF formula (forall (Z_5:int) (Y_5:int) (X_41:int), (((ord_less_eq_int Y_5) X_41)->(((ord_less_eq_int Z_5) Y_5)->((ord_less_eq_int Z_5) X_41)))) of role axiom named fact_360_xt1_I6_J % A new axiom: (forall (Z_5:int) (Y_5:int) (X_41:int), (((ord_less_eq_int Y_5) X_41)->(((ord_less_eq_int Z_5) Y_5)->((ord_less_eq_int Z_5) X_41)))) % FOF formula (forall (Z_5:nat) (Y_5:nat) (X_41:nat), (((ord_less_eq_nat Y_5) X_41)->(((ord_less_eq_nat Z_5) Y_5)->((ord_less_eq_nat Z_5) X_41)))) of role axiom named fact_361_xt1_I6_J % A new axiom: (forall (Z_5:nat) (Y_5:nat) (X_41:nat), (((ord_less_eq_nat Y_5) X_41)->(((ord_less_eq_nat Z_5) Y_5)->((ord_less_eq_nat Z_5) X_41)))) % FOF formula (forall (Z_5:(x_a->Prop)) (Y_5:(x_a->Prop)) (X_41:(x_a->Prop)), (((ord_less_eq_a_o Y_5) X_41)->(((ord_less_eq_a_o Z_5) Y_5)->((ord_less_eq_a_o Z_5) X_41)))) of role axiom named fact_362_xt1_I6_J % A new axiom: (forall (Z_5:(x_a->Prop)) (Y_5:(x_a->Prop)) (X_41:(x_a->Prop)), (((ord_less_eq_a_o Y_5) X_41)->(((ord_less_eq_a_o Z_5) Y_5)->((ord_less_eq_a_o Z_5) X_41)))) % FOF formula (forall (X_40:int) (Y_4:int), ((((ord_less_eq_int X_40) Y_4)->False)->((ord_less_eq_int Y_4) X_40))) of role axiom named fact_363_linorder__le__cases % A new axiom: (forall (X_40:int) (Y_4:int), ((((ord_less_eq_int X_40) Y_4)->False)->((ord_less_eq_int Y_4) X_40))) % FOF formula (forall (X_40:nat) (Y_4:nat), ((((ord_less_eq_nat X_40) Y_4)->False)->((ord_less_eq_nat Y_4) X_40))) of role axiom named fact_364_linorder__le__cases % A new axiom: (forall (X_40:nat) (Y_4:nat), ((((ord_less_eq_nat X_40) Y_4)->False)->((ord_less_eq_nat Y_4) X_40))) % FOF formula (forall (A_135:x_a) (B_73:(x_a->Prop)), ((member_a A_135) ((insert_a A_135) B_73))) of role axiom named fact_365_insertI1 % A new axiom: (forall (A_135:x_a) (B_73:(x_a->Prop)), ((member_a A_135) ((insert_a A_135) B_73))) % FOF formula (forall (A_135:int) (B_73:(int->Prop)), ((member_int A_135) ((insert_int A_135) B_73))) of role axiom named fact_366_insertI1 % A new axiom: (forall (A_135:int) (B_73:(int->Prop)), ((member_int A_135) ((insert_int A_135) B_73))) % FOF formula (forall (A_135:nat) (B_73:(nat->Prop)), ((member_nat A_135) ((insert_nat A_135) B_73))) of role axiom named fact_367_insertI1 % A new axiom: (forall (A_135:nat) (B_73:(nat->Prop)), ((member_nat A_135) ((insert_nat A_135) B_73))) % FOF formula (forall (A_135:pname) (B_73:(pname->Prop)), ((member_pname A_135) ((insert_pname A_135) B_73))) of role axiom named fact_368_insertI1 % A new axiom: (forall (A_135:pname) (B_73:(pname->Prop)), ((member_pname A_135) ((insert_pname A_135) B_73))) % FOF formula (forall (A_134:x_a) (B_72:(x_a->Prop)), (((eq (x_a->Prop)) ((insert_a A_134) B_72)) (collect_a (fun (X_1:x_a)=> ((or (((eq x_a) X_1) A_134)) ((member_a X_1) B_72)))))) of role axiom named fact_369_insert__compr % A new axiom: (forall (A_134:x_a) (B_72:(x_a->Prop)), (((eq (x_a->Prop)) ((insert_a A_134) B_72)) (collect_a (fun (X_1:x_a)=> ((or (((eq x_a) X_1) A_134)) ((member_a X_1) B_72)))))) % FOF formula (forall (A_134:int) (B_72:(int->Prop)), (((eq (int->Prop)) ((insert_int A_134) B_72)) (collect_int (fun (X_1:int)=> ((or (((eq int) X_1) A_134)) ((member_int X_1) B_72)))))) of role axiom named fact_370_insert__compr % A new axiom: (forall (A_134:int) (B_72:(int->Prop)), (((eq (int->Prop)) ((insert_int A_134) B_72)) (collect_int (fun (X_1:int)=> ((or (((eq int) X_1) A_134)) ((member_int X_1) B_72)))))) % FOF formula (forall (A_134:nat) (B_72:(nat->Prop)), (((eq (nat->Prop)) ((insert_nat A_134) B_72)) (collect_nat (fun (X_1:nat)=> ((or (((eq nat) X_1) A_134)) ((member_nat X_1) B_72)))))) of role axiom named fact_371_insert__compr % A new axiom: (forall (A_134:nat) (B_72:(nat->Prop)), (((eq (nat->Prop)) ((insert_nat A_134) B_72)) (collect_nat (fun (X_1:nat)=> ((or (((eq nat) X_1) A_134)) ((member_nat X_1) B_72)))))) % FOF formula (forall (A_134:pname) (B_72:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname A_134) B_72)) (collect_pname (fun (X_1:pname)=> ((or (((eq pname) X_1) A_134)) ((member_pname X_1) B_72)))))) of role axiom named fact_372_insert__compr % A new axiom: (forall (A_134:pname) (B_72:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname A_134) B_72)) (collect_pname (fun (X_1:pname)=> ((or (((eq pname) X_1) A_134)) ((member_pname X_1) B_72)))))) % FOF formula (forall (A_133:x_a) (P_11:(x_a->Prop)), (((eq (x_a->Prop)) ((insert_a A_133) (collect_a P_11))) (collect_a (fun (U_1:x_a)=> (((fun (X:Prop) (Y:Prop)=> (X->Y)) (not (((eq x_a) U_1) A_133))) (P_11 U_1)))))) of role axiom named fact_373_insert__Collect % A new axiom: (forall (A_133:x_a) (P_11:(x_a->Prop)), (((eq (x_a->Prop)) ((insert_a A_133) (collect_a P_11))) (collect_a (fun (U_1:x_a)=> (((fun (X:Prop) (Y:Prop)=> (X->Y)) (not (((eq x_a) U_1) A_133))) (P_11 U_1)))))) % FOF formula (forall (A_133:int) (P_11:(int->Prop)), (((eq (int->Prop)) ((insert_int A_133) (collect_int P_11))) (collect_int (fun (U_1:int)=> (((fun (X:Prop) (Y:Prop)=> (X->Y)) (not (((eq int) U_1) A_133))) (P_11 U_1)))))) of role axiom named fact_374_insert__Collect % A new axiom: (forall (A_133:int) (P_11:(int->Prop)), (((eq (int->Prop)) ((insert_int A_133) (collect_int P_11))) (collect_int (fun (U_1:int)=> (((fun (X:Prop) (Y:Prop)=> (X->Y)) (not (((eq int) U_1) A_133))) (P_11 U_1)))))) % FOF formula (forall (A_133:nat) (P_11:(nat->Prop)), (((eq (nat->Prop)) ((insert_nat A_133) (collect_nat P_11))) (collect_nat (fun (U_1:nat)=> (((fun (X:Prop) (Y:Prop)=> (X->Y)) (not (((eq nat) U_1) A_133))) (P_11 U_1)))))) of role axiom named fact_375_insert__Collect % A new axiom: (forall (A_133:nat) (P_11:(nat->Prop)), (((eq (nat->Prop)) ((insert_nat A_133) (collect_nat P_11))) (collect_nat (fun (U_1:nat)=> (((fun (X:Prop) (Y:Prop)=> (X->Y)) (not (((eq nat) U_1) A_133))) (P_11 U_1)))))) % FOF formula (forall (X_39:int) (A_132:(int->Prop)), ((iff ((member_int X_39) A_132)) (A_132 X_39))) of role axiom named fact_376_mem__def % A new axiom: (forall (X_39:int) (A_132:(int->Prop)), ((iff ((member_int X_39) A_132)) (A_132 X_39))) % FOF formula (forall (X_39:nat) (A_132:(nat->Prop)), ((iff ((member_nat X_39) A_132)) (A_132 X_39))) of role axiom named fact_377_mem__def % A new axiom: (forall (X_39:nat) (A_132:(nat->Prop)), ((iff ((member_nat X_39) A_132)) (A_132 X_39))) % FOF formula (forall (X_39:x_a) (A_132:(x_a->Prop)), ((iff ((member_a X_39) A_132)) (A_132 X_39))) of role axiom named fact_378_mem__def % A new axiom: (forall (X_39:x_a) (A_132:(x_a->Prop)), ((iff ((member_a X_39) A_132)) (A_132 X_39))) % FOF formula (forall (X_39:pname) (A_132:(pname->Prop)), ((iff ((member_pname X_39) A_132)) (A_132 X_39))) of role axiom named fact_379_mem__def % A new axiom: (forall (X_39:pname) (A_132:(pname->Prop)), ((iff ((member_pname X_39) A_132)) (A_132 X_39))) % FOF formula (forall (P_10:(int->Prop)), (((eq (int->Prop)) (collect_int P_10)) P_10)) of role axiom named fact_380_Collect__def % A new axiom: (forall (P_10:(int->Prop)), (((eq (int->Prop)) (collect_int P_10)) P_10)) % FOF formula (forall (P_10:(nat->Prop)), (((eq (nat->Prop)) (collect_nat P_10)) P_10)) of role axiom named fact_381_Collect__def % A new axiom: (forall (P_10:(nat->Prop)), (((eq (nat->Prop)) (collect_nat P_10)) P_10)) % FOF formula (forall (X_38:x_a) (A_131:(x_a->Prop)), (((eq (x_a->Prop)) ((insert_a X_38) ((insert_a X_38) A_131))) ((insert_a X_38) A_131))) of role axiom named fact_382_insert__absorb2 % A new axiom: (forall (X_38:x_a) (A_131:(x_a->Prop)), (((eq (x_a->Prop)) ((insert_a X_38) ((insert_a X_38) A_131))) ((insert_a X_38) A_131))) % FOF formula (forall (X_37:x_a) (Y_3:x_a) (A_130:(x_a->Prop)), (((eq (x_a->Prop)) ((insert_a X_37) ((insert_a Y_3) A_130))) ((insert_a Y_3) ((insert_a X_37) A_130)))) of role axiom named fact_383_insert__commute % A new axiom: (forall (X_37:x_a) (Y_3:x_a) (A_130:(x_a->Prop)), (((eq (x_a->Prop)) ((insert_a X_37) ((insert_a Y_3) A_130))) ((insert_a Y_3) ((insert_a X_37) A_130)))) % FOF formula (forall (A_129:x_a) (B_71:x_a) (A_128:(x_a->Prop)), ((iff ((member_a A_129) ((insert_a B_71) A_128))) ((or (((eq x_a) A_129) B_71)) ((member_a A_129) A_128)))) of role axiom named fact_384_insert__iff % A new axiom: (forall (A_129:x_a) (B_71:x_a) (A_128:(x_a->Prop)), ((iff ((member_a A_129) ((insert_a B_71) A_128))) ((or (((eq x_a) A_129) B_71)) ((member_a A_129) A_128)))) % FOF formula (forall (A_129:int) (B_71:int) (A_128:(int->Prop)), ((iff ((member_int A_129) ((insert_int B_71) A_128))) ((or (((eq int) A_129) B_71)) ((member_int A_129) A_128)))) of role axiom named fact_385_insert__iff % A new axiom: (forall (A_129:int) (B_71:int) (A_128:(int->Prop)), ((iff ((member_int A_129) ((insert_int B_71) A_128))) ((or (((eq int) A_129) B_71)) ((member_int A_129) A_128)))) % FOF formula (forall (A_129:nat) (B_71:nat) (A_128:(nat->Prop)), ((iff ((member_nat A_129) ((insert_nat B_71) A_128))) ((or (((eq nat) A_129) B_71)) ((member_nat A_129) A_128)))) of role axiom named fact_386_insert__iff % A new axiom: (forall (A_129:nat) (B_71:nat) (A_128:(nat->Prop)), ((iff ((member_nat A_129) ((insert_nat B_71) A_128))) ((or (((eq nat) A_129) B_71)) ((member_nat A_129) A_128)))) % FOF formula (forall (A_129:pname) (B_71:pname) (A_128:(pname->Prop)), ((iff ((member_pname A_129) ((insert_pname B_71) A_128))) ((or (((eq pname) A_129) B_71)) ((member_pname A_129) A_128)))) of role axiom named fact_387_insert__iff % A new axiom: (forall (A_129:pname) (B_71:pname) (A_128:(pname->Prop)), ((iff ((member_pname A_129) ((insert_pname B_71) A_128))) ((or (((eq pname) A_129) B_71)) ((member_pname A_129) A_128)))) % FOF formula (forall (Y_2:x_a) (A_127:(x_a->Prop)) (X_36:x_a), ((iff (((insert_a Y_2) A_127) X_36)) ((or (((eq x_a) Y_2) X_36)) (A_127 X_36)))) of role axiom named fact_388_insert__code % A new axiom: (forall (Y_2:x_a) (A_127:(x_a->Prop)) (X_36:x_a), ((iff (((insert_a Y_2) A_127) X_36)) ((or (((eq x_a) Y_2) X_36)) (A_127 X_36)))) % FOF formula (forall (B_70:(x_a->Prop)) (X_35:x_a) (A_126:(x_a->Prop)), ((((member_a X_35) A_126)->False)->((((member_a X_35) B_70)->False)->((iff (((eq (x_a->Prop)) ((insert_a X_35) A_126)) ((insert_a X_35) B_70))) (((eq (x_a->Prop)) A_126) B_70))))) of role axiom named fact_389_insert__ident % A new axiom: (forall (B_70:(x_a->Prop)) (X_35:x_a) (A_126:(x_a->Prop)), ((((member_a X_35) A_126)->False)->((((member_a X_35) B_70)->False)->((iff (((eq (x_a->Prop)) ((insert_a X_35) A_126)) ((insert_a X_35) B_70))) (((eq (x_a->Prop)) A_126) B_70))))) % FOF formula (forall (B_70:(int->Prop)) (X_35:int) (A_126:(int->Prop)), ((((member_int X_35) A_126)->False)->((((member_int X_35) B_70)->False)->((iff (((eq (int->Prop)) ((insert_int X_35) A_126)) ((insert_int X_35) B_70))) (((eq (int->Prop)) A_126) B_70))))) of role axiom named fact_390_insert__ident % A new axiom: (forall (B_70:(int->Prop)) (X_35:int) (A_126:(int->Prop)), ((((member_int X_35) A_126)->False)->((((member_int X_35) B_70)->False)->((iff (((eq (int->Prop)) ((insert_int X_35) A_126)) ((insert_int X_35) B_70))) (((eq (int->Prop)) A_126) B_70))))) % FOF formula (forall (B_70:(nat->Prop)) (X_35:nat) (A_126:(nat->Prop)), ((((member_nat X_35) A_126)->False)->((((member_nat X_35) B_70)->False)->((iff (((eq (nat->Prop)) ((insert_nat X_35) A_126)) ((insert_nat X_35) B_70))) (((eq (nat->Prop)) A_126) B_70))))) of role axiom named fact_391_insert__ident % A new axiom: (forall (B_70:(nat->Prop)) (X_35:nat) (A_126:(nat->Prop)), ((((member_nat X_35) A_126)->False)->((((member_nat X_35) B_70)->False)->((iff (((eq (nat->Prop)) ((insert_nat X_35) A_126)) ((insert_nat X_35) B_70))) (((eq (nat->Prop)) A_126) B_70))))) % FOF formula (forall (B_70:(pname->Prop)) (X_35:pname) (A_126:(pname->Prop)), ((((member_pname X_35) A_126)->False)->((((member_pname X_35) B_70)->False)->((iff (((eq (pname->Prop)) ((insert_pname X_35) A_126)) ((insert_pname X_35) B_70))) (((eq (pname->Prop)) A_126) B_70))))) of role axiom named fact_392_insert__ident % A new axiom: (forall (B_70:(pname->Prop)) (X_35:pname) (A_126:(pname->Prop)), ((((member_pname X_35) A_126)->False)->((((member_pname X_35) B_70)->False)->((iff (((eq (pname->Prop)) ((insert_pname X_35) A_126)) ((insert_pname X_35) B_70))) (((eq (pname->Prop)) A_126) B_70))))) % FOF formula (forall (B_69:x_a) (A_125:x_a) (B_68:(x_a->Prop)), (((member_a A_125) B_68)->((member_a A_125) ((insert_a B_69) B_68)))) of role axiom named fact_393_insertI2 % A new axiom: (forall (B_69:x_a) (A_125:x_a) (B_68:(x_a->Prop)), (((member_a A_125) B_68)->((member_a A_125) ((insert_a B_69) B_68)))) % FOF formula (forall (B_69:int) (A_125:int) (B_68:(int->Prop)), (((member_int A_125) B_68)->((member_int A_125) ((insert_int B_69) B_68)))) of role axiom named fact_394_insertI2 % A new axiom: (forall (B_69:int) (A_125:int) (B_68:(int->Prop)), (((member_int A_125) B_68)->((member_int A_125) ((insert_int B_69) B_68)))) % FOF formula (forall (B_69:nat) (A_125:nat) (B_68:(nat->Prop)), (((member_nat A_125) B_68)->((member_nat A_125) ((insert_nat B_69) B_68)))) of role axiom named fact_395_insertI2 % A new axiom: (forall (B_69:nat) (A_125:nat) (B_68:(nat->Prop)), (((member_nat A_125) B_68)->((member_nat A_125) ((insert_nat B_69) B_68)))) % FOF formula (forall (B_69:pname) (A_125:pname) (B_68:(pname->Prop)), (((member_pname A_125) B_68)->((member_pname A_125) ((insert_pname B_69) B_68)))) of role axiom named fact_396_insertI2 % A new axiom: (forall (B_69:pname) (A_125:pname) (B_68:(pname->Prop)), (((member_pname A_125) B_68)->((member_pname A_125) ((insert_pname B_69) B_68)))) % FOF formula (forall (A_124:x_a) (A_123:(x_a->Prop)), (((member_a A_124) A_123)->(((eq (x_a->Prop)) ((insert_a A_124) A_123)) A_123))) of role axiom named fact_397_insert__absorb % A new axiom: (forall (A_124:x_a) (A_123:(x_a->Prop)), (((member_a A_124) A_123)->(((eq (x_a->Prop)) ((insert_a A_124) A_123)) A_123))) % FOF formula (forall (A_124:int) (A_123:(int->Prop)), (((member_int A_124) A_123)->(((eq (int->Prop)) ((insert_int A_124) A_123)) A_123))) of role axiom named fact_398_insert__absorb % A new axiom: (forall (A_124:int) (A_123:(int->Prop)), (((member_int A_124) A_123)->(((eq (int->Prop)) ((insert_int A_124) A_123)) A_123))) % FOF formula (forall (A_124:nat) (A_123:(nat->Prop)), (((member_nat A_124) A_123)->(((eq (nat->Prop)) ((insert_nat A_124) A_123)) A_123))) of role axiom named fact_399_insert__absorb % A new axiom: (forall (A_124:nat) (A_123:(nat->Prop)), (((member_nat A_124) A_123)->(((eq (nat->Prop)) ((insert_nat A_124) A_123)) A_123))) % FOF formula (forall (A_124:pname) (A_123:(pname->Prop)), (((member_pname A_124) A_123)->(((eq (pname->Prop)) ((insert_pname A_124) A_123)) A_123))) of role axiom named fact_400_insert__absorb % A new axiom: (forall (A_124:pname) (A_123:(pname->Prop)), (((member_pname A_124) A_123)->(((eq (pname->Prop)) ((insert_pname A_124) A_123)) A_123))) % FOF formula (forall (A_122:(int->Prop)), ((ord_less_eq_int_o A_122) A_122)) of role axiom named fact_401_subset__refl % A new axiom: (forall (A_122:(int->Prop)), ((ord_less_eq_int_o A_122) A_122)) % FOF formula (forall (A_122:(nat->Prop)), ((ord_less_eq_nat_o A_122) A_122)) of role axiom named fact_402_subset__refl % A new axiom: (forall (A_122:(nat->Prop)), ((ord_less_eq_nat_o A_122) A_122)) % FOF formula (forall (A_122:(x_a->Prop)), ((ord_less_eq_a_o A_122) A_122)) of role axiom named fact_403_subset__refl % A new axiom: (forall (A_122:(x_a->Prop)), ((ord_less_eq_a_o A_122) A_122)) % FOF formula (forall (A_121:(int->Prop)) (B_67:(int->Prop)), ((iff (((eq (int->Prop)) A_121) B_67)) ((and ((ord_less_eq_int_o A_121) B_67)) ((ord_less_eq_int_o B_67) A_121)))) of role axiom named fact_404_set__eq__subset % A new axiom: (forall (A_121:(int->Prop)) (B_67:(int->Prop)), ((iff (((eq (int->Prop)) A_121) B_67)) ((and ((ord_less_eq_int_o A_121) B_67)) ((ord_less_eq_int_o B_67) A_121)))) % FOF formula (forall (A_121:(nat->Prop)) (B_67:(nat->Prop)), ((iff (((eq (nat->Prop)) A_121) B_67)) ((and ((ord_less_eq_nat_o A_121) B_67)) ((ord_less_eq_nat_o B_67) A_121)))) of role axiom named fact_405_set__eq__subset % A new axiom: (forall (A_121:(nat->Prop)) (B_67:(nat->Prop)), ((iff (((eq (nat->Prop)) A_121) B_67)) ((and ((ord_less_eq_nat_o A_121) B_67)) ((ord_less_eq_nat_o B_67) A_121)))) % FOF formula (forall (A_121:(x_a->Prop)) (B_67:(x_a->Prop)), ((iff (((eq (x_a->Prop)) A_121) B_67)) ((and ((ord_less_eq_a_o A_121) B_67)) ((ord_less_eq_a_o B_67) A_121)))) of role axiom named fact_406_set__eq__subset % A new axiom: (forall (A_121:(x_a->Prop)) (B_67:(x_a->Prop)), ((iff (((eq (x_a->Prop)) A_121) B_67)) ((and ((ord_less_eq_a_o A_121) B_67)) ((ord_less_eq_a_o B_67) A_121)))) % FOF formula (forall (A_120:(int->Prop)) (B_66:(int->Prop)), ((((eq (int->Prop)) A_120) B_66)->((ord_less_eq_int_o A_120) B_66))) of role axiom named fact_407_equalityD1 % A new axiom: (forall (A_120:(int->Prop)) (B_66:(int->Prop)), ((((eq (int->Prop)) A_120) B_66)->((ord_less_eq_int_o A_120) B_66))) % FOF formula (forall (A_120:(nat->Prop)) (B_66:(nat->Prop)), ((((eq (nat->Prop)) A_120) B_66)->((ord_less_eq_nat_o A_120) B_66))) of role axiom named fact_408_equalityD1 % A new axiom: (forall (A_120:(nat->Prop)) (B_66:(nat->Prop)), ((((eq (nat->Prop)) A_120) B_66)->((ord_less_eq_nat_o A_120) B_66))) % FOF formula (forall (A_120:(x_a->Prop)) (B_66:(x_a->Prop)), ((((eq (x_a->Prop)) A_120) B_66)->((ord_less_eq_a_o A_120) B_66))) of role axiom named fact_409_equalityD1 % A new axiom: (forall (A_120:(x_a->Prop)) (B_66:(x_a->Prop)), ((((eq (x_a->Prop)) A_120) B_66)->((ord_less_eq_a_o A_120) B_66))) % FOF formula (forall (A_119:(int->Prop)) (B_65:(int->Prop)), ((((eq (int->Prop)) A_119) B_65)->((ord_less_eq_int_o B_65) A_119))) of role axiom named fact_410_equalityD2 % A new axiom: (forall (A_119:(int->Prop)) (B_65:(int->Prop)), ((((eq (int->Prop)) A_119) B_65)->((ord_less_eq_int_o B_65) A_119))) % FOF formula (forall (A_119:(nat->Prop)) (B_65:(nat->Prop)), ((((eq (nat->Prop)) A_119) B_65)->((ord_less_eq_nat_o B_65) A_119))) of role axiom named fact_411_equalityD2 % A new axiom: (forall (A_119:(nat->Prop)) (B_65:(nat->Prop)), ((((eq (nat->Prop)) A_119) B_65)->((ord_less_eq_nat_o B_65) A_119))) % FOF formula (forall (A_119:(x_a->Prop)) (B_65:(x_a->Prop)), ((((eq (x_a->Prop)) A_119) B_65)->((ord_less_eq_a_o B_65) A_119))) of role axiom named fact_412_equalityD2 % A new axiom: (forall (A_119:(x_a->Prop)) (B_65:(x_a->Prop)), ((((eq (x_a->Prop)) A_119) B_65)->((ord_less_eq_a_o B_65) A_119))) % FOF formula (forall (X_34:int) (A_118:(int->Prop)) (B_64:(int->Prop)), (((ord_less_eq_int_o A_118) B_64)->(((member_int X_34) A_118)->((member_int X_34) B_64)))) of role axiom named fact_413_in__mono % A new axiom: (forall (X_34:int) (A_118:(int->Prop)) (B_64:(int->Prop)), (((ord_less_eq_int_o A_118) B_64)->(((member_int X_34) A_118)->((member_int X_34) B_64)))) % FOF formula (forall (X_34:nat) (A_118:(nat->Prop)) (B_64:(nat->Prop)), (((ord_less_eq_nat_o A_118) B_64)->(((member_nat X_34) A_118)->((member_nat X_34) B_64)))) of role axiom named fact_414_in__mono % A new axiom: (forall (X_34:nat) (A_118:(nat->Prop)) (B_64:(nat->Prop)), (((ord_less_eq_nat_o A_118) B_64)->(((member_nat X_34) A_118)->((member_nat X_34) B_64)))) % FOF formula (forall (X_34:x_a) (A_118:(x_a->Prop)) (B_64:(x_a->Prop)), (((ord_less_eq_a_o A_118) B_64)->(((member_a X_34) A_118)->((member_a X_34) B_64)))) of role axiom named fact_415_in__mono % A new axiom: (forall (X_34:x_a) (A_118:(x_a->Prop)) (B_64:(x_a->Prop)), (((ord_less_eq_a_o A_118) B_64)->(((member_a X_34) A_118)->((member_a X_34) B_64)))) % FOF formula (forall (X_34:pname) (A_118:(pname->Prop)) (B_64:(pname->Prop)), (((ord_less_eq_pname_o A_118) B_64)->(((member_pname X_34) A_118)->((member_pname X_34) B_64)))) of role axiom named fact_416_in__mono % A new axiom: (forall (X_34:pname) (A_118:(pname->Prop)) (B_64:(pname->Prop)), (((ord_less_eq_pname_o A_118) B_64)->(((member_pname X_34) A_118)->((member_pname X_34) B_64)))) % FOF formula (forall (B_63:(int->Prop)) (X_33:int) (A_117:(int->Prop)), (((member_int X_33) A_117)->(((ord_less_eq_int_o A_117) B_63)->((member_int X_33) B_63)))) of role axiom named fact_417_set__rev__mp % A new axiom: (forall (B_63:(int->Prop)) (X_33:int) (A_117:(int->Prop)), (((member_int X_33) A_117)->(((ord_less_eq_int_o A_117) B_63)->((member_int X_33) B_63)))) % FOF formula (forall (B_63:(nat->Prop)) (X_33:nat) (A_117:(nat->Prop)), (((member_nat X_33) A_117)->(((ord_less_eq_nat_o A_117) B_63)->((member_nat X_33) B_63)))) of role axiom named fact_418_set__rev__mp % A new axiom: (forall (B_63:(nat->Prop)) (X_33:nat) (A_117:(nat->Prop)), (((member_nat X_33) A_117)->(((ord_less_eq_nat_o A_117) B_63)->((member_nat X_33) B_63)))) % FOF formula (forall (B_63:(x_a->Prop)) (X_33:x_a) (A_117:(x_a->Prop)), (((member_a X_33) A_117)->(((ord_less_eq_a_o A_117) B_63)->((member_a X_33) B_63)))) of role axiom named fact_419_set__rev__mp % A new axiom: (forall (B_63:(x_a->Prop)) (X_33:x_a) (A_117:(x_a->Prop)), (((member_a X_33) A_117)->(((ord_less_eq_a_o A_117) B_63)->((member_a X_33) B_63)))) % FOF formula (forall (B_63:(pname->Prop)) (X_33:pname) (A_117:(pname->Prop)), (((member_pname X_33) A_117)->(((ord_less_eq_pname_o A_117) B_63)->((member_pname X_33) B_63)))) of role axiom named fact_420_set__rev__mp % A new axiom: (forall (B_63:(pname->Prop)) (X_33:pname) (A_117:(pname->Prop)), (((member_pname X_33) A_117)->(((ord_less_eq_pname_o A_117) B_63)->((member_pname X_33) B_63)))) % FOF formula (forall (X_32:int) (A_116:(int->Prop)) (B_62:(int->Prop)), (((ord_less_eq_int_o A_116) B_62)->(((member_int X_32) A_116)->((member_int X_32) B_62)))) of role axiom named fact_421_set__mp % A new axiom: (forall (X_32:int) (A_116:(int->Prop)) (B_62:(int->Prop)), (((ord_less_eq_int_o A_116) B_62)->(((member_int X_32) A_116)->((member_int X_32) B_62)))) % FOF formula (forall (X_32:nat) (A_116:(nat->Prop)) (B_62:(nat->Prop)), (((ord_less_eq_nat_o A_116) B_62)->(((member_nat X_32) A_116)->((member_nat X_32) B_62)))) of role axiom named fact_422_set__mp % A new axiom: (forall (X_32:nat) (A_116:(nat->Prop)) (B_62:(nat->Prop)), (((ord_less_eq_nat_o A_116) B_62)->(((member_nat X_32) A_116)->((member_nat X_32) B_62)))) % FOF formula (forall (X_32:x_a) (A_116:(x_a->Prop)) (B_62:(x_a->Prop)), (((ord_less_eq_a_o A_116) B_62)->(((member_a X_32) A_116)->((member_a X_32) B_62)))) of role axiom named fact_423_set__mp % A new axiom: (forall (X_32:x_a) (A_116:(x_a->Prop)) (B_62:(x_a->Prop)), (((ord_less_eq_a_o A_116) B_62)->(((member_a X_32) A_116)->((member_a X_32) B_62)))) % FOF formula (forall (X_32:pname) (A_116:(pname->Prop)) (B_62:(pname->Prop)), (((ord_less_eq_pname_o A_116) B_62)->(((member_pname X_32) A_116)->((member_pname X_32) B_62)))) of role axiom named fact_424_set__mp % A new axiom: (forall (X_32:pname) (A_116:(pname->Prop)) (B_62:(pname->Prop)), (((ord_less_eq_pname_o A_116) B_62)->(((member_pname X_32) A_116)->((member_pname X_32) B_62)))) % FOF formula (forall (C_28:(int->Prop)) (A_115:(int->Prop)) (B_61:(int->Prop)), (((ord_less_eq_int_o A_115) B_61)->(((ord_less_eq_int_o B_61) C_28)->((ord_less_eq_int_o A_115) C_28)))) of role axiom named fact_425_subset__trans % A new axiom: (forall (C_28:(int->Prop)) (A_115:(int->Prop)) (B_61:(int->Prop)), (((ord_less_eq_int_o A_115) B_61)->(((ord_less_eq_int_o B_61) C_28)->((ord_less_eq_int_o A_115) C_28)))) % FOF formula (forall (C_28:(nat->Prop)) (A_115:(nat->Prop)) (B_61:(nat->Prop)), (((ord_less_eq_nat_o A_115) B_61)->(((ord_less_eq_nat_o B_61) C_28)->((ord_less_eq_nat_o A_115) C_28)))) of role axiom named fact_426_subset__trans % A new axiom: (forall (C_28:(nat->Prop)) (A_115:(nat->Prop)) (B_61:(nat->Prop)), (((ord_less_eq_nat_o A_115) B_61)->(((ord_less_eq_nat_o B_61) C_28)->((ord_less_eq_nat_o A_115) C_28)))) % FOF formula (forall (C_28:(x_a->Prop)) (A_115:(x_a->Prop)) (B_61:(x_a->Prop)), (((ord_less_eq_a_o A_115) B_61)->(((ord_less_eq_a_o B_61) C_28)->((ord_less_eq_a_o A_115) C_28)))) of role axiom named fact_427_subset__trans % A new axiom: (forall (C_28:(x_a->Prop)) (A_115:(x_a->Prop)) (B_61:(x_a->Prop)), (((ord_less_eq_a_o A_115) B_61)->(((ord_less_eq_a_o B_61) C_28)->((ord_less_eq_a_o A_115) C_28)))) % FOF formula (forall (A_114:(int->Prop)) (B_60:(int->Prop)), ((((eq (int->Prop)) A_114) B_60)->((((ord_less_eq_int_o A_114) B_60)->(((ord_less_eq_int_o B_60) A_114)->False))->False))) of role axiom named fact_428_equalityE % A new axiom: (forall (A_114:(int->Prop)) (B_60:(int->Prop)), ((((eq (int->Prop)) A_114) B_60)->((((ord_less_eq_int_o A_114) B_60)->(((ord_less_eq_int_o B_60) A_114)->False))->False))) % FOF formula (forall (A_114:(nat->Prop)) (B_60:(nat->Prop)), ((((eq (nat->Prop)) A_114) B_60)->((((ord_less_eq_nat_o A_114) B_60)->(((ord_less_eq_nat_o B_60) A_114)->False))->False))) of role axiom named fact_429_equalityE % A new axiom: (forall (A_114:(nat->Prop)) (B_60:(nat->Prop)), ((((eq (nat->Prop)) A_114) B_60)->((((ord_less_eq_nat_o A_114) B_60)->(((ord_less_eq_nat_o B_60) A_114)->False))->False))) % FOF formula (forall (A_114:(x_a->Prop)) (B_60:(x_a->Prop)), ((((eq (x_a->Prop)) A_114) B_60)->((((ord_less_eq_a_o A_114) B_60)->(((ord_less_eq_a_o B_60) A_114)->False))->False))) of role axiom named fact_430_equalityE % A new axiom: (forall (A_114:(x_a->Prop)) (B_60:(x_a->Prop)), ((((eq (x_a->Prop)) A_114) B_60)->((((ord_less_eq_a_o A_114) B_60)->(((ord_less_eq_a_o B_60) A_114)->False))->False))) % FOF formula (forall (Z_4:int) (F_35:(nat->int)) (A_113:(nat->Prop)), ((iff ((member_int Z_4) ((image_nat_int F_35) A_113))) ((ex nat) (fun (X_1:nat)=> ((and ((member_nat X_1) A_113)) (((eq int) Z_4) (F_35 X_1))))))) of role axiom named fact_431_image__iff % A new axiom: (forall (Z_4:int) (F_35:(nat->int)) (A_113:(nat->Prop)), ((iff ((member_int Z_4) ((image_nat_int F_35) A_113))) ((ex nat) (fun (X_1:nat)=> ((and ((member_nat X_1) A_113)) (((eq int) Z_4) (F_35 X_1))))))) % FOF formula (forall (Z_4:x_a) (F_35:(pname->x_a)) (A_113:(pname->Prop)), ((iff ((member_a Z_4) ((image_pname_a F_35) A_113))) ((ex pname) (fun (X_1:pname)=> ((and ((member_pname X_1) A_113)) (((eq x_a) Z_4) (F_35 X_1))))))) of role axiom named fact_432_image__iff % A new axiom: (forall (Z_4:x_a) (F_35:(pname->x_a)) (A_113:(pname->Prop)), ((iff ((member_a Z_4) ((image_pname_a F_35) A_113))) ((ex pname) (fun (X_1:pname)=> ((and ((member_pname X_1) A_113)) (((eq x_a) Z_4) (F_35 X_1))))))) % FOF formula (forall (F_34:(nat->int)) (X_31:nat) (A_112:(nat->Prop)), (((member_nat X_31) A_112)->((member_int (F_34 X_31)) ((image_nat_int F_34) A_112)))) of role axiom named fact_433_imageI % A new axiom: (forall (F_34:(nat->int)) (X_31:nat) (A_112:(nat->Prop)), (((member_nat X_31) A_112)->((member_int (F_34 X_31)) ((image_nat_int F_34) A_112)))) % FOF formula (forall (F_34:(pname->x_a)) (X_31:pname) (A_112:(pname->Prop)), (((member_pname X_31) A_112)->((member_a (F_34 X_31)) ((image_pname_a F_34) A_112)))) of role axiom named fact_434_imageI % A new axiom: (forall (F_34:(pname->x_a)) (X_31:pname) (A_112:(pname->Prop)), (((member_pname X_31) A_112)->((member_a (F_34 X_31)) ((image_pname_a F_34) A_112)))) % FOF formula (forall (B_59:int) (F_33:(nat->int)) (X_30:nat) (A_111:(nat->Prop)), (((member_nat X_30) A_111)->((((eq int) B_59) (F_33 X_30))->((member_int B_59) ((image_nat_int F_33) A_111))))) of role axiom named fact_435_rev__image__eqI % A new axiom: (forall (B_59:int) (F_33:(nat->int)) (X_30:nat) (A_111:(nat->Prop)), (((member_nat X_30) A_111)->((((eq int) B_59) (F_33 X_30))->((member_int B_59) ((image_nat_int F_33) A_111))))) % FOF formula (forall (B_59:x_a) (F_33:(pname->x_a)) (X_30:pname) (A_111:(pname->Prop)), (((member_pname X_30) A_111)->((((eq x_a) B_59) (F_33 X_30))->((member_a B_59) ((image_pname_a F_33) A_111))))) of role axiom named fact_436_rev__image__eqI % A new axiom: (forall (B_59:x_a) (F_33:(pname->x_a)) (X_30:pname) (A_111:(pname->Prop)), (((member_pname X_30) A_111)->((((eq x_a) B_59) (F_33 X_30))->((member_a B_59) ((image_pname_a F_33) A_111))))) % FOF formula (forall (X_1:x_a) (Xa:(x_a->Prop)), (((eq (x_a->Prop)) ((insert_a X_1) Xa)) (collect_a (fun (Y_1:x_a)=> ((or (((eq x_a) Y_1) X_1)) ((member_a Y_1) Xa)))))) of role axiom named fact_437_insert__compr__raw % A new axiom: (forall (X_1:x_a) (Xa:(x_a->Prop)), (((eq (x_a->Prop)) ((insert_a X_1) Xa)) (collect_a (fun (Y_1:x_a)=> ((or (((eq x_a) Y_1) X_1)) ((member_a Y_1) Xa)))))) % FOF formula (forall (X_1:int) (Xa:(int->Prop)), (((eq (int->Prop)) ((insert_int X_1) Xa)) (collect_int (fun (Y_1:int)=> ((or (((eq int) Y_1) X_1)) ((member_int Y_1) Xa)))))) of role axiom named fact_438_insert__compr__raw % A new axiom: (forall (X_1:int) (Xa:(int->Prop)), (((eq (int->Prop)) ((insert_int X_1) Xa)) (collect_int (fun (Y_1:int)=> ((or (((eq int) Y_1) X_1)) ((member_int Y_1) Xa)))))) % FOF formula (forall (X_1:nat) (Xa:(nat->Prop)), (((eq (nat->Prop)) ((insert_nat X_1) Xa)) (collect_nat (fun (Y_1:nat)=> ((or (((eq nat) Y_1) X_1)) ((member_nat Y_1) Xa)))))) of role axiom named fact_439_insert__compr__raw % A new axiom: (forall (X_1:nat) (Xa:(nat->Prop)), (((eq (nat->Prop)) ((insert_nat X_1) Xa)) (collect_nat (fun (Y_1:nat)=> ((or (((eq nat) Y_1) X_1)) ((member_nat Y_1) Xa)))))) % FOF formula (forall (X_1:pname) (Xa:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname X_1) Xa)) (collect_pname (fun (Y_1:pname)=> ((or (((eq pname) Y_1) X_1)) ((member_pname Y_1) Xa)))))) of role axiom named fact_440_insert__compr__raw % A new axiom: (forall (X_1:pname) (Xa:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname X_1) Xa)) (collect_pname (fun (Y_1:pname)=> ((or (((eq pname) Y_1) X_1)) ((member_pname Y_1) Xa)))))) % FOF formula (forall (F_32:(int->Prop)) (G_4:(int->Prop)), ((iff ((ord_less_eq_int_o F_32) G_4)) (forall (X_1:int), ((ord_less_eq_o (F_32 X_1)) (G_4 X_1))))) of role axiom named fact_441_le__fun__def % A new axiom: (forall (F_32:(int->Prop)) (G_4:(int->Prop)), ((iff ((ord_less_eq_int_o F_32) G_4)) (forall (X_1:int), ((ord_less_eq_o (F_32 X_1)) (G_4 X_1))))) % FOF formula (forall (F_32:(nat->Prop)) (G_4:(nat->Prop)), ((iff ((ord_less_eq_nat_o F_32) G_4)) (forall (X_1:nat), ((ord_less_eq_o (F_32 X_1)) (G_4 X_1))))) of role axiom named fact_442_le__fun__def % A new axiom: (forall (F_32:(nat->Prop)) (G_4:(nat->Prop)), ((iff ((ord_less_eq_nat_o F_32) G_4)) (forall (X_1:nat), ((ord_less_eq_o (F_32 X_1)) (G_4 X_1))))) % FOF formula (forall (F_32:(x_a->Prop)) (G_4:(x_a->Prop)), ((iff ((ord_less_eq_a_o F_32) G_4)) (forall (X_1:x_a), ((ord_less_eq_o (F_32 X_1)) (G_4 X_1))))) of role axiom named fact_443_le__fun__def % A new axiom: (forall (F_32:(x_a->Prop)) (G_4:(x_a->Prop)), ((iff ((ord_less_eq_a_o F_32) G_4)) (forall (X_1:x_a), ((ord_less_eq_o (F_32 X_1)) (G_4 X_1))))) % FOF formula (forall (X_29:int) (F_31:(int->Prop)) (G_3:(int->Prop)), (((ord_less_eq_int_o F_31) G_3)->((ord_less_eq_o (F_31 X_29)) (G_3 X_29)))) of role axiom named fact_444_le__funD % A new axiom: (forall (X_29:int) (F_31:(int->Prop)) (G_3:(int->Prop)), (((ord_less_eq_int_o F_31) G_3)->((ord_less_eq_o (F_31 X_29)) (G_3 X_29)))) % FOF formula (forall (X_29:nat) (F_31:(nat->Prop)) (G_3:(nat->Prop)), (((ord_less_eq_nat_o F_31) G_3)->((ord_less_eq_o (F_31 X_29)) (G_3 X_29)))) of role axiom named fact_445_le__funD % A new axiom: (forall (X_29:nat) (F_31:(nat->Prop)) (G_3:(nat->Prop)), (((ord_less_eq_nat_o F_31) G_3)->((ord_less_eq_o (F_31 X_29)) (G_3 X_29)))) % FOF formula (forall (X_29:x_a) (F_31:(x_a->Prop)) (G_3:(x_a->Prop)), (((ord_less_eq_a_o F_31) G_3)->((ord_less_eq_o (F_31 X_29)) (G_3 X_29)))) of role axiom named fact_446_le__funD % A new axiom: (forall (X_29:x_a) (F_31:(x_a->Prop)) (G_3:(x_a->Prop)), (((ord_less_eq_a_o F_31) G_3)->((ord_less_eq_o (F_31 X_29)) (G_3 X_29)))) % FOF formula (forall (X_28:int) (F_30:(int->Prop)) (G_2:(int->Prop)), (((ord_less_eq_int_o F_30) G_2)->((ord_less_eq_o (F_30 X_28)) (G_2 X_28)))) of role axiom named fact_447_le__funE % A new axiom: (forall (X_28:int) (F_30:(int->Prop)) (G_2:(int->Prop)), (((ord_less_eq_int_o F_30) G_2)->((ord_less_eq_o (F_30 X_28)) (G_2 X_28)))) % FOF formula (forall (X_28:nat) (F_30:(nat->Prop)) (G_2:(nat->Prop)), (((ord_less_eq_nat_o F_30) G_2)->((ord_less_eq_o (F_30 X_28)) (G_2 X_28)))) of role axiom named fact_448_le__funE % A new axiom: (forall (X_28:nat) (F_30:(nat->Prop)) (G_2:(nat->Prop)), (((ord_less_eq_nat_o F_30) G_2)->((ord_less_eq_o (F_30 X_28)) (G_2 X_28)))) % FOF formula (forall (X_28:x_a) (F_30:(x_a->Prop)) (G_2:(x_a->Prop)), (((ord_less_eq_a_o F_30) G_2)->((ord_less_eq_o (F_30 X_28)) (G_2 X_28)))) of role axiom named fact_449_le__funE % A new axiom: (forall (X_28:x_a) (F_30:(x_a->Prop)) (G_2:(x_a->Prop)), (((ord_less_eq_a_o F_30) G_2)->((ord_less_eq_o (F_30 X_28)) (G_2 X_28)))) % FOF formula (forall (B_58:(x_a->Prop)) (A_110:x_a), ((ord_less_eq_a_o B_58) ((insert_a A_110) B_58))) of role axiom named fact_450_subset__insertI % A new axiom: (forall (B_58:(x_a->Prop)) (A_110:x_a), ((ord_less_eq_a_o B_58) ((insert_a A_110) B_58))) % FOF formula (forall (B_58:(int->Prop)) (A_110:int), ((ord_less_eq_int_o B_58) ((insert_int A_110) B_58))) of role axiom named fact_451_subset__insertI % A new axiom: (forall (B_58:(int->Prop)) (A_110:int), ((ord_less_eq_int_o B_58) ((insert_int A_110) B_58))) % FOF formula (forall (B_58:(nat->Prop)) (A_110:nat), ((ord_less_eq_nat_o B_58) ((insert_nat A_110) B_58))) of role axiom named fact_452_subset__insertI % A new axiom: (forall (B_58:(nat->Prop)) (A_110:nat), ((ord_less_eq_nat_o B_58) ((insert_nat A_110) B_58))) % FOF formula (forall (X_27:x_a) (A_109:(x_a->Prop)) (B_57:(x_a->Prop)), ((iff ((ord_less_eq_a_o ((insert_a X_27) A_109)) B_57)) ((and ((member_a X_27) B_57)) ((ord_less_eq_a_o A_109) B_57)))) of role axiom named fact_453_insert__subset % A new axiom: (forall (X_27:x_a) (A_109:(x_a->Prop)) (B_57:(x_a->Prop)), ((iff ((ord_less_eq_a_o ((insert_a X_27) A_109)) B_57)) ((and ((member_a X_27) B_57)) ((ord_less_eq_a_o A_109) B_57)))) % FOF formula (forall (X_27:int) (A_109:(int->Prop)) (B_57:(int->Prop)), ((iff ((ord_less_eq_int_o ((insert_int X_27) A_109)) B_57)) ((and ((member_int X_27) B_57)) ((ord_less_eq_int_o A_109) B_57)))) of role axiom named fact_454_insert__subset % A new axiom: (forall (X_27:int) (A_109:(int->Prop)) (B_57:(int->Prop)), ((iff ((ord_less_eq_int_o ((insert_int X_27) A_109)) B_57)) ((and ((member_int X_27) B_57)) ((ord_less_eq_int_o A_109) B_57)))) % FOF formula (forall (X_27:nat) (A_109:(nat->Prop)) (B_57:(nat->Prop)), ((iff ((ord_less_eq_nat_o ((insert_nat X_27) A_109)) B_57)) ((and ((member_nat X_27) B_57)) ((ord_less_eq_nat_o A_109) B_57)))) of role axiom named fact_455_insert__subset % A new axiom: (forall (X_27:nat) (A_109:(nat->Prop)) (B_57:(nat->Prop)), ((iff ((ord_less_eq_nat_o ((insert_nat X_27) A_109)) B_57)) ((and ((member_nat X_27) B_57)) ((ord_less_eq_nat_o A_109) B_57)))) % FOF formula (forall (X_27:pname) (A_109:(pname->Prop)) (B_57:(pname->Prop)), ((iff ((ord_less_eq_pname_o ((insert_pname X_27) A_109)) B_57)) ((and ((member_pname X_27) B_57)) ((ord_less_eq_pname_o A_109) B_57)))) of role axiom named fact_456_insert__subset % A new axiom: (forall (X_27:pname) (A_109:(pname->Prop)) (B_57:(pname->Prop)), ((iff ((ord_less_eq_pname_o ((insert_pname X_27) A_109)) B_57)) ((and ((member_pname X_27) B_57)) ((ord_less_eq_pname_o A_109) B_57)))) % FOF formula (forall (B_56:(x_a->Prop)) (X_26:x_a) (A_108:(x_a->Prop)), ((((member_a X_26) A_108)->False)->((iff ((ord_less_eq_a_o A_108) ((insert_a X_26) B_56))) ((ord_less_eq_a_o A_108) B_56)))) of role axiom named fact_457_subset__insert % A new axiom: (forall (B_56:(x_a->Prop)) (X_26:x_a) (A_108:(x_a->Prop)), ((((member_a X_26) A_108)->False)->((iff ((ord_less_eq_a_o A_108) ((insert_a X_26) B_56))) ((ord_less_eq_a_o A_108) B_56)))) % FOF formula (forall (B_56:(int->Prop)) (X_26:int) (A_108:(int->Prop)), ((((member_int X_26) A_108)->False)->((iff ((ord_less_eq_int_o A_108) ((insert_int X_26) B_56))) ((ord_less_eq_int_o A_108) B_56)))) of role axiom named fact_458_subset__insert % A new axiom: (forall (B_56:(int->Prop)) (X_26:int) (A_108:(int->Prop)), ((((member_int X_26) A_108)->False)->((iff ((ord_less_eq_int_o A_108) ((insert_int X_26) B_56))) ((ord_less_eq_int_o A_108) B_56)))) % FOF formula (forall (B_56:(nat->Prop)) (X_26:nat) (A_108:(nat->Prop)), ((((member_nat X_26) A_108)->False)->((iff ((ord_less_eq_nat_o A_108) ((insert_nat X_26) B_56))) ((ord_less_eq_nat_o A_108) B_56)))) of role axiom named fact_459_subset__insert % A new axiom: (forall (B_56:(nat->Prop)) (X_26:nat) (A_108:(nat->Prop)), ((((member_nat X_26) A_108)->False)->((iff ((ord_less_eq_nat_o A_108) ((insert_nat X_26) B_56))) ((ord_less_eq_nat_o A_108) B_56)))) % FOF formula (forall (B_56:(pname->Prop)) (X_26:pname) (A_108:(pname->Prop)), ((((member_pname X_26) A_108)->False)->((iff ((ord_less_eq_pname_o A_108) ((insert_pname X_26) B_56))) ((ord_less_eq_pname_o A_108) B_56)))) of role axiom named fact_460_subset__insert % A new axiom: (forall (B_56:(pname->Prop)) (X_26:pname) (A_108:(pname->Prop)), ((((member_pname X_26) A_108)->False)->((iff ((ord_less_eq_pname_o A_108) ((insert_pname X_26) B_56))) ((ord_less_eq_pname_o A_108) B_56)))) % FOF formula (forall (B_55:x_a) (A_107:(x_a->Prop)) (B_54:(x_a->Prop)), (((ord_less_eq_a_o A_107) B_54)->((ord_less_eq_a_o A_107) ((insert_a B_55) B_54)))) of role axiom named fact_461_subset__insertI2 % A new axiom: (forall (B_55:x_a) (A_107:(x_a->Prop)) (B_54:(x_a->Prop)), (((ord_less_eq_a_o A_107) B_54)->((ord_less_eq_a_o A_107) ((insert_a B_55) B_54)))) % FOF formula (forall (B_55:int) (A_107:(int->Prop)) (B_54:(int->Prop)), (((ord_less_eq_int_o A_107) B_54)->((ord_less_eq_int_o A_107) ((insert_int B_55) B_54)))) of role axiom named fact_462_subset__insertI2 % A new axiom: (forall (B_55:int) (A_107:(int->Prop)) (B_54:(int->Prop)), (((ord_less_eq_int_o A_107) B_54)->((ord_less_eq_int_o A_107) ((insert_int B_55) B_54)))) % FOF formula (forall (B_55:nat) (A_107:(nat->Prop)) (B_54:(nat->Prop)), (((ord_less_eq_nat_o A_107) B_54)->((ord_less_eq_nat_o A_107) ((insert_nat B_55) B_54)))) of role axiom named fact_463_subset__insertI2 % A new axiom: (forall (B_55:nat) (A_107:(nat->Prop)) (B_54:(nat->Prop)), (((ord_less_eq_nat_o A_107) B_54)->((ord_less_eq_nat_o A_107) ((insert_nat B_55) B_54)))) % FOF formula (forall (A_106:x_a) (C_27:(x_a->Prop)) (D_7:(x_a->Prop)), (((ord_less_eq_a_o C_27) D_7)->((ord_less_eq_a_o ((insert_a A_106) C_27)) ((insert_a A_106) D_7)))) of role axiom named fact_464_insert__mono % A new axiom: (forall (A_106:x_a) (C_27:(x_a->Prop)) (D_7:(x_a->Prop)), (((ord_less_eq_a_o C_27) D_7)->((ord_less_eq_a_o ((insert_a A_106) C_27)) ((insert_a A_106) D_7)))) % FOF formula (forall (A_106:int) (C_27:(int->Prop)) (D_7:(int->Prop)), (((ord_less_eq_int_o C_27) D_7)->((ord_less_eq_int_o ((insert_int A_106) C_27)) ((insert_int A_106) D_7)))) of role axiom named fact_465_insert__mono % A new axiom: (forall (A_106:int) (C_27:(int->Prop)) (D_7:(int->Prop)), (((ord_less_eq_int_o C_27) D_7)->((ord_less_eq_int_o ((insert_int A_106) C_27)) ((insert_int A_106) D_7)))) % FOF formula (forall (A_106:nat) (C_27:(nat->Prop)) (D_7:(nat->Prop)), (((ord_less_eq_nat_o C_27) D_7)->((ord_less_eq_nat_o ((insert_nat A_106) C_27)) ((insert_nat A_106) D_7)))) of role axiom named fact_466_insert__mono % A new axiom: (forall (A_106:nat) (C_27:(nat->Prop)) (D_7:(nat->Prop)), (((ord_less_eq_nat_o C_27) D_7)->((ord_less_eq_nat_o ((insert_nat A_106) C_27)) ((insert_nat A_106) D_7)))) % FOF formula (forall (F_29:(nat->int)) (A_105:nat) (B_53:(nat->Prop)), (((eq (int->Prop)) ((image_nat_int F_29) ((insert_nat A_105) B_53))) ((insert_int (F_29 A_105)) ((image_nat_int F_29) B_53)))) of role axiom named fact_467_image__insert % A new axiom: (forall (F_29:(nat->int)) (A_105:nat) (B_53:(nat->Prop)), (((eq (int->Prop)) ((image_nat_int F_29) ((insert_nat A_105) B_53))) ((insert_int (F_29 A_105)) ((image_nat_int F_29) B_53)))) % FOF formula (forall (F_29:(pname->x_a)) (A_105:pname) (B_53:(pname->Prop)), (((eq (x_a->Prop)) ((image_pname_a F_29) ((insert_pname A_105) B_53))) ((insert_a (F_29 A_105)) ((image_pname_a F_29) B_53)))) of role axiom named fact_468_image__insert % A new axiom: (forall (F_29:(pname->x_a)) (A_105:pname) (B_53:(pname->Prop)), (((eq (x_a->Prop)) ((image_pname_a F_29) ((insert_pname A_105) B_53))) ((insert_a (F_29 A_105)) ((image_pname_a F_29) B_53)))) % FOF formula (forall (F_28:(nat->int)) (X_25:nat) (A_104:(nat->Prop)), (((member_nat X_25) A_104)->(((eq (int->Prop)) ((insert_int (F_28 X_25)) ((image_nat_int F_28) A_104))) ((image_nat_int F_28) A_104)))) of role axiom named fact_469_insert__image % A new axiom: (forall (F_28:(nat->int)) (X_25:nat) (A_104:(nat->Prop)), (((member_nat X_25) A_104)->(((eq (int->Prop)) ((insert_int (F_28 X_25)) ((image_nat_int F_28) A_104))) ((image_nat_int F_28) A_104)))) % FOF formula (forall (F_28:(pname->x_a)) (X_25:pname) (A_104:(pname->Prop)), (((member_pname X_25) A_104)->(((eq (x_a->Prop)) ((insert_a (F_28 X_25)) ((image_pname_a F_28) A_104))) ((image_pname_a F_28) A_104)))) of role axiom named fact_470_insert__image % A new axiom: (forall (F_28:(pname->x_a)) (X_25:pname) (A_104:(pname->Prop)), (((member_pname X_25) A_104)->(((eq (x_a->Prop)) ((insert_a (F_28 X_25)) ((image_pname_a F_28) A_104))) ((image_pname_a F_28) A_104)))) % FOF formula (forall (B_52:(int->Prop)) (F_27:(nat->int)) (A_103:(nat->Prop)), ((iff ((ord_less_eq_int_o B_52) ((image_nat_int F_27) A_103))) ((ex (nat->Prop)) (fun (AA:(nat->Prop))=> ((and ((ord_less_eq_nat_o AA) A_103)) (((eq (int->Prop)) B_52) ((image_nat_int F_27) AA))))))) of role axiom named fact_471_subset__image__iff % A new axiom: (forall (B_52:(int->Prop)) (F_27:(nat->int)) (A_103:(nat->Prop)), ((iff ((ord_less_eq_int_o B_52) ((image_nat_int F_27) A_103))) ((ex (nat->Prop)) (fun (AA:(nat->Prop))=> ((and ((ord_less_eq_nat_o AA) A_103)) (((eq (int->Prop)) B_52) ((image_nat_int F_27) AA))))))) % FOF formula (forall (B_52:(x_a->Prop)) (F_27:(pname->x_a)) (A_103:(pname->Prop)), ((iff ((ord_less_eq_a_o B_52) ((image_pname_a F_27) A_103))) ((ex (pname->Prop)) (fun (AA:(pname->Prop))=> ((and ((ord_less_eq_pname_o AA) A_103)) (((eq (x_a->Prop)) B_52) ((image_pname_a F_27) AA))))))) of role axiom named fact_472_subset__image__iff % A new axiom: (forall (B_52:(x_a->Prop)) (F_27:(pname->x_a)) (A_103:(pname->Prop)), ((iff ((ord_less_eq_a_o B_52) ((image_pname_a F_27) A_103))) ((ex (pname->Prop)) (fun (AA:(pname->Prop))=> ((and ((ord_less_eq_pname_o AA) A_103)) (((eq (x_a->Prop)) B_52) ((image_pname_a F_27) AA))))))) % FOF formula (forall (F_26:(nat->int)) (A_102:(nat->Prop)) (B_51:(nat->Prop)), (((ord_less_eq_nat_o A_102) B_51)->((ord_less_eq_int_o ((image_nat_int F_26) A_102)) ((image_nat_int F_26) B_51)))) of role axiom named fact_473_image__mono % A new axiom: (forall (F_26:(nat->int)) (A_102:(nat->Prop)) (B_51:(nat->Prop)), (((ord_less_eq_nat_o A_102) B_51)->((ord_less_eq_int_o ((image_nat_int F_26) A_102)) ((image_nat_int F_26) B_51)))) % FOF formula (forall (F_26:(pname->x_a)) (A_102:(pname->Prop)) (B_51:(pname->Prop)), (((ord_less_eq_pname_o A_102) B_51)->((ord_less_eq_a_o ((image_pname_a F_26) A_102)) ((image_pname_a F_26) B_51)))) of role axiom named fact_474_image__mono % A new axiom: (forall (F_26:(pname->x_a)) (A_102:(pname->Prop)) (B_51:(pname->Prop)), (((ord_less_eq_pname_o A_102) B_51)->((ord_less_eq_a_o ((image_pname_a F_26) A_102)) ((image_pname_a F_26) B_51)))) % FOF formula (forall (B_50:int) (F_25:(nat->int)) (A_101:(nat->Prop)), (((member_int B_50) ((image_nat_int F_25) A_101))->((forall (X_1:nat), ((((eq int) B_50) (F_25 X_1))->(((member_nat X_1) A_101)->False)))->False))) of role axiom named fact_475_imageE % A new axiom: (forall (B_50:int) (F_25:(nat->int)) (A_101:(nat->Prop)), (((member_int B_50) ((image_nat_int F_25) A_101))->((forall (X_1:nat), ((((eq int) B_50) (F_25 X_1))->(((member_nat X_1) A_101)->False)))->False))) % FOF formula (forall (B_50:x_a) (F_25:(pname->x_a)) (A_101:(pname->Prop)), (((member_a B_50) ((image_pname_a F_25) A_101))->((forall (X_1:pname), ((((eq x_a) B_50) (F_25 X_1))->(((member_pname X_1) A_101)->False)))->False))) of role axiom named fact_476_imageE % A new axiom: (forall (B_50:x_a) (F_25:(pname->x_a)) (A_101:(pname->Prop)), (((member_a B_50) ((image_pname_a F_25) A_101))->((forall (X_1:pname), ((((eq x_a) B_50) (F_25 X_1))->(((member_pname X_1) A_101)->False)))->False))) % FOF formula (forall (B_49:(int->Prop)) (A_100:(int->Prop)), ((forall (X_1:int), (((member_int X_1) A_100)->((member_int X_1) B_49)))->((ord_less_eq_int_o A_100) B_49))) of role axiom named fact_477_subsetI % A new axiom: (forall (B_49:(int->Prop)) (A_100:(int->Prop)), ((forall (X_1:int), (((member_int X_1) A_100)->((member_int X_1) B_49)))->((ord_less_eq_int_o A_100) B_49))) % FOF formula (forall (B_49:(nat->Prop)) (A_100:(nat->Prop)), ((forall (X_1:nat), (((member_nat X_1) A_100)->((member_nat X_1) B_49)))->((ord_less_eq_nat_o A_100) B_49))) of role axiom named fact_478_subsetI % A new axiom: (forall (B_49:(nat->Prop)) (A_100:(nat->Prop)), ((forall (X_1:nat), (((member_nat X_1) A_100)->((member_nat X_1) B_49)))->((ord_less_eq_nat_o A_100) B_49))) % FOF formula (forall (B_49:(x_a->Prop)) (A_100:(x_a->Prop)), ((forall (X_1:x_a), (((member_a X_1) A_100)->((member_a X_1) B_49)))->((ord_less_eq_a_o A_100) B_49))) of role axiom named fact_479_subsetI % A new axiom: (forall (B_49:(x_a->Prop)) (A_100:(x_a->Prop)), ((forall (X_1:x_a), (((member_a X_1) A_100)->((member_a X_1) B_49)))->((ord_less_eq_a_o A_100) B_49))) % FOF formula (forall (B_49:(pname->Prop)) (A_100:(pname->Prop)), ((forall (X_1:pname), (((member_pname X_1) A_100)->((member_pname X_1) B_49)))->((ord_less_eq_pname_o A_100) B_49))) of role axiom named fact_480_subsetI % A new axiom: (forall (B_49:(pname->Prop)) (A_100:(pname->Prop)), ((forall (X_1:pname), (((member_pname X_1) A_100)->((member_pname X_1) B_49)))->((ord_less_eq_pname_o A_100) B_49))) % FOF formula (forall (F_24:(nat->int)) (B_48:(int->Prop)) (A_99:(nat->Prop)), ((forall (X_1:nat), (((member_nat X_1) A_99)->((member_int (F_24 X_1)) B_48)))->((ord_less_eq_int_o ((image_nat_int F_24) A_99)) B_48))) of role axiom named fact_481_image__subsetI % A new axiom: (forall (F_24:(nat->int)) (B_48:(int->Prop)) (A_99:(nat->Prop)), ((forall (X_1:nat), (((member_nat X_1) A_99)->((member_int (F_24 X_1)) B_48)))->((ord_less_eq_int_o ((image_nat_int F_24) A_99)) B_48))) % FOF formula (forall (F_24:(pname->x_a)) (B_48:(x_a->Prop)) (A_99:(pname->Prop)), ((forall (X_1:pname), (((member_pname X_1) A_99)->((member_a (F_24 X_1)) B_48)))->((ord_less_eq_a_o ((image_pname_a F_24) A_99)) B_48))) of role axiom named fact_482_image__subsetI % A new axiom: (forall (F_24:(pname->x_a)) (B_48:(x_a->Prop)) (A_99:(pname->Prop)), ((forall (X_1:pname), (((member_pname X_1) A_99)->((member_a (F_24 X_1)) B_48)))->((ord_less_eq_a_o ((image_pname_a F_24) A_99)) B_48))) % FOF formula (forall (F_23:(int->Prop)) (G_1:(int->Prop)), ((forall (X_1:int), ((ord_less_eq_o (F_23 X_1)) (G_1 X_1)))->((ord_less_eq_int_o F_23) G_1))) of role axiom named fact_483_le__funI % A new axiom: (forall (F_23:(int->Prop)) (G_1:(int->Prop)), ((forall (X_1:int), ((ord_less_eq_o (F_23 X_1)) (G_1 X_1)))->((ord_less_eq_int_o F_23) G_1))) % FOF formula (forall (F_23:(nat->Prop)) (G_1:(nat->Prop)), ((forall (X_1:nat), ((ord_less_eq_o (F_23 X_1)) (G_1 X_1)))->((ord_less_eq_nat_o F_23) G_1))) of role axiom named fact_484_le__funI % A new axiom: (forall (F_23:(nat->Prop)) (G_1:(nat->Prop)), ((forall (X_1:nat), ((ord_less_eq_o (F_23 X_1)) (G_1 X_1)))->((ord_less_eq_nat_o F_23) G_1))) % FOF formula (forall (F_23:(x_a->Prop)) (G_1:(x_a->Prop)), ((forall (X_1:x_a), ((ord_less_eq_o (F_23 X_1)) (G_1 X_1)))->((ord_less_eq_a_o F_23) G_1))) of role axiom named fact_485_le__funI % A new axiom: (forall (F_23:(x_a->Prop)) (G_1:(x_a->Prop)), ((forall (X_1:x_a), ((ord_less_eq_o (F_23 X_1)) (G_1 X_1)))->((ord_less_eq_a_o F_23) G_1))) % FOF formula (forall (N_2:(nat->Prop)), ((iff (finite_finite_nat N_2)) ((ex nat) (fun (M_1:nat)=> (forall (X_1:nat), (((member_nat X_1) N_2)->((ord_less_eq_nat X_1) M_1))))))) of role axiom named fact_486_finite__nat__set__iff__bounded__le % A new axiom: (forall (N_2:(nat->Prop)), ((iff (finite_finite_nat N_2)) ((ex nat) (fun (M_1:nat)=> (forall (X_1:nat), (((member_nat X_1) N_2)->((ord_less_eq_nat X_1) M_1))))))) % FOF formula (forall (G:(x_a->Prop)) (C:com), ((wt C)->((forall (X_1:pname), (((member_pname X_1) u)->((p G) ((insert_a (mgt_call X_1)) bot_bot_a_o))))->((p G) ((insert_a (mgt C)) bot_bot_a_o))))) of role axiom named fact_487_assms_I3_J % A new axiom: (forall (G:(x_a->Prop)) (C:com), ((wt C)->((forall (X_1:pname), (((member_pname X_1) u)->((p G) ((insert_a (mgt_call X_1)) bot_bot_a_o))))->((p G) ((insert_a (mgt C)) bot_bot_a_o))))) % FOF formula (forall (A_98:int) (B_47:int) (C_26:int) (D_6:int), ((((eq int) ((minus_minus_int A_98) B_47)) ((minus_minus_int C_26) D_6))->((iff ((ord_less_eq_int A_98) B_47)) ((ord_less_eq_int C_26) D_6)))) of role axiom named fact_488_diff__eq__diff__less__eq % A new axiom: (forall (A_98:int) (B_47:int) (C_26:int) (D_6:int), ((((eq int) ((minus_minus_int A_98) B_47)) ((minus_minus_int C_26) D_6))->((iff ((ord_less_eq_int A_98) B_47)) ((ord_less_eq_int C_26) D_6)))) % FOF formula (forall (M:nat) (N:nat), ((iff ((ord_less_eq_nat (suc M)) N)) (((nat_case_o False) (ord_less_eq_nat M)) N))) of role axiom named fact_489_less__eq__nat_Osimps_I2_J % A new axiom: (forall (M:nat) (N:nat), ((iff ((ord_less_eq_nat (suc M)) N)) (((nat_case_o False) (ord_less_eq_nat M)) N))) % FOF formula (forall (A_97:int), (((member_int A_97) bot_bot_int_o)->False)) of role axiom named fact_490_emptyE % A new axiom: (forall (A_97:int), (((member_int A_97) bot_bot_int_o)->False)) % FOF formula (forall (A_97:nat), (((member_nat A_97) bot_bot_nat_o)->False)) of role axiom named fact_491_emptyE % A new axiom: (forall (A_97:nat), (((member_nat A_97) bot_bot_nat_o)->False)) % FOF formula (forall (A_97:x_a), (((member_a A_97) bot_bot_a_o)->False)) of role axiom named fact_492_emptyE % A new axiom: (forall (A_97:x_a), (((member_a A_97) bot_bot_a_o)->False)) % FOF formula (forall (A_97:pname), (((member_pname A_97) bot_bot_pname_o)->False)) of role axiom named fact_493_emptyE % A new axiom: (forall (A_97:pname), (((member_pname A_97) bot_bot_pname_o)->False)) % FOF formula (forall (B_46:(int->Prop)) (A_96:(int->Prop)), ((finite_finite_int A_96)->(finite_finite_int ((minus_minus_int_o A_96) B_46)))) of role axiom named fact_494_finite__Diff % A new axiom: (forall (B_46:(int->Prop)) (A_96:(int->Prop)), ((finite_finite_int A_96)->(finite_finite_int ((minus_minus_int_o A_96) B_46)))) % FOF formula (forall (B_46:(nat->Prop)) (A_96:(nat->Prop)), ((finite_finite_nat A_96)->(finite_finite_nat ((minus_minus_nat_o A_96) B_46)))) of role axiom named fact_495_finite__Diff % A new axiom: (forall (B_46:(nat->Prop)) (A_96:(nat->Prop)), ((finite_finite_nat A_96)->(finite_finite_nat ((minus_minus_nat_o A_96) B_46)))) % FOF formula (forall (B_46:(pname->Prop)) (A_96:(pname->Prop)), ((finite_finite_pname A_96)->(finite_finite_pname ((minus_minus_pname_o A_96) B_46)))) of role axiom named fact_496_finite__Diff % A new axiom: (forall (B_46:(pname->Prop)) (A_96:(pname->Prop)), ((finite_finite_pname A_96)->(finite_finite_pname ((minus_minus_pname_o A_96) B_46)))) % FOF formula (finite_finite_int bot_bot_int_o) of role axiom named fact_497_finite_OemptyI % A new axiom: (finite_finite_int bot_bot_int_o) % FOF formula (finite_finite_nat bot_bot_nat_o) of role axiom named fact_498_finite_OemptyI % A new axiom: (finite_finite_nat bot_bot_nat_o) % FOF formula (finite_finite_pname bot_bot_pname_o) of role axiom named fact_499_finite_OemptyI % A new axiom: (finite_finite_pname bot_bot_pname_o) % FOF formula (finite_finite_a bot_bot_a_o) of role axiom named fact_500_finite_OemptyI % A new axiom: (finite_finite_a bot_bot_a_o) % FOF formula (forall (A_95:(nat->Prop)), ((ord_less_eq_nat_o bot_bot_nat_o) A_95)) of role axiom named fact_501_empty__subsetI % A new axiom: (forall (A_95:(nat->Prop)), ((ord_less_eq_nat_o bot_bot_nat_o) A_95)) % FOF formula (forall (A_95:(int->Prop)), ((ord_less_eq_int_o bot_bot_int_o) A_95)) of role axiom named fact_502_empty__subsetI % A new axiom: (forall (A_95:(int->Prop)), ((ord_less_eq_int_o bot_bot_int_o) A_95)) % FOF formula (forall (A_95:(x_a->Prop)), ((ord_less_eq_a_o bot_bot_a_o) A_95)) of role axiom named fact_503_empty__subsetI % A new axiom: (forall (A_95:(x_a->Prop)), ((ord_less_eq_a_o bot_bot_a_o) A_95)) % FOF formula (forall (A_94:int) (A_93:(int->Prop)), ((((eq (int->Prop)) A_93) bot_bot_int_o)->(((member_int A_94) A_93)->False))) of role axiom named fact_504_equals0D % A new axiom: (forall (A_94:int) (A_93:(int->Prop)), ((((eq (int->Prop)) A_93) bot_bot_int_o)->(((member_int A_94) A_93)->False))) % FOF formula (forall (A_94:nat) (A_93:(nat->Prop)), ((((eq (nat->Prop)) A_93) bot_bot_nat_o)->(((member_nat A_94) A_93)->False))) of role axiom named fact_505_equals0D % A new axiom: (forall (A_94:nat) (A_93:(nat->Prop)), ((((eq (nat->Prop)) A_93) bot_bot_nat_o)->(((member_nat A_94) A_93)->False))) % FOF formula (forall (A_94:x_a) (A_93:(x_a->Prop)), ((((eq (x_a->Prop)) A_93) bot_bot_a_o)->(((member_a A_94) A_93)->False))) of role axiom named fact_506_equals0D % A new axiom: (forall (A_94:x_a) (A_93:(x_a->Prop)), ((((eq (x_a->Prop)) A_93) bot_bot_a_o)->(((member_a A_94) A_93)->False))) % FOF formula (forall (A_94:pname) (A_93:(pname->Prop)), ((((eq (pname->Prop)) A_93) bot_bot_pname_o)->(((member_pname A_94) A_93)->False))) of role axiom named fact_507_equals0D % A new axiom: (forall (A_94:pname) (A_93:(pname->Prop)), ((((eq (pname->Prop)) A_93) bot_bot_pname_o)->(((member_pname A_94) A_93)->False))) % FOF formula (forall (P_9:(int->Prop)), ((iff (((eq (int->Prop)) (collect_int P_9)) bot_bot_int_o)) (forall (X_1:int), ((P_9 X_1)->False)))) of role axiom named fact_508_Collect__empty__eq % A new axiom: (forall (P_9:(int->Prop)), ((iff (((eq (int->Prop)) (collect_int P_9)) bot_bot_int_o)) (forall (X_1:int), ((P_9 X_1)->False)))) % FOF formula (forall (P_9:(nat->Prop)), ((iff (((eq (nat->Prop)) (collect_nat P_9)) bot_bot_nat_o)) (forall (X_1:nat), ((P_9 X_1)->False)))) of role axiom named fact_509_Collect__empty__eq % A new axiom: (forall (P_9:(nat->Prop)), ((iff (((eq (nat->Prop)) (collect_nat P_9)) bot_bot_nat_o)) (forall (X_1:nat), ((P_9 X_1)->False)))) % FOF formula (forall (P_9:(x_a->Prop)), ((iff (((eq (x_a->Prop)) (collect_a P_9)) bot_bot_a_o)) (forall (X_1:x_a), ((P_9 X_1)->False)))) of role axiom named fact_510_Collect__empty__eq % A new axiom: (forall (P_9:(x_a->Prop)), ((iff (((eq (x_a->Prop)) (collect_a P_9)) bot_bot_a_o)) (forall (X_1:x_a), ((P_9 X_1)->False)))) % FOF formula (forall (A_92:(nat->Prop)), (((eq (nat->Prop)) ((minus_minus_nat_o A_92) A_92)) bot_bot_nat_o)) of role axiom named fact_511_Diff__cancel % A new axiom: (forall (A_92:(nat->Prop)), (((eq (nat->Prop)) ((minus_minus_nat_o A_92) A_92)) bot_bot_nat_o)) % FOF formula (forall (A_92:(int->Prop)), (((eq (int->Prop)) ((minus_minus_int_o A_92) A_92)) bot_bot_int_o)) of role axiom named fact_512_Diff__cancel % A new axiom: (forall (A_92:(int->Prop)), (((eq (int->Prop)) ((minus_minus_int_o A_92) A_92)) bot_bot_int_o)) % FOF formula (forall (A_92:(x_a->Prop)), (((eq (x_a->Prop)) ((minus_minus_a_o A_92) A_92)) bot_bot_a_o)) of role axiom named fact_513_Diff__cancel % A new axiom: (forall (A_92:(x_a->Prop)), (((eq (x_a->Prop)) ((minus_minus_a_o A_92) A_92)) bot_bot_a_o)) % FOF formula (forall (A_91:(nat->Prop)), (((eq (nat->Prop)) ((minus_minus_nat_o A_91) bot_bot_nat_o)) A_91)) of role axiom named fact_514_Diff__empty % A new axiom: (forall (A_91:(nat->Prop)), (((eq (nat->Prop)) ((minus_minus_nat_o A_91) bot_bot_nat_o)) A_91)) % FOF formula (forall (A_91:(int->Prop)), (((eq (int->Prop)) ((minus_minus_int_o A_91) bot_bot_int_o)) A_91)) of role axiom named fact_515_Diff__empty % A new axiom: (forall (A_91:(int->Prop)), (((eq (int->Prop)) ((minus_minus_int_o A_91) bot_bot_int_o)) A_91)) % FOF formula (forall (A_91:(x_a->Prop)), (((eq (x_a->Prop)) ((minus_minus_a_o A_91) bot_bot_a_o)) A_91)) of role axiom named fact_516_Diff__empty % A new axiom: (forall (A_91:(x_a->Prop)), (((eq (x_a->Prop)) ((minus_minus_a_o A_91) bot_bot_a_o)) A_91)) % FOF formula (forall (C_25:int), (((member_int C_25) bot_bot_int_o)->False)) of role axiom named fact_517_empty__iff % A new axiom: (forall (C_25:int), (((member_int C_25) bot_bot_int_o)->False)) % FOF formula (forall (C_25:nat), (((member_nat C_25) bot_bot_nat_o)->False)) of role axiom named fact_518_empty__iff % A new axiom: (forall (C_25:nat), (((member_nat C_25) bot_bot_nat_o)->False)) % FOF formula (forall (C_25:x_a), (((member_a C_25) bot_bot_a_o)->False)) of role axiom named fact_519_empty__iff % A new axiom: (forall (C_25:x_a), (((member_a C_25) bot_bot_a_o)->False)) % FOF formula (forall (C_25:pname), (((member_pname C_25) bot_bot_pname_o)->False)) of role axiom named fact_520_empty__iff % A new axiom: (forall (C_25:pname), (((member_pname C_25) bot_bot_pname_o)->False)) % FOF formula (forall (P_8:(int->Prop)), ((iff (((eq (int->Prop)) bot_bot_int_o) (collect_int P_8))) (forall (X_1:int), ((P_8 X_1)->False)))) of role axiom named fact_521_empty__Collect__eq % A new axiom: (forall (P_8:(int->Prop)), ((iff (((eq (int->Prop)) bot_bot_int_o) (collect_int P_8))) (forall (X_1:int), ((P_8 X_1)->False)))) % FOF formula (forall (P_8:(nat->Prop)), ((iff (((eq (nat->Prop)) bot_bot_nat_o) (collect_nat P_8))) (forall (X_1:nat), ((P_8 X_1)->False)))) of role axiom named fact_522_empty__Collect__eq % A new axiom: (forall (P_8:(nat->Prop)), ((iff (((eq (nat->Prop)) bot_bot_nat_o) (collect_nat P_8))) (forall (X_1:nat), ((P_8 X_1)->False)))) % FOF formula (forall (P_8:(x_a->Prop)), ((iff (((eq (x_a->Prop)) bot_bot_a_o) (collect_a P_8))) (forall (X_1:x_a), ((P_8 X_1)->False)))) of role axiom named fact_523_empty__Collect__eq % A new axiom: (forall (P_8:(x_a->Prop)), ((iff (((eq (x_a->Prop)) bot_bot_a_o) (collect_a P_8))) (forall (X_1:x_a), ((P_8 X_1)->False)))) % FOF formula (forall (A_90:(nat->Prop)), (((eq (nat->Prop)) ((minus_minus_nat_o bot_bot_nat_o) A_90)) bot_bot_nat_o)) of role axiom named fact_524_empty__Diff % A new axiom: (forall (A_90:(nat->Prop)), (((eq (nat->Prop)) ((minus_minus_nat_o bot_bot_nat_o) A_90)) bot_bot_nat_o)) % FOF formula (forall (A_90:(int->Prop)), (((eq (int->Prop)) ((minus_minus_int_o bot_bot_int_o) A_90)) bot_bot_int_o)) of role axiom named fact_525_empty__Diff % A new axiom: (forall (A_90:(int->Prop)), (((eq (int->Prop)) ((minus_minus_int_o bot_bot_int_o) A_90)) bot_bot_int_o)) % FOF formula (forall (A_90:(x_a->Prop)), (((eq (x_a->Prop)) ((minus_minus_a_o bot_bot_a_o) A_90)) bot_bot_a_o)) of role axiom named fact_526_empty__Diff % A new axiom: (forall (A_90:(x_a->Prop)), (((eq (x_a->Prop)) ((minus_minus_a_o bot_bot_a_o) A_90)) bot_bot_a_o)) % FOF formula (forall (A_89:(int->Prop)), ((iff ((ex int) (fun (X_1:int)=> ((member_int X_1) A_89)))) (not (((eq (int->Prop)) A_89) bot_bot_int_o)))) of role axiom named fact_527_ex__in__conv % A new axiom: (forall (A_89:(int->Prop)), ((iff ((ex int) (fun (X_1:int)=> ((member_int X_1) A_89)))) (not (((eq (int->Prop)) A_89) bot_bot_int_o)))) % FOF formula (forall (A_89:(nat->Prop)), ((iff ((ex nat) (fun (X_1:nat)=> ((member_nat X_1) A_89)))) (not (((eq (nat->Prop)) A_89) bot_bot_nat_o)))) of role axiom named fact_528_ex__in__conv % A new axiom: (forall (A_89:(nat->Prop)), ((iff ((ex nat) (fun (X_1:nat)=> ((member_nat X_1) A_89)))) (not (((eq (nat->Prop)) A_89) bot_bot_nat_o)))) % FOF formula (forall (A_89:(x_a->Prop)), ((iff ((ex x_a) (fun (X_1:x_a)=> ((member_a X_1) A_89)))) (not (((eq (x_a->Prop)) A_89) bot_bot_a_o)))) of role axiom named fact_529_ex__in__conv % A new axiom: (forall (A_89:(x_a->Prop)), ((iff ((ex x_a) (fun (X_1:x_a)=> ((member_a X_1) A_89)))) (not (((eq (x_a->Prop)) A_89) bot_bot_a_o)))) % FOF formula (forall (A_89:(pname->Prop)), ((iff ((ex pname) (fun (X_1:pname)=> ((member_pname X_1) A_89)))) (not (((eq (pname->Prop)) A_89) bot_bot_pname_o)))) of role axiom named fact_530_ex__in__conv % A new axiom: (forall (A_89:(pname->Prop)), ((iff ((ex pname) (fun (X_1:pname)=> ((member_pname X_1) A_89)))) (not (((eq (pname->Prop)) A_89) bot_bot_pname_o)))) % FOF formula (forall (A_88:(int->Prop)), ((iff (forall (X_1:int), (((member_int X_1) A_88)->False))) (((eq (int->Prop)) A_88) bot_bot_int_o))) of role axiom named fact_531_all__not__in__conv % A new axiom: (forall (A_88:(int->Prop)), ((iff (forall (X_1:int), (((member_int X_1) A_88)->False))) (((eq (int->Prop)) A_88) bot_bot_int_o))) % FOF formula (forall (A_88:(nat->Prop)), ((iff (forall (X_1:nat), (((member_nat X_1) A_88)->False))) (((eq (nat->Prop)) A_88) bot_bot_nat_o))) of role axiom named fact_532_all__not__in__conv % A new axiom: (forall (A_88:(nat->Prop)), ((iff (forall (X_1:nat), (((member_nat X_1) A_88)->False))) (((eq (nat->Prop)) A_88) bot_bot_nat_o))) % FOF formula (forall (A_88:(x_a->Prop)), ((iff (forall (X_1:x_a), (((member_a X_1) A_88)->False))) (((eq (x_a->Prop)) A_88) bot_bot_a_o))) of role axiom named fact_533_all__not__in__conv % A new axiom: (forall (A_88:(x_a->Prop)), ((iff (forall (X_1:x_a), (((member_a X_1) A_88)->False))) (((eq (x_a->Prop)) A_88) bot_bot_a_o))) % FOF formula (forall (A_88:(pname->Prop)), ((iff (forall (X_1:pname), (((member_pname X_1) A_88)->False))) (((eq (pname->Prop)) A_88) bot_bot_pname_o))) of role axiom named fact_534_all__not__in__conv % A new axiom: (forall (A_88:(pname->Prop)), ((iff (forall (X_1:pname), (((member_pname X_1) A_88)->False))) (((eq (pname->Prop)) A_88) bot_bot_pname_o))) % FOF formula (forall (X_24:nat), ((iff (bot_bot_nat_o X_24)) bot_bot_o)) of role axiom named fact_535_bot__apply % A new axiom: (forall (X_24:nat), ((iff (bot_bot_nat_o X_24)) bot_bot_o)) % FOF formula (forall (X_24:int), ((iff (bot_bot_int_o X_24)) bot_bot_o)) of role axiom named fact_536_bot__apply % A new axiom: (forall (X_24:int), ((iff (bot_bot_int_o X_24)) bot_bot_o)) % FOF formula (forall (X_24:x_a), ((iff (bot_bot_a_o X_24)) bot_bot_o)) of role axiom named fact_537_bot__apply % A new axiom: (forall (X_24:x_a), ((iff (bot_bot_a_o X_24)) bot_bot_o)) % FOF formula (((eq (int->Prop)) bot_bot_int_o) (collect_int (fun (X_1:int)=> False))) of role axiom named fact_538_empty__def % A new axiom: (((eq (int->Prop)) bot_bot_int_o) (collect_int (fun (X_1:int)=> False))) % FOF formula (((eq (nat->Prop)) bot_bot_nat_o) (collect_nat (fun (X_1:nat)=> False))) of role axiom named fact_539_empty__def % A new axiom: (((eq (nat->Prop)) bot_bot_nat_o) (collect_nat (fun (X_1:nat)=> False))) % FOF formula (((eq (x_a->Prop)) bot_bot_a_o) (collect_a (fun (X_1:x_a)=> False))) of role axiom named fact_540_empty__def % A new axiom: (((eq (x_a->Prop)) bot_bot_a_o) (collect_a (fun (X_1:x_a)=> False))) % FOF formula (forall (X_1:nat), ((iff (bot_bot_nat_o X_1)) bot_bot_o)) of role axiom named fact_541_bot__fun__def % A new axiom: (forall (X_1:nat), ((iff (bot_bot_nat_o X_1)) bot_bot_o)) % FOF formula (forall (X_1:int), ((iff (bot_bot_int_o X_1)) bot_bot_o)) of role axiom named fact_542_bot__fun__def % A new axiom: (forall (X_1:int), ((iff (bot_bot_int_o X_1)) bot_bot_o)) % FOF formula (forall (X_1:x_a), ((iff (bot_bot_a_o X_1)) bot_bot_o)) of role axiom named fact_543_bot__fun__def % A new axiom: (forall (X_1:x_a), ((iff (bot_bot_a_o X_1)) bot_bot_o)) % FOF formula (forall (A_87:x_a) (A_86:(x_a->Prop)), (((member_a A_87) A_86)->(((eq (x_a->Prop)) ((insert_a A_87) ((minus_minus_a_o A_86) ((insert_a A_87) bot_bot_a_o)))) A_86))) of role axiom named fact_544_insert__Diff % A new axiom: (forall (A_87:x_a) (A_86:(x_a->Prop)), (((member_a A_87) A_86)->(((eq (x_a->Prop)) ((insert_a A_87) ((minus_minus_a_o A_86) ((insert_a A_87) bot_bot_a_o)))) A_86))) % FOF formula (forall (A_87:int) (A_86:(int->Prop)), (((member_int A_87) A_86)->(((eq (int->Prop)) ((insert_int A_87) ((minus_minus_int_o A_86) ((insert_int A_87) bot_bot_int_o)))) A_86))) of role axiom named fact_545_insert__Diff % A new axiom: (forall (A_87:int) (A_86:(int->Prop)), (((member_int A_87) A_86)->(((eq (int->Prop)) ((insert_int A_87) ((minus_minus_int_o A_86) ((insert_int A_87) bot_bot_int_o)))) A_86))) % FOF formula (forall (A_87:nat) (A_86:(nat->Prop)), (((member_nat A_87) A_86)->(((eq (nat->Prop)) ((insert_nat A_87) ((minus_minus_nat_o A_86) ((insert_nat A_87) bot_bot_nat_o)))) A_86))) of role axiom named fact_546_insert__Diff % A new axiom: (forall (A_87:nat) (A_86:(nat->Prop)), (((member_nat A_87) A_86)->(((eq (nat->Prop)) ((insert_nat A_87) ((minus_minus_nat_o A_86) ((insert_nat A_87) bot_bot_nat_o)))) A_86))) % FOF formula (forall (A_87:pname) (A_86:(pname->Prop)), (((member_pname A_87) A_86)->(((eq (pname->Prop)) ((insert_pname A_87) ((minus_minus_pname_o A_86) ((insert_pname A_87) bot_bot_pname_o)))) A_86))) of role axiom named fact_547_insert__Diff % A new axiom: (forall (A_87:pname) (A_86:(pname->Prop)), (((member_pname A_87) A_86)->(((eq (pname->Prop)) ((insert_pname A_87) ((minus_minus_pname_o A_86) ((insert_pname A_87) bot_bot_pname_o)))) A_86))) % FOF formula (forall (X_23:x_a) (A_85:(x_a->Prop)), ((((member_a X_23) A_85)->False)->(((eq (x_a->Prop)) ((minus_minus_a_o ((insert_a X_23) A_85)) ((insert_a X_23) bot_bot_a_o))) A_85))) of role axiom named fact_548_Diff__insert__absorb % A new axiom: (forall (X_23:x_a) (A_85:(x_a->Prop)), ((((member_a X_23) A_85)->False)->(((eq (x_a->Prop)) ((minus_minus_a_o ((insert_a X_23) A_85)) ((insert_a X_23) bot_bot_a_o))) A_85))) % FOF formula (forall (X_23:int) (A_85:(int->Prop)), ((((member_int X_23) A_85)->False)->(((eq (int->Prop)) ((minus_minus_int_o ((insert_int X_23) A_85)) ((insert_int X_23) bot_bot_int_o))) A_85))) of role axiom named fact_549_Diff__insert__absorb % A new axiom: (forall (X_23:int) (A_85:(int->Prop)), ((((member_int X_23) A_85)->False)->(((eq (int->Prop)) ((minus_minus_int_o ((insert_int X_23) A_85)) ((insert_int X_23) bot_bot_int_o))) A_85))) % FOF formula (forall (X_23:nat) (A_85:(nat->Prop)), ((((member_nat X_23) A_85)->False)->(((eq (nat->Prop)) ((minus_minus_nat_o ((insert_nat X_23) A_85)) ((insert_nat X_23) bot_bot_nat_o))) A_85))) of role axiom named fact_550_Diff__insert__absorb % A new axiom: (forall (X_23:nat) (A_85:(nat->Prop)), ((((member_nat X_23) A_85)->False)->(((eq (nat->Prop)) ((minus_minus_nat_o ((insert_nat X_23) A_85)) ((insert_nat X_23) bot_bot_nat_o))) A_85))) % FOF formula (forall (X_23:pname) (A_85:(pname->Prop)), ((((member_pname X_23) A_85)->False)->(((eq (pname->Prop)) ((minus_minus_pname_o ((insert_pname X_23) A_85)) ((insert_pname X_23) bot_bot_pname_o))) A_85))) of role axiom named fact_551_Diff__insert__absorb % A new axiom: (forall (X_23:pname) (A_85:(pname->Prop)), ((((member_pname X_23) A_85)->False)->(((eq (pname->Prop)) ((minus_minus_pname_o ((insert_pname X_23) A_85)) ((insert_pname X_23) bot_bot_pname_o))) A_85))) % FOF formula (forall (A_84:x_a) (A_83:(x_a->Prop)), (((eq (x_a->Prop)) ((insert_a A_84) ((minus_minus_a_o A_83) ((insert_a A_84) bot_bot_a_o)))) ((insert_a A_84) A_83))) of role axiom named fact_552_insert__Diff__single % A new axiom: (forall (A_84:x_a) (A_83:(x_a->Prop)), (((eq (x_a->Prop)) ((insert_a A_84) ((minus_minus_a_o A_83) ((insert_a A_84) bot_bot_a_o)))) ((insert_a A_84) A_83))) % FOF formula (forall (A_84:nat) (A_83:(nat->Prop)), (((eq (nat->Prop)) ((insert_nat A_84) ((minus_minus_nat_o A_83) ((insert_nat A_84) bot_bot_nat_o)))) ((insert_nat A_84) A_83))) of role axiom named fact_553_insert__Diff__single % A new axiom: (forall (A_84:nat) (A_83:(nat->Prop)), (((eq (nat->Prop)) ((insert_nat A_84) ((minus_minus_nat_o A_83) ((insert_nat A_84) bot_bot_nat_o)))) ((insert_nat A_84) A_83))) % FOF formula (forall (A_84:int) (A_83:(int->Prop)), (((eq (int->Prop)) ((insert_int A_84) ((minus_minus_int_o A_83) ((insert_int A_84) bot_bot_int_o)))) ((insert_int A_84) A_83))) of role axiom named fact_554_insert__Diff__single % A new axiom: (forall (A_84:int) (A_83:(int->Prop)), (((eq (int->Prop)) ((insert_int A_84) ((minus_minus_int_o A_83) ((insert_int A_84) bot_bot_int_o)))) ((insert_int A_84) A_83))) % FOF formula (forall (A_82:(x_a->Prop)) (A_81:x_a) (B_45:(x_a->Prop)), (((eq (x_a->Prop)) ((minus_minus_a_o A_82) ((insert_a A_81) B_45))) ((minus_minus_a_o ((minus_minus_a_o A_82) ((insert_a A_81) bot_bot_a_o))) B_45))) of role axiom named fact_555_Diff__insert2 % A new axiom: (forall (A_82:(x_a->Prop)) (A_81:x_a) (B_45:(x_a->Prop)), (((eq (x_a->Prop)) ((minus_minus_a_o A_82) ((insert_a A_81) B_45))) ((minus_minus_a_o ((minus_minus_a_o A_82) ((insert_a A_81) bot_bot_a_o))) B_45))) % FOF formula (forall (A_82:(nat->Prop)) (A_81:nat) (B_45:(nat->Prop)), (((eq (nat->Prop)) ((minus_minus_nat_o A_82) ((insert_nat A_81) B_45))) ((minus_minus_nat_o ((minus_minus_nat_o A_82) ((insert_nat A_81) bot_bot_nat_o))) B_45))) of role axiom named fact_556_Diff__insert2 % A new axiom: (forall (A_82:(nat->Prop)) (A_81:nat) (B_45:(nat->Prop)), (((eq (nat->Prop)) ((minus_minus_nat_o A_82) ((insert_nat A_81) B_45))) ((minus_minus_nat_o ((minus_minus_nat_o A_82) ((insert_nat A_81) bot_bot_nat_o))) B_45))) % FOF formula (forall (A_82:(int->Prop)) (A_81:int) (B_45:(int->Prop)), (((eq (int->Prop)) ((minus_minus_int_o A_82) ((insert_int A_81) B_45))) ((minus_minus_int_o ((minus_minus_int_o A_82) ((insert_int A_81) bot_bot_int_o))) B_45))) of role axiom named fact_557_Diff__insert2 % A new axiom: (forall (A_82:(int->Prop)) (A_81:int) (B_45:(int->Prop)), (((eq (int->Prop)) ((minus_minus_int_o A_82) ((insert_int A_81) B_45))) ((minus_minus_int_o ((minus_minus_int_o A_82) ((insert_int A_81) bot_bot_int_o))) B_45))) % FOF formula (forall (A_80:(x_a->Prop)) (A_79:x_a) (B_44:(x_a->Prop)), (((eq (x_a->Prop)) ((minus_minus_a_o A_80) ((insert_a A_79) B_44))) ((minus_minus_a_o ((minus_minus_a_o A_80) B_44)) ((insert_a A_79) bot_bot_a_o)))) of role axiom named fact_558_Diff__insert % A new axiom: (forall (A_80:(x_a->Prop)) (A_79:x_a) (B_44:(x_a->Prop)), (((eq (x_a->Prop)) ((minus_minus_a_o A_80) ((insert_a A_79) B_44))) ((minus_minus_a_o ((minus_minus_a_o A_80) B_44)) ((insert_a A_79) bot_bot_a_o)))) % FOF formula (forall (A_80:(nat->Prop)) (A_79:nat) (B_44:(nat->Prop)), (((eq (nat->Prop)) ((minus_minus_nat_o A_80) ((insert_nat A_79) B_44))) ((minus_minus_nat_o ((minus_minus_nat_o A_80) B_44)) ((insert_nat A_79) bot_bot_nat_o)))) of role axiom named fact_559_Diff__insert % A new axiom: (forall (A_80:(nat->Prop)) (A_79:nat) (B_44:(nat->Prop)), (((eq (nat->Prop)) ((minus_minus_nat_o A_80) ((insert_nat A_79) B_44))) ((minus_minus_nat_o ((minus_minus_nat_o A_80) B_44)) ((insert_nat A_79) bot_bot_nat_o)))) % FOF formula (forall (A_80:(int->Prop)) (A_79:int) (B_44:(int->Prop)), (((eq (int->Prop)) ((minus_minus_int_o A_80) ((insert_int A_79) B_44))) ((minus_minus_int_o ((minus_minus_int_o A_80) B_44)) ((insert_int A_79) bot_bot_int_o)))) of role axiom named fact_560_Diff__insert % A new axiom: (forall (A_80:(int->Prop)) (A_79:int) (B_44:(int->Prop)), (((eq (int->Prop)) ((minus_minus_int_o A_80) ((insert_int A_79) B_44))) ((minus_minus_int_o ((minus_minus_int_o A_80) B_44)) ((insert_int A_79) bot_bot_int_o)))) % FOF formula (forall (A_78:(x_a->Prop)) (X_22:x_a) (B_43:(x_a->Prop)), (((ord_less_eq_a_o ((minus_minus_a_o A_78) ((insert_a X_22) bot_bot_a_o))) B_43)->(((member_a X_22) A_78)->((ord_less_eq_a_o A_78) ((insert_a X_22) B_43))))) of role axiom named fact_561_diff__single__insert % A new axiom: (forall (A_78:(x_a->Prop)) (X_22:x_a) (B_43:(x_a->Prop)), (((ord_less_eq_a_o ((minus_minus_a_o A_78) ((insert_a X_22) bot_bot_a_o))) B_43)->(((member_a X_22) A_78)->((ord_less_eq_a_o A_78) ((insert_a X_22) B_43))))) % FOF formula (forall (A_78:(int->Prop)) (X_22:int) (B_43:(int->Prop)), (((ord_less_eq_int_o ((minus_minus_int_o A_78) ((insert_int X_22) bot_bot_int_o))) B_43)->(((member_int X_22) A_78)->((ord_less_eq_int_o A_78) ((insert_int X_22) B_43))))) of role axiom named fact_562_diff__single__insert % A new axiom: (forall (A_78:(int->Prop)) (X_22:int) (B_43:(int->Prop)), (((ord_less_eq_int_o ((minus_minus_int_o A_78) ((insert_int X_22) bot_bot_int_o))) B_43)->(((member_int X_22) A_78)->((ord_less_eq_int_o A_78) ((insert_int X_22) B_43))))) % FOF formula (forall (A_78:(nat->Prop)) (X_22:nat) (B_43:(nat->Prop)), (((ord_less_eq_nat_o ((minus_minus_nat_o A_78) ((insert_nat X_22) bot_bot_nat_o))) B_43)->(((member_nat X_22) A_78)->((ord_less_eq_nat_o A_78) ((insert_nat X_22) B_43))))) of role axiom named fact_563_diff__single__insert % A new axiom: (forall (A_78:(nat->Prop)) (X_22:nat) (B_43:(nat->Prop)), (((ord_less_eq_nat_o ((minus_minus_nat_o A_78) ((insert_nat X_22) bot_bot_nat_o))) B_43)->(((member_nat X_22) A_78)->((ord_less_eq_nat_o A_78) ((insert_nat X_22) B_43))))) % FOF formula (forall (A_78:(pname->Prop)) (X_22:pname) (B_43:(pname->Prop)), (((ord_less_eq_pname_o ((minus_minus_pname_o A_78) ((insert_pname X_22) bot_bot_pname_o))) B_43)->(((member_pname X_22) A_78)->((ord_less_eq_pname_o A_78) ((insert_pname X_22) B_43))))) of role axiom named fact_564_diff__single__insert % A new axiom: (forall (A_78:(pname->Prop)) (X_22:pname) (B_43:(pname->Prop)), (((ord_less_eq_pname_o ((minus_minus_pname_o A_78) ((insert_pname X_22) bot_bot_pname_o))) B_43)->(((member_pname X_22) A_78)->((ord_less_eq_pname_o A_78) ((insert_pname X_22) B_43))))) % FOF formula (forall (A_77:(x_a->Prop)) (X_21:x_a) (B_42:(x_a->Prop)), ((iff ((ord_less_eq_a_o A_77) ((insert_a X_21) B_42))) ((and (((member_a X_21) A_77)->((ord_less_eq_a_o ((minus_minus_a_o A_77) ((insert_a X_21) bot_bot_a_o))) B_42))) ((((member_a X_21) A_77)->False)->((ord_less_eq_a_o A_77) B_42))))) of role axiom named fact_565_subset__insert__iff % A new axiom: (forall (A_77:(x_a->Prop)) (X_21:x_a) (B_42:(x_a->Prop)), ((iff ((ord_less_eq_a_o A_77) ((insert_a X_21) B_42))) ((and (((member_a X_21) A_77)->((ord_less_eq_a_o ((minus_minus_a_o A_77) ((insert_a X_21) bot_bot_a_o))) B_42))) ((((member_a X_21) A_77)->False)->((ord_less_eq_a_o A_77) B_42))))) % FOF formula (forall (A_77:(int->Prop)) (X_21:int) (B_42:(int->Prop)), ((iff ((ord_less_eq_int_o A_77) ((insert_int X_21) B_42))) ((and (((member_int X_21) A_77)->((ord_less_eq_int_o ((minus_minus_int_o A_77) ((insert_int X_21) bot_bot_int_o))) B_42))) ((((member_int X_21) A_77)->False)->((ord_less_eq_int_o A_77) B_42))))) of role axiom named fact_566_subset__insert__iff % A new axiom: (forall (A_77:(int->Prop)) (X_21:int) (B_42:(int->Prop)), ((iff ((ord_less_eq_int_o A_77) ((insert_int X_21) B_42))) ((and (((member_int X_21) A_77)->((ord_less_eq_int_o ((minus_minus_int_o A_77) ((insert_int X_21) bot_bot_int_o))) B_42))) ((((member_int X_21) A_77)->False)->((ord_less_eq_int_o A_77) B_42))))) % FOF formula (forall (A_77:(nat->Prop)) (X_21:nat) (B_42:(nat->Prop)), ((iff ((ord_less_eq_nat_o A_77) ((insert_nat X_21) B_42))) ((and (((member_nat X_21) A_77)->((ord_less_eq_nat_o ((minus_minus_nat_o A_77) ((insert_nat X_21) bot_bot_nat_o))) B_42))) ((((member_nat X_21) A_77)->False)->((ord_less_eq_nat_o A_77) B_42))))) of role axiom named fact_567_subset__insert__iff % A new axiom: (forall (A_77:(nat->Prop)) (X_21:nat) (B_42:(nat->Prop)), ((iff ((ord_less_eq_nat_o A_77) ((insert_nat X_21) B_42))) ((and (((member_nat X_21) A_77)->((ord_less_eq_nat_o ((minus_minus_nat_o A_77) ((insert_nat X_21) bot_bot_nat_o))) B_42))) ((((member_nat X_21) A_77)->False)->((ord_less_eq_nat_o A_77) B_42))))) % FOF formula (forall (A_77:(pname->Prop)) (X_21:pname) (B_42:(pname->Prop)), ((iff ((ord_less_eq_pname_o A_77) ((insert_pname X_21) B_42))) ((and (((member_pname X_21) A_77)->((ord_less_eq_pname_o ((minus_minus_pname_o A_77) ((insert_pname X_21) bot_bot_pname_o))) B_42))) ((((member_pname X_21) A_77)->False)->((ord_less_eq_pname_o A_77) B_42))))) of role axiom named fact_568_subset__insert__iff % A new axiom: (forall (A_77:(pname->Prop)) (X_21:pname) (B_42:(pname->Prop)), ((iff ((ord_less_eq_pname_o A_77) ((insert_pname X_21) B_42))) ((and (((member_pname X_21) A_77)->((ord_less_eq_pname_o ((minus_minus_pname_o A_77) ((insert_pname X_21) bot_bot_pname_o))) B_42))) ((((member_pname X_21) A_77)->False)->((ord_less_eq_pname_o A_77) B_42))))) % FOF formula (forall (A_76:(int->Prop)) (B_41:(int->Prop)), ((finite_finite_int B_41)->((iff (finite_finite_int ((minus_minus_int_o A_76) B_41))) (finite_finite_int A_76)))) of role axiom named fact_569_finite__Diff2 % A new axiom: (forall (A_76:(int->Prop)) (B_41:(int->Prop)), ((finite_finite_int B_41)->((iff (finite_finite_int ((minus_minus_int_o A_76) B_41))) (finite_finite_int A_76)))) % FOF formula (forall (A_76:(nat->Prop)) (B_41:(nat->Prop)), ((finite_finite_nat B_41)->((iff (finite_finite_nat ((minus_minus_nat_o A_76) B_41))) (finite_finite_nat A_76)))) of role axiom named fact_570_finite__Diff2 % A new axiom: (forall (A_76:(nat->Prop)) (B_41:(nat->Prop)), ((finite_finite_nat B_41)->((iff (finite_finite_nat ((minus_minus_nat_o A_76) B_41))) (finite_finite_nat A_76)))) % FOF formula (forall (A_76:(pname->Prop)) (B_41:(pname->Prop)), ((finite_finite_pname B_41)->((iff (finite_finite_pname ((minus_minus_pname_o A_76) B_41))) (finite_finite_pname A_76)))) of role axiom named fact_571_finite__Diff2 % A new axiom: (forall (A_76:(pname->Prop)) (B_41:(pname->Prop)), ((finite_finite_pname B_41)->((iff (finite_finite_pname ((minus_minus_pname_o A_76) B_41))) (finite_finite_pname A_76)))) % FOF formula (forall (A_75:(x_a->Prop)) (X_20:x_a) (B_40:(x_a->Prop)), (((member_a X_20) B_40)->(((eq (x_a->Prop)) ((minus_minus_a_o ((insert_a X_20) A_75)) B_40)) ((minus_minus_a_o A_75) B_40)))) of role axiom named fact_572_insert__Diff1 % A new axiom: (forall (A_75:(x_a->Prop)) (X_20:x_a) (B_40:(x_a->Prop)), (((member_a X_20) B_40)->(((eq (x_a->Prop)) ((minus_minus_a_o ((insert_a X_20) A_75)) B_40)) ((minus_minus_a_o A_75) B_40)))) % FOF formula (forall (A_75:(int->Prop)) (X_20:int) (B_40:(int->Prop)), (((member_int X_20) B_40)->(((eq (int->Prop)) ((minus_minus_int_o ((insert_int X_20) A_75)) B_40)) ((minus_minus_int_o A_75) B_40)))) of role axiom named fact_573_insert__Diff1 % A new axiom: (forall (A_75:(int->Prop)) (X_20:int) (B_40:(int->Prop)), (((member_int X_20) B_40)->(((eq (int->Prop)) ((minus_minus_int_o ((insert_int X_20) A_75)) B_40)) ((minus_minus_int_o A_75) B_40)))) % FOF formula (forall (A_75:(nat->Prop)) (X_20:nat) (B_40:(nat->Prop)), (((member_nat X_20) B_40)->(((eq (nat->Prop)) ((minus_minus_nat_o ((insert_nat X_20) A_75)) B_40)) ((minus_minus_nat_o A_75) B_40)))) of role axiom named fact_574_insert__Diff1 % A new axiom: (forall (A_75:(nat->Prop)) (X_20:nat) (B_40:(nat->Prop)), (((member_nat X_20) B_40)->(((eq (nat->Prop)) ((minus_minus_nat_o ((insert_nat X_20) A_75)) B_40)) ((minus_minus_nat_o A_75) B_40)))) % FOF formula (forall (A_75:(pname->Prop)) (X_20:pname) (B_40:(pname->Prop)), (((member_pname X_20) B_40)->(((eq (pname->Prop)) ((minus_minus_pname_o ((insert_pname X_20) A_75)) B_40)) ((minus_minus_pname_o A_75) B_40)))) of role axiom named fact_575_insert__Diff1 % A new axiom: (forall (A_75:(pname->Prop)) (X_20:pname) (B_40:(pname->Prop)), (((member_pname X_20) B_40)->(((eq (pname->Prop)) ((minus_minus_pname_o ((insert_pname X_20) A_75)) B_40)) ((minus_minus_pname_o A_75) B_40)))) % FOF formula (forall (A_74:(x_a->Prop)) (X_19:x_a) (B_39:(x_a->Prop)), ((and (((member_a X_19) B_39)->(((eq (x_a->Prop)) ((minus_minus_a_o ((insert_a X_19) A_74)) B_39)) ((minus_minus_a_o A_74) B_39)))) ((((member_a X_19) B_39)->False)->(((eq (x_a->Prop)) ((minus_minus_a_o ((insert_a X_19) A_74)) B_39)) ((insert_a X_19) ((minus_minus_a_o A_74) B_39)))))) of role axiom named fact_576_insert__Diff__if % A new axiom: (forall (A_74:(x_a->Prop)) (X_19:x_a) (B_39:(x_a->Prop)), ((and (((member_a X_19) B_39)->(((eq (x_a->Prop)) ((minus_minus_a_o ((insert_a X_19) A_74)) B_39)) ((minus_minus_a_o A_74) B_39)))) ((((member_a X_19) B_39)->False)->(((eq (x_a->Prop)) ((minus_minus_a_o ((insert_a X_19) A_74)) B_39)) ((insert_a X_19) ((minus_minus_a_o A_74) B_39)))))) % FOF formula (forall (A_74:(int->Prop)) (X_19:int) (B_39:(int->Prop)), ((and (((member_int X_19) B_39)->(((eq (int->Prop)) ((minus_minus_int_o ((insert_int X_19) A_74)) B_39)) ((minus_minus_int_o A_74) B_39)))) ((((member_int X_19) B_39)->False)->(((eq (int->Prop)) ((minus_minus_int_o ((insert_int X_19) A_74)) B_39)) ((insert_int X_19) ((minus_minus_int_o A_74) B_39)))))) of role axiom named fact_577_insert__Diff__if % A new axiom: (forall (A_74:(int->Prop)) (X_19:int) (B_39:(int->Prop)), ((and (((member_int X_19) B_39)->(((eq (int->Prop)) ((minus_minus_int_o ((insert_int X_19) A_74)) B_39)) ((minus_minus_int_o A_74) B_39)))) ((((member_int X_19) B_39)->False)->(((eq (int->Prop)) ((minus_minus_int_o ((insert_int X_19) A_74)) B_39)) ((insert_int X_19) ((minus_minus_int_o A_74) B_39)))))) % FOF formula (forall (A_74:(nat->Prop)) (X_19:nat) (B_39:(nat->Prop)), ((and (((member_nat X_19) B_39)->(((eq (nat->Prop)) ((minus_minus_nat_o ((insert_nat X_19) A_74)) B_39)) ((minus_minus_nat_o A_74) B_39)))) ((((member_nat X_19) B_39)->False)->(((eq (nat->Prop)) ((minus_minus_nat_o ((insert_nat X_19) A_74)) B_39)) ((insert_nat X_19) ((minus_minus_nat_o A_74) B_39)))))) of role axiom named fact_578_insert__Diff__if % A new axiom: (forall (A_74:(nat->Prop)) (X_19:nat) (B_39:(nat->Prop)), ((and (((member_nat X_19) B_39)->(((eq (nat->Prop)) ((minus_minus_nat_o ((insert_nat X_19) A_74)) B_39)) ((minus_minus_nat_o A_74) B_39)))) ((((member_nat X_19) B_39)->False)->(((eq (nat->Prop)) ((minus_minus_nat_o ((insert_nat X_19) A_74)) B_39)) ((insert_nat X_19) ((minus_minus_nat_o A_74) B_39)))))) % FOF formula (forall (A_74:(pname->Prop)) (X_19:pname) (B_39:(pname->Prop)), ((and (((member_pname X_19) B_39)->(((eq (pname->Prop)) ((minus_minus_pname_o ((insert_pname X_19) A_74)) B_39)) ((minus_minus_pname_o A_74) B_39)))) ((((member_pname X_19) B_39)->False)->(((eq (pname->Prop)) ((minus_minus_pname_o ((insert_pname X_19) A_74)) B_39)) ((insert_pname X_19) ((minus_minus_pname_o A_74) B_39)))))) of role axiom named fact_579_insert__Diff__if % A new axiom: (forall (A_74:(pname->Prop)) (X_19:pname) (B_39:(pname->Prop)), ((and (((member_pname X_19) B_39)->(((eq (pname->Prop)) ((minus_minus_pname_o ((insert_pname X_19) A_74)) B_39)) ((minus_minus_pname_o A_74) B_39)))) ((((member_pname X_19) B_39)->False)->(((eq (pname->Prop)) ((minus_minus_pname_o ((insert_pname X_19) A_74)) B_39)) ((insert_pname X_19) ((minus_minus_pname_o A_74) B_39)))))) % FOF formula (forall (C_24:(int->Prop)) (A_73:(int->Prop)) (B_38:(int->Prop)), (((ord_less_eq_int_o A_73) B_38)->(((ord_less_eq_int_o B_38) C_24)->(((eq (int->Prop)) ((minus_minus_int_o B_38) ((minus_minus_int_o C_24) A_73))) A_73)))) of role axiom named fact_580_double__diff % A new axiom: (forall (C_24:(int->Prop)) (A_73:(int->Prop)) (B_38:(int->Prop)), (((ord_less_eq_int_o A_73) B_38)->(((ord_less_eq_int_o B_38) C_24)->(((eq (int->Prop)) ((minus_minus_int_o B_38) ((minus_minus_int_o C_24) A_73))) A_73)))) % FOF formula (forall (C_24:(nat->Prop)) (A_73:(nat->Prop)) (B_38:(nat->Prop)), (((ord_less_eq_nat_o A_73) B_38)->(((ord_less_eq_nat_o B_38) C_24)->(((eq (nat->Prop)) ((minus_minus_nat_o B_38) ((minus_minus_nat_o C_24) A_73))) A_73)))) of role axiom named fact_581_double__diff % A new axiom: (forall (C_24:(nat->Prop)) (A_73:(nat->Prop)) (B_38:(nat->Prop)), (((ord_less_eq_nat_o A_73) B_38)->(((ord_less_eq_nat_o B_38) C_24)->(((eq (nat->Prop)) ((minus_minus_nat_o B_38) ((minus_minus_nat_o C_24) A_73))) A_73)))) % FOF formula (forall (C_24:(x_a->Prop)) (A_73:(x_a->Prop)) (B_38:(x_a->Prop)), (((ord_less_eq_a_o A_73) B_38)->(((ord_less_eq_a_o B_38) C_24)->(((eq (x_a->Prop)) ((minus_minus_a_o B_38) ((minus_minus_a_o C_24) A_73))) A_73)))) of role axiom named fact_582_double__diff % A new axiom: (forall (C_24:(x_a->Prop)) (A_73:(x_a->Prop)) (B_38:(x_a->Prop)), (((ord_less_eq_a_o A_73) B_38)->(((ord_less_eq_a_o B_38) C_24)->(((eq (x_a->Prop)) ((minus_minus_a_o B_38) ((minus_minus_a_o C_24) A_73))) A_73)))) % FOF formula (forall (D_5:(int->Prop)) (B_37:(int->Prop)) (A_72:(int->Prop)) (C_23:(int->Prop)), (((ord_less_eq_int_o A_72) C_23)->(((ord_less_eq_int_o D_5) B_37)->((ord_less_eq_int_o ((minus_minus_int_o A_72) B_37)) ((minus_minus_int_o C_23) D_5))))) of role axiom named fact_583_Diff__mono % A new axiom: (forall (D_5:(int->Prop)) (B_37:(int->Prop)) (A_72:(int->Prop)) (C_23:(int->Prop)), (((ord_less_eq_int_o A_72) C_23)->(((ord_less_eq_int_o D_5) B_37)->((ord_less_eq_int_o ((minus_minus_int_o A_72) B_37)) ((minus_minus_int_o C_23) D_5))))) % FOF formula (forall (D_5:(nat->Prop)) (B_37:(nat->Prop)) (A_72:(nat->Prop)) (C_23:(nat->Prop)), (((ord_less_eq_nat_o A_72) C_23)->(((ord_less_eq_nat_o D_5) B_37)->((ord_less_eq_nat_o ((minus_minus_nat_o A_72) B_37)) ((minus_minus_nat_o C_23) D_5))))) of role axiom named fact_584_Diff__mono % A new axiom: (forall (D_5:(nat->Prop)) (B_37:(nat->Prop)) (A_72:(nat->Prop)) (C_23:(nat->Prop)), (((ord_less_eq_nat_o A_72) C_23)->(((ord_less_eq_nat_o D_5) B_37)->((ord_less_eq_nat_o ((minus_minus_nat_o A_72) B_37)) ((minus_minus_nat_o C_23) D_5))))) % FOF formula (forall (D_5:(x_a->Prop)) (B_37:(x_a->Prop)) (A_72:(x_a->Prop)) (C_23:(x_a->Prop)), (((ord_less_eq_a_o A_72) C_23)->(((ord_less_eq_a_o D_5) B_37)->((ord_less_eq_a_o ((minus_minus_a_o A_72) B_37)) ((minus_minus_a_o C_23) D_5))))) of role axiom named fact_585_Diff__mono % A new axiom: (forall (D_5:(x_a->Prop)) (B_37:(x_a->Prop)) (A_72:(x_a->Prop)) (C_23:(x_a->Prop)), (((ord_less_eq_a_o A_72) C_23)->(((ord_less_eq_a_o D_5) B_37)->((ord_less_eq_a_o ((minus_minus_a_o A_72) B_37)) ((minus_minus_a_o C_23) D_5))))) % FOF formula (forall (A_71:(int->Prop)) (B_36:(int->Prop)), ((ord_less_eq_int_o ((minus_minus_int_o A_71) B_36)) A_71)) of role axiom named fact_586_Diff__subset % A new axiom: (forall (A_71:(int->Prop)) (B_36:(int->Prop)), ((ord_less_eq_int_o ((minus_minus_int_o A_71) B_36)) A_71)) % FOF formula (forall (A_71:(nat->Prop)) (B_36:(nat->Prop)), ((ord_less_eq_nat_o ((minus_minus_nat_o A_71) B_36)) A_71)) of role axiom named fact_587_Diff__subset % A new axiom: (forall (A_71:(nat->Prop)) (B_36:(nat->Prop)), ((ord_less_eq_nat_o ((minus_minus_nat_o A_71) B_36)) A_71)) % FOF formula (forall (A_71:(x_a->Prop)) (B_36:(x_a->Prop)), ((ord_less_eq_a_o ((minus_minus_a_o A_71) B_36)) A_71)) of role axiom named fact_588_Diff__subset % A new axiom: (forall (A_71:(x_a->Prop)) (B_36:(x_a->Prop)), ((ord_less_eq_a_o ((minus_minus_a_o A_71) B_36)) A_71)) % FOF formula (forall (A_70:x_a) (B_35:x_a), ((((eq (x_a->Prop)) ((insert_a A_70) bot_bot_a_o)) ((insert_a B_35) bot_bot_a_o))->(((eq x_a) A_70) B_35))) of role axiom named fact_589_singleton__inject % A new axiom: (forall (A_70:x_a) (B_35:x_a), ((((eq (x_a->Prop)) ((insert_a A_70) bot_bot_a_o)) ((insert_a B_35) bot_bot_a_o))->(((eq x_a) A_70) B_35))) % FOF formula (forall (A_70:nat) (B_35:nat), ((((eq (nat->Prop)) ((insert_nat A_70) bot_bot_nat_o)) ((insert_nat B_35) bot_bot_nat_o))->(((eq nat) A_70) B_35))) of role axiom named fact_590_singleton__inject % A new axiom: (forall (A_70:nat) (B_35:nat), ((((eq (nat->Prop)) ((insert_nat A_70) bot_bot_nat_o)) ((insert_nat B_35) bot_bot_nat_o))->(((eq nat) A_70) B_35))) % FOF formula (forall (A_70:int) (B_35:int), ((((eq (int->Prop)) ((insert_int A_70) bot_bot_int_o)) ((insert_int B_35) bot_bot_int_o))->(((eq int) A_70) B_35))) of role axiom named fact_591_singleton__inject % A new axiom: (forall (A_70:int) (B_35:int), ((((eq (int->Prop)) ((insert_int A_70) bot_bot_int_o)) ((insert_int B_35) bot_bot_int_o))->(((eq int) A_70) B_35))) % FOF formula (forall (B_34:x_a) (A_69:x_a), (((member_a B_34) ((insert_a A_69) bot_bot_a_o))->(((eq x_a) B_34) A_69))) of role axiom named fact_592_singletonE % A new axiom: (forall (B_34:x_a) (A_69:x_a), (((member_a B_34) ((insert_a A_69) bot_bot_a_o))->(((eq x_a) B_34) A_69))) % FOF formula (forall (B_34:int) (A_69:int), (((member_int B_34) ((insert_int A_69) bot_bot_int_o))->(((eq int) B_34) A_69))) of role axiom named fact_593_singletonE % A new axiom: (forall (B_34:int) (A_69:int), (((member_int B_34) ((insert_int A_69) bot_bot_int_o))->(((eq int) B_34) A_69))) % FOF formula (forall (B_34:nat) (A_69:nat), (((member_nat B_34) ((insert_nat A_69) bot_bot_nat_o))->(((eq nat) B_34) A_69))) of role axiom named fact_594_singletonE % A new axiom: (forall (B_34:nat) (A_69:nat), (((member_nat B_34) ((insert_nat A_69) bot_bot_nat_o))->(((eq nat) B_34) A_69))) % FOF formula (forall (B_34:pname) (A_69:pname), (((member_pname B_34) ((insert_pname A_69) bot_bot_pname_o))->(((eq pname) B_34) A_69))) of role axiom named fact_595_singletonE % A new axiom: (forall (B_34:pname) (A_69:pname), (((member_pname B_34) ((insert_pname A_69) bot_bot_pname_o))->(((eq pname) B_34) A_69))) % FOF formula (forall (A_68:x_a) (B_33:x_a) (C_22:x_a) (D_4:x_a), ((iff (((eq (x_a->Prop)) ((insert_a A_68) ((insert_a B_33) bot_bot_a_o))) ((insert_a C_22) ((insert_a D_4) bot_bot_a_o)))) ((or ((and (((eq x_a) A_68) C_22)) (((eq x_a) B_33) D_4))) ((and (((eq x_a) A_68) D_4)) (((eq x_a) B_33) C_22))))) of role axiom named fact_596_doubleton__eq__iff % A new axiom: (forall (A_68:x_a) (B_33:x_a) (C_22:x_a) (D_4:x_a), ((iff (((eq (x_a->Prop)) ((insert_a A_68) ((insert_a B_33) bot_bot_a_o))) ((insert_a C_22) ((insert_a D_4) bot_bot_a_o)))) ((or ((and (((eq x_a) A_68) C_22)) (((eq x_a) B_33) D_4))) ((and (((eq x_a) A_68) D_4)) (((eq x_a) B_33) C_22))))) % FOF formula (forall (A_68:nat) (B_33:nat) (C_22:nat) (D_4:nat), ((iff (((eq (nat->Prop)) ((insert_nat A_68) ((insert_nat B_33) bot_bot_nat_o))) ((insert_nat C_22) ((insert_nat D_4) bot_bot_nat_o)))) ((or ((and (((eq nat) A_68) C_22)) (((eq nat) B_33) D_4))) ((and (((eq nat) A_68) D_4)) (((eq nat) B_33) C_22))))) of role axiom named fact_597_doubleton__eq__iff % A new axiom: (forall (A_68:nat) (B_33:nat) (C_22:nat) (D_4:nat), ((iff (((eq (nat->Prop)) ((insert_nat A_68) ((insert_nat B_33) bot_bot_nat_o))) ((insert_nat C_22) ((insert_nat D_4) bot_bot_nat_o)))) ((or ((and (((eq nat) A_68) C_22)) (((eq nat) B_33) D_4))) ((and (((eq nat) A_68) D_4)) (((eq nat) B_33) C_22))))) % FOF formula (forall (A_68:int) (B_33:int) (C_22:int) (D_4:int), ((iff (((eq (int->Prop)) ((insert_int A_68) ((insert_int B_33) bot_bot_int_o))) ((insert_int C_22) ((insert_int D_4) bot_bot_int_o)))) ((or ((and (((eq int) A_68) C_22)) (((eq int) B_33) D_4))) ((and (((eq int) A_68) D_4)) (((eq int) B_33) C_22))))) of role axiom named fact_598_doubleton__eq__iff % A new axiom: (forall (A_68:int) (B_33:int) (C_22:int) (D_4:int), ((iff (((eq (int->Prop)) ((insert_int A_68) ((insert_int B_33) bot_bot_int_o))) ((insert_int C_22) ((insert_int D_4) bot_bot_int_o)))) ((or ((and (((eq int) A_68) C_22)) (((eq int) B_33) D_4))) ((and (((eq int) A_68) D_4)) (((eq int) B_33) C_22))))) % FOF formula (forall (B_32:x_a) (A_67:x_a), ((iff ((member_a B_32) ((insert_a A_67) bot_bot_a_o))) (((eq x_a) B_32) A_67))) of role axiom named fact_599_singleton__iff % A new axiom: (forall (B_32:x_a) (A_67:x_a), ((iff ((member_a B_32) ((insert_a A_67) bot_bot_a_o))) (((eq x_a) B_32) A_67))) % FOF formula (forall (B_32:int) (A_67:int), ((iff ((member_int B_32) ((insert_int A_67) bot_bot_int_o))) (((eq int) B_32) A_67))) of role axiom named fact_600_singleton__iff % A new axiom: (forall (B_32:int) (A_67:int), ((iff ((member_int B_32) ((insert_int A_67) bot_bot_int_o))) (((eq int) B_32) A_67))) % FOF formula (forall (B_32:nat) (A_67:nat), ((iff ((member_nat B_32) ((insert_nat A_67) bot_bot_nat_o))) (((eq nat) B_32) A_67))) of role axiom named fact_601_singleton__iff % A new axiom: (forall (B_32:nat) (A_67:nat), ((iff ((member_nat B_32) ((insert_nat A_67) bot_bot_nat_o))) (((eq nat) B_32) A_67))) % FOF formula (forall (B_32:pname) (A_67:pname), ((iff ((member_pname B_32) ((insert_pname A_67) bot_bot_pname_o))) (((eq pname) B_32) A_67))) of role axiom named fact_602_singleton__iff % A new axiom: (forall (B_32:pname) (A_67:pname), ((iff ((member_pname B_32) ((insert_pname A_67) bot_bot_pname_o))) (((eq pname) B_32) A_67))) % FOF formula (forall (A_66:x_a) (A_65:(x_a->Prop)), (not (((eq (x_a->Prop)) ((insert_a A_66) A_65)) bot_bot_a_o))) of role axiom named fact_603_insert__not__empty % A new axiom: (forall (A_66:x_a) (A_65:(x_a->Prop)), (not (((eq (x_a->Prop)) ((insert_a A_66) A_65)) bot_bot_a_o))) % FOF formula (forall (A_66:nat) (A_65:(nat->Prop)), (not (((eq (nat->Prop)) ((insert_nat A_66) A_65)) bot_bot_nat_o))) of role axiom named fact_604_insert__not__empty % A new axiom: (forall (A_66:nat) (A_65:(nat->Prop)), (not (((eq (nat->Prop)) ((insert_nat A_66) A_65)) bot_bot_nat_o))) % FOF formula (forall (A_66:int) (A_65:(int->Prop)), (not (((eq (int->Prop)) ((insert_int A_66) A_65)) bot_bot_int_o))) of role axiom named fact_605_insert__not__empty % A new axiom: (forall (A_66:int) (A_65:(int->Prop)), (not (((eq (int->Prop)) ((insert_int A_66) A_65)) bot_bot_int_o))) % FOF formula (forall (A_64:x_a) (A_63:(x_a->Prop)), (not (((eq (x_a->Prop)) bot_bot_a_o) ((insert_a A_64) A_63)))) of role axiom named fact_606_empty__not__insert % A new axiom: (forall (A_64:x_a) (A_63:(x_a->Prop)), (not (((eq (x_a->Prop)) bot_bot_a_o) ((insert_a A_64) A_63)))) % FOF formula (forall (A_64:nat) (A_63:(nat->Prop)), (not (((eq (nat->Prop)) bot_bot_nat_o) ((insert_nat A_64) A_63)))) of role axiom named fact_607_empty__not__insert % A new axiom: (forall (A_64:nat) (A_63:(nat->Prop)), (not (((eq (nat->Prop)) bot_bot_nat_o) ((insert_nat A_64) A_63)))) % FOF formula (forall (A_64:int) (A_63:(int->Prop)), (not (((eq (int->Prop)) bot_bot_int_o) ((insert_int A_64) A_63)))) of role axiom named fact_608_empty__not__insert % A new axiom: (forall (A_64:int) (A_63:(int->Prop)), (not (((eq (int->Prop)) bot_bot_int_o) ((insert_int A_64) A_63)))) % FOF formula (forall (A_62:(nat->Prop)), ((iff ((ord_less_eq_nat_o A_62) bot_bot_nat_o)) (((eq (nat->Prop)) A_62) bot_bot_nat_o))) of role axiom named fact_609_subset__empty % A new axiom: (forall (A_62:(nat->Prop)), ((iff ((ord_less_eq_nat_o A_62) bot_bot_nat_o)) (((eq (nat->Prop)) A_62) bot_bot_nat_o))) % FOF formula (forall (A_62:(int->Prop)), ((iff ((ord_less_eq_int_o A_62) bot_bot_int_o)) (((eq (int->Prop)) A_62) bot_bot_int_o))) of role axiom named fact_610_subset__empty % A new axiom: (forall (A_62:(int->Prop)), ((iff ((ord_less_eq_int_o A_62) bot_bot_int_o)) (((eq (int->Prop)) A_62) bot_bot_int_o))) % FOF formula (forall (A_62:(x_a->Prop)), ((iff ((ord_less_eq_a_o A_62) bot_bot_a_o)) (((eq (x_a->Prop)) A_62) bot_bot_a_o))) of role axiom named fact_611_subset__empty % A new axiom: (forall (A_62:(x_a->Prop)), ((iff ((ord_less_eq_a_o A_62) bot_bot_a_o)) (((eq (x_a->Prop)) A_62) bot_bot_a_o))) % FOF formula (forall (F_22:(nat->int)) (A_61:(nat->Prop)), ((iff (((eq (int->Prop)) ((image_nat_int F_22) A_61)) bot_bot_int_o)) (((eq (nat->Prop)) A_61) bot_bot_nat_o))) of role axiom named fact_612_image__is__empty % A new axiom: (forall (F_22:(nat->int)) (A_61:(nat->Prop)), ((iff (((eq (int->Prop)) ((image_nat_int F_22) A_61)) bot_bot_int_o)) (((eq (nat->Prop)) A_61) bot_bot_nat_o))) % FOF formula (forall (F_22:(pname->x_a)) (A_61:(pname->Prop)), ((iff (((eq (x_a->Prop)) ((image_pname_a F_22) A_61)) bot_bot_a_o)) (((eq (pname->Prop)) A_61) bot_bot_pname_o))) of role axiom named fact_613_image__is__empty % A new axiom: (forall (F_22:(pname->x_a)) (A_61:(pname->Prop)), ((iff (((eq (x_a->Prop)) ((image_pname_a F_22) A_61)) bot_bot_a_o)) (((eq (pname->Prop)) A_61) bot_bot_pname_o))) % FOF formula (forall (F_21:(nat->int)), (((eq (int->Prop)) ((image_nat_int F_21) bot_bot_nat_o)) bot_bot_int_o)) of role axiom named fact_614_image__empty % A new axiom: (forall (F_21:(nat->int)), (((eq (int->Prop)) ((image_nat_int F_21) bot_bot_nat_o)) bot_bot_int_o)) % FOF formula (forall (F_21:(pname->x_a)), (((eq (x_a->Prop)) ((image_pname_a F_21) bot_bot_pname_o)) bot_bot_a_o)) of role axiom named fact_615_image__empty % A new axiom: (forall (F_21:(pname->x_a)), (((eq (x_a->Prop)) ((image_pname_a F_21) bot_bot_pname_o)) bot_bot_a_o)) % FOF formula (forall (F_20:(nat->int)) (A_60:(nat->Prop)), ((iff (((eq (int->Prop)) bot_bot_int_o) ((image_nat_int F_20) A_60))) (((eq (nat->Prop)) A_60) bot_bot_nat_o))) of role axiom named fact_616_empty__is__image % A new axiom: (forall (F_20:(nat->int)) (A_60:(nat->Prop)), ((iff (((eq (int->Prop)) bot_bot_int_o) ((image_nat_int F_20) A_60))) (((eq (nat->Prop)) A_60) bot_bot_nat_o))) % FOF formula (forall (F_20:(pname->x_a)) (A_60:(pname->Prop)), ((iff (((eq (x_a->Prop)) bot_bot_a_o) ((image_pname_a F_20) A_60))) (((eq (pname->Prop)) A_60) bot_bot_pname_o))) of role axiom named fact_617_empty__is__image % A new axiom: (forall (F_20:(pname->x_a)) (A_60:(pname->Prop)), ((iff (((eq (x_a->Prop)) bot_bot_a_o) ((image_pname_a F_20) A_60))) (((eq (pname->Prop)) A_60) bot_bot_pname_o))) % FOF formula (forall (A_59:(nat->Prop)), (((ord_less_eq_nat_o A_59) bot_bot_nat_o)->(((eq (nat->Prop)) A_59) bot_bot_nat_o))) of role axiom named fact_618_le__bot % A new axiom: (forall (A_59:(nat->Prop)), (((ord_less_eq_nat_o A_59) bot_bot_nat_o)->(((eq (nat->Prop)) A_59) bot_bot_nat_o))) % FOF formula (forall (A_59:(int->Prop)), (((ord_less_eq_int_o A_59) bot_bot_int_o)->(((eq (int->Prop)) A_59) bot_bot_int_o))) of role axiom named fact_619_le__bot % A new axiom: (forall (A_59:(int->Prop)), (((ord_less_eq_int_o A_59) bot_bot_int_o)->(((eq (int->Prop)) A_59) bot_bot_int_o))) % FOF formula (forall (A_59:nat), (((ord_less_eq_nat A_59) bot_bot_nat)->(((eq nat) A_59) bot_bot_nat))) of role axiom named fact_620_le__bot % A new axiom: (forall (A_59:nat), (((ord_less_eq_nat A_59) bot_bot_nat)->(((eq nat) A_59) bot_bot_nat))) % FOF formula (forall (A_59:(x_a->Prop)), (((ord_less_eq_a_o A_59) bot_bot_a_o)->(((eq (x_a->Prop)) A_59) bot_bot_a_o))) of role axiom named fact_621_le__bot % A new axiom: (forall (A_59:(x_a->Prop)), (((ord_less_eq_a_o A_59) bot_bot_a_o)->(((eq (x_a->Prop)) A_59) bot_bot_a_o))) % FOF formula (forall (A_58:(nat->Prop)), ((iff ((ord_less_eq_nat_o A_58) bot_bot_nat_o)) (((eq (nat->Prop)) A_58) bot_bot_nat_o))) of role axiom named fact_622_bot__unique % A new axiom: (forall (A_58:(nat->Prop)), ((iff ((ord_less_eq_nat_o A_58) bot_bot_nat_o)) (((eq (nat->Prop)) A_58) bot_bot_nat_o))) % FOF formula (forall (A_58:(int->Prop)), ((iff ((ord_less_eq_int_o A_58) bot_bot_int_o)) (((eq (int->Prop)) A_58) bot_bot_int_o))) of role axiom named fact_623_bot__unique % A new axiom: (forall (A_58:(int->Prop)), ((iff ((ord_less_eq_int_o A_58) bot_bot_int_o)) (((eq (int->Prop)) A_58) bot_bot_int_o))) % FOF formula (forall (A_58:nat), ((iff ((ord_less_eq_nat A_58) bot_bot_nat)) (((eq nat) A_58) bot_bot_nat))) of role axiom named fact_624_bot__unique % A new axiom: (forall (A_58:nat), ((iff ((ord_less_eq_nat A_58) bot_bot_nat)) (((eq nat) A_58) bot_bot_nat))) % FOF formula (forall (A_58:(x_a->Prop)), ((iff ((ord_less_eq_a_o A_58) bot_bot_a_o)) (((eq (x_a->Prop)) A_58) bot_bot_a_o))) of role axiom named fact_625_bot__unique % A new axiom: (forall (A_58:(x_a->Prop)), ((iff ((ord_less_eq_a_o A_58) bot_bot_a_o)) (((eq (x_a->Prop)) A_58) bot_bot_a_o))) % FOF formula (forall (A_57:(nat->Prop)), ((ord_less_eq_nat_o bot_bot_nat_o) A_57)) of role axiom named fact_626_bot__least % A new axiom: (forall (A_57:(nat->Prop)), ((ord_less_eq_nat_o bot_bot_nat_o) A_57)) % FOF formula (forall (A_57:(int->Prop)), ((ord_less_eq_int_o bot_bot_int_o) A_57)) of role axiom named fact_627_bot__least % A new axiom: (forall (A_57:(int->Prop)), ((ord_less_eq_int_o bot_bot_int_o) A_57)) % FOF formula (forall (A_57:nat), ((ord_less_eq_nat bot_bot_nat) A_57)) of role axiom named fact_628_bot__least % A new axiom: (forall (A_57:nat), ((ord_less_eq_nat bot_bot_nat) A_57)) % FOF formula (forall (A_57:(x_a->Prop)), ((ord_less_eq_a_o bot_bot_a_o) A_57)) of role axiom named fact_629_bot__least % A new axiom: (forall (A_57:(x_a->Prop)), ((ord_less_eq_a_o bot_bot_a_o) A_57)) % FOF formula (forall (P_7:(x_a->Prop)) (A_56:x_a), ((and ((P_7 A_56)->(((eq (x_a->Prop)) (collect_a (fun (X_1:x_a)=> ((and (((eq x_a) X_1) A_56)) (P_7 X_1))))) ((insert_a A_56) bot_bot_a_o)))) (((P_7 A_56)->False)->(((eq (x_a->Prop)) (collect_a (fun (X_1:x_a)=> ((and (((eq x_a) X_1) A_56)) (P_7 X_1))))) bot_bot_a_o)))) of role axiom named fact_630_Collect__conv__if % A new axiom: (forall (P_7:(x_a->Prop)) (A_56:x_a), ((and ((P_7 A_56)->(((eq (x_a->Prop)) (collect_a (fun (X_1:x_a)=> ((and (((eq x_a) X_1) A_56)) (P_7 X_1))))) ((insert_a A_56) bot_bot_a_o)))) (((P_7 A_56)->False)->(((eq (x_a->Prop)) (collect_a (fun (X_1:x_a)=> ((and (((eq x_a) X_1) A_56)) (P_7 X_1))))) bot_bot_a_o)))) % FOF formula (forall (P_7:(int->Prop)) (A_56:int), ((and ((P_7 A_56)->(((eq (int->Prop)) (collect_int (fun (X_1:int)=> ((and (((eq int) X_1) A_56)) (P_7 X_1))))) ((insert_int A_56) bot_bot_int_o)))) (((P_7 A_56)->False)->(((eq (int->Prop)) (collect_int (fun (X_1:int)=> ((and (((eq int) X_1) A_56)) (P_7 X_1))))) bot_bot_int_o)))) of role axiom named fact_631_Collect__conv__if % A new axiom: (forall (P_7:(int->Prop)) (A_56:int), ((and ((P_7 A_56)->(((eq (int->Prop)) (collect_int (fun (X_1:int)=> ((and (((eq int) X_1) A_56)) (P_7 X_1))))) ((insert_int A_56) bot_bot_int_o)))) (((P_7 A_56)->False)->(((eq (int->Prop)) (collect_int (fun (X_1:int)=> ((and (((eq int) X_1) A_56)) (P_7 X_1))))) bot_bot_int_o)))) % FOF formula (forall (P_7:(nat->Prop)) (A_56:nat), ((and ((P_7 A_56)->(((eq (nat->Prop)) (collect_nat (fun (X_1:nat)=> ((and (((eq nat) X_1) A_56)) (P_7 X_1))))) ((insert_nat A_56) bot_bot_nat_o)))) (((P_7 A_56)->False)->(((eq (nat->Prop)) (collect_nat (fun (X_1:nat)=> ((and (((eq nat) X_1) A_56)) (P_7 X_1))))) bot_bot_nat_o)))) of role axiom named fact_632_Collect__conv__if % A new axiom: (forall (P_7:(nat->Prop)) (A_56:nat), ((and ((P_7 A_56)->(((eq (nat->Prop)) (collect_nat (fun (X_1:nat)=> ((and (((eq nat) X_1) A_56)) (P_7 X_1))))) ((insert_nat A_56) bot_bot_nat_o)))) (((P_7 A_56)->False)->(((eq (nat->Prop)) (collect_nat (fun (X_1:nat)=> ((and (((eq nat) X_1) A_56)) (P_7 X_1))))) bot_bot_nat_o)))) % FOF formula (forall (P_6:(x_a->Prop)) (A_55:x_a), ((and ((P_6 A_55)->(((eq (x_a->Prop)) (collect_a (fun (X_1:x_a)=> ((and (((eq x_a) A_55) X_1)) (P_6 X_1))))) ((insert_a A_55) bot_bot_a_o)))) (((P_6 A_55)->False)->(((eq (x_a->Prop)) (collect_a (fun (X_1:x_a)=> ((and (((eq x_a) A_55) X_1)) (P_6 X_1))))) bot_bot_a_o)))) of role axiom named fact_633_Collect__conv__if2 % A new axiom: (forall (P_6:(x_a->Prop)) (A_55:x_a), ((and ((P_6 A_55)->(((eq (x_a->Prop)) (collect_a (fun (X_1:x_a)=> ((and (((eq x_a) A_55) X_1)) (P_6 X_1))))) ((insert_a A_55) bot_bot_a_o)))) (((P_6 A_55)->False)->(((eq (x_a->Prop)) (collect_a (fun (X_1:x_a)=> ((and (((eq x_a) A_55) X_1)) (P_6 X_1))))) bot_bot_a_o)))) % FOF formula (forall (P_6:(int->Prop)) (A_55:int), ((and ((P_6 A_55)->(((eq (int->Prop)) (collect_int (fun (X_1:int)=> ((and (((eq int) A_55) X_1)) (P_6 X_1))))) ((insert_int A_55) bot_bot_int_o)))) (((P_6 A_55)->False)->(((eq (int->Prop)) (collect_int (fun (X_1:int)=> ((and (((eq int) A_55) X_1)) (P_6 X_1))))) bot_bot_int_o)))) of role axiom named fact_634_Collect__conv__if2 % A new axiom: (forall (P_6:(int->Prop)) (A_55:int), ((and ((P_6 A_55)->(((eq (int->Prop)) (collect_int (fun (X_1:int)=> ((and (((eq int) A_55) X_1)) (P_6 X_1))))) ((insert_int A_55) bot_bot_int_o)))) (((P_6 A_55)->False)->(((eq (int->Prop)) (collect_int (fun (X_1:int)=> ((and (((eq int) A_55) X_1)) (P_6 X_1))))) bot_bot_int_o)))) % FOF formula (forall (P_6:(nat->Prop)) (A_55:nat), ((and ((P_6 A_55)->(((eq (nat->Prop)) (collect_nat (fun (X_1:nat)=> ((and (((eq nat) A_55) X_1)) (P_6 X_1))))) ((insert_nat A_55) bot_bot_nat_o)))) (((P_6 A_55)->False)->(((eq (nat->Prop)) (collect_nat (fun (X_1:nat)=> ((and (((eq nat) A_55) X_1)) (P_6 X_1))))) bot_bot_nat_o)))) of role axiom named fact_635_Collect__conv__if2 % A new axiom: (forall (P_6:(nat->Prop)) (A_55:nat), ((and ((P_6 A_55)->(((eq (nat->Prop)) (collect_nat (fun (X_1:nat)=> ((and (((eq nat) A_55) X_1)) (P_6 X_1))))) ((insert_nat A_55) bot_bot_nat_o)))) (((P_6 A_55)->False)->(((eq (nat->Prop)) (collect_nat (fun (X_1:nat)=> ((and (((eq nat) A_55) X_1)) (P_6 X_1))))) bot_bot_nat_o)))) % FOF formula (forall (A_54:x_a), (((eq (x_a->Prop)) (collect_a (fun (X_1:x_a)=> (((eq x_a) X_1) A_54)))) ((insert_a A_54) bot_bot_a_o))) of role axiom named fact_636_singleton__conv % A new axiom: (forall (A_54:x_a), (((eq (x_a->Prop)) (collect_a (fun (X_1:x_a)=> (((eq x_a) X_1) A_54)))) ((insert_a A_54) bot_bot_a_o))) % FOF formula (forall (A_54:int), (((eq (int->Prop)) (collect_int (fun (X_1:int)=> (((eq int) X_1) A_54)))) ((insert_int A_54) bot_bot_int_o))) of role axiom named fact_637_singleton__conv % A new axiom: (forall (A_54:int), (((eq (int->Prop)) (collect_int (fun (X_1:int)=> (((eq int) X_1) A_54)))) ((insert_int A_54) bot_bot_int_o))) % FOF formula (forall (A_54:nat), (((eq (nat->Prop)) (collect_nat (fun (X_1:nat)=> (((eq nat) X_1) A_54)))) ((insert_nat A_54) bot_bot_nat_o))) of role axiom named fact_638_singleton__conv % A new axiom: (forall (A_54:nat), (((eq (nat->Prop)) (collect_nat (fun (X_1:nat)=> (((eq nat) X_1) A_54)))) ((insert_nat A_54) bot_bot_nat_o))) % FOF formula (forall (A_53:x_a), (((eq (x_a->Prop)) (collect_a (fequal_a A_53))) ((insert_a A_53) bot_bot_a_o))) of role axiom named fact_639_singleton__conv2 % A new axiom: (forall (A_53:x_a), (((eq (x_a->Prop)) (collect_a (fequal_a A_53))) ((insert_a A_53) bot_bot_a_o))) % FOF formula (forall (A_53:int), (((eq (int->Prop)) (collect_int (fequal_int A_53))) ((insert_int A_53) bot_bot_int_o))) of role axiom named fact_640_singleton__conv2 % A new axiom: (forall (A_53:int), (((eq (int->Prop)) (collect_int (fequal_int A_53))) ((insert_int A_53) bot_bot_int_o))) % FOF formula (forall (A_53:nat), (((eq (nat->Prop)) (collect_nat (fequal_nat A_53))) ((insert_nat A_53) bot_bot_nat_o))) of role axiom named fact_641_singleton__conv2 % A new axiom: (forall (A_53:nat), (((eq (nat->Prop)) (collect_nat (fequal_nat A_53))) ((insert_nat A_53) bot_bot_nat_o))) % FOF formula (forall (X_18:x_a) (A_52:(x_a->Prop)), ((finite_finite_a A_52)->(((member_a X_18) A_52)->(((eq nat) (suc (finite_card_a ((minus_minus_a_o A_52) ((insert_a X_18) bot_bot_a_o))))) (finite_card_a A_52))))) of role axiom named fact_642_card__Suc__Diff1 % A new axiom: (forall (X_18:x_a) (A_52:(x_a->Prop)), ((finite_finite_a A_52)->(((member_a X_18) A_52)->(((eq nat) (suc (finite_card_a ((minus_minus_a_o A_52) ((insert_a X_18) bot_bot_a_o))))) (finite_card_a A_52))))) % FOF formula (forall (X_18:int) (A_52:(int->Prop)), ((finite_finite_int A_52)->(((member_int X_18) A_52)->(((eq nat) (suc (finite_card_int ((minus_minus_int_o A_52) ((insert_int X_18) bot_bot_int_o))))) (finite_card_int A_52))))) of role axiom named fact_643_card__Suc__Diff1 % A new axiom: (forall (X_18:int) (A_52:(int->Prop)), ((finite_finite_int A_52)->(((member_int X_18) A_52)->(((eq nat) (suc (finite_card_int ((minus_minus_int_o A_52) ((insert_int X_18) bot_bot_int_o))))) (finite_card_int A_52))))) % FOF formula (forall (X_18:nat) (A_52:(nat->Prop)), ((finite_finite_nat A_52)->(((member_nat X_18) A_52)->(((eq nat) (suc (finite_card_nat ((minus_minus_nat_o A_52) ((insert_nat X_18) bot_bot_nat_o))))) (finite_card_nat A_52))))) of role axiom named fact_644_card__Suc__Diff1 % A new axiom: (forall (X_18:nat) (A_52:(nat->Prop)), ((finite_finite_nat A_52)->(((member_nat X_18) A_52)->(((eq nat) (suc (finite_card_nat ((minus_minus_nat_o A_52) ((insert_nat X_18) bot_bot_nat_o))))) (finite_card_nat A_52))))) % FOF formula (forall (X_18:pname) (A_52:(pname->Prop)), ((finite_finite_pname A_52)->(((member_pname X_18) A_52)->(((eq nat) (suc (finite_card_pname ((minus_minus_pname_o A_52) ((insert_pname X_18) bot_bot_pname_o))))) (finite_card_pname A_52))))) of role axiom named fact_645_card__Suc__Diff1 % A new axiom: (forall (X_18:pname) (A_52:(pname->Prop)), ((finite_finite_pname A_52)->(((member_pname X_18) A_52)->(((eq nat) (suc (finite_card_pname ((minus_minus_pname_o A_52) ((insert_pname X_18) bot_bot_pname_o))))) (finite_card_pname A_52))))) % FOF formula (forall (X_17:x_a) (A_51:(x_a->Prop)), ((finite_finite_a A_51)->(((eq nat) (finite_card_a ((insert_a X_17) A_51))) (suc (finite_card_a ((minus_minus_a_o A_51) ((insert_a X_17) bot_bot_a_o))))))) of role axiom named fact_646_card__insert % A new axiom: (forall (X_17:x_a) (A_51:(x_a->Prop)), ((finite_finite_a A_51)->(((eq nat) (finite_card_a ((insert_a X_17) A_51))) (suc (finite_card_a ((minus_minus_a_o A_51) ((insert_a X_17) bot_bot_a_o))))))) % FOF formula (forall (X_17:int) (A_51:(int->Prop)), ((finite_finite_int A_51)->(((eq nat) (finite_card_int ((insert_int X_17) A_51))) (suc (finite_card_int ((minus_minus_int_o A_51) ((insert_int X_17) bot_bot_int_o))))))) of role axiom named fact_647_card__insert % A new axiom: (forall (X_17:int) (A_51:(int->Prop)), ((finite_finite_int A_51)->(((eq nat) (finite_card_int ((insert_int X_17) A_51))) (suc (finite_card_int ((minus_minus_int_o A_51) ((insert_int X_17) bot_bot_int_o))))))) % FOF formula (forall (X_17:nat) (A_51:(nat->Prop)), ((finite_finite_nat A_51)->(((eq nat) (finite_card_nat ((insert_nat X_17) A_51))) (suc (finite_card_nat ((minus_minus_nat_o A_51) ((insert_nat X_17) bot_bot_nat_o))))))) of role axiom named fact_648_card__insert % A new axiom: (forall (X_17:nat) (A_51:(nat->Prop)), ((finite_finite_nat A_51)->(((eq nat) (finite_card_nat ((insert_nat X_17) A_51))) (suc (finite_card_nat ((minus_minus_nat_o A_51) ((insert_nat X_17) bot_bot_nat_o))))))) % FOF formula (forall (X_17:pname) (A_51:(pname->Prop)), ((finite_finite_pname A_51)->(((eq nat) (finite_card_pname ((insert_pname X_17) A_51))) (suc (finite_card_pname ((minus_minus_pname_o A_51) ((insert_pname X_17) bot_bot_pname_o))))))) of role axiom named fact_649_card__insert % A new axiom: (forall (X_17:pname) (A_51:(pname->Prop)), ((finite_finite_pname A_51)->(((eq nat) (finite_card_pname ((insert_pname X_17) A_51))) (suc (finite_card_pname ((minus_minus_pname_o A_51) ((insert_pname X_17) bot_bot_pname_o))))))) % FOF formula (forall (X_16:x_a) (A_50:(x_a->Prop)), ((finite_finite_a A_50)->((ord_less_eq_nat (finite_card_a ((minus_minus_a_o A_50) ((insert_a X_16) bot_bot_a_o)))) (finite_card_a A_50)))) of role axiom named fact_650_card__Diff1__le % A new axiom: (forall (X_16:x_a) (A_50:(x_a->Prop)), ((finite_finite_a A_50)->((ord_less_eq_nat (finite_card_a ((minus_minus_a_o A_50) ((insert_a X_16) bot_bot_a_o)))) (finite_card_a A_50)))) % FOF formula (forall (X_16:int) (A_50:(int->Prop)), ((finite_finite_int A_50)->((ord_less_eq_nat (finite_card_int ((minus_minus_int_o A_50) ((insert_int X_16) bot_bot_int_o)))) (finite_card_int A_50)))) of role axiom named fact_651_card__Diff1__le % A new axiom: (forall (X_16:int) (A_50:(int->Prop)), ((finite_finite_int A_50)->((ord_less_eq_nat (finite_card_int ((minus_minus_int_o A_50) ((insert_int X_16) bot_bot_int_o)))) (finite_card_int A_50)))) % FOF formula (forall (X_16:nat) (A_50:(nat->Prop)), ((finite_finite_nat A_50)->((ord_less_eq_nat (finite_card_nat ((minus_minus_nat_o A_50) ((insert_nat X_16) bot_bot_nat_o)))) (finite_card_nat A_50)))) of role axiom named fact_652_card__Diff1__le % A new axiom: (forall (X_16:nat) (A_50:(nat->Prop)), ((finite_finite_nat A_50)->((ord_less_eq_nat (finite_card_nat ((minus_minus_nat_o A_50) ((insert_nat X_16) bot_bot_nat_o)))) (finite_card_nat A_50)))) % FOF formula (forall (X_16:pname) (A_50:(pname->Prop)), ((finite_finite_pname A_50)->((ord_less_eq_nat (finite_card_pname ((minus_minus_pname_o A_50) ((insert_pname X_16) bot_bot_pname_o)))) (finite_card_pname A_50)))) of role axiom named fact_653_card__Diff1__le % A new axiom: (forall (X_16:pname) (A_50:(pname->Prop)), ((finite_finite_pname A_50)->((ord_less_eq_nat (finite_card_pname ((minus_minus_pname_o A_50) ((insert_pname X_16) bot_bot_pname_o)))) (finite_card_pname A_50)))) % FOF formula (forall (A_49:(x_a->Prop)) (A_48:x_a) (B_31:(x_a->Prop)), ((iff (finite_finite_a ((minus_minus_a_o A_49) ((insert_a A_48) B_31)))) (finite_finite_a ((minus_minus_a_o A_49) B_31)))) of role axiom named fact_654_finite__Diff__insert % A new axiom: (forall (A_49:(x_a->Prop)) (A_48:x_a) (B_31:(x_a->Prop)), ((iff (finite_finite_a ((minus_minus_a_o A_49) ((insert_a A_48) B_31)))) (finite_finite_a ((minus_minus_a_o A_49) B_31)))) % FOF formula (forall (A_49:(int->Prop)) (A_48:int) (B_31:(int->Prop)), ((iff (finite_finite_int ((minus_minus_int_o A_49) ((insert_int A_48) B_31)))) (finite_finite_int ((minus_minus_int_o A_49) B_31)))) of role axiom named fact_655_finite__Diff__insert % A new axiom: (forall (A_49:(int->Prop)) (A_48:int) (B_31:(int->Prop)), ((iff (finite_finite_int ((minus_minus_int_o A_49) ((insert_int A_48) B_31)))) (finite_finite_int ((minus_minus_int_o A_49) B_31)))) % FOF formula (forall (A_49:(nat->Prop)) (A_48:nat) (B_31:(nat->Prop)), ((iff (finite_finite_nat ((minus_minus_nat_o A_49) ((insert_nat A_48) B_31)))) (finite_finite_nat ((minus_minus_nat_o A_49) B_31)))) of role axiom named fact_656_finite__Diff__insert % A new axiom: (forall (A_49:(nat->Prop)) (A_48:nat) (B_31:(nat->Prop)), ((iff (finite_finite_nat ((minus_minus_nat_o A_49) ((insert_nat A_48) B_31)))) (finite_finite_nat ((minus_minus_nat_o A_49) B_31)))) % FOF formula (forall (A_49:(pname->Prop)) (A_48:pname) (B_31:(pname->Prop)), ((iff (finite_finite_pname ((minus_minus_pname_o A_49) ((insert_pname A_48) B_31)))) (finite_finite_pname ((minus_minus_pname_o A_49) B_31)))) of role axiom named fact_657_finite__Diff__insert % A new axiom: (forall (A_49:(pname->Prop)) (A_48:pname) (B_31:(pname->Prop)), ((iff (finite_finite_pname ((minus_minus_pname_o A_49) ((insert_pname A_48) B_31)))) (finite_finite_pname ((minus_minus_pname_o A_49) B_31)))) % FOF formula (forall (F_19:(nat->int)) (A_47:(nat->Prop)) (B_30:(nat->Prop)), ((ord_less_eq_int_o ((minus_minus_int_o ((image_nat_int F_19) A_47)) ((image_nat_int F_19) B_30))) ((image_nat_int F_19) ((minus_minus_nat_o A_47) B_30)))) of role axiom named fact_658_image__diff__subset % A new axiom: (forall (F_19:(nat->int)) (A_47:(nat->Prop)) (B_30:(nat->Prop)), ((ord_less_eq_int_o ((minus_minus_int_o ((image_nat_int F_19) A_47)) ((image_nat_int F_19) B_30))) ((image_nat_int F_19) ((minus_minus_nat_o A_47) B_30)))) % FOF formula (forall (F_19:(pname->x_a)) (A_47:(pname->Prop)) (B_30:(pname->Prop)), ((ord_less_eq_a_o ((minus_minus_a_o ((image_pname_a F_19) A_47)) ((image_pname_a F_19) B_30))) ((image_pname_a F_19) ((minus_minus_pname_o A_47) B_30)))) of role axiom named fact_659_image__diff__subset % A new axiom: (forall (F_19:(pname->x_a)) (A_47:(pname->Prop)) (B_30:(pname->Prop)), ((ord_less_eq_a_o ((minus_minus_a_o ((image_pname_a F_19) A_47)) ((image_pname_a F_19) B_30))) ((image_pname_a F_19) ((minus_minus_pname_o A_47) B_30)))) % FOF formula (forall (A_46:(x_a->Prop)) (X_15:x_a), (((ord_less_eq_a_o A_46) ((insert_a X_15) bot_bot_a_o))->((or (((eq (x_a->Prop)) A_46) bot_bot_a_o)) (((eq (x_a->Prop)) A_46) ((insert_a X_15) bot_bot_a_o))))) of role axiom named fact_660_subset__singletonD % A new axiom: (forall (A_46:(x_a->Prop)) (X_15:x_a), (((ord_less_eq_a_o A_46) ((insert_a X_15) bot_bot_a_o))->((or (((eq (x_a->Prop)) A_46) bot_bot_a_o)) (((eq (x_a->Prop)) A_46) ((insert_a X_15) bot_bot_a_o))))) % FOF formula (forall (A_46:(nat->Prop)) (X_15:nat), (((ord_less_eq_nat_o A_46) ((insert_nat X_15) bot_bot_nat_o))->((or (((eq (nat->Prop)) A_46) bot_bot_nat_o)) (((eq (nat->Prop)) A_46) ((insert_nat X_15) bot_bot_nat_o))))) of role axiom named fact_661_subset__singletonD % A new axiom: (forall (A_46:(nat->Prop)) (X_15:nat), (((ord_less_eq_nat_o A_46) ((insert_nat X_15) bot_bot_nat_o))->((or (((eq (nat->Prop)) A_46) bot_bot_nat_o)) (((eq (nat->Prop)) A_46) ((insert_nat X_15) bot_bot_nat_o))))) % FOF formula (forall (A_46:(int->Prop)) (X_15:int), (((ord_less_eq_int_o A_46) ((insert_int X_15) bot_bot_int_o))->((or (((eq (int->Prop)) A_46) bot_bot_int_o)) (((eq (int->Prop)) A_46) ((insert_int X_15) bot_bot_int_o))))) of role axiom named fact_662_subset__singletonD % A new axiom: (forall (A_46:(int->Prop)) (X_15:int), (((ord_less_eq_int_o A_46) ((insert_int X_15) bot_bot_int_o))->((or (((eq (int->Prop)) A_46) bot_bot_int_o)) (((eq (int->Prop)) A_46) ((insert_int X_15) bot_bot_int_o))))) % FOF formula (forall (F1:nat) (F2:(nat->nat)) (Nat_3:nat), (((eq nat) (((nat_case_nat F1) F2) (suc Nat_3))) (F2 Nat_3))) of role axiom named fact_663_nat__case__Suc % A new axiom: (forall (F1:nat) (F2:(nat->nat)) (Nat_3:nat), (((eq nat) (((nat_case_nat F1) F2) (suc Nat_3))) (F2 Nat_3))) % FOF formula (forall (F1:Prop) (F2:(nat->Prop)) (Nat_3:nat), ((iff (((nat_case_o F1) F2) (suc Nat_3))) (F2 Nat_3))) of role axiom named fact_664_nat__case__Suc % A new axiom: (forall (F1:Prop) (F2:(nat->Prop)) (Nat_3:nat), ((iff (((nat_case_o F1) F2) (suc Nat_3))) (F2 Nat_3))) % FOF formula (forall (C_21:int) (X_14:nat) (A_45:(nat->Prop)), (((member_nat X_14) A_45)->(((eq (int->Prop)) ((image_nat_int (fun (X_1:nat)=> C_21)) A_45)) ((insert_int C_21) bot_bot_int_o)))) of role axiom named fact_665_image__constant % A new axiom: (forall (C_21:int) (X_14:nat) (A_45:(nat->Prop)), (((member_nat X_14) A_45)->(((eq (int->Prop)) ((image_nat_int (fun (X_1:nat)=> C_21)) A_45)) ((insert_int C_21) bot_bot_int_o)))) % FOF formula (forall (C_21:x_a) (X_14:pname) (A_45:(pname->Prop)), (((member_pname X_14) A_45)->(((eq (x_a->Prop)) ((image_pname_a (fun (X_1:pname)=> C_21)) A_45)) ((insert_a C_21) bot_bot_a_o)))) of role axiom named fact_666_image__constant % A new axiom: (forall (C_21:x_a) (X_14:pname) (A_45:(pname->Prop)), (((member_pname X_14) A_45)->(((eq (x_a->Prop)) ((image_pname_a (fun (X_1:pname)=> C_21)) A_45)) ((insert_a C_21) bot_bot_a_o)))) % FOF formula (forall (C_20:int) (A_44:(nat->Prop)), ((and ((((eq (nat->Prop)) A_44) bot_bot_nat_o)->(((eq (int->Prop)) ((image_nat_int (fun (X_1:nat)=> C_20)) A_44)) bot_bot_int_o))) ((not (((eq (nat->Prop)) A_44) bot_bot_nat_o))->(((eq (int->Prop)) ((image_nat_int (fun (X_1:nat)=> C_20)) A_44)) ((insert_int C_20) bot_bot_int_o))))) of role axiom named fact_667_image__constant__conv % A new axiom: (forall (C_20:int) (A_44:(nat->Prop)), ((and ((((eq (nat->Prop)) A_44) bot_bot_nat_o)->(((eq (int->Prop)) ((image_nat_int (fun (X_1:nat)=> C_20)) A_44)) bot_bot_int_o))) ((not (((eq (nat->Prop)) A_44) bot_bot_nat_o))->(((eq (int->Prop)) ((image_nat_int (fun (X_1:nat)=> C_20)) A_44)) ((insert_int C_20) bot_bot_int_o))))) % FOF formula (forall (C_20:x_a) (A_44:(pname->Prop)), ((and ((((eq (pname->Prop)) A_44) bot_bot_pname_o)->(((eq (x_a->Prop)) ((image_pname_a (fun (X_1:pname)=> C_20)) A_44)) bot_bot_a_o))) ((not (((eq (pname->Prop)) A_44) bot_bot_pname_o))->(((eq (x_a->Prop)) ((image_pname_a (fun (X_1:pname)=> C_20)) A_44)) ((insert_a C_20) bot_bot_a_o))))) of role axiom named fact_668_image__constant__conv % A new axiom: (forall (C_20:x_a) (A_44:(pname->Prop)), ((and ((((eq (pname->Prop)) A_44) bot_bot_pname_o)->(((eq (x_a->Prop)) ((image_pname_a (fun (X_1:pname)=> C_20)) A_44)) bot_bot_a_o))) ((not (((eq (pname->Prop)) A_44) bot_bot_pname_o))->(((eq (x_a->Prop)) ((image_pname_a (fun (X_1:pname)=> C_20)) A_44)) ((insert_a C_20) bot_bot_a_o))))) % FOF formula (forall (A_43:int) (B_29:int) (C_19:int) (D_3:int), ((((eq int) ((minus_minus_int A_43) B_29)) ((minus_minus_int C_19) D_3))->((iff (((eq int) A_43) B_29)) (((eq int) C_19) D_3)))) of role axiom named fact_669_diff__eq__diff__eq % A new axiom: (forall (A_43:int) (B_29:int) (C_19:int) (D_3:int), ((((eq int) ((minus_minus_int A_43) B_29)) ((minus_minus_int C_19) D_3))->((iff (((eq int) A_43) B_29)) (((eq int) C_19) D_3)))) % FOF formula (forall (A_42:(int->Prop)) (B_28:(int->Prop)), ((finite_finite_int B_28)->(((ord_less_eq_int_o B_28) A_42)->(((eq nat) (finite_card_int ((minus_minus_int_o A_42) B_28))) ((minus_minus_nat (finite_card_int A_42)) (finite_card_int B_28)))))) of role axiom named fact_670_card__Diff__subset % A new axiom: (forall (A_42:(int->Prop)) (B_28:(int->Prop)), ((finite_finite_int B_28)->(((ord_less_eq_int_o B_28) A_42)->(((eq nat) (finite_card_int ((minus_minus_int_o A_42) B_28))) ((minus_minus_nat (finite_card_int A_42)) (finite_card_int B_28)))))) % FOF formula (forall (A_42:(nat->Prop)) (B_28:(nat->Prop)), ((finite_finite_nat B_28)->(((ord_less_eq_nat_o B_28) A_42)->(((eq nat) (finite_card_nat ((minus_minus_nat_o A_42) B_28))) ((minus_minus_nat (finite_card_nat A_42)) (finite_card_nat B_28)))))) of role axiom named fact_671_card__Diff__subset % A new axiom: (forall (A_42:(nat->Prop)) (B_28:(nat->Prop)), ((finite_finite_nat B_28)->(((ord_less_eq_nat_o B_28) A_42)->(((eq nat) (finite_card_nat ((minus_minus_nat_o A_42) B_28))) ((minus_minus_nat (finite_card_nat A_42)) (finite_card_nat B_28)))))) % FOF formula (forall (A_42:(x_a->Prop)) (B_28:(x_a->Prop)), ((finite_finite_a B_28)->(((ord_less_eq_a_o B_28) A_42)->(((eq nat) (finite_card_a ((minus_minus_a_o A_42) B_28))) ((minus_minus_nat (finite_card_a A_42)) (finite_card_a B_28)))))) of role axiom named fact_672_card__Diff__subset % A new axiom: (forall (A_42:(x_a->Prop)) (B_28:(x_a->Prop)), ((finite_finite_a B_28)->(((ord_less_eq_a_o B_28) A_42)->(((eq nat) (finite_card_a ((minus_minus_a_o A_42) B_28))) ((minus_minus_nat (finite_card_a A_42)) (finite_card_a B_28)))))) % FOF formula (forall (A_42:(pname->Prop)) (B_28:(pname->Prop)), ((finite_finite_pname B_28)->(((ord_less_eq_pname_o B_28) A_42)->(((eq nat) (finite_card_pname ((minus_minus_pname_o A_42) B_28))) ((minus_minus_nat (finite_card_pname A_42)) (finite_card_pname B_28)))))) of role axiom named fact_673_card__Diff__subset % A new axiom: (forall (A_42:(pname->Prop)) (B_28:(pname->Prop)), ((finite_finite_pname B_28)->(((ord_less_eq_pname_o B_28) A_42)->(((eq nat) (finite_card_pname ((minus_minus_pname_o A_42) B_28))) ((minus_minus_nat (finite_card_pname A_42)) (finite_card_pname B_28)))))) % FOF formula (forall (A_41:(int->Prop)) (B_27:(int->Prop)), ((finite_finite_int B_27)->((ord_less_eq_nat ((minus_minus_nat (finite_card_int A_41)) (finite_card_int B_27))) (finite_card_int ((minus_minus_int_o A_41) B_27))))) of role axiom named fact_674_diff__card__le__card__Diff % A new axiom: (forall (A_41:(int->Prop)) (B_27:(int->Prop)), ((finite_finite_int B_27)->((ord_less_eq_nat ((minus_minus_nat (finite_card_int A_41)) (finite_card_int B_27))) (finite_card_int ((minus_minus_int_o A_41) B_27))))) % FOF formula (forall (A_41:(nat->Prop)) (B_27:(nat->Prop)), ((finite_finite_nat B_27)->((ord_less_eq_nat ((minus_minus_nat (finite_card_nat A_41)) (finite_card_nat B_27))) (finite_card_nat ((minus_minus_nat_o A_41) B_27))))) of role axiom named fact_675_diff__card__le__card__Diff % A new axiom: (forall (A_41:(nat->Prop)) (B_27:(nat->Prop)), ((finite_finite_nat B_27)->((ord_less_eq_nat ((minus_minus_nat (finite_card_nat A_41)) (finite_card_nat B_27))) (finite_card_nat ((minus_minus_nat_o A_41) B_27))))) % FOF formula (forall (A_41:(x_a->Prop)) (B_27:(x_a->Prop)), ((finite_finite_a B_27)->((ord_less_eq_nat ((minus_minus_nat (finite_card_a A_41)) (finite_card_a B_27))) (finite_card_a ((minus_minus_a_o A_41) B_27))))) of role axiom named fact_676_diff__card__le__card__Diff % A new axiom: (forall (A_41:(x_a->Prop)) (B_27:(x_a->Prop)), ((finite_finite_a B_27)->((ord_less_eq_nat ((minus_minus_nat (finite_card_a A_41)) (finite_card_a B_27))) (finite_card_a ((minus_minus_a_o A_41) B_27))))) % FOF formula (forall (A_41:(pname->Prop)) (B_27:(pname->Prop)), ((finite_finite_pname B_27)->((ord_less_eq_nat ((minus_minus_nat (finite_card_pname A_41)) (finite_card_pname B_27))) (finite_card_pname ((minus_minus_pname_o A_41) B_27))))) of role axiom named fact_677_diff__card__le__card__Diff % A new axiom: (forall (A_41:(pname->Prop)) (B_27:(pname->Prop)), ((finite_finite_pname B_27)->((ord_less_eq_nat ((minus_minus_nat (finite_card_pname A_41)) (finite_card_pname B_27))) (finite_card_pname ((minus_minus_pname_o A_41) B_27))))) % FOF formula (forall (P_5:((x_a->Prop)->Prop)) (A_40:(x_a->Prop)) (F_18:(x_a->Prop)), ((finite_finite_a F_18)->(((ord_less_eq_a_o F_18) A_40)->((P_5 bot_bot_a_o)->((forall (A_37:x_a) (F_2:(x_a->Prop)), ((finite_finite_a F_2)->(((member_a A_37) A_40)->((((member_a A_37) F_2)->False)->((P_5 F_2)->(P_5 ((insert_a A_37) F_2)))))))->(P_5 F_18)))))) of role axiom named fact_678_finite__subset__induct % A new axiom: (forall (P_5:((x_a->Prop)->Prop)) (A_40:(x_a->Prop)) (F_18:(x_a->Prop)), ((finite_finite_a F_18)->(((ord_less_eq_a_o F_18) A_40)->((P_5 bot_bot_a_o)->((forall (A_37:x_a) (F_2:(x_a->Prop)), ((finite_finite_a F_2)->(((member_a A_37) A_40)->((((member_a A_37) F_2)->False)->((P_5 F_2)->(P_5 ((insert_a A_37) F_2)))))))->(P_5 F_18)))))) % FOF formula (forall (P_5:((int->Prop)->Prop)) (A_40:(int->Prop)) (F_18:(int->Prop)), ((finite_finite_int F_18)->(((ord_less_eq_int_o F_18) A_40)->((P_5 bot_bot_int_o)->((forall (A_37:int) (F_2:(int->Prop)), ((finite_finite_int F_2)->(((member_int A_37) A_40)->((((member_int A_37) F_2)->False)->((P_5 F_2)->(P_5 ((insert_int A_37) F_2)))))))->(P_5 F_18)))))) of role axiom named fact_679_finite__subset__induct % A new axiom: (forall (P_5:((int->Prop)->Prop)) (A_40:(int->Prop)) (F_18:(int->Prop)), ((finite_finite_int F_18)->(((ord_less_eq_int_o F_18) A_40)->((P_5 bot_bot_int_o)->((forall (A_37:int) (F_2:(int->Prop)), ((finite_finite_int F_2)->(((member_int A_37) A_40)->((((member_int A_37) F_2)->False)->((P_5 F_2)->(P_5 ((insert_int A_37) F_2)))))))->(P_5 F_18)))))) % FOF formula (forall (P_5:((nat->Prop)->Prop)) (A_40:(nat->Prop)) (F_18:(nat->Prop)), ((finite_finite_nat F_18)->(((ord_less_eq_nat_o F_18) A_40)->((P_5 bot_bot_nat_o)->((forall (A_37:nat) (F_2:(nat->Prop)), ((finite_finite_nat F_2)->(((member_nat A_37) A_40)->((((member_nat A_37) F_2)->False)->((P_5 F_2)->(P_5 ((insert_nat A_37) F_2)))))))->(P_5 F_18)))))) of role axiom named fact_680_finite__subset__induct % A new axiom: (forall (P_5:((nat->Prop)->Prop)) (A_40:(nat->Prop)) (F_18:(nat->Prop)), ((finite_finite_nat F_18)->(((ord_less_eq_nat_o F_18) A_40)->((P_5 bot_bot_nat_o)->((forall (A_37:nat) (F_2:(nat->Prop)), ((finite_finite_nat F_2)->(((member_nat A_37) A_40)->((((member_nat A_37) F_2)->False)->((P_5 F_2)->(P_5 ((insert_nat A_37) F_2)))))))->(P_5 F_18)))))) % FOF formula (forall (P_5:((pname->Prop)->Prop)) (A_40:(pname->Prop)) (F_18:(pname->Prop)), ((finite_finite_pname F_18)->(((ord_less_eq_pname_o F_18) A_40)->((P_5 bot_bot_pname_o)->((forall (A_37:pname) (F_2:(pname->Prop)), ((finite_finite_pname F_2)->(((member_pname A_37) A_40)->((((member_pname A_37) F_2)->False)->((P_5 F_2)->(P_5 ((insert_pname A_37) F_2)))))))->(P_5 F_18)))))) of role axiom named fact_681_finite__subset__induct % A new axiom: (forall (P_5:((pname->Prop)->Prop)) (A_40:(pname->Prop)) (F_18:(pname->Prop)), ((finite_finite_pname F_18)->(((ord_less_eq_pname_o F_18) A_40)->((P_5 bot_bot_pname_o)->((forall (A_37:pname) (F_2:(pname->Prop)), ((finite_finite_pname F_2)->(((member_pname A_37) A_40)->((((member_pname A_37) F_2)->False)->((P_5 F_2)->(P_5 ((insert_pname A_37) F_2)))))))->(P_5 F_18)))))) % FOF formula (forall (Pn:pname) (G:(x_a->Prop)), (((p ((insert_a (mgt_call Pn)) G)) ((insert_a (mgt (the_com (body Pn)))) bot_bot_a_o))->((p G) ((insert_a (mgt_call Pn)) bot_bot_a_o)))) of role axiom named fact_682_assms_I2_J % A new axiom: (forall (Pn:pname) (G:(x_a->Prop)), (((p ((insert_a (mgt_call Pn)) G)) ((insert_a (mgt (the_com (body Pn)))) bot_bot_a_o))->((p G) ((insert_a (mgt_call Pn)) bot_bot_a_o)))) % FOF formula (forall (P_4:((x_a->Prop)->Prop)) (A_39:(x_a->Prop)), ((finite_finite_a A_39)->((P_4 A_39)->((forall (A_37:x_a) (A_38:(x_a->Prop)), ((finite_finite_a A_38)->(((member_a A_37) A_38)->((P_4 A_38)->(P_4 ((minus_minus_a_o A_38) ((insert_a A_37) bot_bot_a_o)))))))->(P_4 bot_bot_a_o))))) of role axiom named fact_683_finite__empty__induct % A new axiom: (forall (P_4:((x_a->Prop)->Prop)) (A_39:(x_a->Prop)), ((finite_finite_a A_39)->((P_4 A_39)->((forall (A_37:x_a) (A_38:(x_a->Prop)), ((finite_finite_a A_38)->(((member_a A_37) A_38)->((P_4 A_38)->(P_4 ((minus_minus_a_o A_38) ((insert_a A_37) bot_bot_a_o)))))))->(P_4 bot_bot_a_o))))) % FOF formula (forall (P_4:((int->Prop)->Prop)) (A_39:(int->Prop)), ((finite_finite_int A_39)->((P_4 A_39)->((forall (A_37:int) (A_38:(int->Prop)), ((finite_finite_int A_38)->(((member_int A_37) A_38)->((P_4 A_38)->(P_4 ((minus_minus_int_o A_38) ((insert_int A_37) bot_bot_int_o)))))))->(P_4 bot_bot_int_o))))) of role axiom named fact_684_finite__empty__induct % A new axiom: (forall (P_4:((int->Prop)->Prop)) (A_39:(int->Prop)), ((finite_finite_int A_39)->((P_4 A_39)->((forall (A_37:int) (A_38:(int->Prop)), ((finite_finite_int A_38)->(((member_int A_37) A_38)->((P_4 A_38)->(P_4 ((minus_minus_int_o A_38) ((insert_int A_37) bot_bot_int_o)))))))->(P_4 bot_bot_int_o))))) % FOF formula (forall (P_4:((nat->Prop)->Prop)) (A_39:(nat->Prop)), ((finite_finite_nat A_39)->((P_4 A_39)->((forall (A_37:nat) (A_38:(nat->Prop)), ((finite_finite_nat A_38)->(((member_nat A_37) A_38)->((P_4 A_38)->(P_4 ((minus_minus_nat_o A_38) ((insert_nat A_37) bot_bot_nat_o)))))))->(P_4 bot_bot_nat_o))))) of role axiom named fact_685_finite__empty__induct % A new axiom: (forall (P_4:((nat->Prop)->Prop)) (A_39:(nat->Prop)), ((finite_finite_nat A_39)->((P_4 A_39)->((forall (A_37:nat) (A_38:(nat->Prop)), ((finite_finite_nat A_38)->(((member_nat A_37) A_38)->((P_4 A_38)->(P_4 ((minus_minus_nat_o A_38) ((insert_nat A_37) bot_bot_nat_o)))))))->(P_4 bot_bot_nat_o))))) % FOF formula (forall (P_4:((pname->Prop)->Prop)) (A_39:(pname->Prop)), ((finite_finite_pname A_39)->((P_4 A_39)->((forall (A_37:pname) (A_38:(pname->Prop)), ((finite_finite_pname A_38)->(((member_pname A_37) A_38)->((P_4 A_38)->(P_4 ((minus_minus_pname_o A_38) ((insert_pname A_37) bot_bot_pname_o)))))))->(P_4 bot_bot_pname_o))))) of role axiom named fact_686_finite__empty__induct % A new axiom: (forall (P_4:((pname->Prop)->Prop)) (A_39:(pname->Prop)), ((finite_finite_pname A_39)->((P_4 A_39)->((forall (A_37:pname) (A_38:(pname->Prop)), ((finite_finite_pname A_38)->(((member_pname A_37) A_38)->((P_4 A_38)->(P_4 ((minus_minus_pname_o A_38) ((insert_pname A_37) bot_bot_pname_o)))))))->(P_4 bot_bot_pname_o))))) % FOF formula (forall (P_3:((x_a->Prop)->Prop)) (F_17:(x_a->Prop)), ((finite_finite_a F_17)->((P_3 bot_bot_a_o)->((forall (X_1:x_a) (F_2:(x_a->Prop)), ((finite_finite_a F_2)->((((member_a X_1) F_2)->False)->((P_3 F_2)->(P_3 ((insert_a X_1) F_2))))))->(P_3 F_17))))) of role axiom named fact_687_finite__induct % A new axiom: (forall (P_3:((x_a->Prop)->Prop)) (F_17:(x_a->Prop)), ((finite_finite_a F_17)->((P_3 bot_bot_a_o)->((forall (X_1:x_a) (F_2:(x_a->Prop)), ((finite_finite_a F_2)->((((member_a X_1) F_2)->False)->((P_3 F_2)->(P_3 ((insert_a X_1) F_2))))))->(P_3 F_17))))) % FOF formula (forall (P_3:((int->Prop)->Prop)) (F_17:(int->Prop)), ((finite_finite_int F_17)->((P_3 bot_bot_int_o)->((forall (X_1:int) (F_2:(int->Prop)), ((finite_finite_int F_2)->((((member_int X_1) F_2)->False)->((P_3 F_2)->(P_3 ((insert_int X_1) F_2))))))->(P_3 F_17))))) of role axiom named fact_688_finite__induct % A new axiom: (forall (P_3:((int->Prop)->Prop)) (F_17:(int->Prop)), ((finite_finite_int F_17)->((P_3 bot_bot_int_o)->((forall (X_1:int) (F_2:(int->Prop)), ((finite_finite_int F_2)->((((member_int X_1) F_2)->False)->((P_3 F_2)->(P_3 ((insert_int X_1) F_2))))))->(P_3 F_17))))) % FOF formula (forall (P_3:((nat->Prop)->Prop)) (F_17:(nat->Prop)), ((finite_finite_nat F_17)->((P_3 bot_bot_nat_o)->((forall (X_1:nat) (F_2:(nat->Prop)), ((finite_finite_nat F_2)->((((member_nat X_1) F_2)->False)->((P_3 F_2)->(P_3 ((insert_nat X_1) F_2))))))->(P_3 F_17))))) of role axiom named fact_689_finite__induct % A new axiom: (forall (P_3:((nat->Prop)->Prop)) (F_17:(nat->Prop)), ((finite_finite_nat F_17)->((P_3 bot_bot_nat_o)->((forall (X_1:nat) (F_2:(nat->Prop)), ((finite_finite_nat F_2)->((((member_nat X_1) F_2)->False)->((P_3 F_2)->(P_3 ((insert_nat X_1) F_2))))))->(P_3 F_17))))) % FOF formula (forall (P_3:((pname->Prop)->Prop)) (F_17:(pname->Prop)), ((finite_finite_pname F_17)->((P_3 bot_bot_pname_o)->((forall (X_1:pname) (F_2:(pname->Prop)), ((finite_finite_pname F_2)->((((member_pname X_1) F_2)->False)->((P_3 F_2)->(P_3 ((insert_pname X_1) F_2))))))->(P_3 F_17))))) of role axiom named fact_690_finite__induct % A new axiom: (forall (P_3:((pname->Prop)->Prop)) (F_17:(pname->Prop)), ((finite_finite_pname F_17)->((P_3 bot_bot_pname_o)->((forall (X_1:pname) (F_2:(pname->Prop)), ((finite_finite_pname F_2)->((((member_pname X_1) F_2)->False)->((P_3 F_2)->(P_3 ((insert_pname X_1) F_2))))))->(P_3 F_17))))) % FOF formula (forall (A_36:(x_a->Prop)), ((iff (finite_finite_a A_36)) ((or (((eq (x_a->Prop)) A_36) bot_bot_a_o)) ((ex (x_a->Prop)) (fun (A_38:(x_a->Prop))=> ((ex x_a) (fun (A_37:x_a)=> ((and (((eq (x_a->Prop)) A_36) ((insert_a A_37) A_38))) (finite_finite_a A_38))))))))) of role axiom named fact_691_finite_Osimps % A new axiom: (forall (A_36:(x_a->Prop)), ((iff (finite_finite_a A_36)) ((or (((eq (x_a->Prop)) A_36) bot_bot_a_o)) ((ex (x_a->Prop)) (fun (A_38:(x_a->Prop))=> ((ex x_a) (fun (A_37:x_a)=> ((and (((eq (x_a->Prop)) A_36) ((insert_a A_37) A_38))) (finite_finite_a A_38))))))))) % FOF formula (forall (A_36:(int->Prop)), ((iff (finite_finite_int A_36)) ((or (((eq (int->Prop)) A_36) bot_bot_int_o)) ((ex (int->Prop)) (fun (A_38:(int->Prop))=> ((ex int) (fun (A_37:int)=> ((and (((eq (int->Prop)) A_36) ((insert_int A_37) A_38))) (finite_finite_int A_38))))))))) of role axiom named fact_692_finite_Osimps % A new axiom: (forall (A_36:(int->Prop)), ((iff (finite_finite_int A_36)) ((or (((eq (int->Prop)) A_36) bot_bot_int_o)) ((ex (int->Prop)) (fun (A_38:(int->Prop))=> ((ex int) (fun (A_37:int)=> ((and (((eq (int->Prop)) A_36) ((insert_int A_37) A_38))) (finite_finite_int A_38))))))))) % FOF formula (forall (A_36:(nat->Prop)), ((iff (finite_finite_nat A_36)) ((or (((eq (nat->Prop)) A_36) bot_bot_nat_o)) ((ex (nat->Prop)) (fun (A_38:(nat->Prop))=> ((ex nat) (fun (A_37:nat)=> ((and (((eq (nat->Prop)) A_36) ((insert_nat A_37) A_38))) (finite_finite_nat A_38))))))))) of role axiom named fact_693_finite_Osimps % A new axiom: (forall (A_36:(nat->Prop)), ((iff (finite_finite_nat A_36)) ((or (((eq (nat->Prop)) A_36) bot_bot_nat_o)) ((ex (nat->Prop)) (fun (A_38:(nat->Prop))=> ((ex nat) (fun (A_37:nat)=> ((and (((eq (nat->Prop)) A_36) ((insert_nat A_37) A_38))) (finite_finite_nat A_38))))))))) % FOF formula (forall (A_36:(pname->Prop)), ((iff (finite_finite_pname A_36)) ((or (((eq (pname->Prop)) A_36) bot_bot_pname_o)) ((ex (pname->Prop)) (fun (A_38:(pname->Prop))=> ((ex pname) (fun (A_37:pname)=> ((and (((eq (pname->Prop)) A_36) ((insert_pname A_37) A_38))) (finite_finite_pname A_38))))))))) of role axiom named fact_694_finite_Osimps % A new axiom: (forall (A_36:(pname->Prop)), ((iff (finite_finite_pname A_36)) ((or (((eq (pname->Prop)) A_36) bot_bot_pname_o)) ((ex (pname->Prop)) (fun (A_38:(pname->Prop))=> ((ex pname) (fun (A_37:pname)=> ((and (((eq (pname->Prop)) A_36) ((insert_pname A_37) A_38))) (finite_finite_pname A_38))))))))) % FOF formula (forall (U:nat) (F:(nat->nat)), ((forall (N_1:nat), ((ord_less_eq_nat N_1) (F N_1)))->(finite_finite_nat (collect_nat (fun (N_1:nat)=> ((ord_less_eq_nat (F N_1)) U)))))) of role axiom named fact_695_finite__less__ub % A new axiom: (forall (U:nat) (F:(nat->nat)), ((forall (N_1:nat), ((ord_less_eq_nat N_1) (F N_1)))->(finite_finite_nat (collect_nat (fun (N_1:nat)=> ((ord_less_eq_nat (F N_1)) U)))))) % FOF formula (forall (X_13:x_a), (((eq x_a) (the_elem_a ((insert_a X_13) bot_bot_a_o))) X_13)) of role axiom named fact_696_the__elem__eq % A new axiom: (forall (X_13:x_a), (((eq x_a) (the_elem_a ((insert_a X_13) bot_bot_a_o))) X_13)) % FOF formula (forall (X_13:nat), (((eq nat) (the_elem_nat ((insert_nat X_13) bot_bot_nat_o))) X_13)) of role axiom named fact_697_the__elem__eq % A new axiom: (forall (X_13:nat), (((eq nat) (the_elem_nat ((insert_nat X_13) bot_bot_nat_o))) X_13)) % FOF formula (forall (X_13:int), (((eq int) (the_elem_int ((insert_int X_13) bot_bot_int_o))) X_13)) of role axiom named fact_698_the__elem__eq % A new axiom: (forall (X_13:int), (((eq int) (the_elem_int ((insert_int X_13) bot_bot_int_o))) X_13)) % FOF formula (forall (A_35:(x_a->Prop)), ((iff (not (((eq (x_a->Prop)) A_35) bot_bot_a_o))) ((ex x_a) (fun (X_1:x_a)=> ((ex (x_a->Prop)) (fun (B_26:(x_a->Prop))=> ((and (((eq (x_a->Prop)) A_35) ((insert_a X_1) B_26))) (((member_a X_1) B_26)->False)))))))) of role axiom named fact_699_nonempty__iff % A new axiom: (forall (A_35:(x_a->Prop)), ((iff (not (((eq (x_a->Prop)) A_35) bot_bot_a_o))) ((ex x_a) (fun (X_1:x_a)=> ((ex (x_a->Prop)) (fun (B_26:(x_a->Prop))=> ((and (((eq (x_a->Prop)) A_35) ((insert_a X_1) B_26))) (((member_a X_1) B_26)->False)))))))) % FOF formula (forall (A_35:(int->Prop)), ((iff (not (((eq (int->Prop)) A_35) bot_bot_int_o))) ((ex int) (fun (X_1:int)=> ((ex (int->Prop)) (fun (B_26:(int->Prop))=> ((and (((eq (int->Prop)) A_35) ((insert_int X_1) B_26))) (((member_int X_1) B_26)->False)))))))) of role axiom named fact_700_nonempty__iff % A new axiom: (forall (A_35:(int->Prop)), ((iff (not (((eq (int->Prop)) A_35) bot_bot_int_o))) ((ex int) (fun (X_1:int)=> ((ex (int->Prop)) (fun (B_26:(int->Prop))=> ((and (((eq (int->Prop)) A_35) ((insert_int X_1) B_26))) (((member_int X_1) B_26)->False)))))))) % FOF formula (forall (A_35:(nat->Prop)), ((iff (not (((eq (nat->Prop)) A_35) bot_bot_nat_o))) ((ex nat) (fun (X_1:nat)=> ((ex (nat->Prop)) (fun (B_26:(nat->Prop))=> ((and (((eq (nat->Prop)) A_35) ((insert_nat X_1) B_26))) (((member_nat X_1) B_26)->False)))))))) of role axiom named fact_701_nonempty__iff % A new axiom: (forall (A_35:(nat->Prop)), ((iff (not (((eq (nat->Prop)) A_35) bot_bot_nat_o))) ((ex nat) (fun (X_1:nat)=> ((ex (nat->Prop)) (fun (B_26:(nat->Prop))=> ((and (((eq (nat->Prop)) A_35) ((insert_nat X_1) B_26))) (((member_nat X_1) B_26)->False)))))))) % FOF formula (forall (A_35:(pname->Prop)), ((iff (not (((eq (pname->Prop)) A_35) bot_bot_pname_o))) ((ex pname) (fun (X_1:pname)=> ((ex (pname->Prop)) (fun (B_26:(pname->Prop))=> ((and (((eq (pname->Prop)) A_35) ((insert_pname X_1) B_26))) (((member_pname X_1) B_26)->False)))))))) of role axiom named fact_702_nonempty__iff % A new axiom: (forall (A_35:(pname->Prop)), ((iff (not (((eq (pname->Prop)) A_35) bot_bot_pname_o))) ((ex pname) (fun (X_1:pname)=> ((ex (pname->Prop)) (fun (B_26:(pname->Prop))=> ((and (((eq (pname->Prop)) A_35) ((insert_pname X_1) B_26))) (((member_pname X_1) B_26)->False)))))))) % FOF formula (forall (Pn:pname), (((member_pname Pn) u)->(wt (the_com (body Pn))))) of role axiom named fact_703_assms_I4_J % A new axiom: (forall (Pn:pname), (((member_pname Pn) u)->(wt (the_com (body Pn))))) % FOF formula (forall (C_18:int) (A_34:(int->Prop)) (B_25:(int->Prop)), (((member_int C_18) ((minus_minus_int_o A_34) B_25))->((((member_int C_18) A_34)->((member_int C_18) B_25))->False))) of role axiom named fact_704_DiffE % A new axiom: (forall (C_18:int) (A_34:(int->Prop)) (B_25:(int->Prop)), (((member_int C_18) ((minus_minus_int_o A_34) B_25))->((((member_int C_18) A_34)->((member_int C_18) B_25))->False))) % FOF formula (forall (C_18:nat) (A_34:(nat->Prop)) (B_25:(nat->Prop)), (((member_nat C_18) ((minus_minus_nat_o A_34) B_25))->((((member_nat C_18) A_34)->((member_nat C_18) B_25))->False))) of role axiom named fact_705_DiffE % A new axiom: (forall (C_18:nat) (A_34:(nat->Prop)) (B_25:(nat->Prop)), (((member_nat C_18) ((minus_minus_nat_o A_34) B_25))->((((member_nat C_18) A_34)->((member_nat C_18) B_25))->False))) % FOF formula (forall (C_18:x_a) (A_34:(x_a->Prop)) (B_25:(x_a->Prop)), (((member_a C_18) ((minus_minus_a_o A_34) B_25))->((((member_a C_18) A_34)->((member_a C_18) B_25))->False))) of role axiom named fact_706_DiffE % A new axiom: (forall (C_18:x_a) (A_34:(x_a->Prop)) (B_25:(x_a->Prop)), (((member_a C_18) ((minus_minus_a_o A_34) B_25))->((((member_a C_18) A_34)->((member_a C_18) B_25))->False))) % FOF formula (forall (C_18:pname) (A_34:(pname->Prop)) (B_25:(pname->Prop)), (((member_pname C_18) ((minus_minus_pname_o A_34) B_25))->((((member_pname C_18) A_34)->((member_pname C_18) B_25))->False))) of role axiom named fact_707_DiffE % A new axiom: (forall (C_18:pname) (A_34:(pname->Prop)) (B_25:(pname->Prop)), (((member_pname C_18) ((minus_minus_pname_o A_34) B_25))->((((member_pname C_18) A_34)->((member_pname C_18) B_25))->False))) % FOF formula (forall (B_24:(int->Prop)) (C_17:int) (A_33:(int->Prop)), (((member_int C_17) A_33)->((((member_int C_17) B_24)->False)->((member_int C_17) ((minus_minus_int_o A_33) B_24))))) of role axiom named fact_708_DiffI % A new axiom: (forall (B_24:(int->Prop)) (C_17:int) (A_33:(int->Prop)), (((member_int C_17) A_33)->((((member_int C_17) B_24)->False)->((member_int C_17) ((minus_minus_int_o A_33) B_24))))) % FOF formula (forall (B_24:(nat->Prop)) (C_17:nat) (A_33:(nat->Prop)), (((member_nat C_17) A_33)->((((member_nat C_17) B_24)->False)->((member_nat C_17) ((minus_minus_nat_o A_33) B_24))))) of role axiom named fact_709_DiffI % A new axiom: (forall (B_24:(nat->Prop)) (C_17:nat) (A_33:(nat->Prop)), (((member_nat C_17) A_33)->((((member_nat C_17) B_24)->False)->((member_nat C_17) ((minus_minus_nat_o A_33) B_24))))) % FOF formula (forall (B_24:(x_a->Prop)) (C_17:x_a) (A_33:(x_a->Prop)), (((member_a C_17) A_33)->((((member_a C_17) B_24)->False)->((member_a C_17) ((minus_minus_a_o A_33) B_24))))) of role axiom named fact_710_DiffI % A new axiom: (forall (B_24:(x_a->Prop)) (C_17:x_a) (A_33:(x_a->Prop)), (((member_a C_17) A_33)->((((member_a C_17) B_24)->False)->((member_a C_17) ((minus_minus_a_o A_33) B_24))))) % FOF formula (forall (B_24:(pname->Prop)) (C_17:pname) (A_33:(pname->Prop)), (((member_pname C_17) A_33)->((((member_pname C_17) B_24)->False)->((member_pname C_17) ((minus_minus_pname_o A_33) B_24))))) of role axiom named fact_711_DiffI % A new axiom: (forall (B_24:(pname->Prop)) (C_17:pname) (A_33:(pname->Prop)), (((member_pname C_17) A_33)->((((member_pname C_17) B_24)->False)->((member_pname C_17) ((minus_minus_pname_o A_33) B_24))))) % FOF formula (forall (C_16:int) (A_32:(int->Prop)) (B_23:(int->Prop)), (((member_int C_16) ((minus_minus_int_o A_32) B_23))->(((member_int C_16) B_23)->False))) of role axiom named fact_712_DiffD2 % A new axiom: (forall (C_16:int) (A_32:(int->Prop)) (B_23:(int->Prop)), (((member_int C_16) ((minus_minus_int_o A_32) B_23))->(((member_int C_16) B_23)->False))) % FOF formula (forall (C_16:nat) (A_32:(nat->Prop)) (B_23:(nat->Prop)), (((member_nat C_16) ((minus_minus_nat_o A_32) B_23))->(((member_nat C_16) B_23)->False))) of role axiom named fact_713_DiffD2 % A new axiom: (forall (C_16:nat) (A_32:(nat->Prop)) (B_23:(nat->Prop)), (((member_nat C_16) ((minus_minus_nat_o A_32) B_23))->(((member_nat C_16) B_23)->False))) % FOF formula (forall (C_16:x_a) (A_32:(x_a->Prop)) (B_23:(x_a->Prop)), (((member_a C_16) ((minus_minus_a_o A_32) B_23))->(((member_a C_16) B_23)->False))) of role axiom named fact_714_DiffD2 % A new axiom: (forall (C_16:x_a) (A_32:(x_a->Prop)) (B_23:(x_a->Prop)), (((member_a C_16) ((minus_minus_a_o A_32) B_23))->(((member_a C_16) B_23)->False))) % FOF formula (forall (C_16:pname) (A_32:(pname->Prop)) (B_23:(pname->Prop)), (((member_pname C_16) ((minus_minus_pname_o A_32) B_23))->(((member_pname C_16) B_23)->False))) of role axiom named fact_715_DiffD2 % A new axiom: (forall (C_16:pname) (A_32:(pname->Prop)) (B_23:(pname->Prop)), (((member_pname C_16) ((minus_minus_pname_o A_32) B_23))->(((member_pname C_16) B_23)->False))) % FOF formula (forall (C_15:int) (A_31:(int->Prop)) (B_22:(int->Prop)), (((member_int C_15) ((minus_minus_int_o A_31) B_22))->((member_int C_15) A_31))) of role axiom named fact_716_DiffD1 % A new axiom: (forall (C_15:int) (A_31:(int->Prop)) (B_22:(int->Prop)), (((member_int C_15) ((minus_minus_int_o A_31) B_22))->((member_int C_15) A_31))) % FOF formula (forall (C_15:nat) (A_31:(nat->Prop)) (B_22:(nat->Prop)), (((member_nat C_15) ((minus_minus_nat_o A_31) B_22))->((member_nat C_15) A_31))) of role axiom named fact_717_DiffD1 % A new axiom: (forall (C_15:nat) (A_31:(nat->Prop)) (B_22:(nat->Prop)), (((member_nat C_15) ((minus_minus_nat_o A_31) B_22))->((member_nat C_15) A_31))) % FOF formula (forall (C_15:x_a) (A_31:(x_a->Prop)) (B_22:(x_a->Prop)), (((member_a C_15) ((minus_minus_a_o A_31) B_22))->((member_a C_15) A_31))) of role axiom named fact_718_DiffD1 % A new axiom: (forall (C_15:x_a) (A_31:(x_a->Prop)) (B_22:(x_a->Prop)), (((member_a C_15) ((minus_minus_a_o A_31) B_22))->((member_a C_15) A_31))) % FOF formula (forall (C_15:pname) (A_31:(pname->Prop)) (B_22:(pname->Prop)), (((member_pname C_15) ((minus_minus_pname_o A_31) B_22))->((member_pname C_15) A_31))) of role axiom named fact_719_DiffD1 % A new axiom: (forall (C_15:pname) (A_31:(pname->Prop)) (B_22:(pname->Prop)), (((member_pname C_15) ((minus_minus_pname_o A_31) B_22))->((member_pname C_15) A_31))) % FOF formula (forall (C_14:int) (A_30:(int->Prop)) (B_21:(int->Prop)), ((iff ((member_int C_14) ((minus_minus_int_o A_30) B_21))) ((and ((member_int C_14) A_30)) (((member_int C_14) B_21)->False)))) of role axiom named fact_720_Diff__iff % A new axiom: (forall (C_14:int) (A_30:(int->Prop)) (B_21:(int->Prop)), ((iff ((member_int C_14) ((minus_minus_int_o A_30) B_21))) ((and ((member_int C_14) A_30)) (((member_int C_14) B_21)->False)))) % FOF formula (forall (C_14:nat) (A_30:(nat->Prop)) (B_21:(nat->Prop)), ((iff ((member_nat C_14) ((minus_minus_nat_o A_30) B_21))) ((and ((member_nat C_14) A_30)) (((member_nat C_14) B_21)->False)))) of role axiom named fact_721_Diff__iff % A new axiom: (forall (C_14:nat) (A_30:(nat->Prop)) (B_21:(nat->Prop)), ((iff ((member_nat C_14) ((minus_minus_nat_o A_30) B_21))) ((and ((member_nat C_14) A_30)) (((member_nat C_14) B_21)->False)))) % FOF formula (forall (C_14:x_a) (A_30:(x_a->Prop)) (B_21:(x_a->Prop)), ((iff ((member_a C_14) ((minus_minus_a_o A_30) B_21))) ((and ((member_a C_14) A_30)) (((member_a C_14) B_21)->False)))) of role axiom named fact_722_Diff__iff % A new axiom: (forall (C_14:x_a) (A_30:(x_a->Prop)) (B_21:(x_a->Prop)), ((iff ((member_a C_14) ((minus_minus_a_o A_30) B_21))) ((and ((member_a C_14) A_30)) (((member_a C_14) B_21)->False)))) % FOF formula (forall (C_14:pname) (A_30:(pname->Prop)) (B_21:(pname->Prop)), ((iff ((member_pname C_14) ((minus_minus_pname_o A_30) B_21))) ((and ((member_pname C_14) A_30)) (((member_pname C_14) B_21)->False)))) of role axiom named fact_723_Diff__iff % A new axiom: (forall (C_14:pname) (A_30:(pname->Prop)) (B_21:(pname->Prop)), ((iff ((member_pname C_14) ((minus_minus_pname_o A_30) B_21))) ((and ((member_pname C_14) A_30)) (((member_pname C_14) B_21)->False)))) % FOF formula (forall (A_29:(int->Prop)) (B_20:(int->Prop)), (((eq (int->Prop)) ((minus_minus_int_o A_29) B_20)) (collect_int (fun (X_1:int)=> ((and ((member_int X_1) A_29)) (not ((member_int X_1) B_20))))))) of role axiom named fact_724_set__diff__eq % A new axiom: (forall (A_29:(int->Prop)) (B_20:(int->Prop)), (((eq (int->Prop)) ((minus_minus_int_o A_29) B_20)) (collect_int (fun (X_1:int)=> ((and ((member_int X_1) A_29)) (not ((member_int X_1) B_20))))))) % FOF formula (forall (A_29:(nat->Prop)) (B_20:(nat->Prop)), (((eq (nat->Prop)) ((minus_minus_nat_o A_29) B_20)) (collect_nat (fun (X_1:nat)=> ((and ((member_nat X_1) A_29)) (not ((member_nat X_1) B_20))))))) of role axiom named fact_725_set__diff__eq % A new axiom: (forall (A_29:(nat->Prop)) (B_20:(nat->Prop)), (((eq (nat->Prop)) ((minus_minus_nat_o A_29) B_20)) (collect_nat (fun (X_1:nat)=> ((and ((member_nat X_1) A_29)) (not ((member_nat X_1) B_20))))))) % FOF formula (forall (A_29:(x_a->Prop)) (B_20:(x_a->Prop)), (((eq (x_a->Prop)) ((minus_minus_a_o A_29) B_20)) (collect_a (fun (X_1:x_a)=> ((and ((member_a X_1) A_29)) (not ((member_a X_1) B_20))))))) of role axiom named fact_726_set__diff__eq % A new axiom: (forall (A_29:(x_a->Prop)) (B_20:(x_a->Prop)), (((eq (x_a->Prop)) ((minus_minus_a_o A_29) B_20)) (collect_a (fun (X_1:x_a)=> ((and ((member_a X_1) A_29)) (not ((member_a X_1) B_20))))))) % FOF formula (forall (A_29:(pname->Prop)) (B_20:(pname->Prop)), (((eq (pname->Prop)) ((minus_minus_pname_o A_29) B_20)) (collect_pname (fun (X_1:pname)=> ((and ((member_pname X_1) A_29)) (not ((member_pname X_1) B_20))))))) of role axiom named fact_727_set__diff__eq % A new axiom: (forall (A_29:(pname->Prop)) (B_20:(pname->Prop)), (((eq (pname->Prop)) ((minus_minus_pname_o A_29) B_20)) (collect_pname (fun (X_1:pname)=> ((and ((member_pname X_1) A_29)) (not ((member_pname X_1) B_20))))))) % FOF formula (forall (X_12:x_a) (A_28:(x_a->Prop)) (F_16:(x_a->(x_a->x_a))) (F_15:((x_a->Prop)->x_a)), (((finite_folding_one_a F_16) F_15)->((finite_finite_a A_28)->((and ((((eq (x_a->Prop)) ((minus_minus_a_o A_28) ((insert_a X_12) bot_bot_a_o))) bot_bot_a_o)->(((eq x_a) (F_15 ((insert_a X_12) A_28))) X_12))) ((not (((eq (x_a->Prop)) ((minus_minus_a_o A_28) ((insert_a X_12) bot_bot_a_o))) bot_bot_a_o))->(((eq x_a) (F_15 ((insert_a X_12) A_28))) ((F_16 X_12) (F_15 ((minus_minus_a_o A_28) ((insert_a X_12) bot_bot_a_o)))))))))) of role axiom named fact_728_folding__one_Oinsert__remove % A new axiom: (forall (X_12:x_a) (A_28:(x_a->Prop)) (F_16:(x_a->(x_a->x_a))) (F_15:((x_a->Prop)->x_a)), (((finite_folding_one_a F_16) F_15)->((finite_finite_a A_28)->((and ((((eq (x_a->Prop)) ((minus_minus_a_o A_28) ((insert_a X_12) bot_bot_a_o))) bot_bot_a_o)->(((eq x_a) (F_15 ((insert_a X_12) A_28))) X_12))) ((not (((eq (x_a->Prop)) ((minus_minus_a_o A_28) ((insert_a X_12) bot_bot_a_o))) bot_bot_a_o))->(((eq x_a) (F_15 ((insert_a X_12) A_28))) ((F_16 X_12) (F_15 ((minus_minus_a_o A_28) ((insert_a X_12) bot_bot_a_o)))))))))) % FOF formula (forall (X_12:int) (A_28:(int->Prop)) (F_16:(int->(int->int))) (F_15:((int->Prop)->int)), (((finite1626084323ne_int F_16) F_15)->((finite_finite_int A_28)->((and ((((eq (int->Prop)) ((minus_minus_int_o A_28) ((insert_int X_12) bot_bot_int_o))) bot_bot_int_o)->(((eq int) (F_15 ((insert_int X_12) A_28))) X_12))) ((not (((eq (int->Prop)) ((minus_minus_int_o A_28) ((insert_int X_12) bot_bot_int_o))) bot_bot_int_o))->(((eq int) (F_15 ((insert_int X_12) A_28))) ((F_16 X_12) (F_15 ((minus_minus_int_o A_28) ((insert_int X_12) bot_bot_int_o)))))))))) of role axiom named fact_729_folding__one_Oinsert__remove % A new axiom: (forall (X_12:int) (A_28:(int->Prop)) (F_16:(int->(int->int))) (F_15:((int->Prop)->int)), (((finite1626084323ne_int F_16) F_15)->((finite_finite_int A_28)->((and ((((eq (int->Prop)) ((minus_minus_int_o A_28) ((insert_int X_12) bot_bot_int_o))) bot_bot_int_o)->(((eq int) (F_15 ((insert_int X_12) A_28))) X_12))) ((not (((eq (int->Prop)) ((minus_minus_int_o A_28) ((insert_int X_12) bot_bot_int_o))) bot_bot_int_o))->(((eq int) (F_15 ((insert_int X_12) A_28))) ((F_16 X_12) (F_15 ((minus_minus_int_o A_28) ((insert_int X_12) bot_bot_int_o)))))))))) % FOF formula (forall (X_12:nat) (A_28:(nat->Prop)) (F_16:(nat->(nat->nat))) (F_15:((nat->Prop)->nat)), (((finite988810631ne_nat F_16) F_15)->((finite_finite_nat A_28)->((and ((((eq (nat->Prop)) ((minus_minus_nat_o A_28) ((insert_nat X_12) bot_bot_nat_o))) bot_bot_nat_o)->(((eq nat) (F_15 ((insert_nat X_12) A_28))) X_12))) ((not (((eq (nat->Prop)) ((minus_minus_nat_o A_28) ((insert_nat X_12) bot_bot_nat_o))) bot_bot_nat_o))->(((eq nat) (F_15 ((insert_nat X_12) A_28))) ((F_16 X_12) (F_15 ((minus_minus_nat_o A_28) ((insert_nat X_12) bot_bot_nat_o)))))))))) of role axiom named fact_730_folding__one_Oinsert__remove % A new axiom: (forall (X_12:nat) (A_28:(nat->Prop)) (F_16:(nat->(nat->nat))) (F_15:((nat->Prop)->nat)), (((finite988810631ne_nat F_16) F_15)->((finite_finite_nat A_28)->((and ((((eq (nat->Prop)) ((minus_minus_nat_o A_28) ((insert_nat X_12) bot_bot_nat_o))) bot_bot_nat_o)->(((eq nat) (F_15 ((insert_nat X_12) A_28))) X_12))) ((not (((eq (nat->Prop)) ((minus_minus_nat_o A_28) ((insert_nat X_12) bot_bot_nat_o))) bot_bot_nat_o))->(((eq nat) (F_15 ((insert_nat X_12) A_28))) ((F_16 X_12) (F_15 ((minus_minus_nat_o A_28) ((insert_nat X_12) bot_bot_nat_o)))))))))) % FOF formula (forall (X_12:pname) (A_28:(pname->Prop)) (F_16:(pname->(pname->pname))) (F_15:((pname->Prop)->pname)), (((finite1282449217_pname F_16) F_15)->((finite_finite_pname A_28)->((and ((((eq (pname->Prop)) ((minus_minus_pname_o A_28) ((insert_pname X_12) bot_bot_pname_o))) bot_bot_pname_o)->(((eq pname) (F_15 ((insert_pname X_12) A_28))) X_12))) ((not (((eq (pname->Prop)) ((minus_minus_pname_o A_28) ((insert_pname X_12) bot_bot_pname_o))) bot_bot_pname_o))->(((eq pname) (F_15 ((insert_pname X_12) A_28))) ((F_16 X_12) (F_15 ((minus_minus_pname_o A_28) ((insert_pname X_12) bot_bot_pname_o)))))))))) of role axiom named fact_731_folding__one_Oinsert__remove % A new axiom: (forall (X_12:pname) (A_28:(pname->Prop)) (F_16:(pname->(pname->pname))) (F_15:((pname->Prop)->pname)), (((finite1282449217_pname F_16) F_15)->((finite_finite_pname A_28)->((and ((((eq (pname->Prop)) ((minus_minus_pname_o A_28) ((insert_pname X_12) bot_bot_pname_o))) bot_bot_pname_o)->(((eq pname) (F_15 ((insert_pname X_12) A_28))) X_12))) ((not (((eq (pname->Prop)) ((minus_minus_pname_o A_28) ((insert_pname X_12) bot_bot_pname_o))) bot_bot_pname_o))->(((eq pname) (F_15 ((insert_pname X_12) A_28))) ((F_16 X_12) (F_15 ((minus_minus_pname_o A_28) ((insert_pname X_12) bot_bot_pname_o)))))))))) % FOF formula (forall (X_11:x_a) (A_27:(x_a->Prop)) (F_14:(x_a->(x_a->x_a))) (F_13:((x_a->Prop)->x_a)), (((finite_folding_one_a F_14) F_13)->((finite_finite_a A_27)->(((member_a X_11) A_27)->((and ((((eq (x_a->Prop)) ((minus_minus_a_o A_27) ((insert_a X_11) bot_bot_a_o))) bot_bot_a_o)->(((eq x_a) (F_13 A_27)) X_11))) ((not (((eq (x_a->Prop)) ((minus_minus_a_o A_27) ((insert_a X_11) bot_bot_a_o))) bot_bot_a_o))->(((eq x_a) (F_13 A_27)) ((F_14 X_11) (F_13 ((minus_minus_a_o A_27) ((insert_a X_11) bot_bot_a_o))))))))))) of role axiom named fact_732_folding__one_Oremove % A new axiom: (forall (X_11:x_a) (A_27:(x_a->Prop)) (F_14:(x_a->(x_a->x_a))) (F_13:((x_a->Prop)->x_a)), (((finite_folding_one_a F_14) F_13)->((finite_finite_a A_27)->(((member_a X_11) A_27)->((and ((((eq (x_a->Prop)) ((minus_minus_a_o A_27) ((insert_a X_11) bot_bot_a_o))) bot_bot_a_o)->(((eq x_a) (F_13 A_27)) X_11))) ((not (((eq (x_a->Prop)) ((minus_minus_a_o A_27) ((insert_a X_11) bot_bot_a_o))) bot_bot_a_o))->(((eq x_a) (F_13 A_27)) ((F_14 X_11) (F_13 ((minus_minus_a_o A_27) ((insert_a X_11) bot_bot_a_o))))))))))) % FOF formula (forall (X_11:int) (A_27:(int->Prop)) (F_14:(int->(int->int))) (F_13:((int->Prop)->int)), (((finite1626084323ne_int F_14) F_13)->((finite_finite_int A_27)->(((member_int X_11) A_27)->((and ((((eq (int->Prop)) ((minus_minus_int_o A_27) ((insert_int X_11) bot_bot_int_o))) bot_bot_int_o)->(((eq int) (F_13 A_27)) X_11))) ((not (((eq (int->Prop)) ((minus_minus_int_o A_27) ((insert_int X_11) bot_bot_int_o))) bot_bot_int_o))->(((eq int) (F_13 A_27)) ((F_14 X_11) (F_13 ((minus_minus_int_o A_27) ((insert_int X_11) bot_bot_int_o))))))))))) of role axiom named fact_733_folding__one_Oremove % A new axiom: (forall (X_11:int) (A_27:(int->Prop)) (F_14:(int->(int->int))) (F_13:((int->Prop)->int)), (((finite1626084323ne_int F_14) F_13)->((finite_finite_int A_27)->(((member_int X_11) A_27)->((and ((((eq (int->Prop)) ((minus_minus_int_o A_27) ((insert_int X_11) bot_bot_int_o))) bot_bot_int_o)->(((eq int) (F_13 A_27)) X_11))) ((not (((eq (int->Prop)) ((minus_minus_int_o A_27) ((insert_int X_11) bot_bot_int_o))) bot_bot_int_o))->(((eq int) (F_13 A_27)) ((F_14 X_11) (F_13 ((minus_minus_int_o A_27) ((insert_int X_11) bot_bot_int_o))))))))))) % FOF formula (forall (X_11:nat) (A_27:(nat->Prop)) (F_14:(nat->(nat->nat))) (F_13:((nat->Prop)->nat)), (((finite988810631ne_nat F_14) F_13)->((finite_finite_nat A_27)->(((member_nat X_11) A_27)->((and ((((eq (nat->Prop)) ((minus_minus_nat_o A_27) ((insert_nat X_11) bot_bot_nat_o))) bot_bot_nat_o)->(((eq nat) (F_13 A_27)) X_11))) ((not (((eq (nat->Prop)) ((minus_minus_nat_o A_27) ((insert_nat X_11) bot_bot_nat_o))) bot_bot_nat_o))->(((eq nat) (F_13 A_27)) ((F_14 X_11) (F_13 ((minus_minus_nat_o A_27) ((insert_nat X_11) bot_bot_nat_o))))))))))) of role axiom named fact_734_folding__one_Oremove % A new axiom: (forall (X_11:nat) (A_27:(nat->Prop)) (F_14:(nat->(nat->nat))) (F_13:((nat->Prop)->nat)), (((finite988810631ne_nat F_14) F_13)->((finite_finite_nat A_27)->(((member_nat X_11) A_27)->((and ((((eq (nat->Prop)) ((minus_minus_nat_o A_27) ((insert_nat X_11) bot_bot_nat_o))) bot_bot_nat_o)->(((eq nat) (F_13 A_27)) X_11))) ((not (((eq (nat->Prop)) ((minus_minus_nat_o A_27) ((insert_nat X_11) bot_bot_nat_o))) bot_bot_nat_o))->(((eq nat) (F_13 A_27)) ((F_14 X_11) (F_13 ((minus_minus_nat_o A_27) ((insert_nat X_11) bot_bot_nat_o))))))))))) % FOF formula (forall (X_11:pname) (A_27:(pname->Prop)) (F_14:(pname->(pname->pname))) (F_13:((pname->Prop)->pname)), (((finite1282449217_pname F_14) F_13)->((finite_finite_pname A_27)->(((member_pname X_11) A_27)->((and ((((eq (pname->Prop)) ((minus_minus_pname_o A_27) ((insert_pname X_11) bot_bot_pname_o))) bot_bot_pname_o)->(((eq pname) (F_13 A_27)) X_11))) ((not (((eq (pname->Prop)) ((minus_minus_pname_o A_27) ((insert_pname X_11) bot_bot_pname_o))) bot_bot_pname_o))->(((eq pname) (F_13 A_27)) ((F_14 X_11) (F_13 ((minus_minus_pname_o A_27) ((insert_pname X_11) bot_bot_pname_o))))))))))) of role axiom named fact_735_folding__one_Oremove % A new axiom: (forall (X_11:pname) (A_27:(pname->Prop)) (F_14:(pname->(pname->pname))) (F_13:((pname->Prop)->pname)), (((finite1282449217_pname F_14) F_13)->((finite_finite_pname A_27)->(((member_pname X_11) A_27)->((and ((((eq (pname->Prop)) ((minus_minus_pname_o A_27) ((insert_pname X_11) bot_bot_pname_o))) bot_bot_pname_o)->(((eq pname) (F_13 A_27)) X_11))) ((not (((eq (pname->Prop)) ((minus_minus_pname_o A_27) ((insert_pname X_11) bot_bot_pname_o))) bot_bot_pname_o))->(((eq pname) (F_13 A_27)) ((F_14 X_11) (F_13 ((minus_minus_pname_o A_27) ((insert_pname X_11) bot_bot_pname_o))))))))))) % FOF formula (forall (X_10:x_a) (A_26:(x_a->Prop)), ((finite_finite_a A_26)->((and (((member_a X_10) A_26)->(((eq nat) (finite_card_a ((minus_minus_a_o A_26) ((insert_a X_10) bot_bot_a_o)))) ((minus_minus_nat (finite_card_a A_26)) one_one_nat)))) ((((member_a X_10) A_26)->False)->(((eq nat) (finite_card_a ((minus_minus_a_o A_26) ((insert_a X_10) bot_bot_a_o)))) (finite_card_a A_26)))))) of role axiom named fact_736_card__Diff__singleton__if % A new axiom: (forall (X_10:x_a) (A_26:(x_a->Prop)), ((finite_finite_a A_26)->((and (((member_a X_10) A_26)->(((eq nat) (finite_card_a ((minus_minus_a_o A_26) ((insert_a X_10) bot_bot_a_o)))) ((minus_minus_nat (finite_card_a A_26)) one_one_nat)))) ((((member_a X_10) A_26)->False)->(((eq nat) (finite_card_a ((minus_minus_a_o A_26) ((insert_a X_10) bot_bot_a_o)))) (finite_card_a A_26)))))) % FOF formula (forall (X_10:int) (A_26:(int->Prop)), ((finite_finite_int A_26)->((and (((member_int X_10) A_26)->(((eq nat) (finite_card_int ((minus_minus_int_o A_26) ((insert_int X_10) bot_bot_int_o)))) ((minus_minus_nat (finite_card_int A_26)) one_one_nat)))) ((((member_int X_10) A_26)->False)->(((eq nat) (finite_card_int ((minus_minus_int_o A_26) ((insert_int X_10) bot_bot_int_o)))) (finite_card_int A_26)))))) of role axiom named fact_737_card__Diff__singleton__if % A new axiom: (forall (X_10:int) (A_26:(int->Prop)), ((finite_finite_int A_26)->((and (((member_int X_10) A_26)->(((eq nat) (finite_card_int ((minus_minus_int_o A_26) ((insert_int X_10) bot_bot_int_o)))) ((minus_minus_nat (finite_card_int A_26)) one_one_nat)))) ((((member_int X_10) A_26)->False)->(((eq nat) (finite_card_int ((minus_minus_int_o A_26) ((insert_int X_10) bot_bot_int_o)))) (finite_card_int A_26)))))) % FOF formula (forall (X_10:nat) (A_26:(nat->Prop)), ((finite_finite_nat A_26)->((and (((member_nat X_10) A_26)->(((eq nat) (finite_card_nat ((minus_minus_nat_o A_26) ((insert_nat X_10) bot_bot_nat_o)))) ((minus_minus_nat (finite_card_nat A_26)) one_one_nat)))) ((((member_nat X_10) A_26)->False)->(((eq nat) (finite_card_nat ((minus_minus_nat_o A_26) ((insert_nat X_10) bot_bot_nat_o)))) (finite_card_nat A_26)))))) of role axiom named fact_738_card__Diff__singleton__if % A new axiom: (forall (X_10:nat) (A_26:(nat->Prop)), ((finite_finite_nat A_26)->((and (((member_nat X_10) A_26)->(((eq nat) (finite_card_nat ((minus_minus_nat_o A_26) ((insert_nat X_10) bot_bot_nat_o)))) ((minus_minus_nat (finite_card_nat A_26)) one_one_nat)))) ((((member_nat X_10) A_26)->False)->(((eq nat) (finite_card_nat ((minus_minus_nat_o A_26) ((insert_nat X_10) bot_bot_nat_o)))) (finite_card_nat A_26)))))) % FOF formula (forall (X_10:pname) (A_26:(pname->Prop)), ((finite_finite_pname A_26)->((and (((member_pname X_10) A_26)->(((eq nat) (finite_card_pname ((minus_minus_pname_o A_26) ((insert_pname X_10) bot_bot_pname_o)))) ((minus_minus_nat (finite_card_pname A_26)) one_one_nat)))) ((((member_pname X_10) A_26)->False)->(((eq nat) (finite_card_pname ((minus_minus_pname_o A_26) ((insert_pname X_10) bot_bot_pname_o)))) (finite_card_pname A_26)))))) of role axiom named fact_739_card__Diff__singleton__if % A new axiom: (forall (X_10:pname) (A_26:(pname->Prop)), ((finite_finite_pname A_26)->((and (((member_pname X_10) A_26)->(((eq nat) (finite_card_pname ((minus_minus_pname_o A_26) ((insert_pname X_10) bot_bot_pname_o)))) ((minus_minus_nat (finite_card_pname A_26)) one_one_nat)))) ((((member_pname X_10) A_26)->False)->(((eq nat) (finite_card_pname ((minus_minus_pname_o A_26) ((insert_pname X_10) bot_bot_pname_o)))) (finite_card_pname A_26)))))) % FOF formula (forall (X_9:x_a) (A_25:(x_a->Prop)), ((finite_finite_a A_25)->(((member_a X_9) A_25)->(((eq nat) (finite_card_a ((minus_minus_a_o A_25) ((insert_a X_9) bot_bot_a_o)))) ((minus_minus_nat (finite_card_a A_25)) one_one_nat))))) of role axiom named fact_740_card__Diff__singleton % A new axiom: (forall (X_9:x_a) (A_25:(x_a->Prop)), ((finite_finite_a A_25)->(((member_a X_9) A_25)->(((eq nat) (finite_card_a ((minus_minus_a_o A_25) ((insert_a X_9) bot_bot_a_o)))) ((minus_minus_nat (finite_card_a A_25)) one_one_nat))))) % FOF formula (forall (X_9:int) (A_25:(int->Prop)), ((finite_finite_int A_25)->(((member_int X_9) A_25)->(((eq nat) (finite_card_int ((minus_minus_int_o A_25) ((insert_int X_9) bot_bot_int_o)))) ((minus_minus_nat (finite_card_int A_25)) one_one_nat))))) of role axiom named fact_741_card__Diff__singleton % A new axiom: (forall (X_9:int) (A_25:(int->Prop)), ((finite_finite_int A_25)->(((member_int X_9) A_25)->(((eq nat) (finite_card_int ((minus_minus_int_o A_25) ((insert_int X_9) bot_bot_int_o)))) ((minus_minus_nat (finite_card_int A_25)) one_one_nat))))) % FOF formula (forall (X_9:nat) (A_25:(nat->Prop)), ((finite_finite_nat A_25)->(((member_nat X_9) A_25)->(((eq nat) (finite_card_nat ((minus_minus_nat_o A_25) ((insert_nat X_9) bot_bot_nat_o)))) ((minus_minus_nat (finite_card_nat A_25)) one_one_nat))))) of role axiom named fact_742_card__Diff__singleton % A new axiom: (forall (X_9:nat) (A_25:(nat->Prop)), ((finite_finite_nat A_25)->(((member_nat X_9) A_25)->(((eq nat) (finite_card_nat ((minus_minus_nat_o A_25) ((insert_nat X_9) bot_bot_nat_o)))) ((minus_minus_nat (finite_card_nat A_25)) one_one_nat))))) % FOF formula (forall (X_9:pname) (A_25:(pname->Prop)), ((finite_finite_pname A_25)->(((member_pname X_9) A_25)->(((eq nat) (finite_card_pname ((minus_minus_pname_o A_25) ((insert_pname X_9) bot_bot_pname_o)))) ((minus_minus_nat (finite_card_pname A_25)) one_one_nat))))) of role axiom named fact_743_card__Diff__singleton % A new axiom: (forall (X_9:pname) (A_25:(pname->Prop)), ((finite_finite_pname A_25)->(((member_pname X_9) A_25)->(((eq nat) (finite_card_pname ((minus_minus_pname_o A_25) ((insert_pname X_9) bot_bot_pname_o)))) ((minus_minus_nat (finite_card_pname A_25)) one_one_nat))))) % FOF formula (forall (X_8:int), ((iff (((eq int) one_one_int) X_8)) (((eq int) X_8) one_one_int))) of role axiom named fact_744_one__reorient % A new axiom: (forall (X_8:int), ((iff (((eq int) one_one_int) X_8)) (((eq int) X_8) one_one_int))) % FOF formula (forall (X_8:nat), ((iff (((eq nat) one_one_nat) X_8)) (((eq nat) X_8) one_one_nat))) of role axiom named fact_745_one__reorient % A new axiom: (forall (X_8:nat), ((iff (((eq nat) one_one_nat) X_8)) (((eq nat) X_8) one_one_nat))) % FOF formula (forall (N:nat), (((eq nat) ((minus_minus_nat (suc N)) one_one_nat)) N)) of role axiom named fact_746_diff__Suc__1 % A new axiom: (forall (N:nat), (((eq nat) ((minus_minus_nat (suc N)) one_one_nat)) N)) % FOF formula (forall (M:nat) (N:nat), (((eq nat) ((minus_minus_nat M) (suc N))) ((minus_minus_nat ((minus_minus_nat M) one_one_nat)) N))) of role axiom named fact_747_diff__Suc__eq__diff__pred % A new axiom: (forall (M:nat) (N:nat), (((eq nat) ((minus_minus_nat M) (suc N))) ((minus_minus_nat ((minus_minus_nat M) one_one_nat)) N))) % FOF formula (forall (X_7:x_a) (F_12:(x_a->(x_a->x_a))) (F_11:((x_a->Prop)->x_a)), (((finite_folding_one_a F_12) F_11)->(((eq x_a) (F_11 ((insert_a X_7) bot_bot_a_o))) X_7))) of role axiom named fact_748_folding__one_Osingleton % A new axiom: (forall (X_7:x_a) (F_12:(x_a->(x_a->x_a))) (F_11:((x_a->Prop)->x_a)), (((finite_folding_one_a F_12) F_11)->(((eq x_a) (F_11 ((insert_a X_7) bot_bot_a_o))) X_7))) % FOF formula (forall (X_7:nat) (F_12:(nat->(nat->nat))) (F_11:((nat->Prop)->nat)), (((finite988810631ne_nat F_12) F_11)->(((eq nat) (F_11 ((insert_nat X_7) bot_bot_nat_o))) X_7))) of role axiom named fact_749_folding__one_Osingleton % A new axiom: (forall (X_7:nat) (F_12:(nat->(nat->nat))) (F_11:((nat->Prop)->nat)), (((finite988810631ne_nat F_12) F_11)->(((eq nat) (F_11 ((insert_nat X_7) bot_bot_nat_o))) X_7))) % FOF formula (forall (X_7:int) (F_12:(int->(int->int))) (F_11:((int->Prop)->int)), (((finite1626084323ne_int F_12) F_11)->(((eq int) (F_11 ((insert_int X_7) bot_bot_int_o))) X_7))) of role axiom named fact_750_folding__one_Osingleton % A new axiom: (forall (X_7:int) (F_12:(int->(int->int))) (F_11:((int->Prop)->int)), (((finite1626084323ne_int F_12) F_11)->(((eq int) (F_11 ((insert_int X_7) bot_bot_int_o))) X_7))) % FOF formula (forall (B_19:(x_a->Prop)) (A_24:x_a) (A_23:(x_a->Prop)), ((finite_finite_a A_23)->(((member_a A_24) A_23)->((((member_a A_24) B_19)->False)->(((eq nat) (finite_card_a ((minus_minus_a_o A_23) ((insert_a A_24) B_19)))) ((minus_minus_nat (finite_card_a ((minus_minus_a_o A_23) B_19))) one_one_nat)))))) of role axiom named fact_751_card__Diff__insert % A new axiom: (forall (B_19:(x_a->Prop)) (A_24:x_a) (A_23:(x_a->Prop)), ((finite_finite_a A_23)->(((member_a A_24) A_23)->((((member_a A_24) B_19)->False)->(((eq nat) (finite_card_a ((minus_minus_a_o A_23) ((insert_a A_24) B_19)))) ((minus_minus_nat (finite_card_a ((minus_minus_a_o A_23) B_19))) one_one_nat)))))) % FOF formula (forall (B_19:(int->Prop)) (A_24:int) (A_23:(int->Prop)), ((finite_finite_int A_23)->(((member_int A_24) A_23)->((((member_int A_24) B_19)->False)->(((eq nat) (finite_card_int ((minus_minus_int_o A_23) ((insert_int A_24) B_19)))) ((minus_minus_nat (finite_card_int ((minus_minus_int_o A_23) B_19))) one_one_nat)))))) of role axiom named fact_752_card__Diff__insert % A new axiom: (forall (B_19:(int->Prop)) (A_24:int) (A_23:(int->Prop)), ((finite_finite_int A_23)->(((member_int A_24) A_23)->((((member_int A_24) B_19)->False)->(((eq nat) (finite_card_int ((minus_minus_int_o A_23) ((insert_int A_24) B_19)))) ((minus_minus_nat (finite_card_int ((minus_minus_int_o A_23) B_19))) one_one_nat)))))) % FOF formula (forall (B_19:(nat->Prop)) (A_24:nat) (A_23:(nat->Prop)), ((finite_finite_nat A_23)->(((member_nat A_24) A_23)->((((member_nat A_24) B_19)->False)->(((eq nat) (finite_card_nat ((minus_minus_nat_o A_23) ((insert_nat A_24) B_19)))) ((minus_minus_nat (finite_card_nat ((minus_minus_nat_o A_23) B_19))) one_one_nat)))))) of role axiom named fact_753_card__Diff__insert % A new axiom: (forall (B_19:(nat->Prop)) (A_24:nat) (A_23:(nat->Prop)), ((finite_finite_nat A_23)->(((member_nat A_24) A_23)->((((member_nat A_24) B_19)->False)->(((eq nat) (finite_card_nat ((minus_minus_nat_o A_23) ((insert_nat A_24) B_19)))) ((minus_minus_nat (finite_card_nat ((minus_minus_nat_o A_23) B_19))) one_one_nat)))))) % FOF formula (forall (B_19:(pname->Prop)) (A_24:pname) (A_23:(pname->Prop)), ((finite_finite_pname A_23)->(((member_pname A_24) A_23)->((((member_pname A_24) B_19)->False)->(((eq nat) (finite_card_pname ((minus_minus_pname_o A_23) ((insert_pname A_24) B_19)))) ((minus_minus_nat (finite_card_pname ((minus_minus_pname_o A_23) B_19))) one_one_nat)))))) of role axiom named fact_754_card__Diff__insert % A new axiom: (forall (B_19:(pname->Prop)) (A_24:pname) (A_23:(pname->Prop)), ((finite_finite_pname A_23)->(((member_pname A_24) A_23)->((((member_pname A_24) B_19)->False)->(((eq nat) (finite_card_pname ((minus_minus_pname_o A_23) ((insert_pname A_24) B_19)))) ((minus_minus_nat (finite_card_pname ((minus_minus_pname_o A_23) B_19))) one_one_nat)))))) % FOF formula (forall (X_6:x_a) (A_22:(x_a->Prop)) (F_10:(x_a->(x_a->x_a))) (F_9:((x_a->Prop)->x_a)), (((finite_folding_one_a F_10) F_9)->((finite_finite_a A_22)->((((member_a X_6) A_22)->False)->((not (((eq (x_a->Prop)) A_22) bot_bot_a_o))->(((eq x_a) (F_9 ((insert_a X_6) A_22))) ((F_10 X_6) (F_9 A_22)))))))) of role axiom named fact_755_folding__one_Oinsert % A new axiom: (forall (X_6:x_a) (A_22:(x_a->Prop)) (F_10:(x_a->(x_a->x_a))) (F_9:((x_a->Prop)->x_a)), (((finite_folding_one_a F_10) F_9)->((finite_finite_a A_22)->((((member_a X_6) A_22)->False)->((not (((eq (x_a->Prop)) A_22) bot_bot_a_o))->(((eq x_a) (F_9 ((insert_a X_6) A_22))) ((F_10 X_6) (F_9 A_22)))))))) % FOF formula (forall (X_6:int) (A_22:(int->Prop)) (F_10:(int->(int->int))) (F_9:((int->Prop)->int)), (((finite1626084323ne_int F_10) F_9)->((finite_finite_int A_22)->((((member_int X_6) A_22)->False)->((not (((eq (int->Prop)) A_22) bot_bot_int_o))->(((eq int) (F_9 ((insert_int X_6) A_22))) ((F_10 X_6) (F_9 A_22)))))))) of role axiom named fact_756_folding__one_Oinsert % A new axiom: (forall (X_6:int) (A_22:(int->Prop)) (F_10:(int->(int->int))) (F_9:((int->Prop)->int)), (((finite1626084323ne_int F_10) F_9)->((finite_finite_int A_22)->((((member_int X_6) A_22)->False)->((not (((eq (int->Prop)) A_22) bot_bot_int_o))->(((eq int) (F_9 ((insert_int X_6) A_22))) ((F_10 X_6) (F_9 A_22)))))))) % FOF formula (forall (X_6:nat) (A_22:(nat->Prop)) (F_10:(nat->(nat->nat))) (F_9:((nat->Prop)->nat)), (((finite988810631ne_nat F_10) F_9)->((finite_finite_nat A_22)->((((member_nat X_6) A_22)->False)->((not (((eq (nat->Prop)) A_22) bot_bot_nat_o))->(((eq nat) (F_9 ((insert_nat X_6) A_22))) ((F_10 X_6) (F_9 A_22)))))))) of role axiom named fact_757_folding__one_Oinsert % A new axiom: (forall (X_6:nat) (A_22:(nat->Prop)) (F_10:(nat->(nat->nat))) (F_9:((nat->Prop)->nat)), (((finite988810631ne_nat F_10) F_9)->((finite_finite_nat A_22)->((((member_nat X_6) A_22)->False)->((not (((eq (nat->Prop)) A_22) bot_bot_nat_o))->(((eq nat) (F_9 ((insert_nat X_6) A_22))) ((F_10 X_6) (F_9 A_22)))))))) % FOF formula (forall (X_6:pname) (A_22:(pname->Prop)) (F_10:(pname->(pname->pname))) (F_9:((pname->Prop)->pname)), (((finite1282449217_pname F_10) F_9)->((finite_finite_pname A_22)->((((member_pname X_6) A_22)->False)->((not (((eq (pname->Prop)) A_22) bot_bot_pname_o))->(((eq pname) (F_9 ((insert_pname X_6) A_22))) ((F_10 X_6) (F_9 A_22)))))))) of role axiom named fact_758_folding__one_Oinsert % A new axiom: (forall (X_6:pname) (A_22:(pname->Prop)) (F_10:(pname->(pname->pname))) (F_9:((pname->Prop)->pname)), (((finite1282449217_pname F_10) F_9)->((finite_finite_pname A_22)->((((member_pname X_6) A_22)->False)->((not (((eq (pname->Prop)) A_22) bot_bot_pname_o))->(((eq pname) (F_9 ((insert_pname X_6) A_22))) ((F_10 X_6) (F_9 A_22)))))))) % FOF formula (forall (A_21:(x_a->Prop)) (F_8:(x_a->(x_a->x_a))) (F_7:((x_a->Prop)->x_a)), (((finite_folding_one_a F_8) F_7)->((finite_finite_a A_21)->((not (((eq (x_a->Prop)) A_21) bot_bot_a_o))->((forall (X_1:x_a) (Y_1:x_a), ((member_a ((F_8 X_1) Y_1)) ((insert_a X_1) ((insert_a Y_1) bot_bot_a_o))))->((member_a (F_7 A_21)) A_21)))))) of role axiom named fact_759_folding__one_Oclosed % A new axiom: (forall (A_21:(x_a->Prop)) (F_8:(x_a->(x_a->x_a))) (F_7:((x_a->Prop)->x_a)), (((finite_folding_one_a F_8) F_7)->((finite_finite_a A_21)->((not (((eq (x_a->Prop)) A_21) bot_bot_a_o))->((forall (X_1:x_a) (Y_1:x_a), ((member_a ((F_8 X_1) Y_1)) ((insert_a X_1) ((insert_a Y_1) bot_bot_a_o))))->((member_a (F_7 A_21)) A_21)))))) % FOF formula (forall (A_21:(int->Prop)) (F_8:(int->(int->int))) (F_7:((int->Prop)->int)), (((finite1626084323ne_int F_8) F_7)->((finite_finite_int A_21)->((not (((eq (int->Prop)) A_21) bot_bot_int_o))->((forall (X_1:int) (Y_1:int), ((member_int ((F_8 X_1) Y_1)) ((insert_int X_1) ((insert_int Y_1) bot_bot_int_o))))->((member_int (F_7 A_21)) A_21)))))) of role axiom named fact_760_folding__one_Oclosed % A new axiom: (forall (A_21:(int->Prop)) (F_8:(int->(int->int))) (F_7:((int->Prop)->int)), (((finite1626084323ne_int F_8) F_7)->((finite_finite_int A_21)->((not (((eq (int->Prop)) A_21) bot_bot_int_o))->((forall (X_1:int) (Y_1:int), ((member_int ((F_8 X_1) Y_1)) ((insert_int X_1) ((insert_int Y_1) bot_bot_int_o))))->((member_int (F_7 A_21)) A_21)))))) % FOF formula (forall (A_21:(nat->Prop)) (F_8:(nat->(nat->nat))) (F_7:((nat->Prop)->nat)), (((finite988810631ne_nat F_8) F_7)->((finite_finite_nat A_21)->((not (((eq (nat->Prop)) A_21) bot_bot_nat_o))->((forall (X_1:nat) (Y_1:nat), ((member_nat ((F_8 X_1) Y_1)) ((insert_nat X_1) ((insert_nat Y_1) bot_bot_nat_o))))->((member_nat (F_7 A_21)) A_21)))))) of role axiom named fact_761_folding__one_Oclosed % A new axiom: (forall (A_21:(nat->Prop)) (F_8:(nat->(nat->nat))) (F_7:((nat->Prop)->nat)), (((finite988810631ne_nat F_8) F_7)->((finite_finite_nat A_21)->((not (((eq (nat->Prop)) A_21) bot_bot_nat_o))->((forall (X_1:nat) (Y_1:nat), ((member_nat ((F_8 X_1) Y_1)) ((insert_nat X_1) ((insert_nat Y_1) bot_bot_nat_o))))->((member_nat (F_7 A_21)) A_21)))))) % FOF formula (forall (A_21:(pname->Prop)) (F_8:(pname->(pname->pname))) (F_7:((pname->Prop)->pname)), (((finite1282449217_pname F_8) F_7)->((finite_finite_pname A_21)->((not (((eq (pname->Prop)) A_21) bot_bot_pname_o))->((forall (X_1:pname) (Y_1:pname), ((member_pname ((F_8 X_1) Y_1)) ((insert_pname X_1) ((insert_pname Y_1) bot_bot_pname_o))))->((member_pname (F_7 A_21)) A_21)))))) of role axiom named fact_762_folding__one_Oclosed % A new axiom: (forall (A_21:(pname->Prop)) (F_8:(pname->(pname->pname))) (F_7:((pname->Prop)->pname)), (((finite1282449217_pname F_8) F_7)->((finite_finite_pname A_21)->((not (((eq (pname->Prop)) A_21) bot_bot_pname_o))->((forall (X_1:pname) (Y_1:pname), ((member_pname ((F_8 X_1) Y_1)) ((insert_pname X_1) ((insert_pname Y_1) bot_bot_pname_o))))->((member_pname (F_7 A_21)) A_21)))))) % FOF formula (forall (X_5:x_a) (A_20:(x_a->Prop)), ((finite_finite_a A_20)->(((member_a X_5) A_20)->(((eq nat) (finite_card_a A_20)) ((plus_plus_nat one_one_nat) (finite_card_a ((minus_minus_a_o A_20) ((insert_a X_5) bot_bot_a_o)))))))) of role axiom named fact_763_card_Oremove % A new axiom: (forall (X_5:x_a) (A_20:(x_a->Prop)), ((finite_finite_a A_20)->(((member_a X_5) A_20)->(((eq nat) (finite_card_a A_20)) ((plus_plus_nat one_one_nat) (finite_card_a ((minus_minus_a_o A_20) ((insert_a X_5) bot_bot_a_o)))))))) % FOF formula (forall (X_5:int) (A_20:(int->Prop)), ((finite_finite_int A_20)->(((member_int X_5) A_20)->(((eq nat) (finite_card_int A_20)) ((plus_plus_nat one_one_nat) (finite_card_int ((minus_minus_int_o A_20) ((insert_int X_5) bot_bot_int_o)))))))) of role axiom named fact_764_card_Oremove % A new axiom: (forall (X_5:int) (A_20:(int->Prop)), ((finite_finite_int A_20)->(((member_int X_5) A_20)->(((eq nat) (finite_card_int A_20)) ((plus_plus_nat one_one_nat) (finite_card_int ((minus_minus_int_o A_20) ((insert_int X_5) bot_bot_int_o)))))))) % FOF formula (forall (X_5:nat) (A_20:(nat->Prop)), ((finite_finite_nat A_20)->(((member_nat X_5) A_20)->(((eq nat) (finite_card_nat A_20)) ((plus_plus_nat one_one_nat) (finite_card_nat ((minus_minus_nat_o A_20) ((insert_nat X_5) bot_bot_nat_o)))))))) of role axiom named fact_765_card_Oremove % A new axiom: (forall (X_5:nat) (A_20:(nat->Prop)), ((finite_finite_nat A_20)->(((member_nat X_5) A_20)->(((eq nat) (finite_card_nat A_20)) ((plus_plus_nat one_one_nat) (finite_card_nat ((minus_minus_nat_o A_20) ((insert_nat X_5) bot_bot_nat_o)))))))) % FOF formula (forall (X_5:pname) (A_20:(pname->Prop)), ((finite_finite_pname A_20)->(((member_pname X_5) A_20)->(((eq nat) (finite_card_pname A_20)) ((plus_plus_nat one_one_nat) (finite_card_pname ((minus_minus_pname_o A_20) ((insert_pname X_5) bot_bot_pname_o)))))))) of role axiom named fact_766_card_Oremove % A new axiom: (forall (X_5:pname) (A_20:(pname->Prop)), ((finite_finite_pname A_20)->(((member_pname X_5) A_20)->(((eq nat) (finite_card_pname A_20)) ((plus_plus_nat one_one_nat) (finite_card_pname ((minus_minus_pname_o A_20) ((insert_pname X_5) bot_bot_pname_o)))))))) % FOF formula (forall (X_4:x_a) (A_19:(x_a->Prop)), ((finite_finite_a A_19)->(((eq nat) (finite_card_a ((insert_a X_4) A_19))) ((plus_plus_nat one_one_nat) (finite_card_a ((minus_minus_a_o A_19) ((insert_a X_4) bot_bot_a_o))))))) of role axiom named fact_767_card_Oinsert__remove % A new axiom: (forall (X_4:x_a) (A_19:(x_a->Prop)), ((finite_finite_a A_19)->(((eq nat) (finite_card_a ((insert_a X_4) A_19))) ((plus_plus_nat one_one_nat) (finite_card_a ((minus_minus_a_o A_19) ((insert_a X_4) bot_bot_a_o))))))) % FOF formula (forall (X_4:int) (A_19:(int->Prop)), ((finite_finite_int A_19)->(((eq nat) (finite_card_int ((insert_int X_4) A_19))) ((plus_plus_nat one_one_nat) (finite_card_int ((minus_minus_int_o A_19) ((insert_int X_4) bot_bot_int_o))))))) of role axiom named fact_768_card_Oinsert__remove % A new axiom: (forall (X_4:int) (A_19:(int->Prop)), ((finite_finite_int A_19)->(((eq nat) (finite_card_int ((insert_int X_4) A_19))) ((plus_plus_nat one_one_nat) (finite_card_int ((minus_minus_int_o A_19) ((insert_int X_4) bot_bot_int_o))))))) % FOF formula (forall (X_4:nat) (A_19:(nat->Prop)), ((finite_finite_nat A_19)->(((eq nat) (finite_card_nat ((insert_nat X_4) A_19))) ((plus_plus_nat one_one_nat) (finite_card_nat ((minus_minus_nat_o A_19) ((insert_nat X_4) bot_bot_nat_o))))))) of role axiom named fact_769_card_Oinsert__remove % A new axiom: (forall (X_4:nat) (A_19:(nat->Prop)), ((finite_finite_nat A_19)->(((eq nat) (finite_card_nat ((insert_nat X_4) A_19))) ((plus_plus_nat one_one_nat) (finite_card_nat ((minus_minus_nat_o A_19) ((insert_nat X_4) bot_bot_nat_o))))))) % FOF formula (forall (X_4:pname) (A_19:(pname->Prop)), ((finite_finite_pname A_19)->(((eq nat) (finite_card_pname ((insert_pname X_4) A_19))) ((plus_plus_nat one_one_nat) (finite_card_pname ((minus_minus_pname_o A_19) ((insert_pname X_4) bot_bot_pname_o))))))) of role axiom named fact_770_card_Oinsert__remove % A new axiom: (forall (X_4:pname) (A_19:(pname->Prop)), ((finite_finite_pname A_19)->(((eq nat) (finite_card_pname ((insert_pname X_4) A_19))) ((plus_plus_nat one_one_nat) (finite_card_pname ((minus_minus_pname_o A_19) ((insert_pname X_4) bot_bot_pname_o))))))) % FOF formula (forall (B_18:(int->Prop)) (A_18:(int->Prop)) (F_6:(int->(int->int))) (F_5:((int->Prop)->int)), (((finite1432773856em_int F_6) F_5)->((finite_finite_int A_18)->((not (((eq (int->Prop)) B_18) bot_bot_int_o))->(((ord_less_eq_int_o B_18) A_18)->(((eq int) ((F_6 (F_5 B_18)) (F_5 A_18))) (F_5 A_18))))))) of role axiom named fact_771_folding__one__idem_Osubset__idem % A new axiom: (forall (B_18:(int->Prop)) (A_18:(int->Prop)) (F_6:(int->(int->int))) (F_5:((int->Prop)->int)), (((finite1432773856em_int F_6) F_5)->((finite_finite_int A_18)->((not (((eq (int->Prop)) B_18) bot_bot_int_o))->(((ord_less_eq_int_o B_18) A_18)->(((eq int) ((F_6 (F_5 B_18)) (F_5 A_18))) (F_5 A_18))))))) % FOF formula (forall (B_18:(nat->Prop)) (A_18:(nat->Prop)) (F_6:(nat->(nat->nat))) (F_5:((nat->Prop)->nat)), (((finite795500164em_nat F_6) F_5)->((finite_finite_nat A_18)->((not (((eq (nat->Prop)) B_18) bot_bot_nat_o))->(((ord_less_eq_nat_o B_18) A_18)->(((eq nat) ((F_6 (F_5 B_18)) (F_5 A_18))) (F_5 A_18))))))) of role axiom named fact_772_folding__one__idem_Osubset__idem % A new axiom: (forall (B_18:(nat->Prop)) (A_18:(nat->Prop)) (F_6:(nat->(nat->nat))) (F_5:((nat->Prop)->nat)), (((finite795500164em_nat F_6) F_5)->((finite_finite_nat A_18)->((not (((eq (nat->Prop)) B_18) bot_bot_nat_o))->(((ord_less_eq_nat_o B_18) A_18)->(((eq nat) ((F_6 (F_5 B_18)) (F_5 A_18))) (F_5 A_18))))))) % FOF formula (forall (B_18:(pname->Prop)) (A_18:(pname->Prop)) (F_6:(pname->(pname->pname))) (F_5:((pname->Prop)->pname)), (((finite89670078_pname F_6) F_5)->((finite_finite_pname A_18)->((not (((eq (pname->Prop)) B_18) bot_bot_pname_o))->(((ord_less_eq_pname_o B_18) A_18)->(((eq pname) ((F_6 (F_5 B_18)) (F_5 A_18))) (F_5 A_18))))))) of role axiom named fact_773_folding__one__idem_Osubset__idem % A new axiom: (forall (B_18:(pname->Prop)) (A_18:(pname->Prop)) (F_6:(pname->(pname->pname))) (F_5:((pname->Prop)->pname)), (((finite89670078_pname F_6) F_5)->((finite_finite_pname A_18)->((not (((eq (pname->Prop)) B_18) bot_bot_pname_o))->(((ord_less_eq_pname_o B_18) A_18)->(((eq pname) ((F_6 (F_5 B_18)) (F_5 A_18))) (F_5 A_18))))))) % FOF formula (forall (B_18:(x_a->Prop)) (A_18:(x_a->Prop)) (F_6:(x_a->(x_a->x_a))) (F_5:((x_a->Prop)->x_a)), (((finite1819937229idem_a F_6) F_5)->((finite_finite_a A_18)->((not (((eq (x_a->Prop)) B_18) bot_bot_a_o))->(((ord_less_eq_a_o B_18) A_18)->(((eq x_a) ((F_6 (F_5 B_18)) (F_5 A_18))) (F_5 A_18))))))) of role axiom named fact_774_folding__one__idem_Osubset__idem % A new axiom: (forall (B_18:(x_a->Prop)) (A_18:(x_a->Prop)) (F_6:(x_a->(x_a->x_a))) (F_5:((x_a->Prop)->x_a)), (((finite1819937229idem_a F_6) F_5)->((finite_finite_a A_18)->((not (((eq (x_a->Prop)) B_18) bot_bot_a_o))->(((ord_less_eq_a_o B_18) A_18)->(((eq x_a) ((F_6 (F_5 B_18)) (F_5 A_18))) (F_5 A_18))))))) % FOF formula (forall (X_3:x_a) (A_17:(x_a->Prop)) (F_4:(x_a->(x_a->x_a))) (F_3:((x_a->Prop)->x_a)), (((finite1819937229idem_a F_4) F_3)->((finite_finite_a A_17)->((not (((eq (x_a->Prop)) A_17) bot_bot_a_o))->(((eq x_a) (F_3 ((insert_a X_3) A_17))) ((F_4 X_3) (F_3 A_17))))))) of role axiom named fact_775_folding__one__idem_Oinsert__idem % A new axiom: (forall (X_3:x_a) (A_17:(x_a->Prop)) (F_4:(x_a->(x_a->x_a))) (F_3:((x_a->Prop)->x_a)), (((finite1819937229idem_a F_4) F_3)->((finite_finite_a A_17)->((not (((eq (x_a->Prop)) A_17) bot_bot_a_o))->(((eq x_a) (F_3 ((insert_a X_3) A_17))) ((F_4 X_3) (F_3 A_17))))))) % FOF formula (forall (X_3:int) (A_17:(int->Prop)) (F_4:(int->(int->int))) (F_3:((int->Prop)->int)), (((finite1432773856em_int F_4) F_3)->((finite_finite_int A_17)->((not (((eq (int->Prop)) A_17) bot_bot_int_o))->(((eq int) (F_3 ((insert_int X_3) A_17))) ((F_4 X_3) (F_3 A_17))))))) of role axiom named fact_776_folding__one__idem_Oinsert__idem % A new axiom: (forall (X_3:int) (A_17:(int->Prop)) (F_4:(int->(int->int))) (F_3:((int->Prop)->int)), (((finite1432773856em_int F_4) F_3)->((finite_finite_int A_17)->((not (((eq (int->Prop)) A_17) bot_bot_int_o))->(((eq int) (F_3 ((insert_int X_3) A_17))) ((F_4 X_3) (F_3 A_17))))))) % FOF formula (forall (X_3:nat) (A_17:(nat->Prop)) (F_4:(nat->(nat->nat))) (F_3:((nat->Prop)->nat)), (((finite795500164em_nat F_4) F_3)->((finite_finite_nat A_17)->((not (((eq (nat->Prop)) A_17) bot_bot_nat_o))->(((eq nat) (F_3 ((insert_nat X_3) A_17))) ((F_4 X_3) (F_3 A_17))))))) of role axiom named fact_777_folding__one__idem_Oinsert__idem % A new axiom: (forall (X_3:nat) (A_17:(nat->Prop)) (F_4:(nat->(nat->nat))) (F_3:((nat->Prop)->nat)), (((finite795500164em_nat F_4) F_3)->((finite_finite_nat A_17)->((not (((eq (nat->Prop)) A_17) bot_bot_nat_o))->(((eq nat) (F_3 ((insert_nat X_3) A_17))) ((F_4 X_3) (F_3 A_17))))))) % FOF formula (forall (X_3:pname) (A_17:(pname->Prop)) (F_4:(pname->(pname->pname))) (F_3:((pname->Prop)->pname)), (((finite89670078_pname F_4) F_3)->((finite_finite_pname A_17)->((not (((eq (pname->Prop)) A_17) bot_bot_pname_o))->(((eq pname) (F_3 ((insert_pname X_3) A_17))) ((F_4 X_3) (F_3 A_17))))))) of role axiom named fact_778_folding__one__idem_Oinsert__idem % A new axiom: (forall (X_3:pname) (A_17:(pname->Prop)) (F_4:(pname->(pname->pname))) (F_3:((pname->Prop)->pname)), (((finite89670078_pname F_4) F_3)->((finite_finite_pname A_17)->((not (((eq (pname->Prop)) A_17) bot_bot_pname_o))->(((eq pname) (F_3 ((insert_pname X_3) A_17))) ((F_4 X_3) (F_3 A_17))))))) % FOF formula (forall (P_2:((x_a->Prop)->Prop)) (F_1:(x_a->Prop)), ((finite_finite_a F_1)->((not (((eq (x_a->Prop)) F_1) bot_bot_a_o))->((forall (X_1:x_a), (P_2 ((insert_a X_1) bot_bot_a_o)))->((forall (X_1:x_a) (F_2:(x_a->Prop)), ((finite_finite_a F_2)->((not (((eq (x_a->Prop)) F_2) bot_bot_a_o))->((((member_a X_1) F_2)->False)->((P_2 F_2)->(P_2 ((insert_a X_1) F_2)))))))->(P_2 F_1)))))) of role axiom named fact_779_finite__ne__induct % A new axiom: (forall (P_2:((x_a->Prop)->Prop)) (F_1:(x_a->Prop)), ((finite_finite_a F_1)->((not (((eq (x_a->Prop)) F_1) bot_bot_a_o))->((forall (X_1:x_a), (P_2 ((insert_a X_1) bot_bot_a_o)))->((forall (X_1:x_a) (F_2:(x_a->Prop)), ((finite_finite_a F_2)->((not (((eq (x_a->Prop)) F_2) bot_bot_a_o))->((((member_a X_1) F_2)->False)->((P_2 F_2)->(P_2 ((insert_a X_1) F_2)))))))->(P_2 F_1)))))) % FOF formula (forall (P_2:((int->Prop)->Prop)) (F_1:(int->Prop)), ((finite_finite_int F_1)->((not (((eq (int->Prop)) F_1) bot_bot_int_o))->((forall (X_1:int), (P_2 ((insert_int X_1) bot_bot_int_o)))->((forall (X_1:int) (F_2:(int->Prop)), ((finite_finite_int F_2)->((not (((eq (int->Prop)) F_2) bot_bot_int_o))->((((member_int X_1) F_2)->False)->((P_2 F_2)->(P_2 ((insert_int X_1) F_2)))))))->(P_2 F_1)))))) of role axiom named fact_780_finite__ne__induct % A new axiom: (forall (P_2:((int->Prop)->Prop)) (F_1:(int->Prop)), ((finite_finite_int F_1)->((not (((eq (int->Prop)) F_1) bot_bot_int_o))->((forall (X_1:int), (P_2 ((insert_int X_1) bot_bot_int_o)))->((forall (X_1:int) (F_2:(int->Prop)), ((finite_finite_int F_2)->((not (((eq (int->Prop)) F_2) bot_bot_int_o))->((((member_int X_1) F_2)->False)->((P_2 F_2)->(P_2 ((insert_int X_1) F_2)))))))->(P_2 F_1)))))) % FOF formula (forall (P_2:((nat->Prop)->Prop)) (F_1:(nat->Prop)), ((finite_finite_nat F_1)->((not (((eq (nat->Prop)) F_1) bot_bot_nat_o))->((forall (X_1:nat), (P_2 ((insert_nat X_1) bot_bot_nat_o)))->((forall (X_1:nat) (F_2:(nat->Prop)), ((finite_finite_nat F_2)->((not (((eq (nat->Prop)) F_2) bot_bot_nat_o))->((((member_nat X_1) F_2)->False)->((P_2 F_2)->(P_2 ((insert_nat X_1) F_2)))))))->(P_2 F_1)))))) of role axiom named fact_781_finite__ne__induct % A new axiom: (forall (P_2:((nat->Prop)->Prop)) (F_1:(nat->Prop)), ((finite_finite_nat F_1)->((not (((eq (nat->Prop)) F_1) bot_bot_nat_o))->((forall (X_1:nat), (P_2 ((insert_nat X_1) bot_bot_nat_o)))->((forall (X_1:nat) (F_2:(nat->Prop)), ((finite_finite_nat F_2)->((not (((eq (nat->Prop)) F_2) bot_bot_nat_o))->((((member_nat X_1) F_2)->False)->((P_2 F_2)->(P_2 ((insert_nat X_1) F_2)))))))->(P_2 F_1)))))) % FOF formula (forall (P_2:((pname->Prop)->Prop)) (F_1:(pname->Prop)), ((finite_finite_pname F_1)->((not (((eq (pname->Prop)) F_1) bot_bot_pname_o))->((forall (X_1:pname), (P_2 ((insert_pname X_1) bot_bot_pname_o)))->((forall (X_1:pname) (F_2:(pname->Prop)), ((finite_finite_pname F_2)->((not (((eq (pname->Prop)) F_2) bot_bot_pname_o))->((((member_pname X_1) F_2)->False)->((P_2 F_2)->(P_2 ((insert_pname X_1) F_2)))))))->(P_2 F_1)))))) of role axiom named fact_782_finite__ne__induct % A new axiom: (forall (P_2:((pname->Prop)->Prop)) (F_1:(pname->Prop)), ((finite_finite_pname F_1)->((not (((eq (pname->Prop)) F_1) bot_bot_pname_o))->((forall (X_1:pname), (P_2 ((insert_pname X_1) bot_bot_pname_o)))->((forall (X_1:pname) (F_2:(pname->Prop)), ((finite_finite_pname F_2)->((not (((eq (pname->Prop)) F_2) bot_bot_pname_o))->((((member_pname X_1) F_2)->False)->((P_2 F_2)->(P_2 ((insert_pname X_1) F_2)))))))->(P_2 F_1)))))) % FOF formula (forall (X_2:(x_a->Prop)), (((eq x_a) (the_elem_a X_2)) (the_a (fun (X_1:x_a)=> (((eq (x_a->Prop)) X_2) ((insert_a X_1) bot_bot_a_o)))))) of role axiom named fact_783_the__elem__def % A new axiom: (forall (X_2:(x_a->Prop)), (((eq x_a) (the_elem_a X_2)) (the_a (fun (X_1:x_a)=> (((eq (x_a->Prop)) X_2) ((insert_a X_1) bot_bot_a_o)))))) % FOF formula (forall (X_2:(nat->Prop)), (((eq nat) (the_elem_nat X_2)) (the_nat (fun (X_1:nat)=> (((eq (nat->Prop)) X_2) ((insert_nat X_1) bot_bot_nat_o)))))) of role axiom named fact_784_the__elem__def % A new axiom: (forall (X_2:(nat->Prop)), (((eq nat) (the_elem_nat X_2)) (the_nat (fun (X_1:nat)=> (((eq (nat->Prop)) X_2) ((insert_nat X_1) bot_bot_nat_o)))))) % FOF formula (forall (X_2:(int->Prop)), (((eq int) (the_elem_int X_2)) (the_int (fun (X_1:int)=> (((eq (int->Prop)) X_2) ((insert_int X_1) bot_bot_int_o)))))) of role axiom named fact_785_the__elem__def % A new axiom: (forall (X_2:(int->Prop)), (((eq int) (the_elem_int X_2)) (the_int (fun (X_1:int)=> (((eq (int->Prop)) X_2) ((insert_int X_1) bot_bot_int_o)))))) % FOF formula (forall (A_16:int) (B_17:int) (C_13:int), (((eq int) ((plus_plus_int ((plus_plus_int A_16) B_17)) C_13)) ((plus_plus_int A_16) ((plus_plus_int B_17) C_13)))) of role axiom named fact_786_ab__semigroup__add__class_Oadd__ac_I1_J % A new axiom: (forall (A_16:int) (B_17:int) (C_13:int), (((eq int) ((plus_plus_int ((plus_plus_int A_16) B_17)) C_13)) ((plus_plus_int A_16) ((plus_plus_int B_17) C_13)))) % FOF formula (forall (A_16:nat) (B_17:nat) (C_13:nat), (((eq nat) ((plus_plus_nat ((plus_plus_nat A_16) B_17)) C_13)) ((plus_plus_nat A_16) ((plus_plus_nat B_17) C_13)))) of role axiom named fact_787_ab__semigroup__add__class_Oadd__ac_I1_J % A new axiom: (forall (A_16:nat) (B_17:nat) (C_13:nat), (((eq nat) ((plus_plus_nat ((plus_plus_nat A_16) B_17)) C_13)) ((plus_plus_nat A_16) ((plus_plus_nat B_17) C_13)))) % FOF formula (forall (A_15:int) (B_16:int) (C_12:int), ((iff (((eq int) ((plus_plus_int A_15) B_16)) ((plus_plus_int A_15) C_12))) (((eq int) B_16) C_12))) of role axiom named fact_788_add__left__cancel % A new axiom: (forall (A_15:int) (B_16:int) (C_12:int), ((iff (((eq int) ((plus_plus_int A_15) B_16)) ((plus_plus_int A_15) C_12))) (((eq int) B_16) C_12))) % FOF formula (forall (A_15:nat) (B_16:nat) (C_12:nat), ((iff (((eq nat) ((plus_plus_nat A_15) B_16)) ((plus_plus_nat A_15) C_12))) (((eq nat) B_16) C_12))) of role axiom named fact_789_add__left__cancel % A new axiom: (forall (A_15:nat) (B_16:nat) (C_12:nat), ((iff (((eq nat) ((plus_plus_nat A_15) B_16)) ((plus_plus_nat A_15) C_12))) (((eq nat) B_16) C_12))) % FOF formula (forall (B_15:int) (A_14:int) (C_11:int), ((iff (((eq int) ((plus_plus_int B_15) A_14)) ((plus_plus_int C_11) A_14))) (((eq int) B_15) C_11))) of role axiom named fact_790_add__right__cancel % A new axiom: (forall (B_15:int) (A_14:int) (C_11:int), ((iff (((eq int) ((plus_plus_int B_15) A_14)) ((plus_plus_int C_11) A_14))) (((eq int) B_15) C_11))) % FOF formula (forall (B_15:nat) (A_14:nat) (C_11:nat), ((iff (((eq nat) ((plus_plus_nat B_15) A_14)) ((plus_plus_nat C_11) A_14))) (((eq nat) B_15) C_11))) of role axiom named fact_791_add__right__cancel % A new axiom: (forall (B_15:nat) (A_14:nat) (C_11:nat), ((iff (((eq nat) ((plus_plus_nat B_15) A_14)) ((plus_plus_nat C_11) A_14))) (((eq nat) B_15) C_11))) % FOF formula (forall (A_13:int) (B_14:int) (C_10:int), ((((eq int) ((plus_plus_int A_13) B_14)) ((plus_plus_int A_13) C_10))->(((eq int) B_14) C_10))) of role axiom named fact_792_add__left__imp__eq % A new axiom: (forall (A_13:int) (B_14:int) (C_10:int), ((((eq int) ((plus_plus_int A_13) B_14)) ((plus_plus_int A_13) C_10))->(((eq int) B_14) C_10))) % FOF formula (forall (A_13:nat) (B_14:nat) (C_10:nat), ((((eq nat) ((plus_plus_nat A_13) B_14)) ((plus_plus_nat A_13) C_10))->(((eq nat) B_14) C_10))) of role axiom named fact_793_add__left__imp__eq % A new axiom: (forall (A_13:nat) (B_14:nat) (C_10:nat), ((((eq nat) ((plus_plus_nat A_13) B_14)) ((plus_plus_nat A_13) C_10))->(((eq nat) B_14) C_10))) % FOF formula (forall (A_12:int) (B_13:int) (C_9:int), ((((eq int) ((plus_plus_int A_12) B_13)) ((plus_plus_int A_12) C_9))->(((eq int) B_13) C_9))) of role axiom named fact_794_add__imp__eq % A new axiom: (forall (A_12:int) (B_13:int) (C_9:int), ((((eq int) ((plus_plus_int A_12) B_13)) ((plus_plus_int A_12) C_9))->(((eq int) B_13) C_9))) % FOF formula (forall (A_12:nat) (B_13:nat) (C_9:nat), ((((eq nat) ((plus_plus_nat A_12) B_13)) ((plus_plus_nat A_12) C_9))->(((eq nat) B_13) C_9))) of role axiom named fact_795_add__imp__eq % A new axiom: (forall (A_12:nat) (B_13:nat) (C_9:nat), ((((eq nat) ((plus_plus_nat A_12) B_13)) ((plus_plus_nat A_12) C_9))->(((eq nat) B_13) C_9))) % FOF formula (forall (B_12:int) (A_11:int) (C_8:int), ((((eq int) ((plus_plus_int B_12) A_11)) ((plus_plus_int C_8) A_11))->(((eq int) B_12) C_8))) of role axiom named fact_796_add__right__imp__eq % A new axiom: (forall (B_12:int) (A_11:int) (C_8:int), ((((eq int) ((plus_plus_int B_12) A_11)) ((plus_plus_int C_8) A_11))->(((eq int) B_12) C_8))) % FOF formula (forall (B_12:nat) (A_11:nat) (C_8:nat), ((((eq nat) ((plus_plus_nat B_12) A_11)) ((plus_plus_nat C_8) A_11))->(((eq nat) B_12) C_8))) of role axiom named fact_797_add__right__imp__eq % A new axiom: (forall (B_12:nat) (A_11:nat) (C_8:nat), ((((eq nat) ((plus_plus_nat B_12) A_11)) ((plus_plus_nat C_8) A_11))->(((eq nat) B_12) C_8))) % FOF formula (forall (M:nat) (N:nat), (((eq nat) ((plus_plus_nat M) N)) ((plus_plus_nat N) M))) of role axiom named fact_798_nat__add__commute % A new axiom: (forall (M:nat) (N:nat), (((eq nat) ((plus_plus_nat M) N)) ((plus_plus_nat N) M))) % FOF formula (forall (X:nat) (Y:nat) (Z:nat), (((eq nat) ((plus_plus_nat X) ((plus_plus_nat Y) Z))) ((plus_plus_nat Y) ((plus_plus_nat X) Z)))) of role axiom named fact_799_nat__add__left__commute % A new axiom: (forall (X:nat) (Y:nat) (Z:nat), (((eq nat) ((plus_plus_nat X) ((plus_plus_nat Y) Z))) ((plus_plus_nat Y) ((plus_plus_nat X) Z)))) % FOF formula (forall (M:nat) (N:nat) (K:nat), (((eq nat) ((plus_plus_nat ((plus_plus_nat M) N)) K)) ((plus_plus_nat M) ((plus_plus_nat N) K)))) of role axiom named fact_800_nat__add__assoc % A new axiom: (forall (M:nat) (N:nat) (K:nat), (((eq nat) ((plus_plus_nat ((plus_plus_nat M) N)) K)) ((plus_plus_nat M) ((plus_plus_nat N) K)))) % FOF formula (forall (K:nat) (M:nat) (N:nat), ((iff (((eq nat) ((plus_plus_nat K) M)) ((plus_plus_nat K) N))) (((eq nat) M) N))) of role axiom named fact_801_nat__add__left__cancel % A new axiom: (forall (K:nat) (M:nat) (N:nat), ((iff (((eq nat) ((plus_plus_nat K) M)) ((plus_plus_nat K) N))) (((eq nat) M) N))) % FOF formula (forall (M:nat) (K:nat) (N:nat), ((iff (((eq nat) ((plus_plus_nat M) K)) ((plus_plus_nat N) K))) (((eq nat) M) N))) of role axiom named fact_802_nat__add__right__cancel % A new axiom: (forall (M:nat) (K:nat) (N:nat), ((iff (((eq nat) ((plus_plus_nat M) K)) ((plus_plus_nat N) K))) (((eq nat) M) N))) % FOF formula (forall (A_10:int) (C_7:int) (B_11:int), ((iff ((ord_less_eq_int ((plus_plus_int A_10) C_7)) ((plus_plus_int B_11) C_7))) ((ord_less_eq_int A_10) B_11))) of role axiom named fact_803_add__le__cancel__right % A new axiom: (forall (A_10:int) (C_7:int) (B_11:int), ((iff ((ord_less_eq_int ((plus_plus_int A_10) C_7)) ((plus_plus_int B_11) C_7))) ((ord_less_eq_int A_10) B_11))) % FOF formula (forall (A_10:nat) (C_7:nat) (B_11:nat), ((iff ((ord_less_eq_nat ((plus_plus_nat A_10) C_7)) ((plus_plus_nat B_11) C_7))) ((ord_less_eq_nat A_10) B_11))) of role axiom named fact_804_add__le__cancel__right % A new axiom: (forall (A_10:nat) (C_7:nat) (B_11:nat), ((iff ((ord_less_eq_nat ((plus_plus_nat A_10) C_7)) ((plus_plus_nat B_11) C_7))) ((ord_less_eq_nat A_10) B_11))) % FOF formula (forall (C_6:int) (A_9:int) (B_10:int), ((iff ((ord_less_eq_int ((plus_plus_int C_6) A_9)) ((plus_plus_int C_6) B_10))) ((ord_less_eq_int A_9) B_10))) of role axiom named fact_805_add__le__cancel__left % A new axiom: (forall (C_6:int) (A_9:int) (B_10:int), ((iff ((ord_less_eq_int ((plus_plus_int C_6) A_9)) ((plus_plus_int C_6) B_10))) ((ord_less_eq_int A_9) B_10))) % FOF formula (forall (C_6:nat) (A_9:nat) (B_10:nat), ((iff ((ord_less_eq_nat ((plus_plus_nat C_6) A_9)) ((plus_plus_nat C_6) B_10))) ((ord_less_eq_nat A_9) B_10))) of role axiom named fact_806_add__le__cancel__left % A new axiom: (forall (C_6:nat) (A_9:nat) (B_10:nat), ((iff ((ord_less_eq_nat ((plus_plus_nat C_6) A_9)) ((plus_plus_nat C_6) B_10))) ((ord_less_eq_nat A_9) B_10))) % FOF formula (forall (C_5:int) (A_8:int) (B_9:int), (((ord_less_eq_int A_8) B_9)->((ord_less_eq_int ((plus_plus_int A_8) C_5)) ((plus_plus_int B_9) C_5)))) of role axiom named fact_807_add__right__mono % A new axiom: (forall (C_5:int) (A_8:int) (B_9:int), (((ord_less_eq_int A_8) B_9)->((ord_less_eq_int ((plus_plus_int A_8) C_5)) ((plus_plus_int B_9) C_5)))) % FOF formula (forall (C_5:nat) (A_8:nat) (B_9:nat), (((ord_less_eq_nat A_8) B_9)->((ord_less_eq_nat ((plus_plus_nat A_8) C_5)) ((plus_plus_nat B_9) C_5)))) of role axiom named fact_808_add__right__mono % A new axiom: (forall (C_5:nat) (A_8:nat) (B_9:nat), (((ord_less_eq_nat A_8) B_9)->((ord_less_eq_nat ((plus_plus_nat A_8) C_5)) ((plus_plus_nat B_9) C_5)))) % FOF formula (forall (C_4:int) (A_7:int) (B_8:int), (((ord_less_eq_int A_7) B_8)->((ord_less_eq_int ((plus_plus_int C_4) A_7)) ((plus_plus_int C_4) B_8)))) of role axiom named fact_809_add__left__mono % A new axiom: (forall (C_4:int) (A_7:int) (B_8:int), (((ord_less_eq_int A_7) B_8)->((ord_less_eq_int ((plus_plus_int C_4) A_7)) ((plus_plus_int C_4) B_8)))) % FOF formula (forall (C_4:nat) (A_7:nat) (B_8:nat), (((ord_less_eq_nat A_7) B_8)->((ord_less_eq_nat ((plus_plus_nat C_4) A_7)) ((plus_plus_nat C_4) B_8)))) of role axiom named fact_810_add__left__mono % A new axiom: (forall (C_4:nat) (A_7:nat) (B_8:nat), (((ord_less_eq_nat A_7) B_8)->((ord_less_eq_nat ((plus_plus_nat C_4) A_7)) ((plus_plus_nat C_4) B_8)))) % FOF formula (forall (C_3:int) (D_2:int) (A_6:int) (B_7:int), (((ord_less_eq_int A_6) B_7)->(((ord_less_eq_int C_3) D_2)->((ord_less_eq_int ((plus_plus_int A_6) C_3)) ((plus_plus_int B_7) D_2))))) of role axiom named fact_811_add__mono % A new axiom: (forall (C_3:int) (D_2:int) (A_6:int) (B_7:int), (((ord_less_eq_int A_6) B_7)->(((ord_less_eq_int C_3) D_2)->((ord_less_eq_int ((plus_plus_int A_6) C_3)) ((plus_plus_int B_7) D_2))))) % FOF formula (forall (C_3:nat) (D_2:nat) (A_6:nat) (B_7:nat), (((ord_less_eq_nat A_6) B_7)->(((ord_less_eq_nat C_3) D_2)->((ord_less_eq_nat ((plus_plus_nat A_6) C_3)) ((plus_plus_nat B_7) D_2))))) of role axiom named fact_812_add__mono % A new axiom: (forall (C_3:nat) (D_2:nat) (A_6:nat) (B_7:nat), (((ord_less_eq_nat A_6) B_7)->(((ord_less_eq_nat C_3) D_2)->((ord_less_eq_nat ((plus_plus_nat A_6) C_3)) ((plus_plus_nat B_7) D_2))))) % FOF formula (forall (A_5:int) (C_2:int) (B_6:int), (((ord_less_eq_int ((plus_plus_int A_5) C_2)) ((plus_plus_int B_6) C_2))->((ord_less_eq_int A_5) B_6))) of role axiom named fact_813_add__le__imp__le__right % A new axiom: (forall (A_5:int) (C_2:int) (B_6:int), (((ord_less_eq_int ((plus_plus_int A_5) C_2)) ((plus_plus_int B_6) C_2))->((ord_less_eq_int A_5) B_6))) % FOF formula (forall (A_5:nat) (C_2:nat) (B_6:nat), (((ord_less_eq_nat ((plus_plus_nat A_5) C_2)) ((plus_plus_nat B_6) C_2))->((ord_less_eq_nat A_5) B_6))) of role axiom named fact_814_add__le__imp__le__right % A new axiom: (forall (A_5:nat) (C_2:nat) (B_6:nat), (((ord_less_eq_nat ((plus_plus_nat A_5) C_2)) ((plus_plus_nat B_6) C_2))->((ord_less_eq_nat A_5) B_6))) % FOF formula (forall (C_1:int) (A_4:int) (B_5:int), (((ord_less_eq_int ((plus_plus_int C_1) A_4)) ((plus_plus_int C_1) B_5))->((ord_less_eq_int A_4) B_5))) of role axiom named fact_815_add__le__imp__le__left % A new axiom: (forall (C_1:int) (A_4:int) (B_5:int), (((ord_less_eq_int ((plus_plus_int C_1) A_4)) ((plus_plus_int C_1) B_5))->((ord_less_eq_int A_4) B_5))) % FOF formula (forall (C_1:nat) (A_4:nat) (B_5:nat), (((ord_less_eq_nat ((plus_plus_nat C_1) A_4)) ((plus_plus_nat C_1) B_5))->((ord_less_eq_nat A_4) B_5))) of role axiom named fact_816_add__le__imp__le__left % A new axiom: (forall (C_1:nat) (A_4:nat) (B_5:nat), (((ord_less_eq_nat ((plus_plus_nat C_1) A_4)) ((plus_plus_nat C_1) B_5))->((ord_less_eq_nat A_4) B_5))) % FOF formula (forall (A_3:int) (B_4:int), (((eq int) ((plus_plus_int ((minus_minus_int A_3) B_4)) B_4)) A_3)) of role axiom named fact_817_diff__add__cancel % A new axiom: (forall (A_3:int) (B_4:int), (((eq int) ((plus_plus_int ((minus_minus_int A_3) B_4)) B_4)) A_3)) % FOF formula (forall (A_2:int) (B_3:int), (((eq int) ((minus_minus_int ((plus_plus_int A_2) B_3)) B_3)) A_2)) of role axiom named fact_818_add__diff__cancel % A new axiom: (forall (A_2:int) (B_3:int), (((eq int) ((minus_minus_int ((plus_plus_int A_2) B_3)) B_3)) A_2)) % FOF formula (forall (M:nat) (N:nat), (((eq nat) ((plus_plus_nat M) (suc N))) (suc ((plus_plus_nat M) N)))) of role axiom named fact_819_add__Suc__right % A new axiom: (forall (M:nat) (N:nat), (((eq nat) ((plus_plus_nat M) (suc N))) (suc ((plus_plus_nat M) N)))) % FOF formula (forall (M:nat) (N:nat), (((eq nat) ((plus_plus_nat (suc M)) N)) (suc ((plus_plus_nat M) N)))) of role axiom named fact_820_add__Suc % A new axiom: (forall (M:nat) (N:nat), (((eq nat) ((plus_plus_nat (suc M)) N)) (suc ((plus_plus_nat M) N)))) % FOF formula (forall (M:nat) (N:nat), (((eq nat) ((plus_plus_nat (suc M)) N)) ((plus_plus_nat M) (suc N)))) of role axiom named fact_821_add__Suc__shift % A new axiom: (forall (M:nat) (N:nat), (((eq nat) ((plus_plus_nat (suc M)) N)) ((plus_plus_nat M) (suc N)))) % FOF formula (forall (N:nat) (M:nat), ((ord_less_eq_nat N) ((plus_plus_nat M) N))) of role axiom named fact_822_le__add2 % A new axiom: (forall (N:nat) (M:nat), ((ord_less_eq_nat N) ((plus_plus_nat M) N))) % FOF formula (forall (N:nat) (M:nat), ((ord_less_eq_nat N) ((plus_plus_nat N) M))) of role axiom named fact_823_le__add1 % A new axiom: (forall (N:nat) (M:nat), ((ord_less_eq_nat N) ((plus_plus_nat N) M))) % FOF formula (forall (M:nat) (N:nat), ((iff ((ord_less_eq_nat M) N)) ((ex nat) (fun (K_1:nat)=> (((eq nat) N) ((plus_plus_nat M) K_1)))))) of role axiom named fact_824_le__iff__add % A new axiom: (forall (M:nat) (N:nat), ((iff ((ord_less_eq_nat M) N)) ((ex nat) (fun (K_1:nat)=> (((eq nat) N) ((plus_plus_nat M) K_1)))))) % FOF formula (forall (K:nat) (M:nat) (N:nat), ((iff ((ord_less_eq_nat ((plus_plus_nat K) M)) ((plus_plus_nat K) N))) ((ord_less_eq_nat M) N))) of role axiom named fact_825_nat__add__left__cancel__le % A new axiom: (forall (K:nat) (M:nat) (N:nat), ((iff ((ord_less_eq_nat ((plus_plus_nat K) M)) ((plus_plus_nat K) N))) ((ord_less_eq_nat M) N))) % FOF formula (forall (M:nat) (I_1:nat) (J:nat), (((ord_less_eq_nat I_1) J)->((ord_less_eq_nat I_1) ((plus_plus_nat J) M)))) of role axiom named fact_826_trans__le__add1 % A new axiom: (forall (M:nat) (I_1:nat) (J:nat), (((ord_less_eq_nat I_1) J)->((ord_less_eq_nat I_1) ((plus_plus_nat J) M)))) % FOF formula (forall (M:nat) (I_1:nat) (J:nat), (((ord_less_eq_nat I_1) J)->((ord_less_eq_nat I_1) ((plus_plus_nat M) J)))) of role axiom named fact_827_trans__le__add2 % A new axiom: (forall (M:nat) (I_1:nat) (J:nat), (((ord_less_eq_nat I_1) J)->((ord_less_eq_nat I_1) ((plus_plus_nat M) J)))) % FOF formula (forall (K:nat) (I_1:nat) (J:nat), (((ord_less_eq_nat I_1) J)->((ord_less_eq_nat ((plus_plus_nat I_1) K)) ((plus_plus_nat J) K)))) of role axiom named fact_828_add__le__mono1 % A new axiom: (forall (K:nat) (I_1:nat) (J:nat), (((ord_less_eq_nat I_1) J)->((ord_less_eq_nat ((plus_plus_nat I_1) K)) ((plus_plus_nat J) K)))) % FOF formula (forall (K:nat) (L:nat) (I_1:nat) (J:nat), (((ord_less_eq_nat I_1) J)->(((ord_less_eq_nat K) L)->((ord_less_eq_nat ((plus_plus_nat I_1) K)) ((plus_plus_nat J) L))))) of role axiom named fact_829_add__le__mono % A new axiom: (forall (K:nat) (L:nat) (I_1:nat) (J:nat), (((ord_less_eq_nat I_1) J)->(((ord_less_eq_nat K) L)->((ord_less_eq_nat ((plus_plus_nat I_1) K)) ((plus_plus_nat J) L))))) % FOF formula (forall (M:nat) (K:nat) (N:nat), (((ord_less_eq_nat ((plus_plus_nat M) K)) N)->((ord_less_eq_nat K) N))) of role axiom named fact_830_add__leD2 % A new axiom: (forall (M:nat) (K:nat) (N:nat), (((ord_less_eq_nat ((plus_plus_nat M) K)) N)->((ord_less_eq_nat K) N))) % FOF formula (forall (M:nat) (K:nat) (N:nat), (((ord_less_eq_nat ((plus_plus_nat M) K)) N)->((ord_less_eq_nat M) N))) of role axiom named fact_831_add__leD1 % A new axiom: (forall (M:nat) (K:nat) (N:nat), (((ord_less_eq_nat ((plus_plus_nat M) K)) N)->((ord_less_eq_nat M) N))) % FOF formula (forall (M:nat) (K:nat) (N:nat), (((ord_less_eq_nat ((plus_plus_nat M) K)) N)->((((ord_less_eq_nat M) N)->(((ord_less_eq_nat K) N)->False))->False))) of role axiom named fact_832_add__leE % A new axiom: (forall (M:nat) (K:nat) (N:nat), (((ord_less_eq_nat ((plus_plus_nat M) K)) N)->((((ord_less_eq_nat M) N)->(((ord_less_eq_nat K) N)->False))->False))) % FOF formula (forall (M:nat) (N:nat), (((eq nat) ((minus_minus_nat ((plus_plus_nat M) N)) N)) M)) of role axiom named fact_833_diff__add__inverse2 % A new axiom: (forall (M:nat) (N:nat), (((eq nat) ((minus_minus_nat ((plus_plus_nat M) N)) N)) M)) % FOF formula (forall (N:nat) (M:nat), (((eq nat) ((minus_minus_nat ((plus_plus_nat N) M)) N)) M)) of role axiom named fact_834_diff__add__inverse % A new axiom: (forall (N:nat) (M:nat), (((eq nat) ((minus_minus_nat ((plus_plus_nat N) M)) N)) M)) % FOF formula (forall (I_1:nat) (J:nat) (K:nat), (((eq nat) ((minus_minus_nat ((minus_minus_nat I_1) J)) K)) ((minus_minus_nat I_1) ((plus_plus_nat J) K)))) of role axiom named fact_835_diff__diff__left % A new axiom: (forall (I_1:nat) (J:nat) (K:nat), (((eq nat) ((minus_minus_nat ((minus_minus_nat I_1) J)) K)) ((minus_minus_nat I_1) ((plus_plus_nat J) K)))) % FOF formula (forall (K:nat) (M:nat) (N:nat), (((eq nat) ((minus_minus_nat ((plus_plus_nat K) M)) ((plus_plus_nat K) N))) ((minus_minus_nat M) N))) of role axiom named fact_836_diff__cancel % A new axiom: (forall (K:nat) (M:nat) (N:nat), (((eq nat) ((minus_minus_nat ((plus_plus_nat K) M)) ((plus_plus_nat K) N))) ((minus_minus_nat M) N))) % FOF formula (forall (M:nat) (K:nat) (N:nat), (((eq nat) ((minus_minus_nat ((plus_plus_nat M) K)) ((plus_plus_nat N) K))) ((minus_minus_nat M) N))) of role axiom named fact_837_diff__cancel2 % A new axiom: (forall (M:nat) (K:nat) (N:nat), (((eq nat) ((minus_minus_nat ((plus_plus_nat M) K)) ((plus_plus_nat N) K))) ((minus_minus_nat M) N))) % FOF formula (forall (I_1:nat) (K:nat) (J:nat), (((ord_less_eq_nat K) J)->(((eq nat) ((minus_minus_nat I_1) ((minus_minus_nat J) K))) ((minus_minus_nat ((plus_plus_nat I_1) K)) J)))) of role axiom named fact_838_diff__diff__right % A new axiom: (forall (I_1:nat) (K:nat) (J:nat), (((ord_less_eq_nat K) J)->(((eq nat) ((minus_minus_nat I_1) ((minus_minus_nat J) K))) ((minus_minus_nat ((plus_plus_nat I_1) K)) J)))) % FOF formula (forall (J:nat) (K:nat) (I_1:nat), ((iff ((ord_less_eq_nat ((minus_minus_nat J) K)) I_1)) ((ord_less_eq_nat J) ((plus_plus_nat I_1) K)))) of role axiom named fact_839_le__diff__conv % A new axiom: (forall (J:nat) (K:nat) (I_1:nat), ((iff ((ord_less_eq_nat ((minus_minus_nat J) K)) I_1)) ((ord_less_eq_nat J) ((plus_plus_nat I_1) K)))) % FOF formula (forall (M:nat) (K:nat) (N:nat), (((ord_less_eq_nat K) N)->((ord_less_eq_nat M) ((minus_minus_nat ((plus_plus_nat N) M)) K)))) of role axiom named fact_840_le__add__diff % A new axiom: (forall (M:nat) (K:nat) (N:nat), (((ord_less_eq_nat K) N)->((ord_less_eq_nat M) ((minus_minus_nat ((plus_plus_nat N) M)) K)))) % FOF formula (forall (N:nat) (M:nat), (((ord_less_eq_nat N) M)->(((eq nat) ((plus_plus_nat N) ((minus_minus_nat M) N))) M))) of role axiom named fact_841_le__add__diff__inverse % A new axiom: (forall (N:nat) (M:nat), (((ord_less_eq_nat N) M)->(((eq nat) ((plus_plus_nat N) ((minus_minus_nat M) N))) M))) % FOF formula (forall (I_1:nat) (K:nat) (J:nat), (((ord_less_eq_nat K) J)->(((eq nat) ((plus_plus_nat I_1) ((minus_minus_nat J) K))) ((minus_minus_nat ((plus_plus_nat I_1) J)) K)))) of role axiom named fact_842_add__diff__assoc % A new axiom: (forall (I_1:nat) (K:nat) (J:nat), (((ord_less_eq_nat K) J)->(((eq nat) ((plus_plus_nat I_1) ((minus_minus_nat J) K))) ((minus_minus_nat ((plus_plus_nat I_1) J)) K)))) % FOF formula (forall (I_1:nat) (K:nat) (J:nat), (((ord_less_eq_nat K) J)->((iff ((ord_less_eq_nat I_1) ((minus_minus_nat J) K))) ((ord_less_eq_nat ((plus_plus_nat I_1) K)) J)))) of role axiom named fact_843_le__diff__conv2 % A new axiom: (forall (I_1:nat) (K:nat) (J:nat), (((ord_less_eq_nat K) J)->((iff ((ord_less_eq_nat I_1) ((minus_minus_nat J) K))) ((ord_less_eq_nat ((plus_plus_nat I_1) K)) J)))) % FOF formula (forall (N:nat) (M:nat), (((ord_less_eq_nat N) M)->(((eq nat) ((plus_plus_nat ((minus_minus_nat M) N)) N)) M))) of role axiom named fact_844_le__add__diff__inverse2 % A new axiom: (forall (N:nat) (M:nat), (((ord_less_eq_nat N) M)->(((eq nat) ((plus_plus_nat ((minus_minus_nat M) N)) N)) M))) % FOF formula (forall (K:nat) (I_1:nat) (J:nat), (((ord_less_eq_nat I_1) J)->((iff (((eq nat) ((minus_minus_nat J) I_1)) K)) (((eq nat) J) ((plus_plus_nat K) I_1))))) of role axiom named fact_845_le__imp__diff__is__add % A new axiom: (forall (K:nat) (I_1:nat) (J:nat), (((ord_less_eq_nat I_1) J)->((iff (((eq nat) ((minus_minus_nat J) I_1)) K)) (((eq nat) J) ((plus_plus_nat K) I_1))))) % FOF formula (forall (I_1:nat) (K:nat) (J:nat), (((ord_less_eq_nat K) J)->(((eq nat) ((minus_minus_nat ((plus_plus_nat I_1) J)) K)) ((plus_plus_nat I_1) ((minus_minus_nat J) K))))) of role axiom named fact_846_diff__add__assoc % A new axiom: (forall (I_1:nat) (K:nat) (J:nat), (((ord_less_eq_nat K) J)->(((eq nat) ((minus_minus_nat ((plus_plus_nat I_1) J)) K)) ((plus_plus_nat I_1) ((minus_minus_nat J) K))))) % FOF formula (forall (I_1:nat) (K:nat) (J:nat), (((ord_less_eq_nat K) J)->(((eq nat) ((plus_plus_nat ((minus_minus_nat J) K)) I_1)) ((minus_minus_nat ((plus_plus_nat J) I_1)) K)))) of role axiom named fact_847_add__diff__assoc2 % A new axiom: (forall (I_1:nat) (K:nat) (J:nat), (((ord_less_eq_nat K) J)->(((eq nat) ((plus_plus_nat ((minus_minus_nat J) K)) I_1)) ((minus_minus_nat ((plus_plus_nat J) I_1)) K)))) % FOF formula (forall (I_1:nat) (K:nat) (J:nat), (((ord_less_eq_nat K) J)->(((eq nat) ((minus_minus_nat ((plus_plus_nat J) I_1)) K)) ((plus_plus_nat ((minus_minus_nat J) K)) I_1)))) of role axiom named fact_848_diff__add__assoc2 % A new axiom: (forall (I_1:nat) (K:nat) (J:nat), (((ord_less_eq_nat K) J)->(((eq nat) ((minus_minus_nat ((plus_plus_nat J) I_1)) K)) ((plus_plus_nat ((minus_minus_nat J) K)) I_1)))) % FOF formula (forall (N:nat), (((eq nat) (suc N)) ((plus_plus_nat one_one_nat) N))) of role axiom named fact_849_Suc__eq__plus1__left % A new axiom: (forall (N:nat), (((eq nat) (suc N)) ((plus_plus_nat one_one_nat) N))) % FOF formula (forall (N:nat), (((eq nat) (suc N)) ((plus_plus_nat N) one_one_nat))) of role axiom named fact_850_Suc__eq__plus1 % A new axiom: (forall (N:nat), (((eq nat) (suc N)) ((plus_plus_nat N) one_one_nat))) % FOF formula (forall (M:nat) (K:nat) (J:nat), (((ord_less_eq_nat K) J)->(((eq nat) ((minus_minus_nat M) (suc ((minus_minus_nat J) K)))) ((minus_minus_nat ((plus_plus_nat M) K)) (suc J))))) of role axiom named fact_851_diff__Suc__diff__eq1 % A new axiom: (forall (M:nat) (K:nat) (J:nat), (((ord_less_eq_nat K) J)->(((eq nat) ((minus_minus_nat M) (suc ((minus_minus_nat J) K)))) ((minus_minus_nat ((plus_plus_nat M) K)) (suc J))))) % FOF formula (forall (M:nat) (K:nat) (J:nat), (((ord_less_eq_nat K) J)->(((eq nat) ((minus_minus_nat (suc ((minus_minus_nat J) K))) M)) ((minus_minus_nat (suc J)) ((plus_plus_nat K) M))))) of role axiom named fact_852_diff__Suc__diff__eq2 % A new axiom: (forall (M:nat) (K:nat) (J:nat), (((ord_less_eq_nat K) J)->(((eq nat) ((minus_minus_nat (suc ((minus_minus_nat J) K))) M)) ((minus_minus_nat (suc J)) ((plus_plus_nat K) M))))) % FOF formula (forall (Y:nat) (X:nat) (Z:nat), (((ord_less_eq_nat X) Z)->((ord_less_eq_nat X) ((plus_plus_nat Y) Z)))) of role axiom named fact_853_termination__basic__simps_I4_J % A new axiom: (forall (Y:nat) (X:nat) (Z:nat), (((ord_less_eq_nat X) Z)->((ord_less_eq_nat X) ((plus_plus_nat Y) Z)))) % FOF formula (forall (Z:nat) (X:nat) (Y:nat), (((ord_less_eq_nat X) Y)->((ord_less_eq_nat X) ((plus_plus_nat Y) Z)))) of role axiom named fact_854_termination__basic__simps_I3_J % A new axiom: (forall (Z:nat) (X:nat) (Y:nat), (((ord_less_eq_nat X) Y)->((ord_less_eq_nat X) ((plus_plus_nat Y) Z)))) % FOF formula (forall (N:nat), ((ord_less_nat N) (suc N))) of role axiom named fact_855_lessI % A new axiom: (forall (N:nat), ((ord_less_nat N) (suc N))) % FOF formula (forall (M:nat) (N:nat), (((ord_less_nat M) N)->((ord_less_nat (suc M)) (suc N)))) of role axiom named fact_856_Suc__mono % A new axiom: (forall (M:nat) (N:nat), (((ord_less_nat M) N)->((ord_less_nat (suc M)) (suc N)))) % FOF formula (forall (K:nat), (finite_finite_nat (collect_nat (fun (N_1:nat)=> ((ord_less_nat N_1) K))))) of role axiom named fact_857_finite__Collect__less__nat % A new axiom: (forall (K:nat), (finite_finite_nat (collect_nat (fun (N_1:nat)=> ((ord_less_nat N_1) K))))) % FOF formula (forall (N:nat), (((ord_less_nat N) N)->False)) of role axiom named fact_858_less__not__refl % A new axiom: (forall (N:nat), (((ord_less_nat N) N)->False)) % FOF formula (forall (M:nat) (N:nat), ((iff (not (((eq nat) M) N))) ((or ((ord_less_nat M) N)) ((ord_less_nat N) M)))) of role axiom named fact_859_nat__neq__iff % A new axiom: (forall (M:nat) (N:nat), ((iff (not (((eq nat) M) N))) ((or ((ord_less_nat M) N)) ((ord_less_nat N) M)))) % FOF formula (forall (X:nat) (Y:nat), ((not (((eq nat) X) Y))->((((ord_less_nat X) Y)->False)->((ord_less_nat Y) X)))) of role axiom named fact_860_linorder__neqE__nat % A new axiom: (forall (X:nat) (Y:nat), ((not (((eq nat) X) Y))->((((ord_less_nat X) Y)->False)->((ord_less_nat Y) X)))) % FOF formula (forall (N:nat), (((ord_less_nat N) N)->False)) of role axiom named fact_861_less__irrefl__nat % A new axiom: (forall (N:nat), (((ord_less_nat N) N)->False)) % FOF formula (forall (N:nat) (M:nat), (((ord_less_nat N) M)->(not (((eq nat) M) N)))) of role axiom named fact_862_less__not__refl2 % A new axiom: (forall (N:nat) (M:nat), (((ord_less_nat N) M)->(not (((eq nat) M) N)))) % FOF formula (forall (S:nat) (T:nat), (((ord_less_nat S) T)->(not (((eq nat) S) T)))) of role axiom named fact_863_less__not__refl3 % A new axiom: (forall (S:nat) (T:nat), (((ord_less_nat S) T)->(not (((eq nat) S) T)))) % FOF formula (forall (P:(nat->(nat->Prop))) (M:nat) (N:nat), ((((ord_less_nat M) N)->((P N) M))->(((((eq nat) M) N)->((P N) M))->((((ord_less_nat N) M)->((P N) M))->((P N) M))))) of role axiom named fact_864_nat__less__cases % A new axiom: (forall (P:(nat->(nat->Prop))) (M:nat) (N:nat), ((((ord_less_nat M) N)->((P N) M))->(((((eq nat) M) N)->((P N) M))->((((ord_less_nat N) M)->((P N) M))->((P N) M))))) % FOF formula (forall (M:nat) (N:nat), ((iff (((ord_less_nat M) N)->False)) ((ord_less_nat N) (suc M)))) of role axiom named fact_865_not__less__eq % A new axiom: (forall (M:nat) (N:nat), ((iff (((ord_less_nat M) N)->False)) ((ord_less_nat N) (suc M)))) % FOF formula (forall (M:nat) (N:nat), ((iff ((ord_less_nat M) (suc N))) ((or ((ord_less_nat M) N)) (((eq nat) M) N)))) of role axiom named fact_866_less__Suc__eq % A new axiom: (forall (M:nat) (N:nat), ((iff ((ord_less_nat M) (suc N))) ((or ((ord_less_nat M) N)) (((eq nat) M) N)))) % FOF formula (forall (M:nat) (N:nat), ((iff ((ord_less_nat (suc M)) (suc N))) ((ord_less_nat M) N))) of role axiom named fact_867_Suc__less__eq % A new axiom: (forall (M:nat) (N:nat), ((iff ((ord_less_nat (suc M)) (suc N))) ((ord_less_nat M) N))) % FOF formula (forall (N:nat) (M:nat), ((((ord_less_nat N) M)->False)->((iff ((ord_less_nat N) (suc M))) (((eq nat) N) M)))) of role axiom named fact_868_not__less__less__Suc__eq % A new axiom: (forall (N:nat) (M:nat), ((((ord_less_nat N) M)->False)->((iff ((ord_less_nat N) (suc M))) (((eq nat) N) M)))) % FOF formula (forall (N:nat) (M:nat), ((((ord_less_nat N) M)->False)->(((ord_less_nat N) (suc M))->(((eq nat) M) N)))) of role axiom named fact_869_less__antisym % A new axiom: (forall (N:nat) (M:nat), ((((ord_less_nat N) M)->False)->(((ord_less_nat N) (suc M))->(((eq nat) M) N)))) % FOF formula (forall (M:nat) (N:nat), (((ord_less_nat M) N)->((ord_less_nat M) (suc N)))) of role axiom named fact_870_less__SucI % A new axiom: (forall (M:nat) (N:nat), (((ord_less_nat M) N)->((ord_less_nat M) (suc N)))) % FOF formula (forall (M:nat) (N:nat), (((ord_less_nat M) N)->((not (((eq nat) (suc M)) N))->((ord_less_nat (suc M)) N)))) of role axiom named fact_871_Suc__lessI % A new axiom: (forall (M:nat) (N:nat), (((ord_less_nat M) N)->((not (((eq nat) (suc M)) N))->((ord_less_nat (suc M)) N)))) % FOF formula (forall (K:nat) (I_1:nat) (J:nat), (((ord_less_nat I_1) J)->(((ord_less_nat J) K)->((ord_less_nat (suc I_1)) K)))) of role axiom named fact_872_less__trans__Suc % A new axiom: (forall (K:nat) (I_1:nat) (J:nat), (((ord_less_nat I_1) J)->(((ord_less_nat J) K)->((ord_less_nat (suc I_1)) K)))) % FOF formula (forall (M:nat) (N:nat), (((ord_less_nat M) (suc N))->((((ord_less_nat M) N)->False)->(((eq nat) M) N)))) of role axiom named fact_873_less__SucE % A new axiom: (forall (M:nat) (N:nat), (((ord_less_nat M) (suc N))->((((ord_less_nat M) N)->False)->(((eq nat) M) N)))) % FOF formula (forall (M:nat) (N:nat), (((ord_less_nat (suc M)) N)->((ord_less_nat M) N))) of role axiom named fact_874_Suc__lessD % A new axiom: (forall (M:nat) (N:nat), (((ord_less_nat (suc M)) N)->((ord_less_nat M) N))) % FOF formula (forall (M:nat) (N:nat), (((ord_less_nat (suc M)) (suc N))->((ord_less_nat M) N))) of role axiom named fact_875_Suc__less__SucD % A new axiom: (forall (M:nat) (N:nat), (((ord_less_nat (suc M)) (suc N))->((ord_less_nat M) N))) % FOF formula (forall (I_1:nat) (J:nat), (((ord_less_nat ((plus_plus_nat I_1) J)) I_1)->False)) of role axiom named fact_876_not__add__less1 % A new axiom: (forall (I_1:nat) (J:nat), (((ord_less_nat ((plus_plus_nat I_1) J)) I_1)->False)) % FOF formula (forall (J:nat) (I_1:nat), (((ord_less_nat ((plus_plus_nat J) I_1)) I_1)->False)) of role axiom named fact_877_not__add__less2 % A new axiom: (forall (J:nat) (I_1:nat), (((ord_less_nat ((plus_plus_nat J) I_1)) I_1)->False)) % FOF formula (forall (K:nat) (M:nat) (N:nat), ((iff ((ord_less_nat ((plus_plus_nat K) M)) ((plus_plus_nat K) N))) ((ord_less_nat M) N))) of role axiom named fact_878_nat__add__left__cancel__less % A new axiom: (forall (K:nat) (M:nat) (N:nat), ((iff ((ord_less_nat ((plus_plus_nat K) M)) ((plus_plus_nat K) N))) ((ord_less_nat M) N))) % FOF formula (forall (M:nat) (I_1:nat) (J:nat), (((ord_less_nat I_1) J)->((ord_less_nat I_1) ((plus_plus_nat J) M)))) of role axiom named fact_879_trans__less__add1 % A new axiom: (forall (M:nat) (I_1:nat) (J:nat), (((ord_less_nat I_1) J)->((ord_less_nat I_1) ((plus_plus_nat J) M)))) % FOF formula (forall (M:nat) (I_1:nat) (J:nat), (((ord_less_nat I_1) J)->((ord_less_nat I_1) ((plus_plus_nat M) J)))) of role axiom named fact_880_trans__less__add2 % A new axiom: (forall (M:nat) (I_1:nat) (J:nat), (((ord_less_nat I_1) J)->((ord_less_nat I_1) ((plus_plus_nat M) J)))) % FOF formula (forall (K:nat) (I_1:nat) (J:nat), (((ord_less_nat I_1) J)->((ord_less_nat ((plus_plus_nat I_1) K)) ((plus_plus_nat J) K)))) of role axiom named fact_881_add__less__mono1 % A new axiom: (forall (K:nat) (I_1:nat) (J:nat), (((ord_less_nat I_1) J)->((ord_less_nat ((plus_plus_nat I_1) K)) ((plus_plus_nat J) K)))) % FOF formula (forall (K:nat) (L:nat) (I_1:nat) (J:nat), (((ord_less_nat I_1) J)->(((ord_less_nat K) L)->((ord_less_nat ((plus_plus_nat I_1) K)) ((plus_plus_nat J) L))))) of role axiom named fact_882_add__less__mono % A new axiom: (forall (K:nat) (L:nat) (I_1:nat) (J:nat), (((ord_less_nat I_1) J)->(((ord_less_nat K) L)->((ord_less_nat ((plus_plus_nat I_1) K)) ((plus_plus_nat J) L))))) % FOF formula (forall (M:nat) (N:nat) (K:nat) (L:nat), (((ord_less_nat K) L)->((((eq nat) ((plus_plus_nat M) L)) ((plus_plus_nat K) N))->((ord_less_nat M) N)))) of role axiom named fact_883_less__add__eq__less % A new axiom: (forall (M:nat) (N:nat) (K:nat) (L:nat), (((ord_less_nat K) L)->((((eq nat) ((plus_plus_nat M) L)) ((plus_plus_nat K) N))->((ord_less_nat M) N)))) % FOF formula (forall (I_1:nat) (J:nat) (K:nat), (((ord_less_nat ((plus_plus_nat I_1) J)) K)->((ord_less_nat I_1) K))) of role axiom named fact_884_add__lessD1 % A new axiom: (forall (I_1:nat) (J:nat) (K:nat), (((ord_less_nat ((plus_plus_nat I_1) J)) K)->((ord_less_nat I_1) K))) % FOF formula (forall (Z:nat) (X:nat) (Y:nat), (((ord_less_nat X) Y)->((ord_less_nat X) ((plus_plus_nat Y) Z)))) of role axiom named fact_885_termination__basic__simps_I1_J % A new axiom: (forall (Z:nat) (X:nat) (Y:nat), (((ord_less_nat X) Y)->((ord_less_nat X) ((plus_plus_nat Y) Z)))) % FOF formula (forall (Y:nat) (X:nat) (Z:nat), (((ord_less_nat X) Z)->((ord_less_nat X) ((plus_plus_nat Y) Z)))) of role axiom named fact_886_termination__basic__simps_I2_J % A new axiom: (forall (Y:nat) (X:nat) (Z:nat), (((ord_less_nat X) Z)->((ord_less_nat X) ((plus_plus_nat Y) Z)))) % FOF formula (forall (M:nat) (N:nat), ((iff ((ord_less_nat M) N)) ((and ((ord_less_eq_nat M) N)) (not (((eq nat) M) N))))) of role axiom named fact_887_nat__less__le % A new axiom: (forall (M:nat) (N:nat), ((iff ((ord_less_nat M) N)) ((and ((ord_less_eq_nat M) N)) (not (((eq nat) M) N))))) % FOF formula (forall (M:nat) (N:nat), ((iff ((ord_less_eq_nat M) N)) ((or ((ord_less_nat M) N)) (((eq nat) M) N)))) of role axiom named fact_888_le__eq__less__or__eq % A new axiom: (forall (M:nat) (N:nat), ((iff ((ord_less_eq_nat M) N)) ((or ((ord_less_nat M) N)) (((eq nat) M) N)))) % FOF formula (forall (M:nat) (N:nat), (((ord_less_nat M) N)->((ord_less_eq_nat M) N))) of role axiom named fact_889_less__imp__le__nat % A new axiom: (forall (M:nat) (N:nat), (((ord_less_nat M) N)->((ord_less_eq_nat M) N))) % FOF formula (forall (M:nat) (N:nat), (((ord_less_eq_nat M) N)->((not (((eq nat) M) N))->((ord_less_nat M) N)))) of role axiom named fact_890_le__neq__implies__less % A new axiom: (forall (M:nat) (N:nat), (((ord_less_eq_nat M) N)->((not (((eq nat) M) N))->((ord_less_nat M) N)))) % FOF formula (forall (M:nat) (N:nat), (((or ((ord_less_nat M) N)) (((eq nat) M) N))->((ord_less_eq_nat M) N))) of role axiom named fact_891_less__or__eq__imp__le % A new axiom: (forall (M:nat) (N:nat), (((or ((ord_less_nat M) N)) (((eq nat) M) N))->((ord_less_eq_nat M) N))) % FOF formula (forall (X:nat) (Y:nat), (((ord_less_nat X) Y)->((ord_less_eq_nat X) Y))) of role axiom named fact_892_termination__basic__simps_I5_J % A new axiom: (forall (X:nat) (Y:nat), (((ord_less_nat X) Y)->((ord_less_eq_nat X) Y))) % FOF formula (forall (N:nat) (J:nat) (K:nat), (((ord_less_nat J) K)->((ord_less_nat ((minus_minus_nat J) N)) K))) of role axiom named fact_893_less__imp__diff__less % A new axiom: (forall (N:nat) (J:nat) (K:nat), (((ord_less_nat J) K)->((ord_less_nat ((minus_minus_nat J) N)) K))) % FOF formula (forall (L:nat) (M:nat) (N:nat), (((ord_less_nat M) N)->(((ord_less_nat M) L)->((ord_less_nat ((minus_minus_nat L) N)) ((minus_minus_nat L) M))))) of role axiom named fact_894_diff__less__mono2 % A new axiom: (forall (L:nat) (M:nat) (N:nat), (((ord_less_nat M) N)->(((ord_less_nat M) L)->((ord_less_nat ((minus_minus_nat L) N)) ((minus_minus_nat L) M))))) % FOF formula (forall (N_2:(nat->Prop)), ((iff (finite_finite_nat N_2)) ((ex nat) (fun (M_1:nat)=> (forall (X_1:nat), (((member_nat X_1) N_2)->((ord_less_nat X_1) M_1))))))) of role axiom named fact_895_finite__nat__set__iff__bounded % A new axiom: (forall (N_2:(nat->Prop)), ((iff (finite_finite_nat N_2)) ((ex nat) (fun (M_1:nat)=> (forall (X_1:nat), (((member_nat X_1) N_2)->((ord_less_nat X_1) M_1))))))) % FOF formula (forall (N:nat), (((eq nat) (finite_card_nat (collect_nat (fun (_TPTP_I:nat)=> ((ord_less_nat _TPTP_I) N))))) N)) of role axiom named fact_896_card__Collect__less__nat % A new axiom: (forall (N:nat), (((eq nat) (finite_card_nat (collect_nat (fun (_TPTP_I:nat)=> ((ord_less_nat _TPTP_I) N))))) N)) % FOF formula (forall (P:(nat->Prop)) (I_1:nat), (finite_finite_nat (collect_nat (fun (K_1:nat)=> ((and (P K_1)) ((ord_less_nat K_1) I_1)))))) of role axiom named fact_897_finite__M__bounded__by__nat % A new axiom: (forall (P:(nat->Prop)) (I_1:nat), (finite_finite_nat (collect_nat (fun (K_1:nat)=> ((and (P K_1)) ((ord_less_nat K_1) I_1)))))) % FOF formula (forall (I_1:nat) (M:nat), ((ord_less_nat I_1) (suc ((plus_plus_nat I_1) M)))) of role axiom named fact_898_less__add__Suc1 % A new axiom: (forall (I_1:nat) (M:nat), ((ord_less_nat I_1) (suc ((plus_plus_nat I_1) M)))) % FOF formula (forall (I_1:nat) (M:nat), ((ord_less_nat I_1) (suc ((plus_plus_nat M) I_1)))) of role axiom named fact_899_less__add__Suc2 % A new axiom: (forall (I_1:nat) (M:nat), ((ord_less_nat I_1) (suc ((plus_plus_nat M) I_1)))) % FOF formula (forall (M:nat) (N:nat), ((iff ((ord_less_nat M) N)) ((ex nat) (fun (K_1:nat)=> (((eq nat) N) (suc ((plus_plus_nat M) K_1))))))) of role axiom named fact_900_less__iff__Suc__add % A new axiom: (forall (M:nat) (N:nat), ((iff ((ord_less_nat M) N)) ((ex nat) (fun (K_1:nat)=> (((eq nat) N) (suc ((plus_plus_nat M) K_1))))))) % FOF formula (forall (N:nat) (M:nat), ((iff ((ord_less_nat N) M)) ((ord_less_eq_nat (suc N)) M))) of role axiom named fact_901_less__eq__Suc__le % A new axiom: (forall (N:nat) (M:nat), ((iff ((ord_less_nat N) M)) ((ord_less_eq_nat (suc N)) M))) % FOF formula (forall (M:nat) (N:nat), ((iff ((ord_less_nat M) (suc N))) ((ord_less_eq_nat M) N))) of role axiom named fact_902_less__Suc__eq__le % A new axiom: (forall (M:nat) (N:nat), ((iff ((ord_less_nat M) (suc N))) ((ord_less_eq_nat M) N))) % FOF formula (forall (M:nat) (N:nat), ((iff ((ord_less_eq_nat (suc M)) N)) ((ord_less_nat M) N))) of role axiom named fact_903_Suc__le__eq % A new axiom: (forall (M:nat) (N:nat), ((iff ((ord_less_eq_nat (suc M)) N)) ((ord_less_nat M) N))) % FOF formula (forall (M:nat) (N:nat), (((ord_less_eq_nat M) N)->((ord_less_nat M) (suc N)))) of role axiom named fact_904_le__imp__less__Suc % A new axiom: (forall (M:nat) (N:nat), (((ord_less_eq_nat M) N)->((ord_less_nat M) (suc N)))) % FOF formula (forall (M:nat) (N:nat), (((ord_less_nat M) N)->((ord_less_eq_nat (suc M)) N))) of role axiom named fact_905_Suc__leI % A new axiom: (forall (M:nat) (N:nat), (((ord_less_nat M) N)->((ord_less_eq_nat (suc M)) N))) % FOF formula (forall (M:nat) (N:nat), (((ord_less_eq_nat M) N)->((iff ((ord_less_nat N) (suc M))) (((eq nat) N) M)))) of role axiom named fact_906_le__less__Suc__eq % A new axiom: (forall (M:nat) (N:nat), (((ord_less_eq_nat M) N)->((iff ((ord_less_nat N) (suc M))) (((eq nat) N) M)))) % FOF formula (forall (M:nat) (N:nat), (((ord_less_eq_nat (suc M)) N)->((ord_less_nat M) N))) of role axiom named fact_907_Suc__le__lessD % A new axiom: (forall (M:nat) (N:nat), (((ord_less_eq_nat (suc M)) N)->((ord_less_nat M) N))) % FOF formula (forall (M:nat) (N:nat), ((ord_less_nat ((minus_minus_nat M) N)) (suc M))) of role axiom named fact_908_diff__less__Suc % A new axiom: (forall (M:nat) (N:nat), ((ord_less_nat ((minus_minus_nat M) N)) (suc M))) % FOF formula (forall (I_1:nat) (J:nat) (K:nat), ((iff ((ord_less_nat I_1) ((minus_minus_nat J) K))) ((ord_less_nat ((plus_plus_nat I_1) K)) J))) of role axiom named fact_909_less__diff__conv % A new axiom: (forall (I_1:nat) (J:nat) (K:nat), ((iff ((ord_less_nat I_1) ((minus_minus_nat J) K))) ((ord_less_nat ((plus_plus_nat I_1) K)) J))) % FOF formula (forall (M:nat) (N:nat), ((((ord_less_nat M) N)->False)->(((eq nat) ((plus_plus_nat N) ((minus_minus_nat M) N))) M))) of role axiom named fact_910_add__diff__inverse % A new axiom: (forall (M:nat) (N:nat), ((((ord_less_nat M) N)->False)->(((eq nat) ((plus_plus_nat N) ((minus_minus_nat M) N))) M))) % FOF formula (forall (C:nat) (A_1:nat) (B_2:nat), (((ord_less_nat A_1) B_2)->(((ord_less_eq_nat C) A_1)->((ord_less_nat ((minus_minus_nat A_1) C)) ((minus_minus_nat B_2) C))))) of role axiom named fact_911_diff__less__mono % A new axiom: (forall (C:nat) (A_1:nat) (B_2:nat), (((ord_less_nat A_1) B_2)->(((ord_less_eq_nat C) A_1)->((ord_less_nat ((minus_minus_nat A_1) C)) ((minus_minus_nat B_2) C))))) % FOF formula (forall (N:nat) (K:nat) (M:nat), (((ord_less_eq_nat K) M)->(((ord_less_eq_nat K) N)->((iff ((ord_less_nat ((minus_minus_nat M) K)) ((minus_minus_nat N) K))) ((ord_less_nat M) N))))) of role axiom named fact_912_less__diff__iff % A new axiom: (forall (N:nat) (K:nat) (M:nat), (((ord_less_eq_nat K) M)->(((ord_less_eq_nat K) N)->((iff ((ord_less_nat ((minus_minus_nat M) K)) ((minus_minus_nat N) K))) ((ord_less_nat M) N))))) % FOF formula (forall (X_1:nat), (((eq (nat->Prop)) (ord_less_nat X_1)) (ord_less_eq_nat (suc X_1)))) of role axiom named fact_913_less__eq__Suc__le__raw % A new axiom: (forall (X_1:nat), (((eq (nat->Prop)) (ord_less_nat X_1)) (ord_less_eq_nat (suc X_1)))) % FOF formula (forall (M:nat) (K:nat) (F:(nat->nat)), ((forall (M_1:nat) (N_1:nat), (((ord_less_nat M_1) N_1)->((ord_less_nat (F M_1)) (F N_1))))->((ord_less_eq_nat ((plus_plus_nat (F M)) K)) (F ((plus_plus_nat M) K))))) of role axiom named fact_914_mono__nat__linear__lb % A new axiom: (forall (M:nat) (K:nat) (F:(nat->nat)), ((forall (M_1:nat) (N_1:nat), (((ord_less_nat M_1) N_1)->((ord_less_nat (F M_1)) (F N_1))))->((ord_less_eq_nat ((plus_plus_nat (F M)) K)) (F ((plus_plus_nat M) K))))) % FOF formula (forall (P:(nat->Prop)) (I_1:nat) (J:nat), (((ord_less_eq_nat I_1) J)->((P J)->((forall (_TPTP_I:nat), (((ord_less_nat _TPTP_I) J)->((P (suc _TPTP_I))->(P _TPTP_I))))->(P I_1))))) of role axiom named fact_915_inc__induct % A new axiom: (forall (P:(nat->Prop)) (I_1:nat) (J:nat), (((ord_less_eq_nat I_1) J)->((P J)->((forall (_TPTP_I:nat), (((ord_less_nat _TPTP_I) J)->((P (suc _TPTP_I))->(P _TPTP_I))))->(P I_1))))) % FOF formula (forall (M:nat) (N:nat), (((ord_less_nat M) N)->((ex nat) (fun (K_1:nat)=> (((eq nat) N) (suc ((plus_plus_nat M) K_1))))))) of role axiom named fact_916_less__imp__Suc__add % A new axiom: (forall (M:nat) (N:nat), (((ord_less_nat M) N)->((ex nat) (fun (K_1:nat)=> (((eq nat) N) (suc ((plus_plus_nat M) K_1))))))) % FOF formula (forall (N:nat) (N_2:(nat->Prop)), ((forall (X_1:nat), (((member_nat X_1) N_2)->((ord_less_nat X_1) N)))->(finite_finite_nat N_2))) of role axiom named fact_917_bounded__nat__set__is__finite % A new axiom: (forall (N:nat) (N_2:(nat->Prop)), ((forall (X_1:nat), (((member_nat X_1) N_2)->((ord_less_nat X_1) N)))->(finite_finite_nat N_2))) % FOF formula (forall (I_1:nat) (J:nat) (F:(nat->nat)), ((forall (_TPTP_I:nat) (J_1:nat), (((ord_less_nat _TPTP_I) J_1)->((ord_less_nat (F _TPTP_I)) (F J_1))))->(((ord_less_eq_nat I_1) J)->((ord_less_eq_nat (F I_1)) (F J))))) of role axiom named fact_918_less__mono__imp__le__mono % A new axiom: (forall (I_1:nat) (J:nat) (F:(nat->nat)), ((forall (_TPTP_I:nat) (J_1:nat), (((ord_less_nat _TPTP_I) J_1)->((ord_less_nat (F _TPTP_I)) (F J_1))))->(((ord_less_eq_nat I_1) J)->((ord_less_eq_nat (F I_1)) (F J))))) % FOF formula (forall (I_1:nat) (K:nat), (((ord_less_nat I_1) K)->((not (((eq nat) K) (suc I_1)))->((forall (J_1:nat), (((ord_less_nat I_1) J_1)->(not (((eq nat) K) (suc J_1)))))->False)))) of role axiom named fact_919_lessE % A new axiom: (forall (I_1:nat) (K:nat), (((ord_less_nat I_1) K)->((not (((eq nat) K) (suc I_1)))->((forall (J_1:nat), (((ord_less_nat I_1) J_1)->(not (((eq nat) K) (suc J_1)))))->False)))) % FOF formula (forall (I_1:nat) (K:nat), (((ord_less_nat (suc I_1)) K)->((forall (J_1:nat), (((ord_less_nat I_1) J_1)->(not (((eq nat) K) (suc J_1)))))->False))) of role axiom named fact_920_Suc__lessE % A new axiom: (forall (I_1:nat) (K:nat), (((ord_less_nat (suc I_1)) K)->((forall (J_1:nat), (((ord_less_nat I_1) J_1)->(not (((eq nat) K) (suc J_1)))))->False))) % FOF formula (forall (N:nat), (((ord_less_nat N) zero_zero_nat)->False)) of role axiom named fact_921_less__zeroE % A new axiom: (forall (N:nat), (((ord_less_nat N) zero_zero_nat)->False)) % FOF formula (forall (N:nat), ((ord_less_eq_nat zero_zero_nat) N)) of role axiom named fact_922_le0 % A new axiom: (forall (N:nat), ((ord_less_eq_nat zero_zero_nat) N)) % FOF formula (forall (N:nat), ((ord_less_nat zero_zero_nat) (suc N))) of role axiom named fact_923_zero__less__Suc % A new axiom: (forall (N:nat), ((ord_less_nat zero_zero_nat) (suc N))) % FOF formula (forall (N:nat), ((iff ((ord_less_eq_nat N) zero_zero_nat)) (((eq nat) N) zero_zero_nat))) of role axiom named fact_924_le__0__eq % A new axiom: (forall (N:nat), ((iff ((ord_less_eq_nat N) zero_zero_nat)) (((eq nat) N) zero_zero_nat))) % FOF formula (forall (N:nat), ((ord_less_eq_nat zero_zero_nat) N)) of role axiom named fact_925_less__eq__nat_Osimps_I1_J % A new axiom: (forall (N:nat), ((ord_less_eq_nat zero_zero_nat) N)) % FOF formula (forall (M:nat) (N:nat), ((((eq nat) ((minus_minus_nat M) N)) zero_zero_nat)->((((eq nat) ((minus_minus_nat N) M)) zero_zero_nat)->(((eq nat) M) N)))) of role axiom named fact_926_diffs0__imp__equal % A new axiom: (forall (M:nat) (N:nat), ((((eq nat) ((minus_minus_nat M) N)) zero_zero_nat)->((((eq nat) ((minus_minus_nat N) M)) zero_zero_nat)->(((eq nat) M) N)))) % FOF formula (forall (M:nat), (((eq nat) ((minus_minus_nat M) M)) zero_zero_nat)) of role axiom named fact_927_diff__self__eq__0 % A new axiom: (forall (M:nat), (((eq nat) ((minus_minus_nat M) M)) zero_zero_nat)) % FOF formula (forall (M:nat), (((eq nat) ((minus_minus_nat M) zero_zero_nat)) M)) of role axiom named fact_928_minus__nat_Odiff__0 % A new axiom: (forall (M:nat), (((eq nat) ((minus_minus_nat M) zero_zero_nat)) M)) % FOF formula (forall (N:nat), (((eq nat) ((minus_minus_nat zero_zero_nat) N)) zero_zero_nat)) of role axiom named fact_929_diff__0__eq__0 % A new axiom: (forall (N:nat), (((eq nat) ((minus_minus_nat zero_zero_nat) N)) zero_zero_nat)) % FOF formula (((eq nat) bot_bot_nat) zero_zero_nat) of role axiom named fact_930_bot__nat__def % A new axiom: (((eq nat) bot_bot_nat) zero_zero_nat) % FOF formula (forall (M:nat) (N:nat), ((((eq nat) ((plus_plus_nat M) N)) M)->(((eq nat) N) zero_zero_nat))) of role axiom named fact_931_add__eq__self__zero % A new axiom: (forall (M:nat) (N:nat), ((((eq nat) ((plus_plus_nat M) N)) M)->(((eq nat) N) zero_zero_nat))) % FOF formula (forall (M:nat) (N:nat), ((iff (((eq nat) ((plus_plus_nat M) N)) zero_zero_nat)) ((and (((eq nat) M) zero_zero_nat)) (((eq nat) N) zero_zero_nat)))) of role axiom named fact_932_add__is__0 % A new axiom: (forall (M:nat) (N:nat), ((iff (((eq nat) ((plus_plus_nat M) N)) zero_zero_nat)) ((and (((eq nat) M) zero_zero_nat)) (((eq nat) N) zero_zero_nat)))) % FOF formula (forall (M:nat), (((eq nat) ((plus_plus_nat M) zero_zero_nat)) M)) of role axiom named fact_933_Nat_Oadd__0__right % A new axiom: (forall (M:nat), (((eq nat) ((plus_plus_nat M) zero_zero_nat)) M)) % FOF formula (forall (N:nat), (((eq nat) ((plus_plus_nat zero_zero_nat) N)) N)) of role axiom named fact_934_plus__nat_Oadd__0 % A new axiom: (forall (N:nat), (((eq nat) ((plus_plus_nat zero_zero_nat) N)) N)) % FOF formula (forall (N:nat), ((not (((eq nat) N) zero_zero_nat))->((ord_less_nat zero_zero_nat) N))) of role axiom named fact_935_gr0I % A new axiom: (forall (N:nat), ((not (((eq nat) N) zero_zero_nat))->((ord_less_nat zero_zero_nat) N))) % FOF formula (forall (M:nat) (N:nat), (((ord_less_nat M) N)->(not (((eq nat) N) zero_zero_nat)))) of role axiom named fact_936_gr__implies__not0 % A new axiom: (forall (M:nat) (N:nat), (((ord_less_nat M) N)->(not (((eq nat) N) zero_zero_nat)))) % FOF formula (forall (N:nat), (((ord_less_nat N) zero_zero_nat)->False)) of role axiom named fact_937_less__nat__zero__code % A new axiom: (forall (N:nat), (((ord_less_nat N) zero_zero_nat)->False)) % FOF formula (forall (N:nat), ((iff (not (((eq nat) N) zero_zero_nat))) ((ord_less_nat zero_zero_nat) N))) of role axiom named fact_938_neq0__conv % A new axiom: (forall (N:nat), ((iff (not (((eq nat) N) zero_zero_nat))) ((ord_less_nat zero_zero_nat) N))) % FOF formula (forall (N:nat), (((ord_less_nat N) zero_zero_nat)->False)) of role axiom named fact_939_not__less0 % A new axiom: (forall (N:nat), (((ord_less_nat N) zero_zero_nat)->False)) % FOF formula (forall (M:nat), (not (((eq nat) (suc M)) zero_zero_nat))) of role axiom named fact_940_Suc__neq__Zero % A new axiom: (forall (M:nat), (not (((eq nat) (suc M)) zero_zero_nat))) % FOF formula (forall (M:nat), (not (((eq nat) zero_zero_nat) (suc M)))) of role axiom named fact_941_Zero__neq__Suc % A new axiom: (forall (M:nat), (not (((eq nat) zero_zero_nat) (suc M)))) % FOF formula (forall (Nat_2:nat), (not (((eq nat) (suc Nat_2)) zero_zero_nat))) of role axiom named fact_942_nat_Osimps_I3_J % A new axiom: (forall (Nat_2:nat), (not (((eq nat) (suc Nat_2)) zero_zero_nat))) % FOF formula (forall (M:nat), (not (((eq nat) (suc M)) zero_zero_nat))) of role axiom named fact_943_Suc__not__Zero % A new axiom: (forall (M:nat), (not (((eq nat) (suc M)) zero_zero_nat))) % FOF formula (forall (Nat_1:nat), (not (((eq nat) zero_zero_nat) (suc Nat_1)))) of role axiom named fact_944_nat_Osimps_I2_J % A new axiom: (forall (Nat_1:nat), (not (((eq nat) zero_zero_nat) (suc Nat_1)))) % FOF formula (forall (M:nat), (not (((eq nat) zero_zero_nat) (suc M)))) of role axiom named fact_945_Zero__not__Suc % A new axiom: (forall (M:nat), (not (((eq nat) zero_zero_nat) (suc M)))) % FOF formula (forall (N:nat), ((iff ((ord_less_nat zero_zero_nat) N)) ((ex nat) (fun (M_1:nat)=> (((eq nat) N) (suc M_1)))))) of role axiom named fact_946_gr0__conv__Suc % A new axiom: (forall (N:nat), ((iff ((ord_less_nat zero_zero_nat) N)) ((ex nat) (fun (M_1:nat)=> (((eq nat) N) (suc M_1)))))) % FOF formula (forall (N:nat), ((iff ((ord_less_nat N) (suc zero_zero_nat))) (((eq nat) N) zero_zero_nat))) of role axiom named fact_947_less__Suc0 % A new axiom: (forall (N:nat), ((iff ((ord_less_nat N) (suc zero_zero_nat))) (((eq nat) N) zero_zero_nat))) % FOF formula (forall (M:nat) (N:nat), ((iff ((ord_less_nat M) (suc N))) ((or (((eq nat) M) zero_zero_nat)) ((ex nat) (fun (J_1:nat)=> ((and (((eq nat) M) (suc J_1))) ((ord_less_nat J_1) N))))))) of role axiom named fact_948_less__Suc__eq__0__disj % A new axiom: (forall (M:nat) (N:nat), ((iff ((ord_less_nat M) (suc N))) ((or (((eq nat) M) zero_zero_nat)) ((ex nat) (fun (J_1:nat)=> ((and (((eq nat) M) (suc J_1))) ((ord_less_nat J_1) N))))))) % FOF formula (forall (M:nat) (N:nat), ((iff (((eq nat) (suc zero_zero_nat)) ((plus_plus_nat M) N))) ((or ((and (((eq nat) M) (suc zero_zero_nat))) (((eq nat) N) zero_zero_nat))) ((and (((eq nat) M) zero_zero_nat)) (((eq nat) N) (suc zero_zero_nat)))))) of role axiom named fact_949_one__is__add % A new axiom: (forall (M:nat) (N:nat), ((iff (((eq nat) (suc zero_zero_nat)) ((plus_plus_nat M) N))) ((or ((and (((eq nat) M) (suc zero_zero_nat))) (((eq nat) N) zero_zero_nat))) ((and (((eq nat) M) zero_zero_nat)) (((eq nat) N) (suc zero_zero_nat)))))) % FOF formula (forall (M:nat) (N:nat), ((iff (((eq nat) ((plus_plus_nat M) N)) (suc zero_zero_nat))) ((or ((and (((eq nat) M) (suc zero_zero_nat))) (((eq nat) N) zero_zero_nat))) ((and (((eq nat) M) zero_zero_nat)) (((eq nat) N) (suc zero_zero_nat)))))) of role axiom named fact_950_add__is__1 % A new axiom: (forall (M:nat) (N:nat), ((iff (((eq nat) ((plus_plus_nat M) N)) (suc zero_zero_nat))) ((or ((and (((eq nat) M) (suc zero_zero_nat))) (((eq nat) N) zero_zero_nat))) ((and (((eq nat) M) zero_zero_nat)) (((eq nat) N) (suc zero_zero_nat)))))) % FOF formula (forall (M:nat) (N:nat), ((iff ((ord_less_nat zero_zero_nat) ((plus_plus_nat M) N))) ((or ((ord_less_nat zero_zero_nat) M)) ((ord_less_nat zero_zero_nat) N)))) of role axiom named fact_951_add__gr__0 % A new axiom: (forall (M:nat) (N:nat), ((iff ((ord_less_nat zero_zero_nat) ((plus_plus_nat M) N))) ((or ((ord_less_nat zero_zero_nat) M)) ((ord_less_nat zero_zero_nat) N)))) % FOF formula (forall (N:nat) (M:nat), ((iff ((ord_less_nat zero_zero_nat) ((minus_minus_nat N) M))) ((ord_less_nat M) N))) of role axiom named fact_952_zero__less__diff % A new axiom: (forall (N:nat) (M:nat), ((iff ((ord_less_nat zero_zero_nat) ((minus_minus_nat N) M))) ((ord_less_nat M) N))) % FOF formula (forall (M:nat) (N:nat), (((ord_less_nat zero_zero_nat) N)->(((ord_less_nat zero_zero_nat) M)->((ord_less_nat ((minus_minus_nat M) N)) M)))) of role axiom named fact_953_diff__less % A new axiom: (forall (M:nat) (N:nat), (((ord_less_nat zero_zero_nat) N)->(((ord_less_nat zero_zero_nat) M)->((ord_less_nat ((minus_minus_nat M) N)) M)))) % FOF formula (forall (N:nat) (M:nat), (((eq nat) ((minus_minus_nat N) ((plus_plus_nat N) M))) zero_zero_nat)) of role axiom named fact_954_diff__add__0 % A new axiom: (forall (N:nat) (M:nat), (((eq nat) ((minus_minus_nat N) ((plus_plus_nat N) M))) zero_zero_nat)) % FOF formula (forall (M:nat) (N:nat), ((iff (((eq nat) ((minus_minus_nat M) N)) zero_zero_nat)) ((ord_less_eq_nat M) N))) of role axiom named fact_955_diff__is__0__eq % A new axiom: (forall (M:nat) (N:nat), ((iff (((eq nat) ((minus_minus_nat M) N)) zero_zero_nat)) ((ord_less_eq_nat M) N))) % FOF formula (forall (M:nat) (N:nat), (((ord_less_eq_nat M) N)->(((eq nat) ((minus_minus_nat M) N)) zero_zero_nat))) of role axiom named fact_956_diff__is__0__eq_H % A new axiom: (forall (M:nat) (N:nat), (((ord_less_eq_nat M) N)->(((eq nat) ((minus_minus_nat M) N)) zero_zero_nat))) % FOF formula (((eq nat) one_one_nat) (suc zero_zero_nat)) of role axiom named fact_957_One__nat__def % A new axiom: (((eq nat) one_one_nat) (suc zero_zero_nat)) % FOF formula (forall (M:nat) (N:nat), (((eq nat) ((minus_minus_nat M) (suc N))) (((nat_case_nat zero_zero_nat) (fun (K_1:nat)=> K_1)) ((minus_minus_nat M) N)))) of role axiom named fact_958_diff__Suc % A new axiom: (forall (M:nat) (N:nat), (((eq nat) ((minus_minus_nat M) (suc N))) (((nat_case_nat zero_zero_nat) (fun (K_1:nat)=> K_1)) ((minus_minus_nat M) N)))) % FOF formula (forall (N:nat), (((ord_less_nat zero_zero_nat) N)->(((eq nat) (suc ((minus_minus_nat N) (suc zero_zero_nat)))) N))) of role axiom named fact_959_Suc__pred % A new axiom: (forall (N:nat), (((ord_less_nat zero_zero_nat) N)->(((eq nat) (suc ((minus_minus_nat N) (suc zero_zero_nat)))) N))) % FOF formula (forall (I_1:nat) (N:nat), (((ord_less_nat zero_zero_nat) N)->((ord_less_nat ((minus_minus_nat N) (suc I_1))) N))) of role axiom named fact_960_diff__Suc__less % A new axiom: (forall (I_1:nat) (N:nat), (((ord_less_nat zero_zero_nat) N)->((ord_less_nat ((minus_minus_nat N) (suc I_1))) N))) % FOF formula (forall (P:(nat->Prop)) (A_1:nat) (B_2:nat), ((iff (P ((minus_minus_nat A_1) B_2))) ((and (((ord_less_nat A_1) B_2)->(P zero_zero_nat))) (forall (D_1:nat), ((((eq nat) A_1) ((plus_plus_nat B_2) D_1))->(P D_1)))))) of role axiom named fact_961_nat__diff__split % A new axiom: (forall (P:(nat->Prop)) (A_1:nat) (B_2:nat), ((iff (P ((minus_minus_nat A_1) B_2))) ((and (((ord_less_nat A_1) B_2)->(P zero_zero_nat))) (forall (D_1:nat), ((((eq nat) A_1) ((plus_plus_nat B_2) D_1))->(P D_1)))))) % FOF formula (forall (P:(nat->Prop)) (A_1:nat) (B_2:nat), ((iff (P ((minus_minus_nat A_1) B_2))) (((or ((and ((ord_less_nat A_1) B_2)) ((P zero_zero_nat)->False))) ((ex nat) (fun (D_1:nat)=> ((and (((eq nat) A_1) ((plus_plus_nat B_2) D_1))) ((P D_1)->False)))))->False))) of role axiom named fact_962_nat__diff__split__asm % A new axiom: (forall (P:(nat->Prop)) (A_1:nat) (B_2:nat), ((iff (P ((minus_minus_nat A_1) B_2))) (((or ((and ((ord_less_nat A_1) B_2)) ((P zero_zero_nat)->False))) ((ex nat) (fun (D_1:nat)=> ((and (((eq nat) A_1) ((plus_plus_nat B_2) D_1))) ((P D_1)->False)))))->False))) % FOF formula (forall (I_1:nat) (M_2:(nat->Prop)), (((member_nat zero_zero_nat) M_2)->(((eq nat) (suc (finite_card_nat (collect_nat (fun (K_1:nat)=> ((and ((member_nat (suc K_1)) M_2)) ((ord_less_nat K_1) I_1))))))) (finite_card_nat (collect_nat (fun (K_1:nat)=> ((and ((member_nat K_1) M_2)) ((ord_less_nat K_1) (suc I_1))))))))) of role axiom named fact_963_card__less__Suc % A new axiom: (forall (I_1:nat) (M_2:(nat->Prop)), (((member_nat zero_zero_nat) M_2)->(((eq nat) (suc (finite_card_nat (collect_nat (fun (K_1:nat)=> ((and ((member_nat (suc K_1)) M_2)) ((ord_less_nat K_1) I_1))))))) (finite_card_nat (collect_nat (fun (K_1:nat)=> ((and ((member_nat K_1) M_2)) ((ord_less_nat K_1) (suc I_1))))))))) % FOF formula (forall (I_1:nat) (M_2:(nat->Prop)), (((member_nat zero_zero_nat) M_2)->(not (((eq nat) (finite_card_nat (collect_nat (fun (K_1:nat)=> ((and ((member_nat K_1) M_2)) ((ord_less_nat K_1) (suc I_1))))))) zero_zero_nat)))) of role axiom named fact_964_card__less % A new axiom: (forall (I_1:nat) (M_2:(nat->Prop)), (((member_nat zero_zero_nat) M_2)->(not (((eq nat) (finite_card_nat (collect_nat (fun (K_1:nat)=> ((and ((member_nat K_1) M_2)) ((ord_less_nat K_1) (suc I_1))))))) zero_zero_nat)))) % FOF formula (forall (I_1:nat) (M_2:(nat->Prop)), ((((member_nat zero_zero_nat) M_2)->False)->(((eq nat) (finite_card_nat (collect_nat (fun (K_1:nat)=> ((and ((member_nat (suc K_1)) M_2)) ((ord_less_nat K_1) I_1)))))) (finite_card_nat (collect_nat (fun (K_1:nat)=> ((and ((member_nat K_1) M_2)) ((ord_less_nat K_1) (suc I_1))))))))) of role axiom named fact_965_card__less__Suc2 % A new axiom: (forall (I_1:nat) (M_2:(nat->Prop)), ((((member_nat zero_zero_nat) M_2)->False)->(((eq nat) (finite_card_nat (collect_nat (fun (K_1:nat)=> ((and ((member_nat (suc K_1)) M_2)) ((ord_less_nat K_1) I_1)))))) (finite_card_nat (collect_nat (fun (K_1:nat)=> ((and ((member_nat K_1) M_2)) ((ord_less_nat K_1) (suc I_1))))))))) % FOF formula (forall (N:nat), (((ord_less_nat zero_zero_nat) N)->(((eq nat) (suc ((minus_minus_nat N) one_one_nat))) N))) of role axiom named fact_966_Suc__diff__1 % A new axiom: (forall (N:nat), (((ord_less_nat zero_zero_nat) N)->(((eq nat) (suc ((minus_minus_nat N) one_one_nat))) N))) % FOF formula (forall (N:nat), (((ord_less_nat zero_zero_nat) N)->(((eq nat) N) (suc ((minus_minus_nat N) one_one_nat))))) of role axiom named fact_967_Suc__pred_H % A new axiom: (forall (N:nat), (((ord_less_nat zero_zero_nat) N)->(((eq nat) N) (suc ((minus_minus_nat N) one_one_nat))))) % FOF formula (forall (N:nat) (M:nat), ((and ((((eq nat) M) zero_zero_nat)->(((eq nat) ((plus_plus_nat M) N)) N))) ((not (((eq nat) M) zero_zero_nat))->(((eq nat) ((plus_plus_nat M) N)) (suc ((plus_plus_nat ((minus_minus_nat M) one_one_nat)) N)))))) of role axiom named fact_968_add__eq__if % A new axiom: (forall (N:nat) (M:nat), ((and ((((eq nat) M) zero_zero_nat)->(((eq nat) ((plus_plus_nat M) N)) N))) ((not (((eq nat) M) zero_zero_nat))->(((eq nat) ((plus_plus_nat M) N)) (suc ((plus_plus_nat ((minus_minus_nat M) one_one_nat)) N)))))) % FOF formula (forall (N:nat) (P:(nat->Prop)), (((P zero_zero_nat)->False)->((P N)->((ex nat) (fun (K_1:nat)=> ((and ((and ((ord_less_nat K_1) N)) (forall (_TPTP_I:nat), (((ord_less_eq_nat _TPTP_I) K_1)->((P _TPTP_I)->False))))) (P ((plus_plus_nat K_1) one_one_nat)))))))) of role axiom named fact_969_ex__least__nat__less % A new axiom: (forall (N:nat) (P:(nat->Prop)), (((P zero_zero_nat)->False)->((P N)->((ex nat) (fun (K_1:nat)=> ((and ((and ((ord_less_nat K_1) N)) (forall (_TPTP_I:nat), (((ord_less_eq_nat _TPTP_I) K_1)->((P _TPTP_I)->False))))) (P ((plus_plus_nat K_1) one_one_nat)))))))) % FOF formula (forall (N:nat) (P:(nat->Prop)), (((P zero_zero_nat)->False)->((P N)->((ex nat) (fun (K_1:nat)=> ((and ((and ((ord_less_eq_nat K_1) N)) (forall (_TPTP_I:nat), (((ord_less_nat _TPTP_I) K_1)->((P _TPTP_I)->False))))) (P K_1))))))) of role axiom named fact_970_ex__least__nat__le % A new axiom: (forall (N:nat) (P:(nat->Prop)), (((P zero_zero_nat)->False)->((P N)->((ex nat) (fun (K_1:nat)=> ((and ((and ((ord_less_eq_nat K_1) N)) (forall (_TPTP_I:nat), (((ord_less_nat _TPTP_I) K_1)->((P _TPTP_I)->False))))) (P K_1))))))) % FOF formula (forall (I_1:nat) (J:nat), (((ord_less_nat I_1) J)->((ex nat) (fun (K_1:nat)=> ((and ((ord_less_nat zero_zero_nat) K_1)) (((eq nat) ((plus_plus_nat I_1) K_1)) J)))))) of role axiom named fact_971_less__imp__add__positive % A new axiom: (forall (I_1:nat) (J:nat), (((ord_less_nat I_1) J)->((ex nat) (fun (K_1:nat)=> ((and ((ord_less_nat zero_zero_nat) K_1)) (((eq nat) ((plus_plus_nat I_1) K_1)) J)))))) % FOF formula (forall (N:nat), (((ord_less_nat zero_zero_nat) N)->((ex nat) (fun (M_1:nat)=> (((eq nat) N) (suc M_1)))))) of role axiom named fact_972_gr0__implies__Suc % A new axiom: (forall (N:nat), (((ord_less_nat zero_zero_nat) N)->((ex nat) (fun (M_1:nat)=> (((eq nat) N) (suc M_1)))))) % FOF formula (forall (Y:nat), ((not (((eq nat) Y) zero_zero_nat))->((forall (Nat:nat), (not (((eq nat) Y) (suc Nat))))->False))) of role axiom named fact_973_nat_Oexhaust % A new axiom: (forall (Y:nat), ((not (((eq nat) Y) zero_zero_nat))->((forall (Nat:nat), (not (((eq nat) Y) (suc Nat))))->False))) % FOF formula (forall (P:(nat->Prop)) (K:nat), ((P K)->((forall (N_1:nat), ((P (suc N_1))->(P N_1)))->(P zero_zero_nat)))) of role axiom named fact_974_zero__induct % A new axiom: (forall (P:(nat->Prop)) (K:nat), ((P K)->((forall (N_1:nat), ((P (suc N_1))->(P N_1)))->(P zero_zero_nat)))) % FOF formula (forall (N:nat), ((not (((eq nat) N) zero_zero_nat))->((ex nat) (fun (M_1:nat)=> (((eq nat) N) (suc M_1)))))) of role axiom named fact_975_not0__implies__Suc % A new axiom: (forall (N:nat), ((not (((eq nat) N) zero_zero_nat))->((ex nat) (fun (M_1:nat)=> (((eq nat) N) (suc M_1)))))) % FOF formula (forall (N:nat) (P:(nat->Prop)), ((P zero_zero_nat)->((forall (N_1:nat), ((P N_1)->(P (suc N_1))))->(P N)))) of role axiom named fact_976_nat__induct % A new axiom: (forall (N:nat) (P:(nat->Prop)), ((P zero_zero_nat)->((forall (N_1:nat), ((P N_1)->(P (suc N_1))))->(P N)))) % FOF formula (forall (V:int), (((ord_less_nat zero_zero_nat) (number_number_of_nat V))->(((eq nat) (number_number_of_nat V)) (suc ((minus_minus_nat (number_number_of_nat V)) one_one_nat))))) of role axiom named fact_977_expand__Suc % A new axiom: (forall (V:int), (((ord_less_nat zero_zero_nat) (number_number_of_nat V))->(((eq nat) (number_number_of_nat V)) (suc ((minus_minus_nat (number_number_of_nat V)) one_one_nat))))) % FOF formula (forall (N:nat), (((eq nat) ((times_times_nat zero_zero_nat) N)) zero_zero_nat)) of role axiom named fact_978_mult__0 % A new axiom: (forall (N:nat), (((eq nat) ((times_times_nat zero_zero_nat) N)) zero_zero_nat)) % FOF formula (forall (M:nat), (((eq nat) ((times_times_nat M) zero_zero_nat)) zero_zero_nat)) of role axiom named fact_979_mult__0__right % A new axiom: (forall (M:nat), (((eq nat) ((times_times_nat M) zero_zero_nat)) zero_zero_nat)) % FOF formula (forall (M:nat) (N:nat), ((iff (((eq nat) ((times_times_nat M) N)) zero_zero_nat)) ((or (((eq nat) M) zero_zero_nat)) (((eq nat) N) zero_zero_nat)))) of role axiom named fact_980_mult__is__0 % A new axiom: (forall (M:nat) (N:nat), ((iff (((eq nat) ((times_times_nat M) N)) zero_zero_nat)) ((or (((eq nat) M) zero_zero_nat)) (((eq nat) N) zero_zero_nat)))) % FOF formula (forall (K:nat) (M:nat) (N:nat), ((iff (((eq nat) ((times_times_nat K) M)) ((times_times_nat K) N))) ((or (((eq nat) M) N)) (((eq nat) K) zero_zero_nat)))) of role axiom named fact_981_mult__cancel1 % A new axiom: (forall (K:nat) (M:nat) (N:nat), ((iff (((eq nat) ((times_times_nat K) M)) ((times_times_nat K) N))) ((or (((eq nat) M) N)) (((eq nat) K) zero_zero_nat)))) % FOF formula (forall (M:nat) (K:nat) (N:nat), ((iff (((eq nat) ((times_times_nat M) K)) ((times_times_nat N) K))) ((or (((eq nat) M) N)) (((eq nat) K) zero_zero_nat)))) of role axiom named fact_982_mult__cancel2 % A new axiom: (forall (M:nat) (K:nat) (N:nat), ((iff (((eq nat) ((times_times_nat M) K)) ((times_times_nat N) K))) ((or (((eq nat) M) N)) (((eq nat) K) zero_zero_nat)))) % FOF formula (forall (K:nat) (M:nat) (N:nat), ((iff (((eq nat) ((times_times_nat (suc K)) M)) ((times_times_nat (suc K)) N))) (((eq nat) M) N))) of role axiom named fact_983_Suc__mult__cancel1 % A new axiom: (forall (K:nat) (M:nat) (N:nat), ((iff (((eq nat) ((times_times_nat (suc K)) M)) ((times_times_nat (suc K)) N))) (((eq nat) M) N))) % FOF formula (forall (M:nat) (N:nat) (K:nat), (((eq nat) ((times_times_nat ((plus_plus_nat M) N)) K)) ((plus_plus_nat ((times_times_nat M) K)) ((times_times_nat N) K)))) of role axiom named fact_984_add__mult__distrib % A new axiom: (forall (M:nat) (N:nat) (K:nat), (((eq nat) ((times_times_nat ((plus_plus_nat M) N)) K)) ((plus_plus_nat ((times_times_nat M) K)) ((times_times_nat N) K)))) % FOF formula (forall (K:nat) (M:nat) (N:nat), (((eq nat) ((times_times_nat K) ((plus_plus_nat M) N))) ((plus_plus_nat ((times_times_nat K) M)) ((times_times_nat K) N)))) of role axiom named fact_985_add__mult__distrib2 % A new axiom: (forall (K:nat) (M:nat) (N:nat), (((eq nat) ((times_times_nat K) ((plus_plus_nat M) N))) ((plus_plus_nat ((times_times_nat K) M)) ((times_times_nat K) N)))) % FOF formula (forall (K:nat) (L:nat) (I_1:nat) (J:nat), (((ord_less_eq_nat I_1) J)->(((ord_less_eq_nat K) L)->((ord_less_eq_nat ((times_times_nat I_1) K)) ((times_times_nat J) L))))) of role axiom named fact_986_mult__le__mono % A new axiom: (forall (K:nat) (L:nat) (I_1:nat) (J:nat), (((ord_less_eq_nat I_1) J)->(((ord_less_eq_nat K) L)->((ord_less_eq_nat ((times_times_nat I_1) K)) ((times_times_nat J) L))))) % FOF formula (forall (K:nat) (I_1:nat) (J:nat), (((ord_less_eq_nat I_1) J)->((ord_less_eq_nat ((times_times_nat K) I_1)) ((times_times_nat K) J)))) of role axiom named fact_987_mult__le__mono2 % A new axiom: (forall (K:nat) (I_1:nat) (J:nat), (((ord_less_eq_nat I_1) J)->((ord_less_eq_nat ((times_times_nat K) I_1)) ((times_times_nat K) J)))) % FOF formula (forall (K:nat) (I_1:nat) (J:nat), (((ord_less_eq_nat I_1) J)->((ord_less_eq_nat ((times_times_nat I_1) K)) ((times_times_nat J) K)))) of role axiom named fact_988_mult__le__mono1 % A new axiom: (forall (K:nat) (I_1:nat) (J:nat), (((ord_less_eq_nat I_1) J)->((ord_less_eq_nat ((times_times_nat I_1) K)) ((times_times_nat J) K)))) % FOF formula (forall (M:nat), ((ord_less_eq_nat M) ((times_times_nat M) ((times_times_nat M) M)))) of role axiom named fact_989_le__cube % A new axiom: (forall (M:nat), ((ord_less_eq_nat M) ((times_times_nat M) ((times_times_nat M) M)))) % FOF formula (forall (M:nat), ((ord_less_eq_nat M) ((times_times_nat M) M))) of role axiom named fact_990_le__square % A new axiom: (forall (M:nat), ((ord_less_eq_nat M) ((times_times_nat M) M))) % FOF formula (forall (M:nat) (N:nat) (K:nat), (((eq nat) ((times_times_nat ((minus_minus_nat M) N)) K)) ((minus_minus_nat ((times_times_nat M) K)) ((times_times_nat N) K)))) of role axiom named fact_991_diff__mult__distrib % A new axiom: (forall (M:nat) (N:nat) (K:nat), (((eq nat) ((times_times_nat ((minus_minus_nat M) N)) K)) ((minus_minus_nat ((times_times_nat M) K)) ((times_times_nat N) K)))) % FOF formula (forall (K:nat) (M:nat) (N:nat), (((eq nat) ((times_times_nat K) ((minus_minus_nat M) N))) ((minus_minus_nat ((times_times_nat K) M)) ((times_times_nat K) N)))) of role axiom named fact_992_diff__mult__distrib2 % A new axiom: (forall (K:nat) (M:nat) (N:nat), (((eq nat) ((times_times_nat K) ((minus_minus_nat M) N))) ((minus_minus_nat ((times_times_nat K) M)) ((times_times_nat K) N)))) % FOF formula (forall (M:nat) (N:nat), ((iff (((eq nat) ((times_times_nat M) N)) one_one_nat)) ((and (((eq nat) M) one_one_nat)) (((eq nat) N) one_one_nat)))) of role axiom named fact_993_nat__mult__eq__1__iff % A new axiom: (forall (M:nat) (N:nat), ((iff (((eq nat) ((times_times_nat M) N)) one_one_nat)) ((and (((eq nat) M) one_one_nat)) (((eq nat) N) one_one_nat)))) % FOF formula (forall (N:nat), (((eq nat) ((times_times_nat N) one_one_nat)) N)) of role axiom named fact_994_nat__mult__1__right % A new axiom: (forall (N:nat), (((eq nat) ((times_times_nat N) one_one_nat)) N)) % FOF formula (forall (M:nat) (N:nat), ((iff (((eq nat) one_one_nat) ((times_times_nat M) N))) ((and (((eq nat) M) one_one_nat)) (((eq nat) N) one_one_nat)))) of role axiom named fact_995_nat__1__eq__mult__iff % A new axiom: (forall (M:nat) (N:nat), ((iff (((eq nat) one_one_nat) ((times_times_nat M) N))) ((and (((eq nat) M) one_one_nat)) (((eq nat) N) one_one_nat)))) % FOF formula (forall (N:nat), (((eq nat) ((times_times_nat one_one_nat) N)) N)) of role axiom named fact_996_nat__mult__1 % A new axiom: (forall (N:nat), (((eq nat) ((times_times_nat one_one_nat) N)) N)) % FOF formula (forall (M:nat) (N:nat), ((iff (((eq nat) ((times_times_nat M) N)) (suc zero_zero_nat))) ((and (((eq nat) M) (suc zero_zero_nat))) (((eq nat) N) (suc zero_zero_nat))))) of role axiom named fact_997_mult__eq__1__iff % A new axiom: (forall (M:nat) (N:nat), ((iff (((eq nat) ((times_times_nat M) N)) (suc zero_zero_nat))) ((and (((eq nat) M) (suc zero_zero_nat))) (((eq nat) N) (suc zero_zero_nat))))) % FOF formula (forall (K:nat) (I_1:nat) (J:nat), (((ord_less_nat I_1) J)->(((ord_less_nat zero_zero_nat) K)->((ord_less_nat ((times_times_nat K) I_1)) ((times_times_nat K) J))))) of role axiom named fact_998_mult__less__mono2 % A new axiom: (forall (K:nat) (I_1:nat) (J:nat), (((ord_less_nat I_1) J)->(((ord_less_nat zero_zero_nat) K)->((ord_less_nat ((times_times_nat K) I_1)) ((times_times_nat K) J))))) % FOF formula (forall (K:nat) (I_1:nat) (J:nat), (((ord_less_nat I_1) J)->(((ord_less_nat zero_zero_nat) K)->((ord_less_nat ((times_times_nat I_1) K)) ((times_times_nat J) K))))) of role axiom named fact_999_mult__less__mono1 % A new axiom: (forall (K:nat) (I_1:nat) (J:nat), (((ord_less_nat I_1) J)->(((ord_less_nat zero_zero_nat) K)->((ord_less_nat ((times_times_nat I_1) K)) ((times_times_nat J) K))))) % FOF formula (forall (M:nat) (K:nat) (N:nat), ((iff ((ord_less_nat ((times_times_nat M) K)) ((times_times_nat N) K))) ((and ((ord_less_nat zero_zero_nat) K)) ((ord_less_nat M) N)))) of role axiom named fact_1000_mult__less__cancel2 % A new axiom: (forall (M:nat) (K:nat) (N:nat), ((iff ((ord_less_nat ((times_times_nat M) K)) ((times_times_nat N) K))) ((and ((ord_less_nat zero_zero_nat) K)) ((ord_less_nat M) N)))) % FOF formula (forall (K:nat) (M:nat) (N:nat), ((iff ((ord_less_nat ((times_times_nat K) M)) ((times_times_nat K) N))) ((and ((ord_less_nat zero_zero_nat) K)) ((ord_less_nat M) N)))) of role axiom named fact_1001_mult__less__cancel1 % A new axiom: (forall (K:nat) (M:nat) (N:nat), ((iff ((ord_less_nat ((times_times_nat K) M)) ((times_times_nat K) N))) ((and ((ord_less_nat zero_zero_nat) K)) ((ord_less_nat M) N)))) % FOF formula (forall (M:nat) (N:nat), ((iff ((ord_less_nat zero_zero_nat) ((times_times_nat M) N))) ((and ((ord_less_nat zero_zero_nat) M)) ((ord_less_nat zero_zero_nat) N)))) of role axiom named fact_1002_nat__0__less__mult__iff % A new axiom: (forall (M:nat) (N:nat), ((iff ((ord_less_nat zero_zero_nat) ((times_times_nat M) N))) ((and ((ord_less_nat zero_zero_nat) M)) ((ord_less_nat zero_zero_nat) N)))) % FOF formula (forall (K:nat) (M:nat) (N:nat), ((iff ((ord_less_nat ((times_times_nat (suc K)) M)) ((times_times_nat (suc K)) N))) ((ord_less_nat M) N))) of role axiom named fact_1003_Suc__mult__less__cancel1 % A new axiom: (forall (K:nat) (M:nat) (N:nat), ((iff ((ord_less_nat ((times_times_nat (suc K)) M)) ((times_times_nat (suc K)) N))) ((ord_less_nat M) N))) % FOF formula (forall (M:nat) (N:nat), (((eq nat) ((times_times_nat M) (suc N))) ((plus_plus_nat M) ((times_times_nat M) N)))) of role axiom named fact_1004_mult__Suc__right % A new axiom: (forall (M:nat) (N:nat), (((eq nat) ((times_times_nat M) (suc N))) ((plus_plus_nat M) ((times_times_nat M) N)))) % FOF formula (forall (M:nat) (N:nat), (((eq nat) ((times_times_nat (suc M)) N)) ((plus_plus_nat N) ((times_times_nat M) N)))) of role axiom named fact_1005_mult__Suc % A new axiom: (forall (M:nat) (N:nat), (((eq nat) ((times_times_nat (suc M)) N)) ((plus_plus_nat N) ((times_times_nat M) N)))) % FOF formula (forall (K:nat) (M:nat) (N:nat), ((iff ((ord_less_eq_nat ((times_times_nat (suc K)) M)) ((times_times_nat (suc K)) N))) ((ord_less_eq_nat M) N))) of role axiom named fact_1006_Suc__mult__le__cancel1 % A new axiom: (forall (K:nat) (M:nat) (N:nat), ((iff ((ord_less_eq_nat ((times_times_nat (suc K)) M)) ((times_times_nat (suc K)) N))) ((ord_less_eq_nat M) N))) % FOF formula (forall (M:nat) (N:nat), ((((eq nat) M) ((times_times_nat M) N))->((or (((eq nat) N) one_one_nat)) (((eq nat) M) zero_zero_nat)))) of role axiom named fact_1007_mult__eq__self__implies__10 % A new axiom: (forall (M:nat) (N:nat), ((((eq nat) M) ((times_times_nat M) N))->((or (((eq nat) N) one_one_nat)) (((eq nat) M) zero_zero_nat)))) % FOF formula (forall (M:nat) (N:nat), (((ord_less_nat (suc zero_zero_nat)) N)->(((ord_less_nat (suc zero_zero_nat)) M)->((ord_less_nat N) ((times_times_nat M) N))))) of role axiom named fact_1008_n__less__m__mult__n % A new axiom: (forall (M:nat) (N:nat), (((ord_less_nat (suc zero_zero_nat)) N)->(((ord_less_nat (suc zero_zero_nat)) M)->((ord_less_nat N) ((times_times_nat M) N))))) % FOF formula (forall (M:nat) (N:nat), (((ord_less_nat (suc zero_zero_nat)) N)->(((ord_less_nat (suc zero_zero_nat)) M)->((ord_less_nat N) ((times_times_nat N) M))))) of role axiom named fact_1009_n__less__n__mult__m % A new axiom: (forall (M:nat) (N:nat), (((ord_less_nat (suc zero_zero_nat)) N)->(((ord_less_nat (suc zero_zero_nat)) M)->((ord_less_nat N) ((times_times_nat N) M))))) % FOF formula (forall (M:nat) (N:nat), (((ord_less_nat (suc zero_zero_nat)) N)->(((ord_less_nat (suc zero_zero_nat)) M)->((ord_less_nat (suc zero_zero_nat)) ((times_times_nat M) N))))) of role axiom named fact_1010_one__less__mult % A new axiom: (forall (M:nat) (N:nat), (((ord_less_nat (suc zero_zero_nat)) N)->(((ord_less_nat (suc zero_zero_nat)) M)->((ord_less_nat (suc zero_zero_nat)) ((times_times_nat M) N))))) % FOF formula (forall (M:nat) (N:nat), ((iff ((ord_less_eq_nat (suc zero_zero_nat)) ((times_times_nat M) N))) ((and ((ord_less_eq_nat (suc zero_zero_nat)) M)) ((ord_less_eq_nat (suc zero_zero_nat)) N)))) of role axiom named fact_1011_one__le__mult__iff % A new axiom: (forall (M:nat) (N:nat), ((iff ((ord_less_eq_nat (suc zero_zero_nat)) ((times_times_nat M) N))) ((and ((ord_less_eq_nat (suc zero_zero_nat)) M)) ((ord_less_eq_nat (suc zero_zero_nat)) N)))) % FOF formula (forall (K:nat) (M:nat) (N:nat), ((iff ((ord_less_eq_nat ((times_times_nat K) M)) ((times_times_nat K) N))) (((ord_less_nat zero_zero_nat) K)->((ord_less_eq_nat M) N)))) of role axiom named fact_1012_mult__le__cancel1 % A new axiom: (forall (K:nat) (M:nat) (N:nat), ((iff ((ord_less_eq_nat ((times_times_nat K) M)) ((times_times_nat K) N))) (((ord_less_nat zero_zero_nat) K)->((ord_less_eq_nat M) N)))) % FOF formula (forall (M:nat) (K:nat) (N:nat), ((iff ((ord_less_eq_nat ((times_times_nat M) K)) ((times_times_nat N) K))) (((ord_less_nat zero_zero_nat) K)->((ord_less_eq_nat M) N)))) of role axiom named fact_1013_mult__le__cancel2 % A new axiom: (forall (M:nat) (K:nat) (N:nat), ((iff ((ord_less_eq_nat ((times_times_nat M) K)) ((times_times_nat N) K))) (((ord_less_nat zero_zero_nat) K)->((ord_less_eq_nat M) N)))) % FOF formula (forall (N:nat) (M:nat), ((and ((((eq nat) M) zero_zero_nat)->(((eq nat) ((times_times_nat M) N)) zero_zero_nat))) ((not (((eq nat) M) zero_zero_nat))->(((eq nat) ((times_times_nat M) N)) ((plus_plus_nat N) ((times_times_nat ((minus_minus_nat M) one_one_nat)) N)))))) of role axiom named fact_1014_mult__eq__if % A new axiom: (forall (N:nat) (M:nat), ((and ((((eq nat) M) zero_zero_nat)->(((eq nat) ((times_times_nat M) N)) zero_zero_nat))) ((not (((eq nat) M) zero_zero_nat))->(((eq nat) ((times_times_nat M) N)) ((plus_plus_nat N) ((times_times_nat ((minus_minus_nat M) one_one_nat)) N)))))) % FOF formula (forall (U:nat) (M:nat) (N:nat) (I_1:nat) (J:nat), (((ord_less_eq_nat I_1) J)->((iff ((ord_less_nat ((plus_plus_nat ((times_times_nat I_1) U)) M)) ((plus_plus_nat ((times_times_nat J) U)) N))) ((ord_less_nat M) ((plus_plus_nat ((times_times_nat ((minus_minus_nat J) I_1)) U)) N))))) of role axiom named fact_1015_nat__less__add__iff2 % A new axiom: (forall (U:nat) (M:nat) (N:nat) (I_1:nat) (J:nat), (((ord_less_eq_nat I_1) J)->((iff ((ord_less_nat ((plus_plus_nat ((times_times_nat I_1) U)) M)) ((plus_plus_nat ((times_times_nat J) U)) N))) ((ord_less_nat M) ((plus_plus_nat ((times_times_nat ((minus_minus_nat J) I_1)) U)) N))))) % FOF formula (forall (M:nat) (N:nat), (((eq nat) ((times_times_nat M) N)) ((times_times_nat N) M))) of role axiom named fact_1016_nat__mult__commute % A new axiom: (forall (M:nat) (N:nat), (((eq nat) ((times_times_nat M) N)) ((times_times_nat N) M))) % FOF formula (forall (M:nat) (N:nat) (K:nat), (((eq nat) ((times_times_nat ((times_times_nat M) N)) K)) ((times_times_nat M) ((times_times_nat N) K)))) of role axiom named fact_1017_nat__mult__assoc % A new axiom: (forall (M:nat) (N:nat) (K:nat), (((eq nat) ((times_times_nat ((times_times_nat M) N)) K)) ((times_times_nat M) ((times_times_nat N) K)))) % FOF formula (forall (K:int) (L:int), ((iff ((ord_less_int (number_number_of_int K)) (number_number_of_int L))) ((ord_less_int K) L))) of role axiom named fact_1018_less__number__of__int__code % A new axiom: (forall (K:int) (L:int), ((iff ((ord_less_int (number_number_of_int K)) (number_number_of_int L))) ((ord_less_int K) L))) % FOF formula (forall (Z:int), (((eq int) ((times_times_int one_one_int) Z)) Z)) of role axiom named fact_1019_zmult__1 % A new axiom: (forall (Z:int), (((eq int) ((times_times_int one_one_int) Z)) Z)) % FOF formula (forall (Z:int), (((eq int) ((times_times_int Z) one_one_int)) Z)) of role axiom named fact_1020_zmult__1__right % A new axiom: (forall (Z:int), (((eq int) ((times_times_int Z) one_one_int)) Z)) % FOF formula (forall (Z:int) (W:int), (((eq int) ((times_times_int Z) W)) ((times_times_int W) Z))) of role axiom named fact_1021_zmult__commute % A new axiom: (forall (Z:int) (W:int), (((eq int) ((times_times_int Z) W)) ((times_times_int W) Z))) % FOF formula (forall (V:int) (W:int), (((eq int) ((times_times_int (number_number_of_int V)) (number_number_of_int W))) (number_number_of_int ((times_times_int V) W)))) of role axiom named fact_1022_times__numeral__code_I5_J % A new axiom: (forall (V:int) (W:int), (((eq int) ((times_times_int (number_number_of_int V)) (number_number_of_int W))) (number_number_of_int ((times_times_int V) W)))) % FOF formula (forall (Z1:int) (Z2:int) (Z3:int), (((eq int) ((times_times_int ((times_times_int Z1) Z2)) Z3)) ((times_times_int Z1) ((times_times_int Z2) Z3)))) of role axiom named fact_1023_zmult__assoc % A new axiom: (forall (Z1:int) (Z2:int) (Z3:int), (((eq int) ((times_times_int ((times_times_int Z1) Z2)) Z3)) ((times_times_int Z1) ((times_times_int Z2) Z3)))) % FOF formula (forall (K:int) (L:int), ((iff ((ord_less_eq_int (number_number_of_int K)) (number_number_of_int L))) ((ord_less_eq_int K) L))) of role axiom named fact_1024_less__eq__number__of__int__code % A new axiom: (forall (K:int) (L:int), ((iff ((ord_less_eq_int (number_number_of_int K)) (number_number_of_int L))) ((ord_less_eq_int K) L))) % FOF formula (forall (Z1:int) (Z2:int) (W:int), (((eq int) ((times_times_int ((minus_minus_int Z1) Z2)) W)) ((minus_minus_int ((times_times_int Z1) W)) ((times_times_int Z2) W)))) of role axiom named fact_1025_zdiff__zmult__distrib % A new axiom: (forall (Z1:int) (Z2:int) (W:int), (((eq int) ((times_times_int ((minus_minus_int Z1) Z2)) W)) ((minus_minus_int ((times_times_int Z1) W)) ((times_times_int Z2) W)))) % FOF formula (forall (W:int) (Z1:int) (Z2:int), (((eq int) ((times_times_int W) ((minus_minus_int Z1) Z2))) ((minus_minus_int ((times_times_int W) Z1)) ((times_times_int W) Z2)))) of role axiom named fact_1026_zdiff__zmult__distrib2 % A new axiom: (forall (W:int) (Z1:int) (Z2:int), (((eq int) ((times_times_int W) ((minus_minus_int Z1) Z2))) ((minus_minus_int ((times_times_int W) Z1)) ((times_times_int W) Z2)))) % FOF formula (forall (W:int) (Z1:int) (Z2:int), (((eq int) ((times_times_int W) ((plus_plus_int Z1) Z2))) ((plus_plus_int ((times_times_int W) Z1)) ((times_times_int W) Z2)))) of role axiom named fact_1027_zadd__zmult__distrib2 % A new axiom: (forall (W:int) (Z1:int) (Z2:int), (((eq int) ((times_times_int W) ((plus_plus_int Z1) Z2))) ((plus_plus_int ((times_times_int W) Z1)) ((times_times_int W) Z2)))) % FOF formula (forall (V:int) (W:int), (((eq int) ((plus_plus_int (number_number_of_int V)) (number_number_of_int W))) (number_number_of_int ((plus_plus_int V) W)))) of role axiom named fact_1028_plus__numeral__code_I9_J % A new axiom: (forall (V:int) (W:int), (((eq int) ((plus_plus_int (number_number_of_int V)) (number_number_of_int W))) (number_number_of_int ((plus_plus_int V) W)))) % FOF formula (forall (Z1:int) (Z2:int) (W:int), (((eq int) ((times_times_int ((plus_plus_int Z1) Z2)) W)) ((plus_plus_int ((times_times_int Z1) W)) ((times_times_int Z2) W)))) of role axiom named fact_1029_zadd__zmult__distrib % A new axiom: (forall (Z1:int) (Z2:int) (W:int), (((eq int) ((times_times_int ((plus_plus_int Z1) Z2)) W)) ((plus_plus_int ((times_times_int Z1) W)) ((times_times_int Z2) W)))) % FOF formula (forall (K:int) (I_1:int) (J:int), (((ord_less_int I_1) J)->(((ord_less_int zero_zero_int) K)->((ord_less_int ((times_times_int K) I_1)) ((times_times_int K) J))))) of role axiom named fact_1030_zmult__zless__mono2 % A new axiom: (forall (K:int) (I_1:int) (J:int), (((ord_less_int I_1) J)->(((ord_less_int zero_zero_int) K)->((ord_less_int ((times_times_int K) I_1)) ((times_times_int K) J))))) % FOF formula (forall (N:int) (M:int), (((ord_less_int zero_zero_int) M)->((iff (((eq int) ((times_times_int M) N)) one_one_int)) ((and (((eq int) M) one_one_int)) (((eq int) N) one_one_int))))) of role axiom named fact_1031_pos__zmult__eq__1__iff % A new axiom: (forall (N:int) (M:int), (((ord_less_int zero_zero_int) M)->((iff (((eq int) ((times_times_int M) N)) one_one_int)) ((and (((eq int) M) one_one_int)) (((eq int) N) one_one_int))))) % FOF formula (forall (Z:int), (not (((eq int) ((plus_plus_int ((plus_plus_int one_one_int) Z)) Z)) zero_zero_int))) of role axiom named fact_1032_odd__nonzero % A new axiom: (forall (Z:int), (not (((eq int) ((plus_plus_int ((plus_plus_int one_one_int) Z)) Z)) zero_zero_int))) % FOF formula (forall (Z:int), (((eq int) ((plus_plus_int Z) zero_zero_int)) Z)) of role axiom named fact_1033_zadd__0__right % A new axiom: (forall (Z:int), (((eq int) ((plus_plus_int Z) zero_zero_int)) Z)) % FOF formula (forall (Z:int), (((eq int) ((plus_plus_int zero_zero_int) Z)) Z)) of role axiom named fact_1034_zadd__0 % A new axiom: (forall (Z:int), (((eq int) ((plus_plus_int zero_zero_int) Z)) Z)) % FOF formula ((ord_less_int zero_zero_int) one_one_int) of role axiom named fact_1035_int__0__less__1 % A new axiom: ((ord_less_int zero_zero_int) one_one_int) % FOF formula (forall (Z:int), ((iff ((ord_less_eq_int one_one_int) Z)) ((ord_less_int zero_zero_int) Z))) of role axiom named fact_1036_int__one__le__iff__zero__less % A new axiom: (forall (Z:int), ((iff ((ord_less_eq_int one_one_int) Z)) ((ord_less_int zero_zero_int) Z))) % FOF formula (forall (K:int) (L:int), ((iff ((ord_less_int K) L)) ((ord_less_int ((minus_minus_int K) L)) zero_zero_int))) of role axiom named fact_1037_less__bin__lemma % A new axiom: (forall (K:int) (L:int), ((iff ((ord_less_int K) L)) ((ord_less_int ((minus_minus_int K) L)) zero_zero_int))) % FOF formula (forall (Z:int), (((ord_less_eq_int zero_zero_int) Z)->((ord_less_int zero_zero_int) ((plus_plus_int one_one_int) Z)))) of role axiom named fact_1038_le__imp__0__less % A new axiom: (forall (Z:int), (((ord_less_eq_int zero_zero_int) Z)->((ord_less_int zero_zero_int) ((plus_plus_int one_one_int) Z)))) % FOF formula (forall (Z:int), ((iff ((ord_less_int ((plus_plus_int ((plus_plus_int one_one_int) Z)) Z)) zero_zero_int)) ((ord_less_int Z) zero_zero_int))) of role axiom named fact_1039_odd__less__0 % A new axiom: (forall (Z:int), ((iff ((ord_less_int ((plus_plus_int ((plus_plus_int one_one_int) Z)) Z)) zero_zero_int)) ((ord_less_int Z) zero_zero_int))) % FOF formula (forall (K:int) (I_1:int) (J:int), (((ord_less_eq_int I_1) J)->((ord_less_eq_int ((plus_plus_int K) I_1)) ((plus_plus_int K) J)))) of role axiom named fact_1040_zadd__left__mono % A new axiom: (forall (K:int) (I_1:int) (J:int), (((ord_less_eq_int I_1) J)->((ord_less_eq_int ((plus_plus_int K) I_1)) ((plus_plus_int K) J)))) % FOF formula (forall (Z1:int) (Z2:int) (Z3:int), (((eq int) ((plus_plus_int ((plus_plus_int Z1) Z2)) Z3)) ((plus_plus_int Z1) ((plus_plus_int Z2) Z3)))) of role axiom named fact_1041_zadd__assoc % A new axiom: (forall (Z1:int) (Z2:int) (Z3:int), (((eq int) ((plus_plus_int ((plus_plus_int Z1) Z2)) Z3)) ((plus_plus_int Z1) ((plus_plus_int Z2) Z3)))) % FOF formula (forall (X:int) (Y:int) (Z:int), (((eq int) ((plus_plus_int X) ((plus_plus_int Y) Z))) ((plus_plus_int Y) ((plus_plus_int X) Z)))) of role axiom named fact_1042_zadd__left__commute % A new axiom: (forall (X:int) (Y:int) (Z:int), (((eq int) ((plus_plus_int X) ((plus_plus_int Y) Z))) ((plus_plus_int Y) ((plus_plus_int X) Z)))) % FOF formula (forall (Z:int) (W:int), (((eq int) ((plus_plus_int Z) W)) ((plus_plus_int W) Z))) of role axiom named fact_1043_zadd__commute % A new axiom: (forall (Z:int) (W:int), (((eq int) ((plus_plus_int Z) W)) ((plus_plus_int W) Z))) % FOF formula (forall (W:int), ((ord_less_eq_int W) W)) of role axiom named fact_1044_zle__refl % A new axiom: (forall (W:int), ((ord_less_eq_int W) W)) % FOF formula (forall (Z:int) (W:int), ((or ((ord_less_eq_int Z) W)) ((ord_less_eq_int W) Z))) of role axiom named fact_1045_zle__linear % A new axiom: (forall (Z:int) (W:int), ((or ((ord_less_eq_int Z) W)) ((ord_less_eq_int W) Z))) % FOF formula (forall (K:int) (I_1:int) (J:int), (((ord_less_eq_int I_1) J)->(((ord_less_eq_int J) K)->((ord_less_eq_int I_1) K)))) of role axiom named fact_1046_zle__trans % A new axiom: (forall (K:int) (I_1:int) (J:int), (((ord_less_eq_int I_1) J)->(((ord_less_eq_int J) K)->((ord_less_eq_int I_1) K)))) % FOF formula (forall (Z:int) (W:int), (((ord_less_eq_int Z) W)->(((ord_less_eq_int W) Z)->(((eq int) Z) W)))) of role axiom named fact_1047_zle__antisym % A new axiom: (forall (Z:int) (W:int), (((ord_less_eq_int Z) W)->(((ord_less_eq_int W) Z)->(((eq int) Z) W)))) % FOF formula (forall (W:int) (Z:int), ((iff ((ord_less_eq_int W) ((minus_minus_int Z) one_one_int))) ((ord_less_int W) Z))) of role axiom named fact_1048_zle__diff1__eq % A new axiom: (forall (W:int) (Z:int), ((iff ((ord_less_eq_int W) ((minus_minus_int Z) one_one_int))) ((ord_less_int W) Z))) % FOF formula (forall (X:int) (Y:int), ((or ((or ((ord_less_int X) Y)) (((eq int) X) Y))) ((ord_less_int Y) X))) of role axiom named fact_1049_zless__linear % A new axiom: (forall (X:int) (Y:int), ((or ((or ((ord_less_int X) Y)) (((eq int) X) Y))) ((ord_less_int Y) X))) % FOF formula (forall (Z:int) (W:int), ((iff ((ord_less_int Z) W)) ((and ((ord_less_eq_int Z) W)) (not (((eq int) Z) W))))) of role axiom named fact_1050_zless__le % A new axiom: (forall (Z:int) (W:int), ((iff ((ord_less_int Z) W)) ((and ((ord_less_eq_int Z) W)) (not (((eq int) Z) W))))) % FOF formula (forall (K:int) (I_1:int) (J:int), (((ord_less_int I_1) J)->((ord_less_int ((plus_plus_int I_1) K)) ((plus_plus_int J) K)))) of role axiom named fact_1051_zadd__strict__right__mono % A new axiom: (forall (K:int) (I_1:int) (J:int), (((ord_less_int I_1) J)->((ord_less_int ((plus_plus_int I_1) K)) ((plus_plus_int J) K)))) % FOF formula (forall (Z_3:int) (Z:int) (W_1:int) (W:int), (((ord_less_int W_1) W)->(((ord_less_eq_int Z_3) Z)->((ord_less_int ((plus_plus_int W_1) Z_3)) ((plus_plus_int W) Z))))) of role axiom named fact_1052_zadd__zless__mono % A new axiom: (forall (Z_3:int) (Z:int) (W_1:int) (W:int), (((ord_less_int W_1) W)->(((ord_less_eq_int Z_3) Z)->((ord_less_int ((plus_plus_int W_1) Z_3)) ((plus_plus_int W) Z))))) % FOF formula (forall (W:int) (Z:int), ((iff ((ord_less_int W) ((plus_plus_int Z) one_one_int))) ((ord_less_eq_int W) Z))) of role axiom named fact_1053_zle__add1__eq__le % A new axiom: (forall (W:int) (Z:int), ((iff ((ord_less_int W) ((plus_plus_int Z) one_one_int))) ((ord_less_eq_int W) Z))) % FOF formula (forall (W:int) (Z:int), ((iff ((ord_less_eq_int ((plus_plus_int W) one_one_int)) Z)) ((ord_less_int W) Z))) of role axiom named fact_1054_add1__zle__eq % A new axiom: (forall (W:int) (Z:int), ((iff ((ord_less_eq_int ((plus_plus_int W) one_one_int)) Z)) ((ord_less_int W) Z))) % FOF formula (forall (W:int) (Z:int), (((ord_less_int W) Z)->((ord_less_eq_int ((plus_plus_int W) one_one_int)) Z))) of role axiom named fact_1055_zless__imp__add1__zle % A new axiom: (forall (W:int) (Z:int), (((ord_less_int W) Z)->((ord_less_eq_int ((plus_plus_int W) one_one_int)) Z))) % FOF formula (forall (W:int) (Z:int), ((iff ((ord_less_int W) ((plus_plus_int Z) one_one_int))) ((or ((ord_less_int W) Z)) (((eq int) W) Z)))) of role axiom named fact_1056_zless__add1__eq % A new axiom: (forall (W:int) (Z:int), ((iff ((ord_less_int W) ((plus_plus_int Z) one_one_int))) ((or ((ord_less_int W) Z)) (((eq int) W) Z)))) % FOF formula (forall (K:nat) (M:nat) (N:nat), ((iff (((eq nat) ((times_times_nat K) M)) ((times_times_nat K) N))) ((or (((eq nat) K) zero_zero_nat)) (((eq nat) M) N)))) of role axiom named fact_1057_nat__mult__eq__cancel__disj % A new axiom: (forall (K:nat) (M:nat) (N:nat), ((iff (((eq nat) ((times_times_nat K) M)) ((times_times_nat K) N))) ((or (((eq nat) K) zero_zero_nat)) (((eq nat) M) N)))) % FOF formula (forall (I_1:nat) (U:nat) (J:nat) (K:nat), (((eq nat) ((plus_plus_nat ((times_times_nat I_1) U)) ((plus_plus_nat ((times_times_nat J) U)) K))) ((plus_plus_nat ((times_times_nat ((plus_plus_nat I_1) J)) U)) K))) of role axiom named fact_1058_left__add__mult__distrib % A new axiom: (forall (I_1:nat) (U:nat) (J:nat) (K:nat), (((eq nat) ((plus_plus_nat ((times_times_nat I_1) U)) ((plus_plus_nat ((times_times_nat J) U)) K))) ((plus_plus_nat ((times_times_nat ((plus_plus_nat I_1) J)) U)) K))) % FOF formula (forall (M:nat) (N:nat) (K:nat), (((ord_less_nat zero_zero_nat) K)->((iff (((eq nat) ((times_times_nat K) M)) ((times_times_nat K) N))) (((eq nat) M) N)))) of role axiom named fact_1059_nat__mult__eq__cancel1 % A new axiom: (forall (M:nat) (N:nat) (K:nat), (((ord_less_nat zero_zero_nat) K)->((iff (((eq nat) ((times_times_nat K) M)) ((times_times_nat K) N))) (((eq nat) M) N)))) % FOF formula (forall (M:nat) (N:nat) (K:nat), (((ord_less_nat zero_zero_nat) K)->((iff ((ord_less_nat ((times_times_nat K) M)) ((times_times_nat K) N))) ((ord_less_nat M) N)))) of role axiom named fact_1060_nat__mult__less__cancel1 % A new axiom: (forall (M:nat) (N:nat) (K:nat), (((ord_less_nat zero_zero_nat) K)->((iff ((ord_less_nat ((times_times_nat K) M)) ((times_times_nat K) N))) ((ord_less_nat M) N)))) % FOF formula (forall (M:nat) (N:nat) (K:nat), (((ord_less_nat zero_zero_nat) K)->((iff ((ord_less_eq_nat ((times_times_nat K) M)) ((times_times_nat K) N))) ((ord_less_eq_nat M) N)))) of role axiom named fact_1061_nat__mult__le__cancel1 % A new axiom: (forall (M:nat) (N:nat) (K:nat), (((ord_less_nat zero_zero_nat) K)->((iff ((ord_less_eq_nat ((times_times_nat K) M)) ((times_times_nat K) N))) ((ord_less_eq_nat M) N)))) % FOF formula (forall (U:nat) (M:nat) (N:nat) (J:nat) (I_1:nat), (((ord_less_eq_nat J) I_1)->((iff ((ord_less_eq_nat ((plus_plus_nat ((times_times_nat I_1) U)) M)) ((plus_plus_nat ((times_times_nat J) U)) N))) ((ord_less_eq_nat ((plus_plus_nat ((times_times_nat ((minus_minus_nat I_1) J)) U)) M)) N)))) of role axiom named fact_1062_nat__le__add__iff1 % A new axiom: (forall (U:nat) (M:nat) (N:nat) (J:nat) (I_1:nat), (((ord_less_eq_nat J) I_1)->((iff ((ord_less_eq_nat ((plus_plus_nat ((times_times_nat I_1) U)) M)) ((plus_plus_nat ((times_times_nat J) U)) N))) ((ord_less_eq_nat ((plus_plus_nat ((times_times_nat ((minus_minus_nat I_1) J)) U)) M)) N)))) % FOF formula (forall (U:nat) (M:nat) (N:nat) (J:nat) (I_1:nat), (((ord_less_eq_nat J) I_1)->(((eq nat) ((minus_minus_nat ((plus_plus_nat ((times_times_nat I_1) U)) M)) ((plus_plus_nat ((times_times_nat J) U)) N))) ((minus_minus_nat ((plus_plus_nat ((times_times_nat ((minus_minus_nat I_1) J)) U)) M)) N)))) of role axiom named fact_1063_nat__diff__add__eq1 % A new axiom: (forall (U:nat) (M:nat) (N:nat) (J:nat) (I_1:nat), (((ord_less_eq_nat J) I_1)->(((eq nat) ((minus_minus_nat ((plus_plus_nat ((times_times_nat I_1) U)) M)) ((plus_plus_nat ((times_times_nat J) U)) N))) ((minus_minus_nat ((plus_plus_nat ((times_times_nat ((minus_minus_nat I_1) J)) U)) M)) N)))) % FOF formula (forall (U:nat) (M:nat) (N:nat) (J:nat) (I_1:nat), (((ord_less_eq_nat J) I_1)->((iff (((eq nat) ((plus_plus_nat ((times_times_nat I_1) U)) M)) ((plus_plus_nat ((times_times_nat J) U)) N))) (((eq nat) ((plus_plus_nat ((times_times_nat ((minus_minus_nat I_1) J)) U)) M)) N)))) of role axiom named fact_1064_nat__eq__add__iff1 % A new axiom: (forall (U:nat) (M:nat) (N:nat) (J:nat) (I_1:nat), (((ord_less_eq_nat J) I_1)->((iff (((eq nat) ((plus_plus_nat ((times_times_nat I_1) U)) M)) ((plus_plus_nat ((times_times_nat J) U)) N))) (((eq nat) ((plus_plus_nat ((times_times_nat ((minus_minus_nat I_1) J)) U)) M)) N)))) % FOF formula (forall (U:nat) (M:nat) (N:nat) (I_1:nat) (J:nat), (((ord_less_eq_nat I_1) J)->((iff ((ord_less_eq_nat ((plus_plus_nat ((times_times_nat I_1) U)) M)) ((plus_plus_nat ((times_times_nat J) U)) N))) ((ord_less_eq_nat M) ((plus_plus_nat ((times_times_nat ((minus_minus_nat J) I_1)) U)) N))))) of role axiom named fact_1065_nat__le__add__iff2 % A new axiom: (forall (U:nat) (M:nat) (N:nat) (I_1:nat) (J:nat), (((ord_less_eq_nat I_1) J)->((iff ((ord_less_eq_nat ((plus_plus_nat ((times_times_nat I_1) U)) M)) ((plus_plus_nat ((times_times_nat J) U)) N))) ((ord_less_eq_nat M) ((plus_plus_nat ((times_times_nat ((minus_minus_nat J) I_1)) U)) N))))) % FOF formula (forall (U:nat) (M:nat) (N:nat) (I_1:nat) (J:nat), (((ord_less_eq_nat I_1) J)->(((eq nat) ((minus_minus_nat ((plus_plus_nat ((times_times_nat I_1) U)) M)) ((plus_plus_nat ((times_times_nat J) U)) N))) ((minus_minus_nat M) ((plus_plus_nat ((times_times_nat ((minus_minus_nat J) I_1)) U)) N))))) of role axiom named fact_1066_nat__diff__add__eq2 % A new axiom: (forall (U:nat) (M:nat) (N:nat) (I_1:nat) (J:nat), (((ord_less_eq_nat I_1) J)->(((eq nat) ((minus_minus_nat ((plus_plus_nat ((times_times_nat I_1) U)) M)) ((plus_plus_nat ((times_times_nat J) U)) N))) ((minus_minus_nat M) ((plus_plus_nat ((times_times_nat ((minus_minus_nat J) I_1)) U)) N))))) % FOF formula (forall (U:nat) (M:nat) (N:nat) (I_1:nat) (J:nat), (((ord_less_eq_nat I_1) J)->((iff (((eq nat) ((plus_plus_nat ((times_times_nat I_1) U)) M)) ((plus_plus_nat ((times_times_nat J) U)) N))) (((eq nat) M) ((plus_plus_nat ((times_times_nat ((minus_minus_nat J) I_1)) U)) N))))) of role axiom named fact_1067_nat__eq__add__iff2 % A new axiom: (forall (U:nat) (M:nat) (N:nat) (I_1:nat) (J:nat), (((ord_less_eq_nat I_1) J)->((iff (((eq nat) ((plus_plus_nat ((times_times_nat I_1) U)) M)) ((plus_plus_nat ((times_times_nat J) U)) N))) (((eq nat) M) ((plus_plus_nat ((times_times_nat ((minus_minus_nat J) I_1)) U)) N))))) % FOF formula (forall (U:nat) (M:nat) (N:nat) (J:nat) (I_1:nat), (((ord_less_eq_nat J) I_1)->((iff ((ord_less_nat ((plus_plus_nat ((times_times_nat I_1) U)) M)) ((plus_plus_nat ((times_times_nat J) U)) N))) ((ord_less_nat ((plus_plus_nat ((times_times_nat ((minus_minus_nat I_1) J)) U)) M)) N)))) of role axiom named fact_1068_nat__less__add__iff1 % A new axiom: (forall (U:nat) (M:nat) (N:nat) (J:nat) (I_1:nat), (((ord_less_eq_nat J) I_1)->((iff ((ord_less_nat ((plus_plus_nat ((times_times_nat I_1) U)) M)) ((plus_plus_nat ((times_times_nat J) U)) N))) ((ord_less_nat ((plus_plus_nat ((times_times_nat ((minus_minus_nat I_1) J)) U)) M)) N)))) % FOF formula (forall (B_2:int) (Q_1:int) (R_1:int) (B_1:int) (Q:int) (R:int), ((((eq int) ((plus_plus_int ((times_times_int B_2) Q_1)) R_1)) ((plus_plus_int ((times_times_int B_1) Q)) R))->(((ord_less_int ((plus_plus_int ((times_times_int B_1) Q)) R)) zero_zero_int)->(((ord_less_int R_1) B_2)->(((ord_less_eq_int zero_zero_int) R)->(((ord_less_int zero_zero_int) B_1)->(((ord_less_eq_int B_1) B_2)->((ord_less_eq_int Q) Q_1)))))))) of role axiom named fact_1069_zdiv__mono2__neg__lemma % A new axiom: (forall (B_2:int) (Q_1:int) (R_1:int) (B_1:int) (Q:int) (R:int), ((((eq int) ((plus_plus_int ((times_times_int B_2) Q_1)) R_1)) ((plus_plus_int ((times_times_int B_1) Q)) R))->(((ord_less_int ((plus_plus_int ((times_times_int B_1) Q)) R)) zero_zero_int)->(((ord_less_int R_1) B_2)->(((ord_less_eq_int zero_zero_int) R)->(((ord_less_int zero_zero_int) B_1)->(((ord_less_eq_int B_1) B_2)->((ord_less_eq_int Q) Q_1)))))))) % FOF formula (forall (B_2:int) (Q:int) (R:int) (Q_1:int) (R_1:int), (((ord_less_eq_int ((plus_plus_int ((times_times_int B_2) Q)) R)) ((plus_plus_int ((times_times_int B_2) Q_1)) R_1))->(((ord_less_eq_int R_1) zero_zero_int)->(((ord_less_int B_2) R_1)->(((ord_less_int B_2) R)->((ord_less_eq_int Q_1) Q)))))) of role axiom named fact_1070_unique__quotient__lemma__neg % A new axiom: (forall (B_2:int) (Q:int) (R:int) (Q_1:int) (R_1:int), (((ord_less_eq_int ((plus_plus_int ((times_times_int B_2) Q)) R)) ((plus_plus_int ((times_times_int B_2) Q_1)) R_1))->(((ord_less_eq_int R_1) zero_zero_int)->(((ord_less_int B_2) R_1)->(((ord_less_int B_2) R)->((ord_less_eq_int Q_1) Q)))))) % FOF formula (forall (K:int), (((eq int) (number_number_of_int K)) K)) of role axiom named fact_1071_number__of__is__id % A new axiom: (forall (K:int), (((eq int) (number_number_of_int K)) K)) % FOF formula (not (((eq int) zero_zero_int) one_one_int)) of role axiom named fact_1072_int__0__neq__1 % A new axiom: (not (((eq int) zero_zero_int) one_one_int)) % FOF formula (forall (R_1:int) (Q_1:int) (A_1:int), (((ord_less_int zero_zero_int) A_1)->((((eq int) A_1) ((plus_plus_int R_1) ((times_times_int A_1) Q_1)))->(((ord_less_int R_1) A_1)->((ord_less_eq_int one_one_int) Q_1))))) of role axiom named fact_1073_self__quotient__aux1 % A new axiom: (forall (R_1:int) (Q_1:int) (A_1:int), (((ord_less_int zero_zero_int) A_1)->((((eq int) A_1) ((plus_plus_int R_1) ((times_times_int A_1) Q_1)))->(((ord_less_int R_1) A_1)->((ord_less_eq_int one_one_int) Q_1))))) % FOF formula (forall (R_1:int) (Q_1:int) (A_1:int), (((ord_less_int zero_zero_int) A_1)->((((eq int) A_1) ((plus_plus_int R_1) ((times_times_int A_1) Q_1)))->(((ord_less_eq_int zero_zero_int) R_1)->((ord_less_eq_int Q_1) one_one_int))))) of role axiom named fact_1074_self__quotient__aux2 % A new axiom: (forall (R_1:int) (Q_1:int) (A_1:int), (((ord_less_int zero_zero_int) A_1)->((((eq int) A_1) ((plus_plus_int R_1) ((times_times_int A_1) Q_1)))->(((ord_less_eq_int zero_zero_int) R_1)->((ord_less_eq_int Q_1) one_one_int))))) % FOF formula (forall (B_1:int) (Q:int) (R:int), (((ord_less_eq_int zero_zero_int) ((plus_plus_int ((times_times_int B_1) Q)) R))->(((ord_less_int R) B_1)->(((ord_less_int zero_zero_int) B_1)->((ord_less_eq_int zero_zero_int) Q))))) of role axiom named fact_1075_q__pos__lemma % A new axiom: (forall (B_1:int) (Q:int) (R:int), (((ord_less_eq_int zero_zero_int) ((plus_plus_int ((times_times_int B_1) Q)) R))->(((ord_less_int R) B_1)->(((ord_less_int zero_zero_int) B_1)->((ord_less_eq_int zero_zero_int) Q))))) % FOF formula (forall (B_1:int) (Q:int) (R:int), (((ord_less_int ((plus_plus_int ((times_times_int B_1) Q)) R)) zero_zero_int)->(((ord_less_eq_int zero_zero_int) R)->(((ord_less_int zero_zero_int) B_1)->((ord_less_eq_int Q) zero_zero_int))))) of role axiom named fact_1076_q__neg__lemma % A new axiom: (forall (B_1:int) (Q:int) (R:int), (((ord_less_int ((plus_plus_int ((times_times_int B_1) Q)) R)) zero_zero_int)->(((ord_less_eq_int zero_zero_int) R)->(((ord_less_int zero_zero_int) B_1)->((ord_less_eq_int Q) zero_zero_int))))) % FOF formula (forall (B_2:int) (Q:int) (R:int) (Q_1:int) (R_1:int), (((ord_less_eq_int ((plus_plus_int ((times_times_int B_2) Q)) R)) ((plus_plus_int ((times_times_int B_2) Q_1)) R_1))->(((ord_less_eq_int zero_zero_int) R)->(((ord_less_int R) B_2)->(((ord_less_int R_1) B_2)->((ord_less_eq_int Q) Q_1)))))) of role axiom named fact_1077_unique__quotient__lemma % A new axiom: (forall (B_2:int) (Q:int) (R:int) (Q_1:int) (R_1:int), (((ord_less_eq_int ((plus_plus_int ((times_times_int B_2) Q)) R)) ((plus_plus_int ((times_times_int B_2) Q_1)) R_1))->(((ord_less_eq_int zero_zero_int) R)->(((ord_less_int R) B_2)->(((ord_less_int R_1) B_2)->((ord_less_eq_int Q) Q_1)))))) % FOF formula (forall (B_2:int) (Q_1:int) (R_1:int) (B_1:int) (Q:int) (R:int), ((((eq int) ((plus_plus_int ((times_times_int B_2) Q_1)) R_1)) ((plus_plus_int ((times_times_int B_1) Q)) R))->(((ord_less_eq_int zero_zero_int) ((plus_plus_int ((times_times_int B_1) Q)) R))->(((ord_less_int R) B_1)->(((ord_less_eq_int zero_zero_int) R_1)->(((ord_less_int zero_zero_int) B_1)->(((ord_less_eq_int B_1) B_2)->((ord_less_eq_int Q_1) Q)))))))) of role axiom named fact_1078_zdiv__mono2__lemma % A new axiom: (forall (B_2:int) (Q_1:int) (R_1:int) (B_1:int) (Q:int) (R:int), ((((eq int) ((plus_plus_int ((times_times_int B_2) Q_1)) R_1)) ((plus_plus_int ((times_times_int B_1) Q)) R))->(((ord_less_eq_int zero_zero_int) ((plus_plus_int ((times_times_int B_1) Q)) R))->(((ord_less_int R) B_1)->(((ord_less_eq_int zero_zero_int) R_1)->(((ord_less_int zero_zero_int) B_1)->(((ord_less_eq_int B_1) B_2)->((ord_less_eq_int Q_1) Q)))))))) % FOF formula (forall (P:(int->Prop)) (I_1:int) (K:int), (((ord_less_int I_1) K)->((P ((minus_minus_int K) one_one_int))->((forall (_TPTP_I:int), (((ord_less_int _TPTP_I) K)->((P _TPTP_I)->(P ((minus_minus_int _TPTP_I) one_one_int)))))->(P I_1))))) of role axiom named fact_1079_int__less__induct % A new axiom: (forall (P:(int->Prop)) (I_1:int) (K:int), (((ord_less_int I_1) K)->((P ((minus_minus_int K) one_one_int))->((forall (_TPTP_I:int), (((ord_less_int _TPTP_I) K)->((P _TPTP_I)->(P ((minus_minus_int _TPTP_I) one_one_int)))))->(P I_1))))) % FOF formula (forall (P:(int->Prop)) (I_1:int) (K:int), (((ord_less_eq_int I_1) K)->((P K)->((forall (_TPTP_I:int), (((ord_less_eq_int _TPTP_I) K)->((P _TPTP_I)->(P ((minus_minus_int _TPTP_I) one_one_int)))))->(P I_1))))) of role axiom named fact_1080_int__le__induct % A new axiom: (forall (P:(int->Prop)) (I_1:int) (K:int), (((ord_less_eq_int I_1) K)->((P K)->((forall (_TPTP_I:int), (((ord_less_eq_int _TPTP_I) K)->((P _TPTP_I)->(P ((minus_minus_int _TPTP_I) one_one_int)))))->(P I_1))))) % FOF formula (forall (P:(int->Prop)) (K:int) (I_1:int), (((ord_less_int K) I_1)->((P ((plus_plus_int K) one_one_int))->((forall (_TPTP_I:int), (((ord_less_int K) _TPTP_I)->((P _TPTP_I)->(P ((plus_plus_int _TPTP_I) one_one_int)))))->(P I_1))))) of role axiom named fact_1081_int__gr__induct % A new axiom: (forall (P:(int->Prop)) (K:int) (I_1:int), (((ord_less_int K) I_1)->((P ((plus_plus_int K) one_one_int))->((forall (_TPTP_I:int), (((ord_less_int K) _TPTP_I)->((P _TPTP_I)->(P ((plus_plus_int _TPTP_I) one_one_int)))))->(P I_1))))) % FOF formula (forall (P:(int->Prop)) (K:int) (I_1:int), (((ord_less_eq_int K) I_1)->((P K)->((forall (_TPTP_I:int), (((ord_less_eq_int K) _TPTP_I)->((P _TPTP_I)->(P ((plus_plus_int _TPTP_I) one_one_int)))))->(P I_1))))) of role axiom named fact_1082_int__ge__induct % A new axiom: (forall (P:(int->Prop)) (K:int) (I_1:int), (((ord_less_eq_int K) I_1)->((P K)->((forall (_TPTP_I:int), (((ord_less_eq_int K) _TPTP_I)->((P _TPTP_I)->(P ((plus_plus_int _TPTP_I) one_one_int)))))->(P I_1))))) % FOF formula (forall (Y:int) (X:int), (((ord_less_eq_int zero_zero_int) X)->(((ord_less_eq_int zero_zero_int) Y)->((ord_less_eq_int zero_zero_int) ((times_times_int X) Y))))) of role axiom named fact_1083_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J % A new axiom: (forall (Y:int) (X:int), (((ord_less_eq_int zero_zero_int) X)->(((ord_less_eq_int zero_zero_int) Y)->((ord_less_eq_int zero_zero_int) ((times_times_int X) Y))))) % FOF formula ((ord_less_eq_int zero_zero_int) zero_zero_int) of role axiom named fact_1084_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J % A new axiom: ((ord_less_eq_int zero_zero_int) zero_zero_int) % FOF formula (forall (Y:int) (X:int), (((ord_less_eq_int zero_zero_int) X)->(((ord_less_eq_int zero_zero_int) Y)->((ord_less_eq_int zero_zero_int) ((plus_plus_int X) Y))))) of role axiom named fact_1085_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J % A new axiom: (forall (Y:int) (X:int), (((ord_less_eq_int zero_zero_int) X)->(((ord_less_eq_int zero_zero_int) Y)->((ord_less_eq_int zero_zero_int) ((plus_plus_int X) Y))))) % FOF formula ((ord_less_eq_int zero_zero_int) one_one_int) of role axiom named fact_1086_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J % A new axiom: ((ord_less_eq_int zero_zero_int) one_one_int) % FOF formula (forall (P_1:(int->Prop)) (P:(int->Prop)), ((forall (X_1:int), (((ord_less_eq_int zero_zero_int) X_1)->((iff (P X_1)) (P_1 X_1))))->(((eq (int->Prop)) (collect_int (fun (X_1:int)=> ((and ((ord_less_eq_int zero_zero_int) X_1)) (P X_1))))) (collect_int (fun (X_1:int)=> ((and ((ord_less_eq_int zero_zero_int) X_1)) (P_1 X_1))))))) of role axiom named fact_1087_transfer__nat__int__set__cong % A new axiom: (forall (P_1:(int->Prop)) (P:(int->Prop)), ((forall (X_1:int), (((ord_less_eq_int zero_zero_int) X_1)->((iff (P X_1)) (P_1 X_1))))->(((eq (int->Prop)) (collect_int (fun (X_1:int)=> ((and ((ord_less_eq_int zero_zero_int) X_1)) (P X_1))))) (collect_int (fun (X_1:int)=> ((and ((ord_less_eq_int zero_zero_int) X_1)) (P_1 X_1))))))) % FOF formula (forall (K:int) (P:(int->Prop)) (D:int), (((ord_less_int zero_zero_int) D)->((forall (X_1:int), ((P X_1)->(P ((minus_minus_int X_1) D))))->(((ord_less_eq_int zero_zero_int) K)->(forall (X_1:int), ((P X_1)->(P ((minus_minus_int X_1) ((times_times_int K) D))))))))) of role axiom named fact_1088_decr__mult__lemma % A new axiom: (forall (K:int) (P:(int->Prop)) (D:int), (((ord_less_int zero_zero_int) D)->((forall (X_1:int), ((P X_1)->(P ((minus_minus_int X_1) D))))->(((ord_less_eq_int zero_zero_int) K)->(forall (X_1:int), ((P X_1)->(P ((minus_minus_int X_1) ((times_times_int K) D))))))))) % FOF formula (forall (P_1:Prop) (P:Prop) (X:int), ((((ord_less_eq_int zero_zero_int) X)->((iff P) P_1))->((iff ((and ((ord_less_eq_int zero_zero_int) X)) P)) ((and ((ord_less_eq_int zero_zero_int) X)) P_1)))) of role axiom named fact_1089_conj__le__cong % A new axiom: (forall (P_1:Prop) (P:Prop) (X:int), ((((ord_less_eq_int zero_zero_int) X)->((iff P) P_1))->((iff ((and ((ord_less_eq_int zero_zero_int) X)) P)) ((and ((ord_less_eq_int zero_zero_int) X)) P_1)))) % FOF formula (forall (P_1:Prop) (P:Prop) (X:int), ((((ord_less_eq_int zero_zero_int) X)->((iff P) P_1))->((iff (((ord_less_eq_int zero_zero_int) X)->P)) (((ord_less_eq_int zero_zero_int) X)->P_1)))) of role axiom named fact_1090_imp__le__cong % A new axiom: (forall (P_1:Prop) (P:Prop) (X:int), ((((ord_less_eq_int zero_zero_int) X)->((iff P) P_1))->((iff (((ord_less_eq_int zero_zero_int) X)->P)) (((ord_less_eq_int zero_zero_int) X)->P_1)))) % FOF formula (forall (K:int) (P:(int->Prop)) (D:int), (((ord_less_int zero_zero_int) D)->((forall (X_1:int), ((P X_1)->(P ((plus_plus_int X_1) D))))->(((ord_less_eq_int zero_zero_int) K)->(forall (X_1:int), ((P X_1)->(P ((plus_plus_int X_1) ((times_times_int K) D))))))))) of role axiom named fact_1091_incr__mult__lemma % A new axiom: (forall (K:int) (P:(int->Prop)) (D:int), (((ord_less_int zero_zero_int) D)->((forall (X_1:int), ((P X_1)->(P ((plus_plus_int X_1) D))))->(((ord_less_eq_int zero_zero_int) K)->(forall (X_1:int), ((P X_1)->(P ((plus_plus_int X_1) ((times_times_int K) D))))))))) % FOF formula (forall (I_1:int) (P:(int->Prop)) (K:int), ((P K)->((forall (_TPTP_I:int), (((ord_less_eq_int K) _TPTP_I)->((P _TPTP_I)->(P ((plus_plus_int _TPTP_I) one_one_int)))))->((forall (_TPTP_I:int), (((ord_less_eq_int _TPTP_I) K)->((P _TPTP_I)->(P ((minus_minus_int _TPTP_I) one_one_int)))))->(P I_1))))) of role axiom named fact_1092_int__induct % A new axiom: (forall (I_1:int) (P:(int->Prop)) (K:int), ((P K)->((forall (_TPTP_I:int), (((ord_less_eq_int K) _TPTP_I)->((P _TPTP_I)->(P ((plus_plus_int _TPTP_I) one_one_int)))))->((forall (_TPTP_I:int), (((ord_less_eq_int _TPTP_I) K)->((P _TPTP_I)->(P ((minus_minus_int _TPTP_I) one_one_int)))))->(P I_1))))) % FOF formula (forall (P:(int->Prop)) (P1:(int->Prop)) (D:int), (((ord_less_int zero_zero_int) D)->((forall (X_1:int) (K_1:int), ((iff (P1 X_1)) (P1 ((minus_minus_int X_1) ((times_times_int K_1) D)))))->(((ex int) (fun (Z_2:int)=> (forall (X_1:int), (((ord_less_int X_1) Z_2)->((iff (P X_1)) (P1 X_1))))))->((_TPTP_ex P1)->(_TPTP_ex P)))))) of role axiom named fact_1093_minusinfinity % A new axiom: (forall (P:(int->Prop)) (P1:(int->Prop)) (D:int), (((ord_less_int zero_zero_int) D)->((forall (X_1:int) (K_1:int), ((iff (P1 X_1)) (P1 ((minus_minus_int X_1) ((times_times_int K_1) D)))))->(((ex int) (fun (Z_2:int)=> (forall (X_1:int), (((ord_less_int X_1) Z_2)->((iff (P X_1)) (P1 X_1))))))->((_TPTP_ex P1)->(_TPTP_ex P)))))) % FOF formula (forall (P:(int->Prop)) (P_1:(int->Prop)) (D:int), (((ord_less_int zero_zero_int) D)->((forall (X_1:int) (K_1:int), ((iff (P_1 X_1)) (P_1 ((minus_minus_int X_1) ((times_times_int K_1) D)))))->(((ex int) (fun (Z_2:int)=> (forall (X_1:int), (((ord_less_int Z_2) X_1)->((iff (P X_1)) (P_1 X_1))))))->((_TPTP_ex P_1)->(_TPTP_ex P)))))) of role axiom named fact_1094_plusinfinity % A new axiom: (forall (P:(int->Prop)) (P_1:(int->Prop)) (D:int), (((ord_less_int zero_zero_int) D)->((forall (X_1:int) (K_1:int), ((iff (P_1 X_1)) (P_1 ((minus_minus_int X_1) ((times_times_int K_1) D)))))->(((ex int) (fun (Z_2:int)=> (forall (X_1:int), (((ord_less_int Z_2) X_1)->((iff (P X_1)) (P_1 X_1))))))->((_TPTP_ex P_1)->(_TPTP_ex P)))))) % FOF formula (forall (Y:int) (X:int), ((and (((ord_less_eq_int Y) X)->(((eq int) ((nat_tsub X) Y)) ((minus_minus_int X) Y)))) ((((ord_less_eq_int Y) X)->False)->(((eq int) ((nat_tsub X) Y)) zero_zero_int)))) of role axiom named fact_1095_tsub__def % A new axiom: (forall (Y:int) (X:int), ((and (((ord_less_eq_int Y) X)->(((eq int) ((nat_tsub X) Y)) ((minus_minus_int X) Y)))) ((((ord_less_eq_int Y) X)->False)->(((eq int) ((nat_tsub X) Y)) zero_zero_int)))) % FOF formula (forall (N:nat), ((ord_less_eq_int zero_zero_int) (semiri1621563631at_int N))) of role axiom named fact_1096_zero__zle__int % A new axiom: (forall (N:nat), ((ord_less_eq_int zero_zero_int) (semiri1621563631at_int N))) % FOF formula (forall (K:nat), (((ord_less_int (semiri1621563631at_int K)) zero_zero_int)->False)) of role axiom named fact_1097_int__less__0__conv % A new axiom: (forall (K:nat), (((ord_less_int (semiri1621563631at_int K)) zero_zero_int)->False)) % FOF formula (((eq int) (semiri1621563631at_int one_one_nat)) one_one_int) of role axiom named fact_1098_int__1 % A new axiom: (((eq int) (semiri1621563631at_int one_one_nat)) one_one_int) % FOF formula (((eq int) (semiri1621563631at_int zero_zero_nat)) zero_zero_int) of role axiom named fact_1099_int__0 % A new axiom: (((eq int) (semiri1621563631at_int zero_zero_nat)) zero_zero_int) % FOF formula (forall (N:nat), ((iff (((eq int) (semiri1621563631at_int N)) zero_zero_int)) (((eq nat) N) zero_zero_nat))) of role axiom named fact_1100_int__eq__0__conv % A new axiom: (forall (N:nat), ((iff (((eq int) (semiri1621563631at_int N)) zero_zero_int)) (((eq nat) N) zero_zero_nat))) % FOF formula (forall (M:nat) (N:nat), ((iff ((ord_less_int (semiri1621563631at_int M)) (semiri1621563631at_int N))) ((ord_less_nat M) N))) of role axiom named fact_1101_zless__int % A new axiom: (forall (M:nat) (N:nat), ((iff ((ord_less_int (semiri1621563631at_int M)) (semiri1621563631at_int N))) ((ord_less_nat M) N))) % FOF formula (forall (M:nat) (N:nat), ((iff ((ord_less_eq_int (semiri1621563631at_int M)) (semiri1621563631at_int N))) ((ord_less_eq_nat M) N))) of role axiom named fact_1102_zle__int % A new axiom: (forall (M:nat) (N:nat), ((iff ((ord_less_eq_int (semiri1621563631at_int M)) (semiri1621563631at_int N))) ((ord_less_eq_nat M) N))) % FOF formula (forall (M:nat) (N:nat), (((eq int) ((plus_plus_int (semiri1621563631at_int M)) (semiri1621563631at_int N))) (semiri1621563631at_int ((plus_plus_nat M) N)))) of role axiom named fact_1103_zadd__int % A new axiom: (forall (M:nat) (N:nat), (((eq int) ((plus_plus_int (semiri1621563631at_int M)) (semiri1621563631at_int N))) (semiri1621563631at_int ((plus_plus_nat M) N)))) % FOF formula (forall (M:nat) (N:nat) (Z:int), (((eq int) ((plus_plus_int (semiri1621563631at_int M)) ((plus_plus_int (semiri1621563631at_int N)) Z))) ((plus_plus_int (semiri1621563631at_int ((plus_plus_nat M) N))) Z))) of role axiom named fact_1104_zadd__int__left % A new axiom: (forall (M:nat) (N:nat) (Z:int), (((eq int) ((plus_plus_int (semiri1621563631at_int M)) ((plus_plus_int (semiri1621563631at_int N)) Z))) ((plus_plus_int (semiri1621563631at_int ((plus_plus_nat M) N))) Z))) % FOF formula (forall (W:int) (Z:int), ((iff ((ord_less_eq_int W) Z)) ((ex nat) (fun (N_1:nat)=> (((eq int) Z) ((plus_plus_int W) (semiri1621563631at_int N_1))))))) of role axiom named fact_1105_zle__iff__zadd % A new axiom: (forall (W:int) (Z:int), ((iff ((ord_less_eq_int W) Z)) ((ex nat) (fun (N_1:nat)=> (((eq int) Z) ((plus_plus_int W) (semiri1621563631at_int N_1))))))) % FOF formula (forall (M:nat) (N:nat), (((eq int) ((times_times_int (semiri1621563631at_int M)) (semiri1621563631at_int N))) (semiri1621563631at_int ((times_times_nat M) N)))) of role axiom named fact_1106_zmult__int % A new axiom: (forall (M:nat) (N:nat), (((eq int) ((times_times_int (semiri1621563631at_int M)) (semiri1621563631at_int N))) (semiri1621563631at_int ((times_times_nat M) N)))) % FOF formula (forall (M:nat) (N:nat), (((eq int) (semiri1621563631at_int ((times_times_nat M) N))) ((times_times_int (semiri1621563631at_int M)) (semiri1621563631at_int N)))) of role axiom named fact_1107_int__mult % A new axiom: (forall (M:nat) (N:nat), (((eq int) (semiri1621563631at_int ((times_times_nat M) N))) ((times_times_int (semiri1621563631at_int M)) (semiri1621563631at_int N)))) % FOF formula (forall (X:nat) (Y:nat), (((eq int) ((times_times_int (semiri1621563631at_int X)) (semiri1621563631at_int Y))) (semiri1621563631at_int ((times_times_nat X) Y)))) of role axiom named fact_1108_Nat__Transfer_Otransfer__int__nat__functions_I2_J % A new axiom: (forall (X:nat) (Y:nat), (((eq int) ((times_times_int (semiri1621563631at_int X)) (semiri1621563631at_int Y))) (semiri1621563631at_int ((times_times_nat X) Y)))) % FOF formula (forall (X:nat) (Y:nat), ((iff ((ord_less_int (semiri1621563631at_int X)) (semiri1621563631at_int Y))) ((ord_less_nat X) Y))) of role axiom named fact_1109_transfer__int__nat__relations_I2_J % A new axiom: (forall (X:nat) (Y:nat), ((iff ((ord_less_int (semiri1621563631at_int X)) (semiri1621563631at_int Y))) ((ord_less_nat X) Y))) % FOF formula (forall (X:nat) (Y:nat), ((iff ((ord_less_eq_int (semiri1621563631at_int X)) (semiri1621563631at_int Y))) ((ord_less_eq_nat X) Y))) of role axiom named fact_1110_transfer__int__nat__relations_I3_J % A new axiom: (forall (X:nat) (Y:nat), ((iff ((ord_less_eq_int (semiri1621563631at_int X)) (semiri1621563631at_int Y))) ((ord_less_eq_nat X) Y))) % FOF formula (forall (X:nat) (Y:nat), (((eq int) ((nat_tsub (semiri1621563631at_int X)) (semiri1621563631at_int Y))) (semiri1621563631at_int ((minus_minus_nat X) Y)))) of role axiom named fact_1111_Nat__Transfer_Otransfer__int__nat__functions_I3_J % A new axiom: (forall (X:nat) (Y:nat), (((eq int) ((nat_tsub (semiri1621563631at_int X)) (semiri1621563631at_int Y))) (semiri1621563631at_int ((minus_minus_nat X) Y)))) % FOF formula (forall (X:nat) (Y:nat), (((eq int) ((plus_plus_int (semiri1621563631at_int X)) (semiri1621563631at_int Y))) (semiri1621563631at_int ((plus_plus_nat X) Y)))) of role axiom named fact_1112_Nat__Transfer_Otransfer__int__nat__functions_I1_J % A new axiom: (forall (X:nat) (Y:nat), (((eq int) ((plus_plus_int (semiri1621563631at_int X)) (semiri1621563631at_int Y))) (semiri1621563631at_int ((plus_plus_nat X) Y)))) % FOF formula (forall (A:(nat->Prop)), (((eq nat) (finite_card_nat A)) (finite_card_int ((image_nat_int semiri1621563631at_int) A)))) of role axiom named fact_1113_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J % A new axiom: (forall (A:(nat->Prop)), (((eq nat) (finite_card_nat A)) (finite_card_int ((image_nat_int semiri1621563631at_int) A)))) % FOF formula (forall (A:(nat->Prop)), ((iff (finite_finite_nat A)) (finite_finite_int ((image_nat_int semiri1621563631at_int) A)))) of role axiom named fact_1114_transfer__nat__int__set__relations_I1_J % A new axiom: (forall (A:(nat->Prop)), ((iff (finite_finite_nat A)) (finite_finite_int ((image_nat_int semiri1621563631at_int) A)))) % FOF formula (((eq int) one_one_int) (semiri1621563631at_int one_one_nat)) of role axiom named fact_1115_transfer__int__nat__numerals_I2_J % A new axiom: (((eq int) one_one_int) (semiri1621563631at_int one_one_nat)) % FOF formula (((eq int) zero_zero_int) (semiri1621563631at_int zero_zero_nat)) of role axiom named fact_1116_transfer__int__nat__numerals_I1_J % A new axiom: (((eq int) zero_zero_int) (semiri1621563631at_int zero_zero_nat)) % FOF formula (forall (P:(int->Prop)), (((eq (int->Prop)) (collect_int (fun (X_1:int)=> ((and ((ord_less_eq_int zero_zero_int) X_1)) (P X_1))))) ((image_nat_int semiri1621563631at_int) (collect_nat (fun (X_1:nat)=> (P (semiri1621563631at_int X_1))))))) of role axiom named fact_1117_Nat__Transfer_Otransfer__int__nat__set__functions_I5_J % A new axiom: (forall (P:(int->Prop)), (((eq (int->Prop)) (collect_int (fun (X_1:int)=> ((and ((ord_less_eq_int zero_zero_int) X_1)) (P X_1))))) ((image_nat_int semiri1621563631at_int) (collect_nat (fun (X_1:nat)=> (P (semiri1621563631at_int X_1))))))) % FOF formula (forall (Z:nat), ((ord_less_eq_int zero_zero_int) (semiri1621563631at_int Z))) of role axiom named fact_1118_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J % A new axiom: (forall (Z:nat), ((ord_less_eq_int zero_zero_int) (semiri1621563631at_int Z))) % FOF formula (forall (P:(int->Prop)), ((iff ((ex int) (fun (X_1:int)=> ((and ((ord_less_eq_int zero_zero_int) X_1)) (P X_1))))) ((ex nat) (fun (X_1:nat)=> (P (semiri1621563631at_int X_1)))))) of role axiom named fact_1119_transfer__int__nat__quantifiers_I2_J % A new axiom: (forall (P:(int->Prop)), ((iff ((ex int) (fun (X_1:int)=> ((and ((ord_less_eq_int zero_zero_int) X_1)) (P X_1))))) ((ex nat) (fun (X_1:nat)=> (P (semiri1621563631at_int X_1)))))) % FOF formula (forall (P:(int->Prop)), ((iff (forall (X_1:int), (((ord_less_eq_int zero_zero_int) X_1)->(P X_1)))) (forall (X_1:nat), (P (semiri1621563631at_int X_1))))) of role axiom named fact_1120_transfer__int__nat__quantifiers_I1_J % A new axiom: (forall (P:(int->Prop)), ((iff (forall (X_1:int), (((ord_less_eq_int zero_zero_int) X_1)->(P X_1)))) (forall (X_1:nat), (P (semiri1621563631at_int X_1))))) % FOF formula (forall (N:nat), ((iff ((ord_less_eq_int (semiri1621563631at_int N)) zero_zero_int)) (((eq nat) N) zero_zero_nat))) of role axiom named fact_1121_int__le__0__conv % A new axiom: (forall (N:nat), ((iff ((ord_less_eq_int (semiri1621563631at_int N)) zero_zero_int)) (((eq nat) N) zero_zero_nat))) % FOF formula (((eq int) (semiri1621563631at_int (suc zero_zero_nat))) one_one_int) of role axiom named fact_1122_int__Suc0__eq__1 % A new axiom: (((eq int) (semiri1621563631at_int (suc zero_zero_nat))) one_one_int) % FOF formula (forall (W:int) (Z:int), ((iff ((ord_less_int W) Z)) ((ex nat) (fun (N_1:nat)=> (((eq int) Z) ((plus_plus_int W) (semiri1621563631at_int (suc N_1)))))))) of role axiom named fact_1123_zless__iff__Suc__zadd % A new axiom: (forall (W:int) (Z:int), ((iff ((ord_less_int W) Z)) ((ex nat) (fun (N_1:nat)=> (((eq int) Z) ((plus_plus_int W) (semiri1621563631at_int (suc N_1)))))))) % FOF formula (forall (M:nat), (((eq int) (semiri1621563631at_int (suc M))) ((plus_plus_int one_one_int) (semiri1621563631at_int M)))) of role axiom named fact_1124_int__Suc % A new axiom: (forall (M:nat), (((eq int) (semiri1621563631at_int (suc M))) ((plus_plus_int one_one_int) (semiri1621563631at_int M)))) % FOF formula (forall (N:nat) (M:nat), (((ord_less_eq_nat N) M)->(((eq int) ((minus_minus_int (semiri1621563631at_int M)) (semiri1621563631at_int N))) (semiri1621563631at_int ((minus_minus_nat M) N))))) of role axiom named fact_1125_zdiff__int % A new axiom: (forall (N:nat) (M:nat), (((ord_less_eq_nat N) M)->(((eq int) ((minus_minus_int (semiri1621563631at_int M)) (semiri1621563631at_int N))) (semiri1621563631at_int ((minus_minus_nat M) N))))) % FOF formula (forall (N:nat), ((iff ((ord_less_int zero_zero_int) (semiri1621563631at_int N))) ((ord_less_nat zero_zero_nat) N))) of role axiom named fact_1126_zero__less__int__conv % A new axiom: (forall (N:nat), ((iff ((ord_less_int zero_zero_int) (semiri1621563631at_int N))) ((ord_less_nat zero_zero_nat) N))) % FOF formula (forall (K:nat) (I_1:int) (J:int), (((ord_less_int I_1) J)->(((ord_less_nat zero_zero_nat) K)->((ord_less_int ((times_times_int (semiri1621563631at_int K)) I_1)) ((times_times_int (semiri1621563631at_int K)) J))))) of role axiom named fact_1127_zmult__zless__mono2__lemma % A new axiom: (forall (K:nat) (I_1:int) (J:int), (((ord_less_int I_1) J)->(((ord_less_nat zero_zero_nat) K)->((ord_less_int ((times_times_int (semiri1621563631at_int K)) I_1)) ((times_times_int (semiri1621563631at_int K)) J))))) % FOF formula (forall (Y:int) (X:int), (((ord_less_eq_int zero_zero_int) X)->(((ord_less_eq_int zero_zero_int) Y)->((ord_less_eq_int zero_zero_int) ((nat_tsub X) Y))))) of role axiom named fact_1128_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J % A new axiom: (forall (Y:int) (X:int), (((ord_less_eq_int zero_zero_int) X)->(((ord_less_eq_int zero_zero_int) Y)->((ord_less_eq_int zero_zero_int) ((nat_tsub X) Y))))) % FOF formula (forall (P:(int->Prop)) (X:nat) (Y:nat), ((iff (P (semiri1621563631at_int ((minus_minus_nat X) Y)))) ((and (((ord_less_eq_nat Y) X)->(P ((minus_minus_int (semiri1621563631at_int X)) (semiri1621563631at_int Y))))) (((ord_less_nat X) Y)->(P zero_zero_int))))) of role axiom named fact_1129_zdiff__int__split % A new axiom: (forall (P:(int->Prop)) (X:nat) (Y:nat), ((iff (P (semiri1621563631at_int ((minus_minus_nat X) Y)))) ((and (((ord_less_eq_nat Y) X)->(P ((minus_minus_int (semiri1621563631at_int X)) (semiri1621563631at_int Y))))) (((ord_less_nat X) Y)->(P zero_zero_int))))) % FOF formula (forall (Y:int) (X:int), (((ord_less_eq_int Y) X)->(((eq int) ((nat_tsub X) Y)) ((minus_minus_int X) Y)))) of role axiom named fact_1130_tsub__eq % A new axiom: (forall (Y:int) (X:int), (((ord_less_eq_int Y) X)->(((eq int) ((nat_tsub X) Y)) ((minus_minus_int X) Y)))) % FOF formula (forall (K:int), (((ord_less_int zero_zero_int) K)->((ex nat) (fun (N_1:nat)=> ((and ((ord_less_nat zero_zero_nat) N_1)) (((eq int) K) (semiri1621563631at_int N_1))))))) of role axiom named fact_1131_zero__less__imp__eq__int % A new axiom: (forall (K:int), (((ord_less_int zero_zero_int) K)->((ex nat) (fun (N_1:nat)=> ((and ((ord_less_nat zero_zero_nat) N_1)) (((eq int) K) (semiri1621563631at_int N_1))))))) % FOF formula (forall (M:nat) (N:nat), ((iff (((eq int) (semiri1621563631at_int M)) (semiri1621563631at_int N))) (((eq nat) M) N))) of role axiom named fact_1132_int__int__eq % A new axiom: (forall (M:nat) (N:nat), ((iff (((eq int) (semiri1621563631at_int M)) (semiri1621563631at_int N))) (((eq nat) M) N))) % FOF formula (forall (A:(nat->Prop)) (B:(nat->Prop)), ((iff ((ord_less_nat_o A) B)) ((ord_less_int_o ((image_nat_int semiri1621563631at_int) A)) ((image_nat_int semiri1621563631at_int) B)))) of role axiom named fact_1133_transfer__nat__int__set__relations_I4_J % A new axiom: (forall (A:(nat->Prop)) (B:(nat->Prop)), ((iff ((ord_less_nat_o A) B)) ((ord_less_int_o ((image_nat_int semiri1621563631at_int) A)) ((image_nat_int semiri1621563631at_int) B)))) % FOF formula (forall (A:(nat->Prop)) (B:(nat->Prop)), ((iff ((ord_less_eq_nat_o A) B)) ((ord_less_eq_int_o ((image_nat_int semiri1621563631at_int) A)) ((image_nat_int semiri1621563631at_int) B)))) of role axiom named fact_1134_transfer__nat__int__set__relations_I5_J % A new axiom: (forall (A:(nat->Prop)) (B:(nat->Prop)), ((iff ((ord_less_eq_nat_o A) B)) ((ord_less_eq_int_o ((image_nat_int semiri1621563631at_int) A)) ((image_nat_int semiri1621563631at_int) B)))) % FOF formula (((eq (int->Prop)) bot_bot_int_o) ((image_nat_int semiri1621563631at_int) bot_bot_nat_o)) of role axiom named fact_1135_Nat__Transfer_Otransfer__int__nat__set__functions_I2_J % A new axiom: (((eq (int->Prop)) bot_bot_int_o) ((image_nat_int semiri1621563631at_int) bot_bot_nat_o)) % FOF formula (forall (A:(nat->Prop)) (B:(nat->Prop)), ((iff (((eq (nat->Prop)) A) B)) (((eq (int->Prop)) ((image_nat_int semiri1621563631at_int) A)) ((image_nat_int semiri1621563631at_int) B)))) of role axiom named fact_1136_transfer__nat__int__set__relations_I3_J % A new axiom: (forall (A:(nat->Prop)) (B:(nat->Prop)), ((iff (((eq (nat->Prop)) A) B)) (((eq (int->Prop)) ((image_nat_int semiri1621563631at_int) A)) ((image_nat_int semiri1621563631at_int) B)))) % FOF formula (forall (X:nat) (A:(nat->Prop)), ((iff ((member_nat X) A)) ((member_int (semiri1621563631at_int X)) ((image_nat_int semiri1621563631at_int) A)))) of role axiom named fact_1137_transfer__nat__int__set__relations_I2_J % A new axiom: (forall (X:nat) (A:(nat->Prop)), ((iff ((member_nat X) A)) ((member_int (semiri1621563631at_int X)) ((image_nat_int semiri1621563631at_int) A)))) % FOF formula (forall (X:nat) (Y:nat) (P:Prop), ((and (P->(((eq int) (semiri1621563631at_int X)) (semiri1621563631at_int (((if_nat P) X) Y))))) ((P->False)->(((eq int) (semiri1621563631at_int Y)) (semiri1621563631at_int (((if_nat P) X) Y)))))) of role axiom named fact_1138_int__if__cong % A new axiom: (forall (X:nat) (Y:nat) (P:Prop), ((and (P->(((eq int) (semiri1621563631at_int X)) (semiri1621563631at_int (((if_nat P) X) Y))))) ((P->False)->(((eq int) (semiri1621563631at_int Y)) (semiri1621563631at_int (((if_nat P) X) Y)))))) % FOF formula (forall (X:nat) (Y:nat), ((iff (((eq int) (semiri1621563631at_int X)) (semiri1621563631at_int Y))) (((eq nat) X) Y))) of role axiom named fact_1139_transfer__int__nat__relations_I1_J % A new axiom: (forall (X:nat) (Y:nat), ((iff (((eq int) (semiri1621563631at_int X)) (semiri1621563631at_int Y))) (((eq nat) X) Y))) % FOF formula (forall (K:int), (((ord_less_eq_int zero_zero_int) K)->((forall (N_1:nat), (not (((eq int) K) (semiri1621563631at_int N_1))))->False))) of role axiom named fact_1140_nonneg__int__cases % A new axiom: (forall (K:int), (((ord_less_eq_int zero_zero_int) K)->((forall (N_1:nat), (not (((eq int) K) (semiri1621563631at_int N_1))))->False))) % FOF formula (forall (Z:int), (((ord_less_eq_int zero_zero_int) Z)->((forall (M_1:nat), (not (((eq int) Z) (semiri1621563631at_int M_1))))->False))) of role axiom named fact_1141_nonneg__eq__int % A new axiom: (forall (Z:int), (((ord_less_eq_int zero_zero_int) Z)->((forall (M_1:nat), (not (((eq int) Z) (semiri1621563631at_int M_1))))->False))) % FOF formula (forall (K:int), (((ord_less_eq_int zero_zero_int) K)->((ex nat) (fun (N_1:nat)=> (((eq int) K) (semiri1621563631at_int N_1)))))) of role axiom named fact_1142_zero__le__imp__eq__int % A new axiom: (forall (K:int), (((ord_less_eq_int zero_zero_int) K)->((ex nat) (fun (N_1:nat)=> (((eq int) K) (semiri1621563631at_int N_1)))))) % FOF formula (forall (Z:int), ((forall (M_1:nat) (N_1:nat), (not (((eq int) Z) ((minus_minus_int (semiri1621563631at_int M_1)) (semiri1621563631at_int N_1)))))->False)) of role axiom named fact_1143_int__diff__cases % A new axiom: (forall (Z:int), ((forall (M_1:nat) (N_1:nat), (not (((eq int) Z) ((minus_minus_int (semiri1621563631at_int M_1)) (semiri1621563631at_int N_1)))))->False)) % FOF formula (forall (X:int) (Z:int) (D:int), (((ord_less_int zero_zero_int) D)->((ord_less_int ((minus_minus_int X) ((times_times_int ((plus_plus_int (abs_abs_int ((minus_minus_int X) Z))) one_one_int)) D))) Z))) of role axiom named fact_1144_decr__lemma % A new axiom: (forall (X:int) (Z:int) (D:int), (((ord_less_int zero_zero_int) D)->((ord_less_int ((minus_minus_int X) ((times_times_int ((plus_plus_int (abs_abs_int ((minus_minus_int X) Z))) one_one_int)) D))) Z))) % FOF formula (forall (Z:int), ((iff ((ord_less_int (abs_abs_int Z)) one_one_int)) (((eq int) Z) zero_zero_int))) of role axiom named fact_1145_zabs__less__one__iff % A new axiom: (forall (Z:int), ((iff ((ord_less_int (abs_abs_int Z)) one_one_int)) (((eq int) Z) zero_zero_int))) % FOF formula (forall (Z_1:int), ((iff (nat_neg Z_1)) ((ord_less_int Z_1) zero_zero_int))) of role axiom named fact_1146_neg__def % A new axiom: (forall (Z_1:int), ((iff (nat_neg Z_1)) ((ord_less_int Z_1) zero_zero_int))) % FOF formula (forall (X:int), ((iff ((nat_neg X)->False)) ((ord_less_eq_int zero_zero_int) X))) of role axiom named fact_1147_not__neg__eq__ge__0 % A new axiom: (forall (X:int), ((iff ((nat_neg X)->False)) ((ord_less_eq_int zero_zero_int) X))) % FOF formula ((nat_neg one_one_int)->False) of role axiom named fact_1148_not__neg__1 % A new axiom: ((nat_neg one_one_int)->False) % FOF formula ((nat_neg zero_zero_int)->False) of role axiom named fact_1149_not__neg__0 % A new axiom: ((nat_neg zero_zero_int)->False) % FOF formula (forall (M:int) (N:int), ((((eq int) (abs_abs_int ((times_times_int M) N))) one_one_int)->(((eq int) (abs_abs_int M)) one_one_int))) of role axiom named fact_1150_abs__zmult__eq__1 % A new axiom: (forall (M:int) (N:int), ((((eq int) (abs_abs_int ((times_times_int M) N))) one_one_int)->(((eq int) (abs_abs_int M)) one_one_int))) % FOF formula (forall (N:nat), ((nat_neg (semiri1621563631at_int N))->False)) of role axiom named fact_1151_not__neg__int % A new axiom: (forall (N:nat), ((nat_neg (semiri1621563631at_int N))->False)) % FOF formula (forall (M:nat), (((eq int) (abs_abs_int (semiri1621563631at_int M))) (semiri1621563631at_int M))) of role axiom named fact_1152_abs__int__eq % A new axiom: (forall (M:nat), (((eq int) (abs_abs_int (semiri1621563631at_int M))) (semiri1621563631at_int M))) % FOF formula (forall (V:int), ((nat_neg (number_number_of_int V))->(((eq nat) (number_number_of_nat V)) zero_zero_nat))) of role axiom named fact_1153_neg__imp__number__of__eq__0 % A new axiom: (forall (V:int), ((nat_neg (number_number_of_int V))->(((eq nat) (number_number_of_nat V)) zero_zero_nat))) % FOF formula (forall (V:int) (V_1:int), ((iff (((eq nat) (number_number_of_nat V)) (number_number_of_nat V_1))) ((and ((nat_neg (number_number_of_int V))->((ord_less_eq_int (number_number_of_int V_1)) zero_zero_int))) (((nat_neg (number_number_of_int V))->False)->((and ((nat_neg (number_number_of_int V_1))->(((eq int) (number_number_of_int V)) zero_zero_int))) (((nat_neg (number_number_of_int V_1))->False)->(((eq int) V) V_1))))))) of role axiom named fact_1154_eq__nat__number__of % A new axiom: (forall (V:int) (V_1:int), ((iff (((eq nat) (number_number_of_nat V)) (number_number_of_nat V_1))) ((and ((nat_neg (number_number_of_int V))->((ord_less_eq_int (number_number_of_int V_1)) zero_zero_int))) (((nat_neg (number_number_of_int V))->False)->((and ((nat_neg (number_number_of_int V_1))->(((eq int) (number_number_of_int V)) zero_zero_int))) (((nat_neg (number_number_of_int V_1))->False)->(((eq int) V) V_1))))))) % FOF formula (forall (V_1:int) (K:nat) (V:int), ((and ((nat_neg (number_number_of_int V))->(((eq nat) ((plus_plus_nat (number_number_of_nat V)) ((plus_plus_nat (number_number_of_nat V_1)) K))) ((plus_plus_nat (number_number_of_nat V_1)) K)))) (((nat_neg (number_number_of_int V))->False)->((and ((nat_neg (number_number_of_int V_1))->(((eq nat) ((plus_plus_nat (number_number_of_nat V)) ((plus_plus_nat (number_number_of_nat V_1)) K))) ((plus_plus_nat (number_number_of_nat V)) K)))) (((nat_neg (number_number_of_int V_1))->False)->(((eq nat) ((plus_plus_nat (number_number_of_nat V)) ((plus_plus_nat (number_number_of_nat V_1)) K))) ((plus_plus_nat (number_number_of_nat ((plus_plus_int V) V_1))) K))))))) of role axiom named fact_1155_nat__number__of__add__left % A new axiom: (forall (V_1:int) (K:nat) (V:int), ((and ((nat_neg (number_number_of_int V))->(((eq nat) ((plus_plus_nat (number_number_of_nat V)) ((plus_plus_nat (number_number_of_nat V_1)) K))) ((plus_plus_nat (number_number_of_nat V_1)) K)))) (((nat_neg (number_number_of_int V))->False)->((and ((nat_neg (number_number_of_int V_1))->(((eq nat) ((plus_plus_nat (number_number_of_nat V)) ((plus_plus_nat (number_number_of_nat V_1)) K))) ((plus_plus_nat (number_number_of_nat V)) K)))) (((nat_neg (number_number_of_int V_1))->False)->(((eq nat) ((plus_plus_nat (number_number_of_nat V)) ((plus_plus_nat (number_number_of_nat V_1)) K))) ((plus_plus_nat (number_number_of_nat ((plus_plus_int V) V_1))) K))))))) % FOF formula (forall (V:int), ((and ((nat_neg (number_number_of_int V))->(((eq int) (semiri1621563631at_int (number_number_of_nat V))) zero_zero_int))) (((nat_neg (number_number_of_int V))->False)->(((eq int) (semiri1621563631at_int (number_number_of_nat V))) (number_number_of_int V))))) of role axiom named fact_1156_int__nat__number__of % A new axiom: (forall (V:int), ((and ((nat_neg (number_number_of_int V))->(((eq int) (semiri1621563631at_int (number_number_of_nat V))) zero_zero_int))) (((nat_neg (number_number_of_int V))->False)->(((eq int) (semiri1621563631at_int (number_number_of_nat V))) (number_number_of_int V))))) % FOF formula (forall (Z:int) (X:int) (D:int), (((ord_less_int zero_zero_int) D)->((ord_less_int Z) ((plus_plus_int X) ((times_times_int ((plus_plus_int (abs_abs_int ((minus_minus_int X) Z))) one_one_int)) D))))) of role axiom named fact_1157_incr__lemma % A new axiom: (forall (Z:int) (X:int) (D:int), (((ord_less_int zero_zero_int) D)->((ord_less_int Z) ((plus_plus_int X) ((times_times_int ((plus_plus_int (abs_abs_int ((minus_minus_int X) Z))) one_one_int)) D))))) % FOF formula (forall (K:int) (F:(nat->int)) (N:nat), ((forall (_TPTP_I:nat), (((ord_less_nat _TPTP_I) N)->((ord_less_eq_int (abs_abs_int ((minus_minus_int (F ((plus_plus_nat _TPTP_I) one_one_nat))) (F _TPTP_I)))) one_one_int)))->(((ord_less_eq_int (F zero_zero_nat)) K)->(((ord_less_eq_int K) (F N))->((ex nat) (fun (_TPTP_I:nat)=> ((and ((ord_less_eq_nat _TPTP_I) N)) (((eq int) (F _TPTP_I)) K)))))))) of role axiom named fact_1158_int__val__lemma % A new axiom: (forall (K:int) (F:(nat->int)) (N:nat), ((forall (_TPTP_I:nat), (((ord_less_nat _TPTP_I) N)->((ord_less_eq_int (abs_abs_int ((minus_minus_int (F ((plus_plus_nat _TPTP_I) one_one_nat))) (F _TPTP_I)))) one_one_int)))->(((ord_less_eq_int (F zero_zero_nat)) K)->(((ord_less_eq_int K) (F N))->((ex nat) (fun (_TPTP_I:nat)=> ((and ((ord_less_eq_nat _TPTP_I) N)) (((eq int) (F _TPTP_I)) K)))))))) % FOF formula (forall (K:int) (F:(nat->int)) (N:nat), ((forall (_TPTP_I:nat), (((ord_less_nat _TPTP_I) N)->((ord_less_eq_int (abs_abs_int ((minus_minus_int (F ((plus_plus_nat _TPTP_I) one_one_nat))) (F _TPTP_I)))) one_one_int)))->(((ord_less_eq_int (F zero_zero_nat)) K)->(((ord_less_eq_int K) (F N))->((ex nat) (fun (_TPTP_I:nat)=> ((and ((ord_less_eq_nat _TPTP_I) N)) (((eq int) (F _TPTP_I)) K)))))))) of role axiom named fact_1159_nat0__intermed__int__val % A new axiom: (forall (K:int) (F:(nat->int)) (N:nat), ((forall (_TPTP_I:nat), (((ord_less_nat _TPTP_I) N)->((ord_less_eq_int (abs_abs_int ((minus_minus_int (F ((plus_plus_nat _TPTP_I) one_one_nat))) (F _TPTP_I)))) one_one_int)))->(((ord_less_eq_int (F zero_zero_nat)) K)->(((ord_less_eq_int K) (F N))->((ex nat) (fun (_TPTP_I:nat)=> ((and ((ord_less_eq_nat _TPTP_I) N)) (((eq int) (F _TPTP_I)) K)))))))) % FOF formula (forall (K:int) (F:(nat->int)) (N:nat) (M:nat), ((forall (_TPTP_I:nat), (((and ((ord_less_eq_nat M) _TPTP_I)) ((ord_less_nat _TPTP_I) N))->((ord_less_eq_int (abs_abs_int ((minus_minus_int (F ((plus_plus_nat _TPTP_I) one_one_nat))) (F _TPTP_I)))) one_one_int)))->(((ord_less_nat M) N)->(((ord_less_eq_int (F M)) K)->(((ord_less_eq_int K) (F N))->((ex nat) (fun (_TPTP_I:nat)=> ((and ((and ((ord_less_eq_nat M) _TPTP_I)) ((ord_less_eq_nat _TPTP_I) N))) (((eq int) (F _TPTP_I)) K))))))))) of role axiom named fact_1160_nat__intermed__int__val % A new axiom: (forall (K:int) (F:(nat->int)) (N:nat) (M:nat), ((forall (_TPTP_I:nat), (((and ((ord_less_eq_nat M) _TPTP_I)) ((ord_less_nat _TPTP_I) N))->((ord_less_eq_int (abs_abs_int ((minus_minus_int (F ((plus_plus_nat _TPTP_I) one_one_nat))) (F _TPTP_I)))) one_one_int)))->(((ord_less_nat M) N)->(((ord_less_eq_int (F M)) K)->(((ord_less_eq_int K) (F N))->((ex nat) (fun (_TPTP_I:nat)=> ((and ((and ((ord_less_eq_nat M) _TPTP_I)) ((ord_less_eq_nat _TPTP_I) N))) (((eq int) (F _TPTP_I)) K))))))))) % FOF formula (forall (N:nat) (V:int), ((and ((nat_neg (number_number_of_int V))->(((eq nat) (suc ((plus_plus_nat (number_number_of_nat V)) N))) ((plus_plus_nat one_one_nat) N)))) (((nat_neg (number_number_of_int V))->False)->(((eq nat) (suc ((plus_plus_nat (number_number_of_nat V)) N))) ((plus_plus_nat (number_number_of_nat (succ V))) N))))) of role axiom named fact_1161_Suc__nat__number__of__add % A new axiom: (forall (N:nat) (V:int), ((and ((nat_neg (number_number_of_int V))->(((eq nat) (suc ((plus_plus_nat (number_number_of_nat V)) N))) ((plus_plus_nat one_one_nat) N)))) (((nat_neg (number_number_of_int V))->False)->(((eq nat) (suc ((plus_plus_nat (number_number_of_nat V)) N))) ((plus_plus_nat (number_number_of_nat (succ V))) N))))) % FOF formula (forall (K:int), (((eq int) (succ K)) ((plus_plus_int K) one_one_int))) of role axiom named fact_1162_succ__def % A new axiom: (forall (K:int), (((eq int) (succ K)) ((plus_plus_int K) one_one_int))) % FOF formula (forall (V:int), ((and ((nat_neg (number_number_of_int V))->(((eq nat) (suc (number_number_of_nat V))) one_one_nat))) (((nat_neg (number_number_of_int V))->False)->(((eq nat) (suc (number_number_of_nat V))) (number_number_of_nat (succ V)))))) of role axiom named fact_1163_Suc__nat__number__of % A new axiom: (forall (V:int), ((and ((nat_neg (number_number_of_int V))->(((eq nat) (suc (number_number_of_nat V))) one_one_nat))) (((nat_neg (number_number_of_int V))->False)->(((eq nat) (suc (number_number_of_nat V))) (number_number_of_nat (succ V)))))) % FOF formula (forall (W:int), ((and ((nat_neg (number_number_of_int W))->(((eq nat) (number_number_of_nat (bit1 W))) zero_zero_nat))) (((nat_neg (number_number_of_int W))->False)->(((eq nat) (number_number_of_nat (bit1 W))) (suc ((plus_plus_nat (number_number_of_nat W)) (number_number_of_nat W))))))) of role axiom named fact_1164_nat__number__of__Bit1 % A new axiom: (forall (W:int), ((and ((nat_neg (number_number_of_int W))->(((eq nat) (number_number_of_nat (bit1 W))) zero_zero_nat))) (((nat_neg (number_number_of_int W))->False)->(((eq nat) (number_number_of_nat (bit1 W))) (suc ((plus_plus_nat (number_number_of_nat W)) (number_number_of_nat W))))))) % FOF formula (forall (V:int), ((and (((ord_less_int V) pls)->(((eq nat) ((plus_plus_nat one_one_nat) (number_number_of_nat V))) one_one_nat))) ((((ord_less_int V) pls)->False)->(((eq nat) ((plus_plus_nat one_one_nat) (number_number_of_nat V))) (number_number_of_nat (succ V)))))) of role axiom named fact_1165_nat__1__add__number__of % A new axiom: (forall (V:int), ((and (((ord_less_int V) pls)->(((eq nat) ((plus_plus_nat one_one_nat) (number_number_of_nat V))) one_one_nat))) ((((ord_less_int V) pls)->False)->(((eq nat) ((plus_plus_nat one_one_nat) (number_number_of_nat V))) (number_number_of_nat (succ V)))))) % FOF formula (((eq int) (succ pls)) (bit1 pls)) of role axiom named fact_1166_succ__Pls % A new axiom: (((eq int) (succ pls)) (bit1 pls)) % FOF formula (forall (W:int), ((iff (nat_neg (number_number_of_int (bit1 W)))) (nat_neg (number_number_of_int W)))) of role axiom named fact_1167_neg__number__of__Bit1 % A new axiom: (forall (W:int), ((iff (nat_neg (number_number_of_int (bit1 W)))) (nat_neg (number_number_of_int W)))) % FOF formula ((nat_neg (number_number_of_int pls))->False) of role axiom named fact_1168_not__neg__number__of__Pls % A new axiom: ((nat_neg (number_number_of_int pls))->False) % FOF formula (((eq int) (number_number_of_int (bit1 (bit1 pls)))) (semiri1621563631at_int (number_number_of_nat (bit1 (bit1 pls))))) of role axiom named fact_1169_transfer__int__nat__numerals_I4_J % A new axiom: (((eq int) (number_number_of_int (bit1 (bit1 pls)))) (semiri1621563631at_int (number_number_of_nat (bit1 (bit1 pls))))) % FOF formula (((eq nat) (number_number_of_nat (bit1 pls))) (suc zero_zero_nat)) of role axiom named fact_1170_numeral__1__eq__Suc__0 % A new axiom: (((eq nat) (number_number_of_nat (bit1 pls))) (suc zero_zero_nat)) % FOF formula (((eq nat) (number_number_of_nat (bit1 (bit1 pls)))) (suc (suc (suc zero_zero_nat)))) of role axiom named fact_1171_numeral__3__eq__3 % A new axiom: (((eq nat) (number_number_of_nat (bit1 (bit1 pls)))) (suc (suc (suc zero_zero_nat)))) % FOF formula (forall (N:nat), (((eq nat) (suc (suc (suc N)))) ((plus_plus_nat (number_number_of_nat (bit1 (bit1 pls)))) N))) of role axiom named fact_1172_Suc3__eq__add__3 % A new axiom: (forall (N:nat), (((eq nat) (suc (suc (suc N)))) ((plus_plus_nat (number_number_of_nat (bit1 (bit1 pls)))) N))) % FOF formula (((eq nat) one_one_nat) (number_number_of_nat (bit1 pls))) of role axiom named fact_1173_Numeral1__eq1__nat % A new axiom: (((eq nat) one_one_nat) (number_number_of_nat (bit1 pls))) % FOF formula (((eq nat) (number_number_of_nat (bit1 pls))) one_one_nat) of role axiom named fact_1174_nat__numeral__1__eq__1 % A new axiom: (((eq nat) (number_number_of_nat (bit1 pls))) one_one_nat) % FOF formula (((eq int) one_one_int) (number_number_of_int (bit1 pls))) of role axiom named fact_1175_one__is__num__one % A new axiom: (((eq int) one_one_int) (number_number_of_int (bit1 pls))) % FOF formula (((eq int) zero_zero_int) (number_number_of_int pls)) of role axiom named fact_1176_zero__is__num__zero % A new axiom: (((eq int) zero_zero_int) (number_number_of_int pls)) % FOF formula (forall (K:int), (((eq int) (bit1 K)) ((plus_plus_int ((plus_plus_int one_one_int) K)) K))) of role axiom named fact_1177_Bit1__def % A new axiom: (forall (K:int), (((eq int) (bit1 K)) ((plus_plus_int ((plus_plus_int one_one_int) K)) K))) % FOF formula (((eq nat) (number_number_of_nat pls)) zero_zero_nat) of role axiom named fact_1178_nat__number__of__Pls % A new axiom: (((eq nat) (number_number_of_nat pls)) zero_zero_nat) % FOF formula (((eq nat) zero_zero_nat) (number_number_of_nat pls)) of role axiom named fact_1179_semiring__norm_I113_J % A new axiom: (((eq nat) zero_zero_nat) (number_number_of_nat pls)) % FOF formula (((eq int) pls) zero_zero_int) of role axiom named fact_1180_Pls__def % A new axiom: (((eq int) pls) zero_zero_int) % FOF formula (forall (K:int) (L:int), ((iff (((eq int) (bit1 K)) (bit1 L))) (((eq int) K) L))) of role axiom named fact_1181_rel__simps_I51_J % A new axiom: (forall (K:int) (L:int), ((iff (((eq int) (bit1 K)) (bit1 L))) (((eq int) K) L))) % FOF formula (forall (K:int), (not (((eq int) (bit1 K)) pls))) of role axiom named fact_1182_rel__simps_I46_J % A new axiom: (forall (K:int), (not (((eq int) (bit1 K)) pls))) % FOF formula (forall (L:int), (not (((eq int) pls) (bit1 L)))) of role axiom named fact_1183_rel__simps_I39_J % A new axiom: (forall (L:int), (not (((eq int) pls) (bit1 L)))) % FOF formula (forall (K:int), (((eq int) ((minus_minus_int K) pls)) K)) of role axiom named fact_1184_diff__bin__simps_I1_J % A new axiom: (forall (K:int), (((eq int) ((minus_minus_int K) pls)) K)) % FOF formula (forall (K:int), (((eq int) ((plus_plus_int pls) K)) K)) of role axiom named fact_1185_add__Pls % A new axiom: (forall (K:int), (((eq int) ((plus_plus_int pls) K)) K)) % FOF formula (forall (K:int), (((eq int) ((plus_plus_int K) pls)) K)) of role axiom named fact_1186_add__Pls__right % A new axiom: (forall (K:int), (((eq int) ((plus_plus_int K) pls)) K)) % FOF formula (forall (W:int), (((eq int) ((times_times_int pls) W)) pls)) of role axiom named fact_1187_mult__Pls % A new axiom: (forall (W:int), (((eq int) ((times_times_int pls) W)) pls)) % FOF formula ((ord_less_eq_int zero_zero_int) (number_number_of_int (bit1 (bit1 pls)))) of role axiom named fact_1188_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J % A new axiom: ((ord_less_eq_int zero_zero_int) (number_number_of_int (bit1 (bit1 pls)))) % FOF formula ((ord_less_eq_int pls) pls) of role axiom named fact_1189_rel__simps_I19_J % A new axiom: ((ord_less_eq_int pls) pls) % FOF formula (forall (K:int), ((iff ((ord_less_eq_int pls) (bit1 K))) ((ord_less_eq_int pls) K))) of role axiom named fact_1190_rel__simps_I22_J % A new axiom: (forall (K:int), ((iff ((ord_less_eq_int pls) (bit1 K))) ((ord_less_eq_int pls) K))) % FOF formula (forall (K:int) (L:int), ((iff ((ord_less_eq_int (bit1 K)) (bit1 L))) ((ord_less_eq_int K) L))) of role axiom named fact_1191_rel__simps_I34_J % A new axiom: (forall (K:int) (L:int), ((iff ((ord_less_eq_int (bit1 K)) (bit1 L))) ((ord_less_eq_int K) L))) % FOF formula (forall (K1:int) (K2:int), ((iff ((ord_less_eq_int (bit1 K1)) (bit1 K2))) ((ord_less_eq_int K1) K2))) of role axiom named fact_1192_less__eq__int__code_I16_J % A new axiom: (forall (K1:int) (K2:int), ((iff ((ord_less_eq_int (bit1 K1)) (bit1 K2))) ((ord_less_eq_int K1) K2))) % FOF formula (((ord_less_int pls) pls)->False) of role axiom named fact_1193_rel__simps_I2_J % A new axiom: (((ord_less_int pls) pls)->False) % FOF formula (forall (K:int), ((iff ((ord_less_int (bit1 K)) pls)) ((ord_less_int K) pls))) of role axiom named fact_1194_rel__simps_I12_J % A new axiom: (forall (K:int), ((iff ((ord_less_int (bit1 K)) pls)) ((ord_less_int K) pls))) % FOF formula (forall (K:int) (L:int), ((iff ((ord_less_int (bit1 K)) (bit1 L))) ((ord_less_int K) L))) of role axiom named fact_1195_rel__simps_I17_J % A new axiom: (forall (K:int) (L:int), ((iff ((ord_less_int (bit1 K)) (bit1 L))) ((ord_less_int K) L))) % FOF formula (forall (K1:int) (K2:int), ((iff ((ord_less_int (bit1 K1)) (bit1 K2))) ((ord_less_int K1) K2))) of role axiom named fact_1196_less__int__code_I16_J % A new axiom: (forall (K1:int) (K2:int), ((iff ((ord_less_int (bit1 K1)) (bit1 K2))) ((ord_less_int K1) K2))) % FOF formula (forall (K:int), ((iff ((ord_less_eq_int (bit1 K)) pls)) ((ord_less_int K) pls))) of role axiom named fact_1197_rel__simps_I29_J % A new axiom: (forall (K:int), ((iff ((ord_less_eq_int (bit1 K)) pls)) ((ord_less_int K) pls))) % FOF formula (forall (K:int), ((iff ((ord_less_int pls) (bit1 K))) ((ord_less_eq_int pls) K))) of role axiom named fact_1198_rel__simps_I5_J % A new axiom: (forall (K:int), ((iff ((ord_less_int pls) (bit1 K))) ((ord_less_eq_int pls) K))) % FOF formula (forall (X:x_a) (Y:x_a), ((or (((fequal_a X) Y)->False)) (((eq x_a) X) Y))) of role axiom named help_fequal_1_1_fequal_000t__a_T % A new axiom: (forall (X:x_a) (Y:x_a), ((or (((fequal_a X) Y)->False)) (((eq x_a) X) Y))) % FOF formula (forall (X:x_a) (Y:x_a), ((or (not (((eq x_a) X) Y))) ((fequal_a X) Y))) of role axiom named help_fequal_2_1_fequal_000t__a_T % A new axiom: (forall (X:x_a) (Y:x_a), ((or (not (((eq x_a) X) Y))) ((fequal_a X) Y))) % FOF formula (forall (X:nat) (Y:nat), (((eq nat) (((if_nat True) X) Y)) X)) of role axiom named help_If_1_1_If_000tc__Nat__Onat_T % A new axiom: (forall (X:nat) (Y:nat), (((eq nat) (((if_nat True) X) Y)) X)) % FOF formula (forall (X:nat) (Y:nat), (((eq nat) (((if_nat False) X) Y)) Y)) of role axiom named help_If_2_1_If_000tc__Nat__Onat_T % A new axiom: (forall (X:nat) (Y:nat), (((eq nat) (((if_nat False) X) Y)) Y)) % FOF formula (forall (P:Prop), ((or (((eq Prop) P) True)) (((eq Prop) P) False))) of role axiom named help_If_3_1_If_000tc__Nat__Onat_T % A new axiom: (forall (P:Prop), ((or (((eq Prop) P) True)) (((eq Prop) P) False))) % FOF formula (forall (X:int) (Y:int), ((or (((fequal_int X) Y)->False)) (((eq int) X) Y))) of role axiom named help_fequal_1_1_fequal_000tc__Int__Oint_T % A new axiom: (forall (X:int) (Y:int), ((or (((fequal_int X) Y)->False)) (((eq int) X) Y))) % FOF formula (forall (X:int) (Y:int), ((or (not (((eq int) X) Y))) ((fequal_int X) Y))) of role axiom named help_fequal_2_1_fequal_000tc__Int__Oint_T % A new axiom: (forall (X:int) (Y:int), ((or (not (((eq int) X) Y))) ((fequal_int X) Y))) % FOF formula (forall (X:nat) (Y:nat), ((or (((fequal_nat X) Y)->False)) (((eq nat) X) Y))) of role axiom named help_fequal_1_1_fequal_000tc__Nat__Onat_T % A new axiom: (forall (X:nat) (Y:nat), ((or (((fequal_nat X) Y)->False)) (((eq nat) X) Y))) % FOF formula (forall (X:nat) (Y:nat), ((or (not (((eq nat) X) Y))) ((fequal_nat X) Y))) of role axiom named help_fequal_2_1_fequal_000tc__Nat__Onat_T % A new axiom: (forall (X:nat) (Y:nat), ((or (not (((eq nat) X) Y))) ((fequal_nat X) Y))) % FOF formula (finite_finite_pname u) of role hypothesis named conj_0 % A new axiom: (finite_finite_pname u) % FOF formula ((ord_less_eq_a_o g) ((image_pname_a mgt_call) u)) of role hypothesis named conj_1 % A new axiom: ((ord_less_eq_a_o g) ((image_pname_a mgt_call) u)) % FOF formula ((ord_less_eq_nat (suc na)) (finite_card_a ((image_pname_a mgt_call) u))) of role hypothesis named conj_2 % A new axiom: ((ord_less_eq_nat (suc na)) (finite_card_a ((image_pname_a mgt_call) u))) % FOF formula (((eq nat) (finite_card_a g)) ((minus_minus_nat (finite_card_a ((image_pname_a mgt_call) u))) (suc na))) of role hypothesis named conj_3 % A new axiom: (((eq nat) (finite_card_a g)) ((minus_minus_nat (finite_card_a ((image_pname_a mgt_call) u))) (suc na))) % FOF formula ((member_pname pn) u) of role hypothesis named conj_4 % A new axiom: ((member_pname pn) u) % FOF formula (((member_a (mgt_call pn)) g)->False) of role hypothesis named conj_5 % A new axiom: (((member_a (mgt_call pn)) g)->False) % FOF formula ((ord_less_eq_a_o ((insert_a (mgt_call pn)) g)) ((image_pname_a mgt_call) u)) of role conjecture named conj_6 % Conjecture to prove = ((ord_less_eq_a_o ((insert_a (mgt_call pn)) g)) ((image_pname_a mgt_call) u)):Prop % Parameter x_a_DUMMY:x_a. % Parameter com_DUMMY:com. % Parameter option_com_DUMMY:option_com. % We need to prove ['((ord_less_eq_a_o ((insert_a (mgt_call pn)) g)) ((image_pname_a mgt_call) u))'] % Parameter x_a:Type. % Parameter com:Type. % Parameter pname:Type. % Parameter int:Type. % Parameter nat:Type. % Parameter option_com:Type. % Parameter body:(pname->option_com). % Parameter _TPTP_ex:((int->Prop)->Prop). % Parameter finite_card_a_o:(((x_a->Prop)->Prop)->nat). % Parameter finite_card_pname_o:(((pname->Prop)->Prop)->nat). % Parameter finite_card_int_o:(((int->Prop)->Prop)->nat). % Parameter finite_card_nat_o:(((nat->Prop)->Prop)->nat). % Parameter finite_card_a:((x_a->Prop)->nat). % Parameter finite_card_pname:((pname->Prop)->nat). % Parameter finite_card_int:((int->Prop)->nat). % Parameter finite_card_nat:((nat->Prop)->nat). % Parameter finite_finite_a_o_o:((((x_a->Prop)->Prop)->Prop)->Prop). % Parameter finite1066544169me_o_o:((((pname->Prop)->Prop)->Prop)->Prop). % Parameter finite229719499nt_o_o:((((int->Prop)->Prop)->Prop)->Prop). % Parameter finite1676163439at_o_o:((((nat->Prop)->Prop)->Prop)->Prop). % Parameter finite_finite_a_o:(((x_a->Prop)->Prop)->Prop). % Parameter finite297249702name_o:(((pname->Prop)->Prop)->Prop). % Parameter finite_finite_int_o:(((int->Prop)->Prop)->Prop). % Parameter finite_finite_nat_o:(((nat->Prop)->Prop)->Prop). % Parameter finite_finite_a:((x_a->Prop)->Prop). % Parameter finite_finite_pname:((pname->Prop)->Prop). % Parameter finite_finite_int:((int->Prop)->Prop). % Parameter finite_finite_nat:((nat->Prop)->Prop). % Parameter finite_folding_one_a:((x_a->(x_a->x_a))->(((x_a->Prop)->x_a)->Prop)). % Parameter finite1282449217_pname:((pname->(pname->pname))->(((pname->Prop)->pname)->Prop)). % Parameter finite1626084323ne_int:((int->(int->int))->(((int->Prop)->int)->Prop)). % Parameter finite988810631ne_nat:((nat->(nat->nat))->(((nat->Prop)->nat)->Prop)). % Parameter finite1819937229idem_a:((x_a->(x_a->x_a))->(((x_a->Prop)->x_a)->Prop)). % Parameter finite89670078_pname:((pname->(pname->pname))->(((pname->Prop)->pname)->Prop)). % Parameter finite1432773856em_int:((int->(int->int))->(((int->Prop)->int)->Prop)). % Parameter finite795500164em_nat:((nat->(nat->nat))->(((nat->Prop)->nat)->Prop)). % Parameter abs_abs_int:(int->int). % Parameter minus_minus_a_o:((x_a->Prop)->((x_a->Prop)->(x_a->Prop))). % Parameter minus_minus_pname_o:((pname->Prop)->((pname->Prop)->(pname->Prop))). % Parameter minus_minus_int_o:((int->Prop)->((int->Prop)->(int->Prop))). % Parameter minus_minus_nat_o:((nat->Prop)->((nat->Prop)->(nat->Prop))). % Parameter minus_minus_int:(int->(int->int)). % Parameter minus_minus_nat:(nat->(nat->nat)). % Parameter one_one_int:int. % Parameter one_one_nat:nat. % Parameter plus_plus_int:(int->(int->int)). % Parameter plus_plus_nat:(nat->(nat->nat)). % Parameter times_times_int:(int->(int->int)). % Parameter times_times_nat:(nat->(nat->nat)). % Parameter zero_zero_int:int. % Parameter zero_zero_nat:nat. % Parameter the_a:((x_a->Prop)->x_a). % Parameter the_int:((int->Prop)->int). % Parameter the_nat:((nat->Prop)->nat). % Parameter if_nat:(Prop->(nat->(nat->nat))). % Parameter bit1:(int->int). % Parameter pls:int. % Parameter number_number_of_int:(int->int). % Parameter number_number_of_nat:(int->nat). % Parameter succ:(int->int). % Parameter suc:(nat->nat). % Parameter nat_case_o:(Prop->((nat->Prop)->(nat->Prop))). % Parameter nat_case_nat:(nat->((nat->nat)->(nat->nat))). % Parameter semiri1621563631at_int:(nat->int). % Parameter nat_neg:(int->Prop). % Parameter nat_tsub:(int->(int->int)). % Parameter the_com:(option_com->com). % Parameter bot_bot_a_o:(x_a->Prop). % Parameter bot_bot_pname_o:(pname->Prop). % Parameter bot_bot_int_o:(int->Prop). % Parameter bot_bot_nat_o:(nat->Prop). % Parameter bot_bot_o:Prop. % Parameter bot_bot_nat:nat. % Parameter ord_less_int_o:((int->Prop)->((int->Prop)->Prop)). % Parameter ord_less_nat_o:((nat->Prop)->((nat->Prop)->Prop)). % Parameter ord_less_int:(int->(int->Prop)). % Parameter ord_less_nat:(nat->(nat->Prop)). % Parameter ord_less_eq_a_o_o:(((x_a->Prop)->Prop)->(((x_a->Prop)->Prop)->Prop)). % Parameter ord_le1205211808me_o_o:(((pname->Prop)->Prop)->(((pname->Prop)->Prop)->Prop)). % Parameter ord_less_eq_int_o_o:(((int->Prop)->Prop)->(((int->Prop)->Prop)->Prop)). % Parameter ord_less_eq_nat_o_o:(((nat->Prop)->Prop)->(((nat->Prop)->Prop)->Prop)). % Parameter ord_less_eq_a_o:((x_a->Prop)->((x_a->Prop)->Prop)). % Parameter ord_less_eq_pname_o:((pname->Prop)->((pname->Prop)->Prop)). % Parameter ord_less_eq_int_o:((int->Prop)->((int->Prop)->Prop)). % Parameter ord_less_eq_nat_o:((nat->Prop)->((nat->Prop)->Prop)). % Parameter ord_less_eq_o:(Prop->(Prop->Prop)). % Parameter ord_less_eq_int:(int->(int->Prop)). % Parameter ord_less_eq_nat:(nat->(nat->Prop)). % Parameter collect_a_o_o:((((x_a->Prop)->Prop)->Prop)->(((x_a->Prop)->Prop)->Prop)). % Parameter collect_pname_o_o:((((pname->Prop)->Prop)->Prop)->(((pname->Prop)->Prop)->Prop)). % Parameter collect_int_o_o:((((int->Prop)->Prop)->Prop)->(((int->Prop)->Prop)->Prop)). % Parameter collect_nat_o_o:((((nat->Prop)->Prop)->Prop)->(((nat->Prop)->Prop)->Prop)). % Parameter collect_a_o:(((x_a->Prop)->Prop)->((x_a->Prop)->Prop)). % Parameter collect_pname_o:(((pname->Prop)->Prop)->((pname->Prop)->Prop)). % Parameter collect_int_o:(((int->Prop)->Prop)->((int->Prop)->Prop)). % Parameter collect_nat_o:(((nat->Prop)->Prop)->((nat->Prop)->Prop)). % Parameter collect_a:((x_a->Prop)->(x_a->Prop)). % Parameter collect_pname:((pname->Prop)->(pname->Prop)). % Parameter collect_int:((int->Prop)->(int->Prop)). % Parameter collect_nat:((nat->Prop)->(nat->Prop)). % Parameter image_a_o_a:(((x_a->Prop)->x_a)->(((x_a->Prop)->Prop)->(x_a->Prop))). % Parameter image_a_o_pname:(((x_a->Prop)->pname)->(((x_a->Prop)->Prop)->(pname->Prop))). % Parameter image_a_o_int:(((x_a->Prop)->int)->(((x_a->Prop)->Prop)->(int->Prop))). % Parameter image_a_o_nat:(((x_a->Prop)->nat)->(((x_a->Prop)->Prop)->(nat->Prop))). % Parameter image_pname_o_a:(((pname->Prop)->x_a)->(((pname->Prop)->Prop)->(x_a->Prop))). % Parameter image_pname_o_pname:(((pname->Prop)->pname)->(((pname->Prop)->Prop)->(pname->Prop))). % Parameter image_pname_o_int:(((pname->Prop)->int)->(((pname->Prop)->Prop)->(int->Prop))). % Parameter image_pname_o_nat:(((pname->Prop)->nat)->(((pname->Prop)->Prop)->(nat->Prop))). % Parameter image_int_o_a:(((int->Prop)->x_a)->(((int->Prop)->Prop)->(x_a->Prop))). % Parameter image_int_o_pname:(((int->Prop)->pname)->(((int->Prop)->Prop)->(pname->Prop))). % Parameter image_int_o_int:(((int->Prop)->int)->(((int->Prop)->Prop)->(int->Prop))). % Parameter image_int_o_nat:(((int->Prop)->nat)->(((int->Prop)->Prop)->(nat->Prop))). % Parameter image_nat_o_a:(((nat->Prop)->x_a)->(((nat->Prop)->Prop)->(x_a->Prop))). % Parameter image_nat_o_pname:(((nat->Prop)->pname)->(((nat->Prop)->Prop)->(pname->Prop))). % Parameter image_nat_o_int:(((nat->Prop)->int)->(((nat->Prop)->Prop)->(int->Prop))). % Parameter image_nat_o_nat:(((nat->Prop)->nat)->(((nat->Prop)->Prop)->(nat->Prop))). % Parameter image_a_a_o:((x_a->(x_a->Prop))->((x_a->Prop)->((x_a->Prop)->Prop))). % Parameter image_a_pname_o:((x_a->(pname->Prop))->((x_a->Prop)->((pname->Prop)->Prop))). % Parameter image_a_int_o:((x_a->(int->Prop))->((x_a->Prop)->((int->Prop)->Prop))). % Parameter image_a_nat_o:((x_a->(nat->Prop))->((x_a->Prop)->((nat->Prop)->Prop))). % Parameter image_a_a:((x_a->x_a)->((x_a->Prop)->(x_a->Prop))). % Parameter image_a_pname:((x_a->pname)->((x_a->Prop)->(pname->Prop))). % Parameter image_a_int:((x_a->int)->((x_a->Prop)->(int->Prop))). % Parameter image_a_nat:((x_a->nat)->((x_a->Prop)->(nat->Prop))). % Parameter image_pname_a_o:((pname->(x_a->Prop))->((pname->Prop)->((x_a->Prop)->Prop))). % Parameter image_pname_pname_o:((pname->(pname->Prop))->((pname->Prop)->((pname->Prop)->Prop))). % Parameter image_pname_int_o:((pname->(int->Prop))->((pname->Prop)->((int->Prop)->Prop))). % Parameter image_pname_nat_o:((pname->(nat->Prop))->((pname->Prop)->((nat->Prop)->Prop))). % Parameter image_pname_a:((pname->x_a)->((pname->Prop)->(x_a->Prop))). % Parameter image_pname_pname:((pname->pname)->((pname->Prop)->(pname->Prop))). % Parameter image_pname_int:((pname->int)->((pname->Prop)->(int->Prop))). % Parameter image_pname_nat:((pname->nat)->((pname->Prop)->(nat->Prop))). % Parameter image_int_a_o:((int->(x_a->Prop))->((int->Prop)->((x_a->Prop)->Prop))). % Parameter image_int_pname_o:((int->(pname->Prop))->((int->Prop)->((pname->Prop)->Prop))). % Parameter image_int_int_o:((int->(int->Prop))->((int->Prop)->((int->Prop)->Prop))). % Parameter image_int_nat_o:((int->(nat->Prop))->((int->Prop)->((nat->Prop)->Prop))). % Parameter image_int_a:((int->x_a)->((int->Prop)->(x_a->Prop))). % Parameter image_int_pname:((int->pname)->((int->Prop)->(pname->Prop))). % Parameter image_nat_a_o:((nat->(x_a->Prop))->((nat->Prop)->((x_a->Prop)->Prop))). % Parameter image_nat_pname_o:((nat->(pname->Prop))->((nat->Prop)->((pname->Prop)->Prop))). % Parameter image_nat_int_o:((nat->(int->Prop))->((nat->Prop)->((int->Prop)->Prop))). % Parameter image_nat_nat_o:((nat->(nat->Prop))->((nat->Prop)->((nat->Prop)->Prop))). % Parameter image_nat_a:((nat->x_a)->((nat->Prop)->(x_a->Prop))). % Parameter image_nat_pname:((nat->pname)->((nat->Prop)->(pname->Prop))). % Parameter image_nat_int:((nat->int)->((nat->Prop)->(int->Prop))). % Parameter insert_a_o:((x_a->Prop)->(((x_a->Prop)->Prop)->((x_a->Prop)->Prop))). % Parameter insert_pname_o:((pname->Prop)->(((pname->Prop)->Prop)->((pname->Prop)->Prop))). % Parameter insert_int_o:((int->Prop)->(((int->Prop)->Prop)->((int->Prop)->Prop))). % Parameter insert_nat_o:((nat->Prop)->(((nat->Prop)->Prop)->((nat->Prop)->Prop))). % Parameter insert_a:(x_a->((x_a->Prop)->(x_a->Prop))). % Parameter insert_pname:(pname->((pname->Prop)->(pname->Prop))). % Parameter insert_int:(int->((int->Prop)->(int->Prop))). % Parameter insert_nat:(nat->((nat->Prop)->(nat->Prop))). % Parameter the_elem_a:((x_a->Prop)->x_a). % Parameter the_elem_int:((int->Prop)->int). % Parameter the_elem_nat:((nat->Prop)->nat). % Parameter fequal_a:(x_a->(x_a->Prop)). % Parameter fequal_int:(int->(int->Prop)). % Parameter fequal_nat:(nat->(nat->Prop)). % Parameter member_a_o:((x_a->Prop)->(((x_a->Prop)->Prop)->Prop)). % Parameter member_pname_o:((pname->Prop)->(((pname->Prop)->Prop)->Prop)). % Parameter member_int_o:((int->Prop)->(((int->Prop)->Prop)->Prop)). % Parameter member_nat_o:((nat->Prop)->(((nat->Prop)->Prop)->Prop)). % Parameter member_a:(x_a->((x_a->Prop)->Prop)). % Parameter member_pname:(pname->((pname->Prop)->Prop)). % Parameter member_int:(int->((int->Prop)->Prop)). % Parameter member_nat:(nat->((nat->Prop)->Prop)). % Parameter g:(x_a->Prop). % Parameter p:((x_a->Prop)->((x_a->Prop)->Prop)). % Parameter u:(pname->Prop). % Parameter mgt:(com->x_a). % Parameter mgt_call:(pname->x_a). % Parameter na:nat. % Parameter pn:pname. % Parameter wt:(com->Prop). % Axiom fact_0_assms_I1_J:(forall (Ts:(x_a->Prop)) (G:(x_a->Prop)), (((ord_less_eq_a_o Ts) G)->((p G) Ts))). % Axiom fact_1_finite__Collect__subsets:(forall (A_161:((int->Prop)->Prop)), ((finite_finite_int_o A_161)->(finite229719499nt_o_o (collect_int_o_o (fun (B_26:((int->Prop)->Prop))=> ((ord_less_eq_int_o_o B_26) A_161)))))). % Axiom fact_2_finite__Collect__subsets:(forall (A_161:((nat->Prop)->Prop)), ((finite_finite_nat_o A_161)->(finite1676163439at_o_o (collect_nat_o_o (fun (B_26:((nat->Prop)->Prop))=> ((ord_less_eq_nat_o_o B_26) A_161)))))). % Axiom fact_3_finite__Collect__subsets:(forall (A_161:((pname->Prop)->Prop)), ((finite297249702name_o A_161)->(finite1066544169me_o_o (collect_pname_o_o (fun (B_26:((pname->Prop)->Prop))=> ((ord_le1205211808me_o_o B_26) A_161)))))). % Axiom fact_4_finite__Collect__subsets:(forall (A_161:((x_a->Prop)->Prop)), ((finite_finite_a_o A_161)->(finite_finite_a_o_o (collect_a_o_o (fun (B_26:((x_a->Prop)->Prop))=> ((ord_less_eq_a_o_o B_26) A_161)))))). % Axiom fact_5_finite__Collect__subsets:(forall (A_161:(x_a->Prop)), ((finite_finite_a A_161)->(finite_finite_a_o (collect_a_o (fun (B_26:(x_a->Prop))=> ((ord_less_eq_a_o B_26) A_161)))))). % Axiom fact_6_finite__Collect__subsets:(forall (A_161:(pname->Prop)), ((finite_finite_pname A_161)->(finite297249702name_o (collect_pname_o (fun (B_26:(pname->Prop))=> ((ord_less_eq_pname_o B_26) A_161)))))). % Axiom fact_7_finite__Collect__subsets:(forall (A_161:(nat->Prop)), ((finite_finite_nat A_161)->(finite_finite_nat_o (collect_nat_o (fun (B_26:(nat->Prop))=> ((ord_less_eq_nat_o B_26) A_161)))))). % Axiom fact_8_finite__Collect__subsets:(forall (A_161:(int->Prop)), ((finite_finite_int A_161)->(finite_finite_int_o (collect_int_o (fun (B_26:(int->Prop))=> ((ord_less_eq_int_o B_26) A_161)))))). % Axiom fact_9_finite__imageI:(forall (H:(pname->(int->Prop))) (F_42:(pname->Prop)), ((finite_finite_pname F_42)->(finite_finite_int_o ((image_pname_int_o H) F_42)))). % Axiom fact_10_finite__imageI:(forall (H:(pname->(nat->Prop))) (F_42:(pname->Prop)), ((finite_finite_pname F_42)->(finite_finite_nat_o ((image_pname_nat_o H) F_42)))). % Axiom fact_11_finite__imageI:(forall (H:(pname->(pname->Prop))) (F_42:(pname->Prop)), ((finite_finite_pname F_42)->(finite297249702name_o ((image_pname_pname_o H) F_42)))). % Axiom fact_12_finite__imageI:(forall (H:(pname->(x_a->Prop))) (F_42:(pname->Prop)), ((finite_finite_pname F_42)->(finite_finite_a_o ((image_pname_a_o H) F_42)))). % Axiom fact_13_finite__imageI:(forall (H:(nat->x_a)) (F_42:(nat->Prop)), ((finite_finite_nat F_42)->(finite_finite_a ((image_nat_a H) F_42)))). % Axiom fact_14_finite__imageI:(forall (H:(nat->(int->Prop))) (F_42:(nat->Prop)), ((finite_finite_nat F_42)->(finite_finite_int_o ((image_nat_int_o H) F_42)))). % Axiom fact_15_finite__imageI:(forall (H:(nat->(nat->Prop))) (F_42:(nat->Prop)), ((finite_finite_nat F_42)->(finite_finite_nat_o ((image_nat_nat_o H) F_42)))). % Axiom fact_16_finite__imageI:(forall (H:(nat->(pname->Prop))) (F_42:(nat->Prop)), ((finite_finite_nat F_42)->(finite297249702name_o ((image_nat_pname_o H) F_42)))). % Axiom fact_17_finite__imageI:(forall (H:(nat->(x_a->Prop))) (F_42:(nat->Prop)), ((finite_finite_nat F_42)->(finite_finite_a_o ((image_nat_a_o H) F_42)))). % Axiom fact_18_finite__imageI:(forall (H:(int->x_a)) (F_42:(int->Prop)), ((finite_finite_int F_42)->(finite_finite_a ((image_int_a H) F_42)))). % Axiom fact_19_finite__imageI:(forall (H:(int->(int->Prop))) (F_42:(int->Prop)), ((finite_finite_int F_42)->(finite_finite_int_o ((image_int_int_o H) F_42)))). % Axiom fact_20_finite__imageI:(forall (H:(int->(nat->Prop))) (F_42:(int->Prop)), ((finite_finite_int F_42)->(finite_finite_nat_o ((image_int_nat_o H) F_42)))). % Axiom fact_21_finite__imageI:(forall (H:(int->(pname->Prop))) (F_42:(int->Prop)), ((finite_finite_int F_42)->(finite297249702name_o ((image_int_pname_o H) F_42)))). % Axiom fact_22_finite__imageI:(forall (H:(int->(x_a->Prop))) (F_42:(int->Prop)), ((finite_finite_int F_42)->(finite_finite_a_o ((image_int_a_o H) F_42)))). % Axiom fact_23_finite__imageI:(forall (H:(x_a->pname)) (F_42:(x_a->Prop)), ((finite_finite_a F_42)->(finite_finite_pname ((image_a_pname H) F_42)))). % Axiom fact_24_finite__imageI:(forall (H:((int->Prop)->pname)) (F_42:((int->Prop)->Prop)), ((finite_finite_int_o F_42)->(finite_finite_pname ((image_int_o_pname H) F_42)))). % Axiom fact_25_finite__imageI:(forall (H:((nat->Prop)->pname)) (F_42:((nat->Prop)->Prop)), ((finite_finite_nat_o F_42)->(finite_finite_pname ((image_nat_o_pname H) F_42)))). % Axiom fact_26_finite__imageI:(forall (H:((pname->Prop)->pname)) (F_42:((pname->Prop)->Prop)), ((finite297249702name_o F_42)->(finite_finite_pname ((image_pname_o_pname H) F_42)))). % Axiom fact_27_finite__imageI:(forall (H:((x_a->Prop)->pname)) (F_42:((x_a->Prop)->Prop)), ((finite_finite_a_o F_42)->(finite_finite_pname ((image_a_o_pname H) F_42)))). % Axiom fact_28_finite__imageI:(forall (H:(x_a->nat)) (F_42:(x_a->Prop)), ((finite_finite_a F_42)->(finite_finite_nat ((image_a_nat H) F_42)))). % Axiom fact_29_finite__imageI:(forall (H:((int->Prop)->nat)) (F_42:((int->Prop)->Prop)), ((finite_finite_int_o F_42)->(finite_finite_nat ((image_int_o_nat H) F_42)))). % Axiom fact_30_finite__imageI:(forall (H:((nat->Prop)->nat)) (F_42:((nat->Prop)->Prop)), ((finite_finite_nat_o F_42)->(finite_finite_nat ((image_nat_o_nat H) F_42)))). % Axiom fact_31_finite__imageI:(forall (H:((pname->Prop)->nat)) (F_42:((pname->Prop)->Prop)), ((finite297249702name_o F_42)->(finite_finite_nat ((image_pname_o_nat H) F_42)))). % Axiom fact_32_finite__imageI:(forall (H:((x_a->Prop)->nat)) (F_42:((x_a->Prop)->Prop)), ((finite_finite_a_o F_42)->(finite_finite_nat ((image_a_o_nat H) F_42)))). % Axiom fact_33_finite__imageI:(forall (H:(x_a->int)) (F_42:(x_a->Prop)), ((finite_finite_a F_42)->(finite_finite_int ((image_a_int H) F_42)))). % Axiom fact_34_finite__imageI:(forall (H:((int->Prop)->int)) (F_42:((int->Prop)->Prop)), ((finite_finite_int_o F_42)->(finite_finite_int ((image_int_o_int H) F_42)))). % Axiom fact_35_finite__imageI:(forall (H:((nat->Prop)->int)) (F_42:((nat->Prop)->Prop)), ((finite_finite_nat_o F_42)->(finite_finite_int ((image_nat_o_int H) F_42)))). % Axiom fact_36_finite__imageI:(forall (H:((pname->Prop)->int)) (F_42:((pname->Prop)->Prop)), ((finite297249702name_o F_42)->(finite_finite_int ((image_pname_o_int H) F_42)))). % Axiom fact_37_finite__imageI:(forall (H:((x_a->Prop)->int)) (F_42:((x_a->Prop)->Prop)), ((finite_finite_a_o F_42)->(finite_finite_int ((image_a_o_int H) F_42)))). % Axiom fact_38_finite__imageI:(forall (H:(pname->x_a)) (F_42:(pname->Prop)), ((finite_finite_pname F_42)->(finite_finite_a ((image_pname_a H) F_42)))). % Axiom fact_39_finite__imageI:(forall (H:(nat->int)) (F_42:(nat->Prop)), ((finite_finite_nat F_42)->(finite_finite_int ((image_nat_int H) F_42)))). % Axiom fact_40_finite_OinsertI:(forall (A_160:(int->Prop)) (A_159:((int->Prop)->Prop)), ((finite_finite_int_o A_159)->(finite_finite_int_o ((insert_int_o A_160) A_159)))). % Axiom fact_41_finite_OinsertI:(forall (A_160:(nat->Prop)) (A_159:((nat->Prop)->Prop)), ((finite_finite_nat_o A_159)->(finite_finite_nat_o ((insert_nat_o A_160) A_159)))). % Axiom fact_42_finite_OinsertI:(forall (A_160:(pname->Prop)) (A_159:((pname->Prop)->Prop)), ((finite297249702name_o A_159)->(finite297249702name_o ((insert_pname_o A_160) A_159)))). % Axiom fact_43_finite_OinsertI:(forall (A_160:(x_a->Prop)) (A_159:((x_a->Prop)->Prop)), ((finite_finite_a_o A_159)->(finite_finite_a_o ((insert_a_o A_160) A_159)))). % Axiom fact_44_finite_OinsertI:(forall (A_160:pname) (A_159:(pname->Prop)), ((finite_finite_pname A_159)->(finite_finite_pname ((insert_pname A_160) A_159)))). % Axiom fact_45_finite_OinsertI:(forall (A_160:nat) (A_159:(nat->Prop)), ((finite_finite_nat A_159)->(finite_finite_nat ((insert_nat A_160) A_159)))). % Axiom fact_46_finite_OinsertI:(forall (A_160:int) (A_159:(int->Prop)), ((finite_finite_int A_159)->(finite_finite_int ((insert_int A_160) A_159)))). % Axiom fact_47_finite_OinsertI:(forall (A_160:x_a) (A_159:(x_a->Prop)), ((finite_finite_a A_159)->(finite_finite_a ((insert_a A_160) A_159)))). % Axiom fact_48_card__image__le:(forall (F_41:(pname->pname)) (A_158:(pname->Prop)), ((finite_finite_pname A_158)->((ord_less_eq_nat (finite_card_pname ((image_pname_pname F_41) A_158))) (finite_card_pname A_158)))). % Axiom fact_49_card__image__le:(forall (F_41:(x_a->x_a)) (A_158:(x_a->Prop)), ((finite_finite_a A_158)->((ord_less_eq_nat (finite_card_a ((image_a_a F_41) A_158))) (finite_card_a A_158)))). % Axiom fact_50_card__image__le:(forall (F_41:((int->Prop)->x_a)) (A_158:((int->Prop)->Prop)), ((finite_finite_int_o A_158)->((ord_less_eq_nat (finite_card_a ((image_int_o_a F_41) A_158))) (finite_card_int_o A_158)))). % Axiom fact_51_card__image__le:(forall (F_41:((nat->Prop)->x_a)) (A_158:((nat->Prop)->Prop)), ((finite_finite_nat_o A_158)->((ord_less_eq_nat (finite_card_a ((image_nat_o_a F_41) A_158))) (finite_card_nat_o A_158)))). % Axiom fact_52_card__image__le:(forall (F_41:((pname->Prop)->x_a)) (A_158:((pname->Prop)->Prop)), ((finite297249702name_o A_158)->((ord_less_eq_nat (finite_card_a ((image_pname_o_a F_41) A_158))) (finite_card_pname_o A_158)))). % Axiom fact_53_card__image__le:(forall (F_41:((x_a->Prop)->x_a)) (A_158:((x_a->Prop)->Prop)), ((finite_finite_a_o A_158)->((ord_less_eq_nat (finite_card_a ((image_a_o_a F_41) A_158))) (finite_card_a_o A_158)))). % Axiom fact_54_card__image__le:(forall (F_41:(pname->nat)) (A_158:(pname->Prop)), ((finite_finite_pname A_158)->((ord_less_eq_nat (finite_card_nat ((image_pname_nat F_41) A_158))) (finite_card_pname A_158)))). % Axiom fact_55_card__image__le:(forall (F_41:(x_a->nat)) (A_158:(x_a->Prop)), ((finite_finite_a A_158)->((ord_less_eq_nat (finite_card_nat ((image_a_nat F_41) A_158))) (finite_card_a A_158)))). % Axiom fact_56_card__image__le:(forall (F_41:((int->Prop)->nat)) (A_158:((int->Prop)->Prop)), ((finite_finite_int_o A_158)->((ord_less_eq_nat (finite_card_nat ((image_int_o_nat F_41) A_158))) (finite_card_int_o A_158)))). % Axiom fact_57_card__image__le:(forall (F_41:((nat->Prop)->nat)) (A_158:((nat->Prop)->Prop)), ((finite_finite_nat_o A_158)->((ord_less_eq_nat (finite_card_nat ((image_nat_o_nat F_41) A_158))) (finite_card_nat_o A_158)))). % Axiom fact_58_card__image__le:(forall (F_41:((pname->Prop)->nat)) (A_158:((pname->Prop)->Prop)), ((finite297249702name_o A_158)->((ord_less_eq_nat (finite_card_nat ((image_pname_o_nat F_41) A_158))) (finite_card_pname_o A_158)))). % Axiom fact_59_card__image__le:(forall (F_41:((x_a->Prop)->nat)) (A_158:((x_a->Prop)->Prop)), ((finite_finite_a_o A_158)->((ord_less_eq_nat (finite_card_nat ((image_a_o_nat F_41) A_158))) (finite_card_a_o A_158)))). % Axiom fact_60_card__image__le:(forall (F_41:(pname->int)) (A_158:(pname->Prop)), ((finite_finite_pname A_158)->((ord_less_eq_nat (finite_card_int ((image_pname_int F_41) A_158))) (finite_card_pname A_158)))). % Axiom fact_61_card__image__le:(forall (F_41:(x_a->int)) (A_158:(x_a->Prop)), ((finite_finite_a A_158)->((ord_less_eq_nat (finite_card_int ((image_a_int F_41) A_158))) (finite_card_a A_158)))). % Axiom fact_62_card__image__le:(forall (F_41:((int->Prop)->int)) (A_158:((int->Prop)->Prop)), ((finite_finite_int_o A_158)->((ord_less_eq_nat (finite_card_int ((image_int_o_int F_41) A_158))) (finite_card_int_o A_158)))). % Axiom fact_63_card__image__le:(forall (F_41:((nat->Prop)->int)) (A_158:((nat->Prop)->Prop)), ((finite_finite_nat_o A_158)->((ord_less_eq_nat (finite_card_int ((image_nat_o_int F_41) A_158))) (finite_card_nat_o A_158)))). % Axiom fact_64_card__image__le:(forall (F_41:((pname->Prop)->int)) (A_158:((pname->Prop)->Prop)), ((finite297249702name_o A_158)->((ord_less_eq_nat (finite_card_int ((image_pname_o_int F_41) A_158))) (finite_card_pname_o A_158)))). % Axiom fact_65_card__image__le:(forall (F_41:((x_a->Prop)->int)) (A_158:((x_a->Prop)->Prop)), ((finite_finite_a_o A_158)->((ord_less_eq_nat (finite_card_int ((image_a_o_int F_41) A_158))) (finite_card_a_o A_158)))). % Axiom fact_66_card__image__le:(forall (F_41:(x_a->pname)) (A_158:(x_a->Prop)), ((finite_finite_a A_158)->((ord_less_eq_nat (finite_card_pname ((image_a_pname F_41) A_158))) (finite_card_a A_158)))). % Axiom fact_67_card__image__le:(forall (F_41:(nat->pname)) (A_158:(nat->Prop)), ((finite_finite_nat A_158)->((ord_less_eq_nat (finite_card_pname ((image_nat_pname F_41) A_158))) (finite_card_nat A_158)))). % Axiom fact_68_card__image__le:(forall (F_41:(int->pname)) (A_158:(int->Prop)), ((finite_finite_int A_158)->((ord_less_eq_nat (finite_card_pname ((image_int_pname F_41) A_158))) (finite_card_int A_158)))). % Axiom fact_69_card__image__le:(forall (F_41:(pname->x_a)) (A_158:(pname->Prop)), ((finite_finite_pname A_158)->((ord_less_eq_nat (finite_card_a ((image_pname_a F_41) A_158))) (finite_card_pname A_158)))). % Axiom fact_70_card__image__le:(forall (F_41:(nat->int)) (A_158:(nat->Prop)), ((finite_finite_nat A_158)->((ord_less_eq_nat (finite_card_int ((image_nat_int F_41) A_158))) (finite_card_nat A_158)))). % Axiom fact_71_card__mono:(forall (A_157:((int->Prop)->Prop)) (B_89:((int->Prop)->Prop)), ((finite_finite_int_o B_89)->(((ord_less_eq_int_o_o A_157) B_89)->((ord_less_eq_nat (finite_card_int_o A_157)) (finite_card_int_o B_89))))). % Axiom fact_72_card__mono:(forall (A_157:((nat->Prop)->Prop)) (B_89:((nat->Prop)->Prop)), ((finite_finite_nat_o B_89)->(((ord_less_eq_nat_o_o A_157) B_89)->((ord_less_eq_nat (finite_card_nat_o A_157)) (finite_card_nat_o B_89))))). % Axiom fact_73_card__mono:(forall (A_157:((pname->Prop)->Prop)) (B_89:((pname->Prop)->Prop)), ((finite297249702name_o B_89)->(((ord_le1205211808me_o_o A_157) B_89)->((ord_less_eq_nat (finite_card_pname_o A_157)) (finite_card_pname_o B_89))))). % Axiom fact_74_card__mono:(forall (A_157:((x_a->Prop)->Prop)) (B_89:((x_a->Prop)->Prop)), ((finite_finite_a_o B_89)->(((ord_less_eq_a_o_o A_157) B_89)->((ord_less_eq_nat (finite_card_a_o A_157)) (finite_card_a_o B_89))))). % Axiom fact_75_card__mono:(forall (A_157:(pname->Prop)) (B_89:(pname->Prop)), ((finite_finite_pname B_89)->(((ord_less_eq_pname_o A_157) B_89)->((ord_less_eq_nat (finite_card_pname A_157)) (finite_card_pname B_89))))). % Axiom fact_76_card__mono:(forall (A_157:(x_a->Prop)) (B_89:(x_a->Prop)), ((finite_finite_a B_89)->(((ord_less_eq_a_o A_157) B_89)->((ord_less_eq_nat (finite_card_a A_157)) (finite_card_a B_89))))). % Axiom fact_77_card__mono:(forall (A_157:(nat->Prop)) (B_89:(nat->Prop)), ((finite_finite_nat B_89)->(((ord_less_eq_nat_o A_157) B_89)->((ord_less_eq_nat (finite_card_nat A_157)) (finite_card_nat B_89))))). % Axiom fact_78_card__mono:(forall (A_157:(int->Prop)) (B_89:(int->Prop)), ((finite_finite_int B_89)->(((ord_less_eq_int_o A_157) B_89)->((ord_less_eq_nat (finite_card_int A_157)) (finite_card_int B_89))))). % Axiom fact_79_card__seteq:(forall (A_156:((int->Prop)->Prop)) (B_88:((int->Prop)->Prop)), ((finite_finite_int_o B_88)->(((ord_less_eq_int_o_o A_156) B_88)->(((ord_less_eq_nat (finite_card_int_o B_88)) (finite_card_int_o A_156))->(((eq ((int->Prop)->Prop)) A_156) B_88))))). % Axiom fact_80_card__seteq:(forall (A_156:((nat->Prop)->Prop)) (B_88:((nat->Prop)->Prop)), ((finite_finite_nat_o B_88)->(((ord_less_eq_nat_o_o A_156) B_88)->(((ord_less_eq_nat (finite_card_nat_o B_88)) (finite_card_nat_o A_156))->(((eq ((nat->Prop)->Prop)) A_156) B_88))))). % Axiom fact_81_card__seteq:(forall (A_156:((pname->Prop)->Prop)) (B_88:((pname->Prop)->Prop)), ((finite297249702name_o B_88)->(((ord_le1205211808me_o_o A_156) B_88)->(((ord_less_eq_nat (finite_card_pname_o B_88)) (finite_card_pname_o A_156))->(((eq ((pname->Prop)->Prop)) A_156) B_88))))). % Axiom fact_82_card__seteq:(forall (A_156:((x_a->Prop)->Prop)) (B_88:((x_a->Prop)->Prop)), ((finite_finite_a_o B_88)->(((ord_less_eq_a_o_o A_156) B_88)->(((ord_less_eq_nat (finite_card_a_o B_88)) (finite_card_a_o A_156))->(((eq ((x_a->Prop)->Prop)) A_156) B_88))))). % Axiom fact_83_card__seteq:(forall (A_156:(pname->Prop)) (B_88:(pname->Prop)), ((finite_finite_pname B_88)->(((ord_less_eq_pname_o A_156) B_88)->(((ord_less_eq_nat (finite_card_pname B_88)) (finite_card_pname A_156))->(((eq (pname->Prop)) A_156) B_88))))). % Axiom fact_84_card__seteq:(forall (A_156:(x_a->Prop)) (B_88:(x_a->Prop)), ((finite_finite_a B_88)->(((ord_less_eq_a_o A_156) B_88)->(((ord_less_eq_nat (finite_card_a B_88)) (finite_card_a A_156))->(((eq (x_a->Prop)) A_156) B_88))))). % Axiom fact_85_card__seteq:(forall (A_156:(nat->Prop)) (B_88:(nat->Prop)), ((finite_finite_nat B_88)->(((ord_less_eq_nat_o A_156) B_88)->(((ord_less_eq_nat (finite_card_nat B_88)) (finite_card_nat A_156))->(((eq (nat->Prop)) A_156) B_88))))). % Axiom fact_86_card__seteq:(forall (A_156:(int->Prop)) (B_88:(int->Prop)), ((finite_finite_int B_88)->(((ord_less_eq_int_o A_156) B_88)->(((ord_less_eq_nat (finite_card_int B_88)) (finite_card_int A_156))->(((eq (int->Prop)) A_156) B_88))))). % Axiom fact_87_card__insert__le:(forall (X_53:(int->Prop)) (A_155:((int->Prop)->Prop)), ((finite_finite_int_o A_155)->((ord_less_eq_nat (finite_card_int_o A_155)) (finite_card_int_o ((insert_int_o X_53) A_155))))). % Axiom fact_88_card__insert__le:(forall (X_53:(nat->Prop)) (A_155:((nat->Prop)->Prop)), ((finite_finite_nat_o A_155)->((ord_less_eq_nat (finite_card_nat_o A_155)) (finite_card_nat_o ((insert_nat_o X_53) A_155))))). % Axiom fact_89_card__insert__le:(forall (X_53:(pname->Prop)) (A_155:((pname->Prop)->Prop)), ((finite297249702name_o A_155)->((ord_less_eq_nat (finite_card_pname_o A_155)) (finite_card_pname_o ((insert_pname_o X_53) A_155))))). % Axiom fact_90_card__insert__le:(forall (X_53:(x_a->Prop)) (A_155:((x_a->Prop)->Prop)), ((finite_finite_a_o A_155)->((ord_less_eq_nat (finite_card_a_o A_155)) (finite_card_a_o ((insert_a_o X_53) A_155))))). % Axiom fact_91_card__insert__le:(forall (X_53:pname) (A_155:(pname->Prop)), ((finite_finite_pname A_155)->((ord_less_eq_nat (finite_card_pname A_155)) (finite_card_pname ((insert_pname X_53) A_155))))). % Axiom fact_92_card__insert__le:(forall (X_53:nat) (A_155:(nat->Prop)), ((finite_finite_nat A_155)->((ord_less_eq_nat (finite_card_nat A_155)) (finite_card_nat ((insert_nat X_53) A_155))))). % Axiom fact_93_card__insert__le:(forall (X_53:int) (A_155:(int->Prop)), ((finite_finite_int A_155)->((ord_less_eq_nat (finite_card_int A_155)) (finite_card_int ((insert_int X_53) A_155))))). % Axiom fact_94_card__insert__le:(forall (X_53:x_a) (A_155:(x_a->Prop)), ((finite_finite_a A_155)->((ord_less_eq_nat (finite_card_a A_155)) (finite_card_a ((insert_a X_53) A_155))))). % Axiom fact_95_card__insert__if:(forall (X_52:(int->Prop)) (A_154:((int->Prop)->Prop)), ((finite_finite_int_o A_154)->((and (((member_int_o X_52) A_154)->(((eq nat) (finite_card_int_o ((insert_int_o X_52) A_154))) (finite_card_int_o A_154)))) ((((member_int_o X_52) A_154)->False)->(((eq nat) (finite_card_int_o ((insert_int_o X_52) A_154))) (suc (finite_card_int_o A_154))))))). % Axiom fact_96_card__insert__if:(forall (X_52:(nat->Prop)) (A_154:((nat->Prop)->Prop)), ((finite_finite_nat_o A_154)->((and (((member_nat_o X_52) A_154)->(((eq nat) (finite_card_nat_o ((insert_nat_o X_52) A_154))) (finite_card_nat_o A_154)))) ((((member_nat_o X_52) A_154)->False)->(((eq nat) (finite_card_nat_o ((insert_nat_o X_52) A_154))) (suc (finite_card_nat_o A_154))))))). % Axiom fact_97_card__insert__if:(forall (X_52:(pname->Prop)) (A_154:((pname->Prop)->Prop)), ((finite297249702name_o A_154)->((and (((member_pname_o X_52) A_154)->(((eq nat) (finite_card_pname_o ((insert_pname_o X_52) A_154))) (finite_card_pname_o A_154)))) ((((member_pname_o X_52) A_154)->False)->(((eq nat) (finite_card_pname_o ((insert_pname_o X_52) A_154))) (suc (finite_card_pname_o A_154))))))). % Axiom fact_98_card__insert__if:(forall (X_52:(x_a->Prop)) (A_154:((x_a->Prop)->Prop)), ((finite_finite_a_o A_154)->((and (((member_a_o X_52) A_154)->(((eq nat) (finite_card_a_o ((insert_a_o X_52) A_154))) (finite_card_a_o A_154)))) ((((member_a_o X_52) A_154)->False)->(((eq nat) (finite_card_a_o ((insert_a_o X_52) A_154))) (suc (finite_card_a_o A_154))))))). % Axiom fact_99_card__insert__if:(forall (X_52:pname) (A_154:(pname->Prop)), ((finite_finite_pname A_154)->((and (((member_pname X_52) A_154)->(((eq nat) (finite_card_pname ((insert_pname X_52) A_154))) (finite_card_pname A_154)))) ((((member_pname X_52) A_154)->False)->(((eq nat) (finite_card_pname ((insert_pname X_52) A_154))) (suc (finite_card_pname A_154))))))). % Axiom fact_100_card__insert__if:(forall (X_52:nat) (A_154:(nat->Prop)), ((finite_finite_nat A_154)->((and (((member_nat X_52) A_154)->(((eq nat) (finite_card_nat ((insert_nat X_52) A_154))) (finite_card_nat A_154)))) ((((member_nat X_52) A_154)->False)->(((eq nat) (finite_card_nat ((insert_nat X_52) A_154))) (suc (finite_card_nat A_154))))))). % Axiom fact_101_card__insert__if:(forall (X_52:int) (A_154:(int->Prop)), ((finite_finite_int A_154)->((and (((member_int X_52) A_154)->(((eq nat) (finite_card_int ((insert_int X_52) A_154))) (finite_card_int A_154)))) ((((member_int X_52) A_154)->False)->(((eq nat) (finite_card_int ((insert_int X_52) A_154))) (suc (finite_card_int A_154))))))). % Axiom fact_102_card__insert__if:(forall (X_52:x_a) (A_154:(x_a->Prop)), ((finite_finite_a A_154)->((and (((member_a X_52) A_154)->(((eq nat) (finite_card_a ((insert_a X_52) A_154))) (finite_card_a A_154)))) ((((member_a X_52) A_154)->False)->(((eq nat) (finite_card_a ((insert_a X_52) A_154))) (suc (finite_card_a A_154))))))). % Axiom fact_103_card__insert__disjoint:(forall (X_51:(int->Prop)) (A_153:((int->Prop)->Prop)), ((finite_finite_int_o A_153)->((((member_int_o X_51) A_153)->False)->(((eq nat) (finite_card_int_o ((insert_int_o X_51) A_153))) (suc (finite_card_int_o A_153)))))). % Axiom fact_104_card__insert__disjoint:(forall (X_51:(nat->Prop)) (A_153:((nat->Prop)->Prop)), ((finite_finite_nat_o A_153)->((((member_nat_o X_51) A_153)->False)->(((eq nat) (finite_card_nat_o ((insert_nat_o X_51) A_153))) (suc (finite_card_nat_o A_153)))))). % Axiom fact_105_card__insert__disjoint:(forall (X_51:(pname->Prop)) (A_153:((pname->Prop)->Prop)), ((finite297249702name_o A_153)->((((member_pname_o X_51) A_153)->False)->(((eq nat) (finite_card_pname_o ((insert_pname_o X_51) A_153))) (suc (finite_card_pname_o A_153)))))). % Axiom fact_106_card__insert__disjoint:(forall (X_51:(x_a->Prop)) (A_153:((x_a->Prop)->Prop)), ((finite_finite_a_o A_153)->((((member_a_o X_51) A_153)->False)->(((eq nat) (finite_card_a_o ((insert_a_o X_51) A_153))) (suc (finite_card_a_o A_153)))))). % Axiom fact_107_card__insert__disjoint:(forall (X_51:pname) (A_153:(pname->Prop)), ((finite_finite_pname A_153)->((((member_pname X_51) A_153)->False)->(((eq nat) (finite_card_pname ((insert_pname X_51) A_153))) (suc (finite_card_pname A_153)))))). % Axiom fact_108_card__insert__disjoint:(forall (X_51:nat) (A_153:(nat->Prop)), ((finite_finite_nat A_153)->((((member_nat X_51) A_153)->False)->(((eq nat) (finite_card_nat ((insert_nat X_51) A_153))) (suc (finite_card_nat A_153)))))). % Axiom fact_109_card__insert__disjoint:(forall (X_51:int) (A_153:(int->Prop)), ((finite_finite_int A_153)->((((member_int X_51) A_153)->False)->(((eq nat) (finite_card_int ((insert_int X_51) A_153))) (suc (finite_card_int A_153)))))). % Axiom fact_110_card__insert__disjoint:(forall (X_51:x_a) (A_153:(x_a->Prop)), ((finite_finite_a A_153)->((((member_a X_51) A_153)->False)->(((eq nat) (finite_card_a ((insert_a X_51) A_153))) (suc (finite_card_a A_153)))))). % Axiom fact_111_finite__Collect__conjI:(forall (Q_3:(x_a->Prop)) (P_13:(x_a->Prop)), (((or (finite_finite_a (collect_a P_13))) (finite_finite_a (collect_a Q_3)))->(finite_finite_a (collect_a (fun (X_1:x_a)=> ((and (P_13 X_1)) (Q_3 X_1))))))). % Axiom fact_112_finite__Collect__conjI:(forall (Q_3:((int->Prop)->Prop)) (P_13:((int->Prop)->Prop)), (((or (finite_finite_int_o (collect_int_o P_13))) (finite_finite_int_o (collect_int_o Q_3)))->(finite_finite_int_o (collect_int_o (fun (X_1:(int->Prop))=> ((and (P_13 X_1)) (Q_3 X_1))))))). % Axiom fact_113_finite__Collect__conjI:(forall (Q_3:((nat->Prop)->Prop)) (P_13:((nat->Prop)->Prop)), (((or (finite_finite_nat_o (collect_nat_o P_13))) (finite_finite_nat_o (collect_nat_o Q_3)))->(finite_finite_nat_o (collect_nat_o (fun (X_1:(nat->Prop))=> ((and (P_13 X_1)) (Q_3 X_1))))))). % Axiom fact_114_finite__Collect__conjI:(forall (Q_3:((pname->Prop)->Prop)) (P_13:((pname->Prop)->Prop)), (((or (finite297249702name_o (collect_pname_o P_13))) (finite297249702name_o (collect_pname_o Q_3)))->(finite297249702name_o (collect_pname_o (fun (X_1:(pname->Prop))=> ((and (P_13 X_1)) (Q_3 X_1))))))). % Axiom fact_115_finite__Collect__conjI:(forall (Q_3:((x_a->Prop)->Prop)) (P_13:((x_a->Prop)->Prop)), (((or (finite_finite_a_o (collect_a_o P_13))) (finite_finite_a_o (collect_a_o Q_3)))->(finite_finite_a_o (collect_a_o (fun (X_1:(x_a->Prop))=> ((and (P_13 X_1)) (Q_3 X_1))))))). % Axiom fact_116_finite__Collect__conjI:(forall (Q_3:(pname->Prop)) (P_13:(pname->Prop)), (((or (finite_finite_pname (collect_pname P_13))) (finite_finite_pname (collect_pname Q_3)))->(finite_finite_pname (collect_pname (fun (X_1:pname)=> ((and (P_13 X_1)) (Q_3 X_1))))))). % Axiom fact_117_finite__Collect__conjI:(forall (Q_3:(nat->Prop)) (P_13:(nat->Prop)), (((or (finite_finite_nat (collect_nat P_13))) (finite_finite_nat (collect_nat Q_3)))->(finite_finite_nat (collect_nat (fun (X_1:nat)=> ((and (P_13 X_1)) (Q_3 X_1))))))). % Axiom fact_118_finite__Collect__conjI:(forall (Q_3:(int->Prop)) (P_13:(int->Prop)), (((or (finite_finite_int (collect_int P_13))) (finite_finite_int (collect_int Q_3)))->(finite_finite_int (collect_int (fun (X_1:int)=> ((and (P_13 X_1)) (Q_3 X_1))))))). % Axiom fact_119_Suc__diff__le:(forall (N:nat) (M:nat), (((ord_less_eq_nat N) M)->(((eq nat) ((minus_minus_nat (suc M)) N)) (suc ((minus_minus_nat M) N))))). % Axiom fact_120_finite__Collect__le__nat:(forall (K:nat), (finite_finite_nat (collect_nat (fun (N_1:nat)=> ((ord_less_eq_nat N_1) K))))). % Axiom fact_121_card__Collect__le__nat:(forall (N:nat), (((eq nat) (finite_card_nat (collect_nat (fun (_TPTP_I:nat)=> ((ord_less_eq_nat _TPTP_I) N))))) (suc N))). % Axiom fact_122_Suc__inject:(forall (X:nat) (Y:nat), ((((eq nat) (suc X)) (suc Y))->(((eq nat) X) Y))). % Axiom fact_123_nat_Oinject:(forall (Nat_4:nat) (Nat_1:nat), ((iff (((eq nat) (suc Nat_4)) (suc Nat_1))) (((eq nat) Nat_4) Nat_1))). % Axiom fact_124_Suc__n__not__n:(forall (N:nat), (not (((eq nat) (suc N)) N))). % Axiom fact_125_n__not__Suc__n:(forall (N:nat), (not (((eq nat) N) (suc N)))). % Axiom fact_126_le__antisym:(forall (M:nat) (N:nat), (((ord_less_eq_nat M) N)->(((ord_less_eq_nat N) M)->(((eq nat) M) N)))). % Axiom fact_127_le__trans:(forall (K:nat) (I_1:nat) (J:nat), (((ord_less_eq_nat I_1) J)->(((ord_less_eq_nat J) K)->((ord_less_eq_nat I_1) K)))). % Axiom fact_128_eq__imp__le:(forall (M:nat) (N:nat), ((((eq nat) M) N)->((ord_less_eq_nat M) N))). % Axiom fact_129_nat__le__linear:(forall (M:nat) (N:nat), ((or ((ord_less_eq_nat M) N)) ((ord_less_eq_nat N) M))). % Axiom fact_130_le__refl:(forall (N:nat), ((ord_less_eq_nat N) N)). % Axiom fact_131_diff__commute:(forall (I_1:nat) (J:nat) (K:nat), (((eq nat) ((minus_minus_nat ((minus_minus_nat I_1) J)) K)) ((minus_minus_nat ((minus_minus_nat I_1) K)) J))). % Axiom fact_132_finite__Collect__disjI:(forall (P_12:(x_a->Prop)) (Q_2:(x_a->Prop)), ((iff (finite_finite_a (collect_a (fun (X_1:x_a)=> ((or (P_12 X_1)) (Q_2 X_1)))))) ((and (finite_finite_a (collect_a P_12))) (finite_finite_a (collect_a Q_2))))). % Axiom fact_133_finite__Collect__disjI:(forall (P_12:((int->Prop)->Prop)) (Q_2:((int->Prop)->Prop)), ((iff (finite_finite_int_o (collect_int_o (fun (X_1:(int->Prop))=> ((or (P_12 X_1)) (Q_2 X_1)))))) ((and (finite_finite_int_o (collect_int_o P_12))) (finite_finite_int_o (collect_int_o Q_2))))). % Axiom fact_134_finite__Collect__disjI:(forall (P_12:((nat->Prop)->Prop)) (Q_2:((nat->Prop)->Prop)), ((iff (finite_finite_nat_o (collect_nat_o (fun (X_1:(nat->Prop))=> ((or (P_12 X_1)) (Q_2 X_1)))))) ((and (finite_finite_nat_o (collect_nat_o P_12))) (finite_finite_nat_o (collect_nat_o Q_2))))). % Axiom fact_135_finite__Collect__disjI:(forall (P_12:((pname->Prop)->Prop)) (Q_2:((pname->Prop)->Prop)), ((iff (finite297249702name_o (collect_pname_o (fun (X_1:(pname->Prop))=> ((or (P_12 X_1)) (Q_2 X_1)))))) ((and (finite297249702name_o (collect_pname_o P_12))) (finite297249702name_o (collect_pname_o Q_2))))). % Axiom fact_136_finite__Collect__disjI:(forall (P_12:((x_a->Prop)->Prop)) (Q_2:((x_a->Prop)->Prop)), ((iff (finite_finite_a_o (collect_a_o (fun (X_1:(x_a->Prop))=> ((or (P_12 X_1)) (Q_2 X_1)))))) ((and (finite_finite_a_o (collect_a_o P_12))) (finite_finite_a_o (collect_a_o Q_2))))). % Axiom fact_137_finite__Collect__disjI:(forall (P_12:(pname->Prop)) (Q_2:(pname->Prop)), ((iff (finite_finite_pname (collect_pname (fun (X_1:pname)=> ((or (P_12 X_1)) (Q_2 X_1)))))) ((and (finite_finite_pname (collect_pname P_12))) (finite_finite_pname (collect_pname Q_2))))). % Axiom fact_138_finite__Collect__disjI:(forall (P_12:(nat->Prop)) (Q_2:(nat->Prop)), ((iff (finite_finite_nat (collect_nat (fun (X_1:nat)=> ((or (P_12 X_1)) (Q_2 X_1)))))) ((and (finite_finite_nat (collect_nat P_12))) (finite_finite_nat (collect_nat Q_2))))). % Axiom fact_139_finite__Collect__disjI:(forall (P_12:(int->Prop)) (Q_2:(int->Prop)), ((iff (finite_finite_int (collect_int (fun (X_1:int)=> ((or (P_12 X_1)) (Q_2 X_1)))))) ((and (finite_finite_int (collect_int P_12))) (finite_finite_int (collect_int Q_2))))). % Axiom fact_140_finite__insert:(forall (A_152:(int->Prop)) (A_151:((int->Prop)->Prop)), ((iff (finite_finite_int_o ((insert_int_o A_152) A_151))) (finite_finite_int_o A_151))). % Axiom fact_141_finite__insert:(forall (A_152:(nat->Prop)) (A_151:((nat->Prop)->Prop)), ((iff (finite_finite_nat_o ((insert_nat_o A_152) A_151))) (finite_finite_nat_o A_151))). % Axiom fact_142_finite__insert:(forall (A_152:(pname->Prop)) (A_151:((pname->Prop)->Prop)), ((iff (finite297249702name_o ((insert_pname_o A_152) A_151))) (finite297249702name_o A_151))). % Axiom fact_143_finite__insert:(forall (A_152:(x_a->Prop)) (A_151:((x_a->Prop)->Prop)), ((iff (finite_finite_a_o ((insert_a_o A_152) A_151))) (finite_finite_a_o A_151))). % Axiom fact_144_finite__insert:(forall (A_152:pname) (A_151:(pname->Prop)), ((iff (finite_finite_pname ((insert_pname A_152) A_151))) (finite_finite_pname A_151))). % Axiom fact_145_finite__insert:(forall (A_152:nat) (A_151:(nat->Prop)), ((iff (finite_finite_nat ((insert_nat A_152) A_151))) (finite_finite_nat A_151))). % Axiom fact_146_finite__insert:(forall (A_152:int) (A_151:(int->Prop)), ((iff (finite_finite_int ((insert_int A_152) A_151))) (finite_finite_int A_151))). % Axiom fact_147_finite__insert:(forall (A_152:x_a) (A_151:(x_a->Prop)), ((iff (finite_finite_a ((insert_a A_152) A_151))) (finite_finite_a A_151))). % Axiom fact_148_finite__subset:(forall (A_150:((int->Prop)->Prop)) (B_87:((int->Prop)->Prop)), (((ord_less_eq_int_o_o A_150) B_87)->((finite_finite_int_o B_87)->(finite_finite_int_o A_150)))). % Axiom fact_149_finite__subset:(forall (A_150:((nat->Prop)->Prop)) (B_87:((nat->Prop)->Prop)), (((ord_less_eq_nat_o_o A_150) B_87)->((finite_finite_nat_o B_87)->(finite_finite_nat_o A_150)))). % Axiom fact_150_finite__subset:(forall (A_150:((pname->Prop)->Prop)) (B_87:((pname->Prop)->Prop)), (((ord_le1205211808me_o_o A_150) B_87)->((finite297249702name_o B_87)->(finite297249702name_o A_150)))). % Axiom fact_151_finite__subset:(forall (A_150:((x_a->Prop)->Prop)) (B_87:((x_a->Prop)->Prop)), (((ord_less_eq_a_o_o A_150) B_87)->((finite_finite_a_o B_87)->(finite_finite_a_o A_150)))). % Axiom fact_152_finite__subset:(forall (A_150:(x_a->Prop)) (B_87:(x_a->Prop)), (((ord_less_eq_a_o A_150) B_87)->((finite_finite_a B_87)->(finite_finite_a A_150)))). % Axiom fact_153_finite__subset:(forall (A_150:(pname->Prop)) (B_87:(pname->Prop)), (((ord_less_eq_pname_o A_150) B_87)->((finite_finite_pname B_87)->(finite_finite_pname A_150)))). % Axiom fact_154_finite__subset:(forall (A_150:(nat->Prop)) (B_87:(nat->Prop)), (((ord_less_eq_nat_o A_150) B_87)->((finite_finite_nat B_87)->(finite_finite_nat A_150)))). % Axiom fact_155_finite__subset:(forall (A_150:(int->Prop)) (B_87:(int->Prop)), (((ord_less_eq_int_o A_150) B_87)->((finite_finite_int B_87)->(finite_finite_int A_150)))). % Axiom fact_156_rev__finite__subset:(forall (A_149:((int->Prop)->Prop)) (B_86:((int->Prop)->Prop)), ((finite_finite_int_o B_86)->(((ord_less_eq_int_o_o A_149) B_86)->(finite_finite_int_o A_149)))). % Axiom fact_157_rev__finite__subset:(forall (A_149:((nat->Prop)->Prop)) (B_86:((nat->Prop)->Prop)), ((finite_finite_nat_o B_86)->(((ord_less_eq_nat_o_o A_149) B_86)->(finite_finite_nat_o A_149)))). % Axiom fact_158_rev__finite__subset:(forall (A_149:((pname->Prop)->Prop)) (B_86:((pname->Prop)->Prop)), ((finite297249702name_o B_86)->(((ord_le1205211808me_o_o A_149) B_86)->(finite297249702name_o A_149)))). % Axiom fact_159_rev__finite__subset:(forall (A_149:((x_a->Prop)->Prop)) (B_86:((x_a->Prop)->Prop)), ((finite_finite_a_o B_86)->(((ord_less_eq_a_o_o A_149) B_86)->(finite_finite_a_o A_149)))). % Axiom fact_160_rev__finite__subset:(forall (A_149:(x_a->Prop)) (B_86:(x_a->Prop)), ((finite_finite_a B_86)->(((ord_less_eq_a_o A_149) B_86)->(finite_finite_a A_149)))). % Axiom fact_161_rev__finite__subset:(forall (A_149:(pname->Prop)) (B_86:(pname->Prop)), ((finite_finite_pname B_86)->(((ord_less_eq_pname_o A_149) B_86)->(finite_finite_pname A_149)))). % Axiom fact_162_rev__finite__subset:(forall (A_149:(nat->Prop)) (B_86:(nat->Prop)), ((finite_finite_nat B_86)->(((ord_less_eq_nat_o A_149) B_86)->(finite_finite_nat A_149)))). % Axiom fact_163_rev__finite__subset:(forall (A_149:(int->Prop)) (B_86:(int->Prop)), ((finite_finite_int B_86)->(((ord_less_eq_int_o A_149) B_86)->(finite_finite_int A_149)))). % Axiom fact_164_Suc__leD:(forall (M:nat) (N:nat), (((ord_less_eq_nat (suc M)) N)->((ord_less_eq_nat M) N))). % Axiom fact_165_le__SucE:(forall (M:nat) (N:nat), (((ord_less_eq_nat M) (suc N))->((((ord_less_eq_nat M) N)->False)->(((eq nat) M) (suc N))))). % Axiom fact_166_le__SucI:(forall (M:nat) (N:nat), (((ord_less_eq_nat M) N)->((ord_less_eq_nat M) (suc N)))). % Axiom fact_167_Suc__le__mono:(forall (N:nat) (M:nat), ((iff ((ord_less_eq_nat (suc N)) (suc M))) ((ord_less_eq_nat N) M))). % Axiom fact_168_le__Suc__eq:(forall (M:nat) (N:nat), ((iff ((ord_less_eq_nat M) (suc N))) ((or ((ord_less_eq_nat M) N)) (((eq nat) M) (suc N))))). % Axiom fact_169_not__less__eq__eq:(forall (M:nat) (N:nat), ((iff (((ord_less_eq_nat M) N)->False)) ((ord_less_eq_nat (suc N)) M))). % Axiom fact_170_Suc__n__not__le__n:(forall (N:nat), (((ord_less_eq_nat (suc N)) N)->False)). % Axiom fact_171_Suc__diff__diff:(forall (M:nat) (N:nat) (K:nat), (((eq nat) ((minus_minus_nat ((minus_minus_nat (suc M)) N)) (suc K))) ((minus_minus_nat ((minus_minus_nat M) N)) K))). % Axiom fact_172_diff__Suc__Suc:(forall (M:nat) (N:nat), (((eq nat) ((minus_minus_nat (suc M)) (suc N))) ((minus_minus_nat M) N))). % Axiom fact_173_le__diff__iff:(forall (N:nat) (K:nat) (M:nat), (((ord_less_eq_nat K) M)->(((ord_less_eq_nat K) N)->((iff ((ord_less_eq_nat ((minus_minus_nat M) K)) ((minus_minus_nat N) K))) ((ord_less_eq_nat M) N))))). % Axiom fact_174_Nat_Odiff__diff__eq:(forall (N:nat) (K:nat) (M:nat), (((ord_less_eq_nat K) M)->(((ord_less_eq_nat K) N)->(((eq nat) ((minus_minus_nat ((minus_minus_nat M) K)) ((minus_minus_nat N) K))) ((minus_minus_nat M) N))))). % Axiom fact_175_eq__diff__iff:(forall (N:nat) (K:nat) (M:nat), (((ord_less_eq_nat K) M)->(((ord_less_eq_nat K) N)->((iff (((eq nat) ((minus_minus_nat M) K)) ((minus_minus_nat N) K))) (((eq nat) M) N))))). % Axiom fact_176_diff__diff__cancel:(forall (I_1:nat) (N:nat), (((ord_less_eq_nat I_1) N)->(((eq nat) ((minus_minus_nat N) ((minus_minus_nat N) I_1))) I_1))). % Axiom fact_177_diff__le__mono:(forall (L:nat) (M:nat) (N:nat), (((ord_less_eq_nat M) N)->((ord_less_eq_nat ((minus_minus_nat M) L)) ((minus_minus_nat N) L)))). % Axiom fact_178_diff__le__mono2:(forall (L:nat) (M:nat) (N:nat), (((ord_less_eq_nat M) N)->((ord_less_eq_nat ((minus_minus_nat L) N)) ((minus_minus_nat L) M)))). % Axiom fact_179_diff__le__self:(forall (M:nat) (N:nat), ((ord_less_eq_nat ((minus_minus_nat M) N)) M)). % Axiom fact_180_finite__surj:(forall (B_85:(x_a->Prop)) (F_40:(x_a->x_a)) (A_148:(x_a->Prop)), ((finite_finite_a A_148)->(((ord_less_eq_a_o B_85) ((image_a_a F_40) A_148))->(finite_finite_a B_85)))). % Axiom fact_181_finite__surj:(forall (B_85:(x_a->Prop)) (F_40:((int->Prop)->x_a)) (A_148:((int->Prop)->Prop)), ((finite_finite_int_o A_148)->(((ord_less_eq_a_o B_85) ((image_int_o_a F_40) A_148))->(finite_finite_a B_85)))). % Axiom fact_182_finite__surj:(forall (B_85:(x_a->Prop)) (F_40:((nat->Prop)->x_a)) (A_148:((nat->Prop)->Prop)), ((finite_finite_nat_o A_148)->(((ord_less_eq_a_o B_85) ((image_nat_o_a F_40) A_148))->(finite_finite_a B_85)))). % Axiom fact_183_finite__surj:(forall (B_85:(x_a->Prop)) (F_40:((pname->Prop)->x_a)) (A_148:((pname->Prop)->Prop)), ((finite297249702name_o A_148)->(((ord_less_eq_a_o B_85) ((image_pname_o_a F_40) A_148))->(finite_finite_a B_85)))). % Axiom fact_184_finite__surj:(forall (B_85:(x_a->Prop)) (F_40:((x_a->Prop)->x_a)) (A_148:((x_a->Prop)->Prop)), ((finite_finite_a_o A_148)->(((ord_less_eq_a_o B_85) ((image_a_o_a F_40) A_148))->(finite_finite_a B_85)))). % Axiom fact_185_finite__surj:(forall (B_85:((int->Prop)->Prop)) (F_40:(pname->(int->Prop))) (A_148:(pname->Prop)), ((finite_finite_pname A_148)->(((ord_less_eq_int_o_o B_85) ((image_pname_int_o F_40) A_148))->(finite_finite_int_o B_85)))). % Axiom fact_186_finite__surj:(forall (B_85:((nat->Prop)->Prop)) (F_40:(pname->(nat->Prop))) (A_148:(pname->Prop)), ((finite_finite_pname A_148)->(((ord_less_eq_nat_o_o B_85) ((image_pname_nat_o F_40) A_148))->(finite_finite_nat_o B_85)))). % Axiom fact_187_finite__surj:(forall (B_85:((pname->Prop)->Prop)) (F_40:(pname->(pname->Prop))) (A_148:(pname->Prop)), ((finite_finite_pname A_148)->(((ord_le1205211808me_o_o B_85) ((image_pname_pname_o F_40) A_148))->(finite297249702name_o B_85)))). % Axiom fact_188_finite__surj:(forall (B_85:((x_a->Prop)->Prop)) (F_40:(pname->(x_a->Prop))) (A_148:(pname->Prop)), ((finite_finite_pname A_148)->(((ord_less_eq_a_o_o B_85) ((image_pname_a_o F_40) A_148))->(finite_finite_a_o B_85)))). % Axiom fact_189_finite__surj:(forall (B_85:(pname->Prop)) (F_40:(pname->pname)) (A_148:(pname->Prop)), ((finite_finite_pname A_148)->(((ord_less_eq_pname_o B_85) ((image_pname_pname F_40) A_148))->(finite_finite_pname B_85)))). % Axiom fact_190_finite__surj:(forall (B_85:(x_a->Prop)) (F_40:(nat->x_a)) (A_148:(nat->Prop)), ((finite_finite_nat A_148)->(((ord_less_eq_a_o B_85) ((image_nat_a F_40) A_148))->(finite_finite_a B_85)))). % Axiom fact_191_finite__surj:(forall (B_85:((int->Prop)->Prop)) (F_40:(nat->(int->Prop))) (A_148:(nat->Prop)), ((finite_finite_nat A_148)->(((ord_less_eq_int_o_o B_85) ((image_nat_int_o F_40) A_148))->(finite_finite_int_o B_85)))). % Axiom fact_192_finite__surj:(forall (B_85:((nat->Prop)->Prop)) (F_40:(nat->(nat->Prop))) (A_148:(nat->Prop)), ((finite_finite_nat A_148)->(((ord_less_eq_nat_o_o B_85) ((image_nat_nat_o F_40) A_148))->(finite_finite_nat_o B_85)))). % Axiom fact_193_finite__surj:(forall (B_85:((pname->Prop)->Prop)) (F_40:(nat->(pname->Prop))) (A_148:(nat->Prop)), ((finite_finite_nat A_148)->(((ord_le1205211808me_o_o B_85) ((image_nat_pname_o F_40) A_148))->(finite297249702name_o B_85)))). % Axiom fact_194_finite__surj:(forall (B_85:((x_a->Prop)->Prop)) (F_40:(nat->(x_a->Prop))) (A_148:(nat->Prop)), ((finite_finite_nat A_148)->(((ord_less_eq_a_o_o B_85) ((image_nat_a_o F_40) A_148))->(finite_finite_a_o B_85)))). % Axiom fact_195_finite__surj:(forall (B_85:(pname->Prop)) (F_40:(nat->pname)) (A_148:(nat->Prop)), ((finite_finite_nat A_148)->(((ord_less_eq_pname_o B_85) ((image_nat_pname F_40) A_148))->(finite_finite_pname B_85)))). % Axiom fact_196_finite__surj:(forall (B_85:(x_a->Prop)) (F_40:(int->x_a)) (A_148:(int->Prop)), ((finite_finite_int A_148)->(((ord_less_eq_a_o B_85) ((image_int_a F_40) A_148))->(finite_finite_a B_85)))). % Axiom fact_197_finite__surj:(forall (B_85:((int->Prop)->Prop)) (F_40:(int->(int->Prop))) (A_148:(int->Prop)), ((finite_finite_int A_148)->(((ord_less_eq_int_o_o B_85) ((image_int_int_o F_40) A_148))->(finite_finite_int_o B_85)))). % Axiom fact_198_finite__surj:(forall (B_85:((nat->Prop)->Prop)) (F_40:(int->(nat->Prop))) (A_148:(int->Prop)), ((finite_finite_int A_148)->(((ord_less_eq_nat_o_o B_85) ((image_int_nat_o F_40) A_148))->(finite_finite_nat_o B_85)))). % Axiom fact_199_finite__surj:(forall (B_85:((pname->Prop)->Prop)) (F_40:(int->(pname->Prop))) (A_148:(int->Prop)), ((finite_finite_int A_148)->(((ord_le1205211808me_o_o B_85) ((image_int_pname_o F_40) A_148))->(finite297249702name_o B_85)))). % Axiom fact_200_finite__surj:(forall (B_85:((x_a->Prop)->Prop)) (F_40:(int->(x_a->Prop))) (A_148:(int->Prop)), ((finite_finite_int A_148)->(((ord_less_eq_a_o_o B_85) ((image_int_a_o F_40) A_148))->(finite_finite_a_o B_85)))). % Axiom fact_201_finite__surj:(forall (B_85:(pname->Prop)) (F_40:(int->pname)) (A_148:(int->Prop)), ((finite_finite_int A_148)->(((ord_less_eq_pname_o B_85) ((image_int_pname F_40) A_148))->(finite_finite_pname B_85)))). % Axiom fact_202_finite__surj:(forall (B_85:(pname->Prop)) (F_40:(x_a->pname)) (A_148:(x_a->Prop)), ((finite_finite_a A_148)->(((ord_less_eq_pname_o B_85) ((image_a_pname F_40) A_148))->(finite_finite_pname B_85)))). % Axiom fact_203_finite__surj:(forall (B_85:(pname->Prop)) (F_40:((int->Prop)->pname)) (A_148:((int->Prop)->Prop)), ((finite_finite_int_o A_148)->(((ord_less_eq_pname_o B_85) ((image_int_o_pname F_40) A_148))->(finite_finite_pname B_85)))). % Axiom fact_204_finite__surj:(forall (B_85:(pname->Prop)) (F_40:((nat->Prop)->pname)) (A_148:((nat->Prop)->Prop)), ((finite_finite_nat_o A_148)->(((ord_less_eq_pname_o B_85) ((image_nat_o_pname F_40) A_148))->(finite_finite_pname B_85)))). % Axiom fact_205_finite__surj:(forall (B_85:(pname->Prop)) (F_40:((pname->Prop)->pname)) (A_148:((pname->Prop)->Prop)), ((finite297249702name_o A_148)->(((ord_less_eq_pname_o B_85) ((image_pname_o_pname F_40) A_148))->(finite_finite_pname B_85)))). % Axiom fact_206_finite__surj:(forall (B_85:(pname->Prop)) (F_40:((x_a->Prop)->pname)) (A_148:((x_a->Prop)->Prop)), ((finite_finite_a_o A_148)->(((ord_less_eq_pname_o B_85) ((image_a_o_pname F_40) A_148))->(finite_finite_pname B_85)))). % Axiom fact_207_finite__surj:(forall (B_85:(nat->Prop)) (F_40:(x_a->nat)) (A_148:(x_a->Prop)), ((finite_finite_a A_148)->(((ord_less_eq_nat_o B_85) ((image_a_nat F_40) A_148))->(finite_finite_nat B_85)))). % Axiom fact_208_finite__surj:(forall (B_85:(nat->Prop)) (F_40:((int->Prop)->nat)) (A_148:((int->Prop)->Prop)), ((finite_finite_int_o A_148)->(((ord_less_eq_nat_o B_85) ((image_int_o_nat F_40) A_148))->(finite_finite_nat B_85)))). % Axiom fact_209_finite__surj:(forall (B_85:(nat->Prop)) (F_40:((nat->Prop)->nat)) (A_148:((nat->Prop)->Prop)), ((finite_finite_nat_o A_148)->(((ord_less_eq_nat_o B_85) ((image_nat_o_nat F_40) A_148))->(finite_finite_nat B_85)))). % Axiom fact_210_finite__surj:(forall (B_85:(nat->Prop)) (F_40:((pname->Prop)->nat)) (A_148:((pname->Prop)->Prop)), ((finite297249702name_o A_148)->(((ord_less_eq_nat_o B_85) ((image_pname_o_nat F_40) A_148))->(finite_finite_nat B_85)))). % Axiom fact_211_finite__surj:(forall (B_85:(nat->Prop)) (F_40:((x_a->Prop)->nat)) (A_148:((x_a->Prop)->Prop)), ((finite_finite_a_o A_148)->(((ord_less_eq_nat_o B_85) ((image_a_o_nat F_40) A_148))->(finite_finite_nat B_85)))). % Axiom fact_212_finite__surj:(forall (B_85:(int->Prop)) (F_40:(x_a->int)) (A_148:(x_a->Prop)), ((finite_finite_a A_148)->(((ord_less_eq_int_o B_85) ((image_a_int F_40) A_148))->(finite_finite_int B_85)))). % Axiom fact_213_finite__surj:(forall (B_85:(int->Prop)) (F_40:((int->Prop)->int)) (A_148:((int->Prop)->Prop)), ((finite_finite_int_o A_148)->(((ord_less_eq_int_o B_85) ((image_int_o_int F_40) A_148))->(finite_finite_int B_85)))). % Axiom fact_214_finite__surj:(forall (B_85:(int->Prop)) (F_40:((nat->Prop)->int)) (A_148:((nat->Prop)->Prop)), ((finite_finite_nat_o A_148)->(((ord_less_eq_int_o B_85) ((image_nat_o_int F_40) A_148))->(finite_finite_int B_85)))). % Axiom fact_215_finite__surj:(forall (B_85:(int->Prop)) (F_40:((pname->Prop)->int)) (A_148:((pname->Prop)->Prop)), ((finite297249702name_o A_148)->(((ord_less_eq_int_o B_85) ((image_pname_o_int F_40) A_148))->(finite_finite_int B_85)))). % Axiom fact_216_finite__surj:(forall (B_85:(int->Prop)) (F_40:((x_a->Prop)->int)) (A_148:((x_a->Prop)->Prop)), ((finite_finite_a_o A_148)->(((ord_less_eq_int_o B_85) ((image_a_o_int F_40) A_148))->(finite_finite_int B_85)))). % Axiom fact_217_finite__surj:(forall (B_85:(x_a->Prop)) (F_40:(pname->x_a)) (A_148:(pname->Prop)), ((finite_finite_pname A_148)->(((ord_less_eq_a_o B_85) ((image_pname_a F_40) A_148))->(finite_finite_a B_85)))). % Axiom fact_218_finite__surj:(forall (B_85:(int->Prop)) (F_40:(nat->int)) (A_148:(nat->Prop)), ((finite_finite_nat A_148)->(((ord_less_eq_int_o B_85) ((image_nat_int F_40) A_148))->(finite_finite_int B_85)))). % Axiom fact_219_finite__subset__image:(forall (F_39:((int->Prop)->x_a)) (A_147:((int->Prop)->Prop)) (B_84:(x_a->Prop)), ((finite_finite_a B_84)->(((ord_less_eq_a_o B_84) ((image_int_o_a F_39) A_147))->((ex ((int->Prop)->Prop)) (fun (C_34:((int->Prop)->Prop))=> ((and ((and ((ord_less_eq_int_o_o C_34) A_147)) (finite_finite_int_o C_34))) (((eq (x_a->Prop)) B_84) ((image_int_o_a F_39) C_34)))))))). % Axiom fact_220_finite__subset__image:(forall (F_39:((nat->Prop)->x_a)) (A_147:((nat->Prop)->Prop)) (B_84:(x_a->Prop)), ((finite_finite_a B_84)->(((ord_less_eq_a_o B_84) ((image_nat_o_a F_39) A_147))->((ex ((nat->Prop)->Prop)) (fun (C_34:((nat->Prop)->Prop))=> ((and ((and ((ord_less_eq_nat_o_o C_34) A_147)) (finite_finite_nat_o C_34))) (((eq (x_a->Prop)) B_84) ((image_nat_o_a F_39) C_34)))))))). % Axiom fact_221_finite__subset__image:(forall (F_39:((pname->Prop)->x_a)) (A_147:((pname->Prop)->Prop)) (B_84:(x_a->Prop)), ((finite_finite_a B_84)->(((ord_less_eq_a_o B_84) ((image_pname_o_a F_39) A_147))->((ex ((pname->Prop)->Prop)) (fun (C_34:((pname->Prop)->Prop))=> ((and ((and ((ord_le1205211808me_o_o C_34) A_147)) (finite297249702name_o C_34))) (((eq (x_a->Prop)) B_84) ((image_pname_o_a F_39) C_34)))))))). % Axiom fact_222_finite__subset__image:(forall (F_39:((x_a->Prop)->x_a)) (A_147:((x_a->Prop)->Prop)) (B_84:(x_a->Prop)), ((finite_finite_a B_84)->(((ord_less_eq_a_o B_84) ((image_a_o_a F_39) A_147))->((ex ((x_a->Prop)->Prop)) (fun (C_34:((x_a->Prop)->Prop))=> ((and ((and ((ord_less_eq_a_o_o C_34) A_147)) (finite_finite_a_o C_34))) (((eq (x_a->Prop)) B_84) ((image_a_o_a F_39) C_34)))))))). % Axiom fact_223_finite__subset__image:(forall (F_39:(x_a->x_a)) (A_147:(x_a->Prop)) (B_84:(x_a->Prop)), ((finite_finite_a B_84)->(((ord_less_eq_a_o B_84) ((image_a_a F_39) A_147))->((ex (x_a->Prop)) (fun (C_34:(x_a->Prop))=> ((and ((and ((ord_less_eq_a_o C_34) A_147)) (finite_finite_a C_34))) (((eq (x_a->Prop)) B_84) ((image_a_a F_39) C_34)))))))). % Axiom fact_224_finite__subset__image:(forall (F_39:(x_a->(int->Prop))) (A_147:(x_a->Prop)) (B_84:((int->Prop)->Prop)), ((finite_finite_int_o B_84)->(((ord_less_eq_int_o_o B_84) ((image_a_int_o F_39) A_147))->((ex (x_a->Prop)) (fun (C_34:(x_a->Prop))=> ((and ((and ((ord_less_eq_a_o C_34) A_147)) (finite_finite_a C_34))) (((eq ((int->Prop)->Prop)) B_84) ((image_a_int_o F_39) C_34)))))))). % Axiom fact_225_finite__subset__image:(forall (F_39:(x_a->(nat->Prop))) (A_147:(x_a->Prop)) (B_84:((nat->Prop)->Prop)), ((finite_finite_nat_o B_84)->(((ord_less_eq_nat_o_o B_84) ((image_a_nat_o F_39) A_147))->((ex (x_a->Prop)) (fun (C_34:(x_a->Prop))=> ((and ((and ((ord_less_eq_a_o C_34) A_147)) (finite_finite_a C_34))) (((eq ((nat->Prop)->Prop)) B_84) ((image_a_nat_o F_39) C_34)))))))). % Axiom fact_226_finite__subset__image:(forall (F_39:(x_a->(pname->Prop))) (A_147:(x_a->Prop)) (B_84:((pname->Prop)->Prop)), ((finite297249702name_o B_84)->(((ord_le1205211808me_o_o B_84) ((image_a_pname_o F_39) A_147))->((ex (x_a->Prop)) (fun (C_34:(x_a->Prop))=> ((and ((and ((ord_less_eq_a_o C_34) A_147)) (finite_finite_a C_34))) (((eq ((pname->Prop)->Prop)) B_84) ((image_a_pname_o F_39) C_34)))))))). % Axiom fact_227_finite__subset__image:(forall (F_39:(x_a->(x_a->Prop))) (A_147:(x_a->Prop)) (B_84:((x_a->Prop)->Prop)), ((finite_finite_a_o B_84)->(((ord_less_eq_a_o_o B_84) ((image_a_a_o F_39) A_147))->((ex (x_a->Prop)) (fun (C_34:(x_a->Prop))=> ((and ((and ((ord_less_eq_a_o C_34) A_147)) (finite_finite_a C_34))) (((eq ((x_a->Prop)->Prop)) B_84) ((image_a_a_o F_39) C_34)))))))). % Axiom fact_228_finite__subset__image:(forall (F_39:(x_a->pname)) (A_147:(x_a->Prop)) (B_84:(pname->Prop)), ((finite_finite_pname B_84)->(((ord_less_eq_pname_o B_84) ((image_a_pname F_39) A_147))->((ex (x_a->Prop)) (fun (C_34:(x_a->Prop))=> ((and ((and ((ord_less_eq_a_o C_34) A_147)) (finite_finite_a C_34))) (((eq (pname->Prop)) B_84) ((image_a_pname F_39) C_34)))))))). % Axiom fact_229_finite__subset__image:(forall (F_39:((int->Prop)->pname)) (A_147:((int->Prop)->Prop)) (B_84:(pname->Prop)), ((finite_finite_pname B_84)->(((ord_less_eq_pname_o B_84) ((image_int_o_pname F_39) A_147))->((ex ((int->Prop)->Prop)) (fun (C_34:((int->Prop)->Prop))=> ((and ((and ((ord_less_eq_int_o_o C_34) A_147)) (finite_finite_int_o C_34))) (((eq (pname->Prop)) B_84) ((image_int_o_pname F_39) C_34)))))))). % Axiom fact_230_finite__subset__image:(forall (F_39:((nat->Prop)->pname)) (A_147:((nat->Prop)->Prop)) (B_84:(pname->Prop)), ((finite_finite_pname B_84)->(((ord_less_eq_pname_o B_84) ((image_nat_o_pname F_39) A_147))->((ex ((nat->Prop)->Prop)) (fun (C_34:((nat->Prop)->Prop))=> ((and ((and ((ord_less_eq_nat_o_o C_34) A_147)) (finite_finite_nat_o C_34))) (((eq (pname->Prop)) B_84) ((image_nat_o_pname F_39) C_34)))))))). % Axiom fact_231_finite__subset__image:(forall (F_39:((pname->Prop)->pname)) (A_147:((pname->Prop)->Prop)) (B_84:(pname->Prop)), ((finite_finite_pname B_84)->(((ord_less_eq_pname_o B_84) ((image_pname_o_pname F_39) A_147))->((ex ((pname->Prop)->Prop)) (fun (C_34:((pname->Prop)->Prop))=> ((and ((and ((ord_le1205211808me_o_o C_34) A_147)) (finite297249702name_o C_34))) (((eq (pname->Prop)) B_84) ((image_pname_o_pname F_39) C_34)))))))). % Axiom fact_232_finite__subset__image:(forall (F_39:((x_a->Prop)->pname)) (A_147:((x_a->Prop)->Prop)) (B_84:(pname->Prop)), ((finite_finite_pname B_84)->(((ord_less_eq_pname_o B_84) ((image_a_o_pname F_39) A_147))->((ex ((x_a->Prop)->Prop)) (fun (C_34:((x_a->Prop)->Prop))=> ((and ((and ((ord_less_eq_a_o_o C_34) A_147)) (finite_finite_a_o C_34))) (((eq (pname->Prop)) B_84) ((image_a_o_pname F_39) C_34)))))))). % Axiom fact_233_finite__subset__image:(forall (F_39:(x_a->nat)) (A_147:(x_a->Prop)) (B_84:(nat->Prop)), ((finite_finite_nat B_84)->(((ord_less_eq_nat_o B_84) ((image_a_nat F_39) A_147))->((ex (x_a->Prop)) (fun (C_34:(x_a->Prop))=> ((and ((and ((ord_less_eq_a_o C_34) A_147)) (finite_finite_a C_34))) (((eq (nat->Prop)) B_84) ((image_a_nat F_39) C_34)))))))). % Axiom fact_234_finite__subset__image:(forall (F_39:((int->Prop)->nat)) (A_147:((int->Prop)->Prop)) (B_84:(nat->Prop)), ((finite_finite_nat B_84)->(((ord_less_eq_nat_o B_84) ((image_int_o_nat F_39) A_147))->((ex ((int->Prop)->Prop)) (fun (C_34:((int->Prop)->Prop))=> ((and ((and ((ord_less_eq_int_o_o C_34) A_147)) (finite_finite_int_o C_34))) (((eq (nat->Prop)) B_84) ((image_int_o_nat F_39) C_34)))))))). % Axiom fact_235_finite__subset__image:(forall (F_39:((nat->Prop)->nat)) (A_147:((nat->Prop)->Prop)) (B_84:(nat->Prop)), ((finite_finite_nat B_84)->(((ord_less_eq_nat_o B_84) ((image_nat_o_nat F_39) A_147))->((ex ((nat->Prop)->Prop)) (fun (C_34:((nat->Prop)->Prop))=> ((and ((and ((ord_less_eq_nat_o_o C_34) A_147)) (finite_finite_nat_o C_34))) (((eq (nat->Prop)) B_84) ((image_nat_o_nat F_39) C_34)))))))). % Axiom fact_236_finite__subset__image:(forall (F_39:((pname->Prop)->nat)) (A_147:((pname->Prop)->Prop)) (B_84:(nat->Prop)), ((finite_finite_nat B_84)->(((ord_less_eq_nat_o B_84) ((image_pname_o_nat F_39) A_147))->((ex ((pname->Prop)->Prop)) (fun (C_34:((pname->Prop)->Prop))=> ((and ((and ((ord_le1205211808me_o_o C_34) A_147)) (finite297249702name_o C_34))) (((eq (nat->Prop)) B_84) ((image_pname_o_nat F_39) C_34)))))))). % Axiom fact_237_finite__subset__image:(forall (F_39:((x_a->Prop)->nat)) (A_147:((x_a->Prop)->Prop)) (B_84:(nat->Prop)), ((finite_finite_nat B_84)->(((ord_less_eq_nat_o B_84) ((image_a_o_nat F_39) A_147))->((ex ((x_a->Prop)->Prop)) (fun (C_34:((x_a->Prop)->Prop))=> ((and ((and ((ord_less_eq_a_o_o C_34) A_147)) (finite_finite_a_o C_34))) (((eq (nat->Prop)) B_84) ((image_a_o_nat F_39) C_34)))))))). % Axiom fact_238_finite__subset__image:(forall (F_39:(pname->nat)) (A_147:(pname->Prop)) (B_84:(nat->Prop)), ((finite_finite_nat B_84)->(((ord_less_eq_nat_o B_84) ((image_pname_nat F_39) A_147))->((ex (pname->Prop)) (fun (C_34:(pname->Prop))=> ((and ((and ((ord_less_eq_pname_o C_34) A_147)) (finite_finite_pname C_34))) (((eq (nat->Prop)) B_84) ((image_pname_nat F_39) C_34)))))))). % Axiom fact_239_finite__subset__image:(forall (F_39:(x_a->int)) (A_147:(x_a->Prop)) (B_84:(int->Prop)), ((finite_finite_int B_84)->(((ord_less_eq_int_o B_84) ((image_a_int F_39) A_147))->((ex (x_a->Prop)) (fun (C_34:(x_a->Prop))=> ((and ((and ((ord_less_eq_a_o C_34) A_147)) (finite_finite_a C_34))) (((eq (int->Prop)) B_84) ((image_a_int F_39) C_34)))))))). % Axiom fact_240_finite__subset__image:(forall (F_39:((int->Prop)->int)) (A_147:((int->Prop)->Prop)) (B_84:(int->Prop)), ((finite_finite_int B_84)->(((ord_less_eq_int_o B_84) ((image_int_o_int F_39) A_147))->((ex ((int->Prop)->Prop)) (fun (C_34:((int->Prop)->Prop))=> ((and ((and ((ord_less_eq_int_o_o C_34) A_147)) (finite_finite_int_o C_34))) (((eq (int->Prop)) B_84) ((image_int_o_int F_39) C_34)))))))). % Axiom fact_241_finite__subset__image:(forall (F_39:((nat->Prop)->int)) (A_147:((nat->Prop)->Prop)) (B_84:(int->Prop)), ((finite_finite_int B_84)->(((ord_less_eq_int_o B_84) ((image_nat_o_int F_39) A_147))->((ex ((nat->Prop)->Prop)) (fun (C_34:((nat->Prop)->Prop))=> ((and ((and ((ord_less_eq_nat_o_o C_34) A_147)) (finite_finite_nat_o C_34))) (((eq (int->Prop)) B_84) ((image_nat_o_int F_39) C_34)))))))). % Axiom fact_242_finite__subset__image:(forall (F_39:((pname->Prop)->int)) (A_147:((pname->Prop)->Prop)) (B_84:(int->Prop)), ((finite_finite_int B_84)->(((ord_less_eq_int_o B_84) ((image_pname_o_int F_39) A_147))->((ex ((pname->Prop)->Prop)) (fun (C_34:((pname->Prop)->Prop))=> ((and ((and ((ord_le1205211808me_o_o C_34) A_147)) (finite297249702name_o C_34))) (((eq (int->Prop)) B_84) ((image_pname_o_int F_39) C_34)))))))). % Axiom fact_243_finite__subset__image:(forall (F_39:((x_a->Prop)->int)) (A_147:((x_a->Prop)->Prop)) (B_84:(int->Prop)), ((finite_finite_int B_84)->(((ord_less_eq_int_o B_84) ((image_a_o_int F_39) A_147))->((ex ((x_a->Prop)->Prop)) (fun (C_34:((x_a->Prop)->Prop))=> ((and ((and ((ord_less_eq_a_o_o C_34) A_147)) (finite_finite_a_o C_34))) (((eq (int->Prop)) B_84) ((image_a_o_int F_39) C_34)))))))). % Axiom fact_244_finite__subset__image:(forall (F_39:(pname->int)) (A_147:(pname->Prop)) (B_84:(int->Prop)), ((finite_finite_int B_84)->(((ord_less_eq_int_o B_84) ((image_pname_int F_39) A_147))->((ex (pname->Prop)) (fun (C_34:(pname->Prop))=> ((and ((and ((ord_less_eq_pname_o C_34) A_147)) (finite_finite_pname C_34))) (((eq (int->Prop)) B_84) ((image_pname_int F_39) C_34)))))))). % Axiom fact_245_finite__subset__image:(forall (F_39:(pname->(int->Prop))) (A_147:(pname->Prop)) (B_84:((int->Prop)->Prop)), ((finite_finite_int_o B_84)->(((ord_less_eq_int_o_o B_84) ((image_pname_int_o F_39) A_147))->((ex (pname->Prop)) (fun (C_34:(pname->Prop))=> ((and ((and ((ord_less_eq_pname_o C_34) A_147)) (finite_finite_pname C_34))) (((eq ((int->Prop)->Prop)) B_84) ((image_pname_int_o F_39) C_34)))))))). % Axiom fact_246_finite__subset__image:(forall (F_39:(pname->(nat->Prop))) (A_147:(pname->Prop)) (B_84:((nat->Prop)->Prop)), ((finite_finite_nat_o B_84)->(((ord_less_eq_nat_o_o B_84) ((image_pname_nat_o F_39) A_147))->((ex (pname->Prop)) (fun (C_34:(pname->Prop))=> ((and ((and ((ord_less_eq_pname_o C_34) A_147)) (finite_finite_pname C_34))) (((eq ((nat->Prop)->Prop)) B_84) ((image_pname_nat_o F_39) C_34)))))))). % Axiom fact_247_finite__subset__image:(forall (F_39:(pname->(pname->Prop))) (A_147:(pname->Prop)) (B_84:((pname->Prop)->Prop)), ((finite297249702name_o B_84)->(((ord_le1205211808me_o_o B_84) ((image_pname_pname_o F_39) A_147))->((ex (pname->Prop)) (fun (C_34:(pname->Prop))=> ((and ((and ((ord_less_eq_pname_o C_34) A_147)) (finite_finite_pname C_34))) (((eq ((pname->Prop)->Prop)) B_84) ((image_pname_pname_o F_39) C_34)))))))). % Axiom fact_248_finite__subset__image:(forall (F_39:(pname->(x_a->Prop))) (A_147:(pname->Prop)) (B_84:((x_a->Prop)->Prop)), ((finite_finite_a_o B_84)->(((ord_less_eq_a_o_o B_84) ((image_pname_a_o F_39) A_147))->((ex (pname->Prop)) (fun (C_34:(pname->Prop))=> ((and ((and ((ord_less_eq_pname_o C_34) A_147)) (finite_finite_pname C_34))) (((eq ((x_a->Prop)->Prop)) B_84) ((image_pname_a_o F_39) C_34)))))))). % Axiom fact_249_finite__subset__image:(forall (F_39:(pname->pname)) (A_147:(pname->Prop)) (B_84:(pname->Prop)), ((finite_finite_pname B_84)->(((ord_less_eq_pname_o B_84) ((image_pname_pname F_39) A_147))->((ex (pname->Prop)) (fun (C_34:(pname->Prop))=> ((and ((and ((ord_less_eq_pname_o C_34) A_147)) (finite_finite_pname C_34))) (((eq (pname->Prop)) B_84) ((image_pname_pname F_39) C_34)))))))). % Axiom fact_250_finite__subset__image:(forall (F_39:(nat->x_a)) (A_147:(nat->Prop)) (B_84:(x_a->Prop)), ((finite_finite_a B_84)->(((ord_less_eq_a_o B_84) ((image_nat_a F_39) A_147))->((ex (nat->Prop)) (fun (C_34:(nat->Prop))=> ((and ((and ((ord_less_eq_nat_o C_34) A_147)) (finite_finite_nat C_34))) (((eq (x_a->Prop)) B_84) ((image_nat_a F_39) C_34)))))))). % Axiom fact_251_finite__subset__image:(forall (F_39:(nat->(int->Prop))) (A_147:(nat->Prop)) (B_84:((int->Prop)->Prop)), ((finite_finite_int_o B_84)->(((ord_less_eq_int_o_o B_84) ((image_nat_int_o F_39) A_147))->((ex (nat->Prop)) (fun (C_34:(nat->Prop))=> ((and ((and ((ord_less_eq_nat_o C_34) A_147)) (finite_finite_nat C_34))) (((eq ((int->Prop)->Prop)) B_84) ((image_nat_int_o F_39) C_34)))))))). % Axiom fact_252_finite__subset__image:(forall (F_39:(nat->(nat->Prop))) (A_147:(nat->Prop)) (B_84:((nat->Prop)->Prop)), ((finite_finite_nat_o B_84)->(((ord_less_eq_nat_o_o B_84) ((image_nat_nat_o F_39) A_147))->((ex (nat->Prop)) (fun (C_34:(nat->Prop))=> ((and ((and ((ord_less_eq_nat_o C_34) A_147)) (finite_finite_nat C_34))) (((eq ((nat->Prop)->Prop)) B_84) ((image_nat_nat_o F_39) C_34)))))))). % Axiom fact_253_finite__subset__image:(forall (F_39:(nat->(pname->Prop))) (A_147:(nat->Prop)) (B_84:((pname->Prop)->Prop)), ((finite297249702name_o B_84)->(((ord_le1205211808me_o_o B_84) ((image_nat_pname_o F_39) A_147))->((ex (nat->Prop)) (fun (C_34:(nat->Prop))=> ((and ((and ((ord_less_eq_nat_o C_34) A_147)) (finite_finite_nat C_34))) (((eq ((pname->Prop)->Prop)) B_84) ((image_nat_pname_o F_39) C_34)))))))). % Axiom fact_254_finite__subset__image:(forall (F_39:(nat->(x_a->Prop))) (A_147:(nat->Prop)) (B_84:((x_a->Prop)->Prop)), ((finite_finite_a_o B_84)->(((ord_less_eq_a_o_o B_84) ((image_nat_a_o F_39) A_147))->((ex (nat->Prop)) (fun (C_34:(nat->Prop))=> ((and ((and ((ord_less_eq_nat_o C_34) A_147)) (finite_finite_nat C_34))) (((eq ((x_a->Prop)->Prop)) B_84) ((image_nat_a_o F_39) C_34)))))))). % Axiom fact_255_finite__subset__image:(forall (F_39:(nat->pname)) (A_147:(nat->Prop)) (B_84:(pname->Prop)), ((finite_finite_pname B_84)->(((ord_less_eq_pname_o B_84) ((image_nat_pname F_39) A_147))->((ex (nat->Prop)) (fun (C_34:(nat->Prop))=> ((and ((and ((ord_less_eq_nat_o C_34) A_147)) (finite_finite_nat C_34))) (((eq (pname->Prop)) B_84) ((image_nat_pname F_39) C_34)))))))). % Axiom fact_256_finite__subset__image:(forall (F_39:(int->x_a)) (A_147:(int->Prop)) (B_84:(x_a->Prop)), ((finite_finite_a B_84)->(((ord_less_eq_a_o B_84) ((image_int_a F_39) A_147))->((ex (int->Prop)) (fun (C_34:(int->Prop))=> ((and ((and ((ord_less_eq_int_o C_34) A_147)) (finite_finite_int C_34))) (((eq (x_a->Prop)) B_84) ((image_int_a F_39) C_34)))))))). % Axiom fact_257_finite__subset__image:(forall (F_39:(int->(int->Prop))) (A_147:(int->Prop)) (B_84:((int->Prop)->Prop)), ((finite_finite_int_o B_84)->(((ord_less_eq_int_o_o B_84) ((image_int_int_o F_39) A_147))->((ex (int->Prop)) (fun (C_34:(int->Prop))=> ((and ((and ((ord_less_eq_int_o C_34) A_147)) (finite_finite_int C_34))) (((eq ((int->Prop)->Prop)) B_84) ((image_int_int_o F_39) C_34)))))))). % Axiom fact_258_finite__subset__image:(forall (F_39:(int->(nat->Prop))) (A_147:(int->Prop)) (B_84:((nat->Prop)->Prop)), ((finite_finite_nat_o B_84)->(((ord_less_eq_nat_o_o B_84) ((image_int_nat_o F_39) A_147))->((ex (int->Prop)) (fun (C_34:(int->Prop))=> ((and ((and ((ord_less_eq_int_o C_34) A_147)) (finite_finite_int C_34))) (((eq ((nat->Prop)->Prop)) B_84) ((image_int_nat_o F_39) C_34)))))))). % Axiom fact_259_finite__subset__image:(forall (F_39:(int->(pname->Prop))) (A_147:(int->Prop)) (B_84:((pname->Prop)->Prop)), ((finite297249702name_o B_84)->(((ord_le1205211808me_o_o B_84) ((image_int_pname_o F_39) A_147))->((ex (int->Prop)) (fun (C_34:(int->Prop))=> ((and ((and ((ord_less_eq_int_o C_34) A_147)) (finite_finite_int C_34))) (((eq ((pname->Prop)->Prop)) B_84) ((image_int_pname_o F_39) C_34)))))))). % Axiom fact_260_finite__subset__image:(forall (F_39:(int->(x_a->Prop))) (A_147:(int->Prop)) (B_84:((x_a->Prop)->Prop)), ((finite_finite_a_o B_84)->(((ord_less_eq_a_o_o B_84) ((image_int_a_o F_39) A_147))->((ex (int->Prop)) (fun (C_34:(int->Prop))=> ((and ((and ((ord_less_eq_int_o C_34) A_147)) (finite_finite_int C_34))) (((eq ((x_a->Prop)->Prop)) B_84) ((image_int_a_o F_39) C_34)))))))). % Axiom fact_261_finite__subset__image:(forall (F_39:(int->pname)) (A_147:(int->Prop)) (B_84:(pname->Prop)), ((finite_finite_pname B_84)->(((ord_less_eq_pname_o B_84) ((image_int_pname F_39) A_147))->((ex (int->Prop)) (fun (C_34:(int->Prop))=> ((and ((and ((ord_less_eq_int_o C_34) A_147)) (finite_finite_int C_34))) (((eq (pname->Prop)) B_84) ((image_int_pname F_39) C_34)))))))). % Axiom fact_262_finite__subset__image:(forall (F_39:(pname->x_a)) (A_147:(pname->Prop)) (B_84:(x_a->Prop)), ((finite_finite_a B_84)->(((ord_less_eq_a_o B_84) ((image_pname_a F_39) A_147))->((ex (pname->Prop)) (fun (C_34:(pname->Prop))=> ((and ((and ((ord_less_eq_pname_o C_34) A_147)) (finite_finite_pname C_34))) (((eq (x_a->Prop)) B_84) ((image_pname_a F_39) C_34)))))))). % Axiom fact_263_finite__subset__image:(forall (F_39:(nat->int)) (A_147:(nat->Prop)) (B_84:(int->Prop)), ((finite_finite_int B_84)->(((ord_less_eq_int_o B_84) ((image_nat_int F_39) A_147))->((ex (nat->Prop)) (fun (C_34:(nat->Prop))=> ((and ((and ((ord_less_eq_nat_o C_34) A_147)) (finite_finite_nat C_34))) (((eq (int->Prop)) B_84) ((image_nat_int F_39) C_34)))))))). % Axiom fact_264_lift__Suc__mono__le:(forall (N_4:nat) (N_3:nat) (F_38:(nat->(pname->Prop))), ((forall (N_1:nat), ((ord_less_eq_pname_o (F_38 N_1)) (F_38 (suc N_1))))->(((ord_less_eq_nat N_4) N_3)->((ord_less_eq_pname_o (F_38 N_4)) (F_38 N_3))))). % Axiom fact_265_lift__Suc__mono__le:(forall (N_4:nat) (N_3:nat) (F_38:(nat->Prop)), ((forall (N_1:nat), ((ord_less_eq_o (F_38 N_1)) (F_38 (suc N_1))))->(((ord_less_eq_nat N_4) N_3)->((ord_less_eq_o (F_38 N_4)) (F_38 N_3))))). % Axiom fact_266_lift__Suc__mono__le:(forall (N_4:nat) (N_3:nat) (F_38:(nat->(x_a->Prop))), ((forall (N_1:nat), ((ord_less_eq_a_o (F_38 N_1)) (F_38 (suc N_1))))->(((ord_less_eq_nat N_4) N_3)->((ord_less_eq_a_o (F_38 N_4)) (F_38 N_3))))). % Axiom fact_267_lift__Suc__mono__le:(forall (N_4:nat) (N_3:nat) (F_38:(nat->nat)), ((forall (N_1:nat), ((ord_less_eq_nat (F_38 N_1)) (F_38 (suc N_1))))->(((ord_less_eq_nat N_4) N_3)->((ord_less_eq_nat (F_38 N_4)) (F_38 N_3))))). % Axiom fact_268_lift__Suc__mono__le:(forall (N_4:nat) (N_3:nat) (F_38:(nat->int)), ((forall (N_1:nat), ((ord_less_eq_int (F_38 N_1)) (F_38 (suc N_1))))->(((ord_less_eq_nat N_4) N_3)->((ord_less_eq_int (F_38 N_4)) (F_38 N_3))))). % Axiom fact_269_lift__Suc__mono__le:(forall (N_4:nat) (N_3:nat) (F_38:(nat->(nat->Prop))), ((forall (N_1:nat), ((ord_less_eq_nat_o (F_38 N_1)) (F_38 (suc N_1))))->(((ord_less_eq_nat N_4) N_3)->((ord_less_eq_nat_o (F_38 N_4)) (F_38 N_3))))). % Axiom fact_270_lift__Suc__mono__le:(forall (N_4:nat) (N_3:nat) (F_38:(nat->(int->Prop))), ((forall (N_1:nat), ((ord_less_eq_int_o (F_38 N_1)) (F_38 (suc N_1))))->(((ord_less_eq_nat N_4) N_3)->((ord_less_eq_int_o (F_38 N_4)) (F_38 N_3))))). % Axiom fact_271_pigeonhole__infinite:(forall (F_37:(nat->(int->Prop))) (A_146:(nat->Prop)), (((finite_finite_nat A_146)->False)->((finite_finite_int_o ((image_nat_int_o F_37) A_146))->((ex nat) (fun (X_1:nat)=> ((and ((member_nat X_1) A_146)) ((finite_finite_nat (collect_nat (fun (A_37:nat)=> ((and ((member_nat A_37) A_146)) (((eq (int->Prop)) (F_37 A_37)) (F_37 X_1))))))->False))))))). % Axiom fact_272_pigeonhole__infinite:(forall (F_37:(nat->(nat->Prop))) (A_146:(nat->Prop)), (((finite_finite_nat A_146)->False)->((finite_finite_nat_o ((image_nat_nat_o F_37) A_146))->((ex nat) (fun (X_1:nat)=> ((and ((member_nat X_1) A_146)) ((finite_finite_nat (collect_nat (fun (A_37:nat)=> ((and ((member_nat A_37) A_146)) (((eq (nat->Prop)) (F_37 A_37)) (F_37 X_1))))))->False))))))). % Axiom fact_273_pigeonhole__infinite:(forall (F_37:(nat->(pname->Prop))) (A_146:(nat->Prop)), (((finite_finite_nat A_146)->False)->((finite297249702name_o ((image_nat_pname_o F_37) A_146))->((ex nat) (fun (X_1:nat)=> ((and ((member_nat X_1) A_146)) ((finite_finite_nat (collect_nat (fun (A_37:nat)=> ((and ((member_nat A_37) A_146)) (((eq (pname->Prop)) (F_37 A_37)) (F_37 X_1))))))->False))))))). % Axiom fact_274_pigeonhole__infinite:(forall (F_37:(nat->(x_a->Prop))) (A_146:(nat->Prop)), (((finite_finite_nat A_146)->False)->((finite_finite_a_o ((image_nat_a_o F_37) A_146))->((ex nat) (fun (X_1:nat)=> ((and ((member_nat X_1) A_146)) ((finite_finite_nat (collect_nat (fun (A_37:nat)=> ((and ((member_nat A_37) A_146)) (((eq (x_a->Prop)) (F_37 A_37)) (F_37 X_1))))))->False))))))). % Axiom fact_275_pigeonhole__infinite:(forall (F_37:(int->x_a)) (A_146:(int->Prop)), (((finite_finite_int A_146)->False)->((finite_finite_a ((image_int_a F_37) A_146))->((ex int) (fun (X_1:int)=> ((and ((member_int X_1) A_146)) ((finite_finite_int (collect_int (fun (A_37:int)=> ((and ((member_int A_37) A_146)) (((eq x_a) (F_37 A_37)) (F_37 X_1))))))->False))))))). % Axiom fact_276_pigeonhole__infinite:(forall (F_37:(int->(int->Prop))) (A_146:(int->Prop)), (((finite_finite_int A_146)->False)->((finite_finite_int_o ((image_int_int_o F_37) A_146))->((ex int) (fun (X_1:int)=> ((and ((member_int X_1) A_146)) ((finite_finite_int (collect_int (fun (A_37:int)=> ((and ((member_int A_37) A_146)) (((eq (int->Prop)) (F_37 A_37)) (F_37 X_1))))))->False))))))). % Axiom fact_277_pigeonhole__infinite:(forall (F_37:(int->(nat->Prop))) (A_146:(int->Prop)), (((finite_finite_int A_146)->False)->((finite_finite_nat_o ((image_int_nat_o F_37) A_146))->((ex int) (fun (X_1:int)=> ((and ((member_int X_1) A_146)) ((finite_finite_int (collect_int (fun (A_37:int)=> ((and ((member_int A_37) A_146)) (((eq (nat->Prop)) (F_37 A_37)) (F_37 X_1))))))->False))))))). % Axiom fact_278_pigeonhole__infinite:(forall (F_37:(int->(pname->Prop))) (A_146:(int->Prop)), (((finite_finite_int A_146)->False)->((finite297249702name_o ((image_int_pname_o F_37) A_146))->((ex int) (fun (X_1:int)=> ((and ((member_int X_1) A_146)) ((finite_finite_int (collect_int (fun (A_37:int)=> ((and ((member_int A_37) A_146)) (((eq (pname->Prop)) (F_37 A_37)) (F_37 X_1))))))->False))))))). % Axiom fact_279_pigeonhole__infinite:(forall (F_37:(int->(x_a->Prop))) (A_146:(int->Prop)), (((finite_finite_int A_146)->False)->((finite_finite_a_o ((image_int_a_o F_37) A_146))->((ex int) (fun (X_1:int)=> ((and ((member_int X_1) A_146)) ((finite_finite_int (collect_int (fun (A_37:int)=> ((and ((member_int A_37) A_146)) (((eq (x_a->Prop)) (F_37 A_37)) (F_37 X_1))))))->False))))))). % Axiom fact_280_pigeonhole__infinite:(forall (F_37:(pname->x_a)) (A_146:(pname->Prop)), (((finite_finite_pname A_146)->False)->((finite_finite_a ((image_pname_a F_37) A_146))->((ex pname) (fun (X_1:pname)=> ((and ((member_pname X_1) A_146)) ((finite_finite_pname (collect_pname (fun (A_37:pname)=> ((and ((member_pname A_37) A_146)) (((eq x_a) (F_37 A_37)) (F_37 X_1))))))->False))))))). % Axiom fact_281_pigeonhole__infinite:(forall (F_37:(nat->int)) (A_146:(nat->Prop)), (((finite_finite_nat A_146)->False)->((finite_finite_int ((image_nat_int F_37) A_146))->((ex nat) (fun (X_1:nat)=> ((and ((member_nat X_1) A_146)) ((finite_finite_nat (collect_nat (fun (A_37:nat)=> ((and ((member_nat A_37) A_146)) (((eq int) (F_37 A_37)) (F_37 X_1))))))->False))))))). % Axiom fact_282_image__eqI:(forall (A_145:(nat->Prop)) (B_83:int) (F_36:(nat->int)) (X_50:nat), ((((eq int) B_83) (F_36 X_50))->(((member_nat X_50) A_145)->((member_int B_83) ((image_nat_int F_36) A_145))))). % Axiom fact_283_image__eqI:(forall (A_145:(pname->Prop)) (B_83:x_a) (F_36:(pname->x_a)) (X_50:pname), ((((eq x_a) B_83) (F_36 X_50))->(((member_pname X_50) A_145)->((member_a B_83) ((image_pname_a F_36) A_145))))). % Axiom fact_284_equalityI:(forall (A_144:(int->Prop)) (B_82:(int->Prop)), (((ord_less_eq_int_o A_144) B_82)->(((ord_less_eq_int_o B_82) A_144)->(((eq (int->Prop)) A_144) B_82)))). % Axiom fact_285_equalityI:(forall (A_144:(nat->Prop)) (B_82:(nat->Prop)), (((ord_less_eq_nat_o A_144) B_82)->(((ord_less_eq_nat_o B_82) A_144)->(((eq (nat->Prop)) A_144) B_82)))). % Axiom fact_286_equalityI:(forall (A_144:(x_a->Prop)) (B_82:(x_a->Prop)), (((ord_less_eq_a_o A_144) B_82)->(((ord_less_eq_a_o B_82) A_144)->(((eq (x_a->Prop)) A_144) B_82)))). % Axiom fact_287_subsetD:(forall (C_33:int) (A_143:(int->Prop)) (B_81:(int->Prop)), (((ord_less_eq_int_o A_143) B_81)->(((member_int C_33) A_143)->((member_int C_33) B_81)))). % Axiom fact_288_subsetD:(forall (C_33:nat) (A_143:(nat->Prop)) (B_81:(nat->Prop)), (((ord_less_eq_nat_o A_143) B_81)->(((member_nat C_33) A_143)->((member_nat C_33) B_81)))). % Axiom fact_289_subsetD:(forall (C_33:x_a) (A_143:(x_a->Prop)) (B_81:(x_a->Prop)), (((ord_less_eq_a_o A_143) B_81)->(((member_a C_33) A_143)->((member_a C_33) B_81)))). % Axiom fact_290_subsetD:(forall (C_33:pname) (A_143:(pname->Prop)) (B_81:(pname->Prop)), (((ord_less_eq_pname_o A_143) B_81)->(((member_pname C_33) A_143)->((member_pname C_33) B_81)))). % Axiom fact_291_insertCI:(forall (B_80:x_a) (A_142:x_a) (B_79:(x_a->Prop)), (((((member_a A_142) B_79)->False)->(((eq x_a) A_142) B_80))->((member_a A_142) ((insert_a B_80) B_79)))). % Axiom fact_292_insertCI:(forall (B_80:int) (A_142:int) (B_79:(int->Prop)), (((((member_int A_142) B_79)->False)->(((eq int) A_142) B_80))->((member_int A_142) ((insert_int B_80) B_79)))). % Axiom fact_293_insertCI:(forall (B_80:nat) (A_142:nat) (B_79:(nat->Prop)), (((((member_nat A_142) B_79)->False)->(((eq nat) A_142) B_80))->((member_nat A_142) ((insert_nat B_80) B_79)))). % Axiom fact_294_insertCI:(forall (B_80:pname) (A_142:pname) (B_79:(pname->Prop)), (((((member_pname A_142) B_79)->False)->(((eq pname) A_142) B_80))->((member_pname A_142) ((insert_pname B_80) B_79)))). % Axiom fact_295_insertE:(forall (A_141:x_a) (B_78:x_a) (A_140:(x_a->Prop)), (((member_a A_141) ((insert_a B_78) A_140))->((not (((eq x_a) A_141) B_78))->((member_a A_141) A_140)))). % Axiom fact_296_insertE:(forall (A_141:int) (B_78:int) (A_140:(int->Prop)), (((member_int A_141) ((insert_int B_78) A_140))->((not (((eq int) A_141) B_78))->((member_int A_141) A_140)))). % Axiom fact_297_insertE:(forall (A_141:nat) (B_78:nat) (A_140:(nat->Prop)), (((member_nat A_141) ((insert_nat B_78) A_140))->((not (((eq nat) A_141) B_78))->((member_nat A_141) A_140)))). % Axiom fact_298_insertE:(forall (A_141:pname) (B_78:pname) (A_140:(pname->Prop)), (((member_pname A_141) ((insert_pname B_78) A_140))->((not (((eq pname) A_141) B_78))->((member_pname A_141) A_140)))). % Axiom fact_299_zero__induct__lemma:(forall (I_1:nat) (P:(nat->Prop)) (K:nat), ((P K)->((forall (N_1:nat), ((P (suc N_1))->(P N_1)))->(P ((minus_minus_nat K) I_1))))). % Axiom fact_300_Suc__le__D:(forall (N:nat) (M_3:nat), (((ord_less_eq_nat (suc N)) M_3)->((ex nat) (fun (M_1:nat)=> (((eq nat) M_3) (suc M_1)))))). % Axiom fact_301_order__refl:(forall (X_49:(int->Prop)), ((ord_less_eq_int_o X_49) X_49)). % Axiom fact_302_order__refl:(forall (X_49:(nat->Prop)), ((ord_less_eq_nat_o X_49) X_49)). % Axiom fact_303_order__refl:(forall (X_49:int), ((ord_less_eq_int X_49) X_49)). % Axiom fact_304_order__refl:(forall (X_49:nat), ((ord_less_eq_nat X_49) X_49)). % Axiom fact_305_order__refl:(forall (X_49:(x_a->Prop)), ((ord_less_eq_a_o X_49) X_49)). % Axiom fact_306_linorder__linear:(forall (X_48:int) (Y_12:int), ((or ((ord_less_eq_int X_48) Y_12)) ((ord_less_eq_int Y_12) X_48))). % Axiom fact_307_linorder__linear:(forall (X_48:nat) (Y_12:nat), ((or ((ord_less_eq_nat X_48) Y_12)) ((ord_less_eq_nat Y_12) X_48))). % Axiom fact_308_order__eq__iff:(forall (X_47:(int->Prop)) (Y_11:(int->Prop)), ((iff (((eq (int->Prop)) X_47) Y_11)) ((and ((ord_less_eq_int_o X_47) Y_11)) ((ord_less_eq_int_o Y_11) X_47)))). % Axiom fact_309_order__eq__iff:(forall (X_47:(nat->Prop)) (Y_11:(nat->Prop)), ((iff (((eq (nat->Prop)) X_47) Y_11)) ((and ((ord_less_eq_nat_o X_47) Y_11)) ((ord_less_eq_nat_o Y_11) X_47)))). % Axiom fact_310_order__eq__iff:(forall (X_47:int) (Y_11:int), ((iff (((eq int) X_47) Y_11)) ((and ((ord_less_eq_int X_47) Y_11)) ((ord_less_eq_int Y_11) X_47)))). % Axiom fact_311_order__eq__iff:(forall (X_47:nat) (Y_11:nat), ((iff (((eq nat) X_47) Y_11)) ((and ((ord_less_eq_nat X_47) Y_11)) ((ord_less_eq_nat Y_11) X_47)))). % Axiom fact_312_order__eq__iff:(forall (X_47:(x_a->Prop)) (Y_11:(x_a->Prop)), ((iff (((eq (x_a->Prop)) X_47) Y_11)) ((and ((ord_less_eq_a_o X_47) Y_11)) ((ord_less_eq_a_o Y_11) X_47)))). % Axiom fact_313_order__eq__refl:(forall (X_46:(int->Prop)) (Y_10:(int->Prop)), ((((eq (int->Prop)) X_46) Y_10)->((ord_less_eq_int_o X_46) Y_10))). % Axiom fact_314_order__eq__refl:(forall (X_46:(nat->Prop)) (Y_10:(nat->Prop)), ((((eq (nat->Prop)) X_46) Y_10)->((ord_less_eq_nat_o X_46) Y_10))). % Axiom fact_315_order__eq__refl:(forall (X_46:int) (Y_10:int), ((((eq int) X_46) Y_10)->((ord_less_eq_int X_46) Y_10))). % Axiom fact_316_order__eq__refl:(forall (X_46:nat) (Y_10:nat), ((((eq nat) X_46) Y_10)->((ord_less_eq_nat X_46) Y_10))). % Axiom fact_317_order__eq__refl:(forall (X_46:(x_a->Prop)) (Y_10:(x_a->Prop)), ((((eq (x_a->Prop)) X_46) Y_10)->((ord_less_eq_a_o X_46) Y_10))). % Axiom fact_318_order__antisym__conv:(forall (Y_9:(int->Prop)) (X_45:(int->Prop)), (((ord_less_eq_int_o Y_9) X_45)->((iff ((ord_less_eq_int_o X_45) Y_9)) (((eq (int->Prop)) X_45) Y_9)))). % Axiom fact_319_order__antisym__conv:(forall (Y_9:(nat->Prop)) (X_45:(nat->Prop)), (((ord_less_eq_nat_o Y_9) X_45)->((iff ((ord_less_eq_nat_o X_45) Y_9)) (((eq (nat->Prop)) X_45) Y_9)))). % Axiom fact_320_order__antisym__conv:(forall (Y_9:int) (X_45:int), (((ord_less_eq_int Y_9) X_45)->((iff ((ord_less_eq_int X_45) Y_9)) (((eq int) X_45) Y_9)))). % Axiom fact_321_order__antisym__conv:(forall (Y_9:nat) (X_45:nat), (((ord_less_eq_nat Y_9) X_45)->((iff ((ord_less_eq_nat X_45) Y_9)) (((eq nat) X_45) Y_9)))). % Axiom fact_322_order__antisym__conv:(forall (Y_9:(x_a->Prop)) (X_45:(x_a->Prop)), (((ord_less_eq_a_o Y_9) X_45)->((iff ((ord_less_eq_a_o X_45) Y_9)) (((eq (x_a->Prop)) X_45) Y_9)))). % Axiom fact_323_ord__eq__le__trans:(forall (C_32:(int->Prop)) (A_139:(int->Prop)) (B_77:(int->Prop)), ((((eq (int->Prop)) A_139) B_77)->(((ord_less_eq_int_o B_77) C_32)->((ord_less_eq_int_o A_139) C_32)))). % Axiom fact_324_ord__eq__le__trans:(forall (C_32:(nat->Prop)) (A_139:(nat->Prop)) (B_77:(nat->Prop)), ((((eq (nat->Prop)) A_139) B_77)->(((ord_less_eq_nat_o B_77) C_32)->((ord_less_eq_nat_o A_139) C_32)))). % Axiom fact_325_ord__eq__le__trans:(forall (C_32:int) (A_139:int) (B_77:int), ((((eq int) A_139) B_77)->(((ord_less_eq_int B_77) C_32)->((ord_less_eq_int A_139) C_32)))). % Axiom fact_326_ord__eq__le__trans:(forall (C_32:nat) (A_139:nat) (B_77:nat), ((((eq nat) A_139) B_77)->(((ord_less_eq_nat B_77) C_32)->((ord_less_eq_nat A_139) C_32)))). % Axiom fact_327_ord__eq__le__trans:(forall (C_32:(x_a->Prop)) (A_139:(x_a->Prop)) (B_77:(x_a->Prop)), ((((eq (x_a->Prop)) A_139) B_77)->(((ord_less_eq_a_o B_77) C_32)->((ord_less_eq_a_o A_139) C_32)))). % Axiom fact_328_xt1_I3_J:(forall (C_31:(int->Prop)) (A_138:(int->Prop)) (B_76:(int->Prop)), ((((eq (int->Prop)) A_138) B_76)->(((ord_less_eq_int_o C_31) B_76)->((ord_less_eq_int_o C_31) A_138)))). % Axiom fact_329_xt1_I3_J:(forall (C_31:(nat->Prop)) (A_138:(nat->Prop)) (B_76:(nat->Prop)), ((((eq (nat->Prop)) A_138) B_76)->(((ord_less_eq_nat_o C_31) B_76)->((ord_less_eq_nat_o C_31) A_138)))). % Axiom fact_330_xt1_I3_J:(forall (C_31:int) (A_138:int) (B_76:int), ((((eq int) A_138) B_76)->(((ord_less_eq_int C_31) B_76)->((ord_less_eq_int C_31) A_138)))). % Axiom fact_331_xt1_I3_J:(forall (C_31:nat) (A_138:nat) (B_76:nat), ((((eq nat) A_138) B_76)->(((ord_less_eq_nat C_31) B_76)->((ord_less_eq_nat C_31) A_138)))). % Axiom fact_332_xt1_I3_J:(forall (C_31:(x_a->Prop)) (A_138:(x_a->Prop)) (B_76:(x_a->Prop)), ((((eq (x_a->Prop)) A_138) B_76)->(((ord_less_eq_a_o C_31) B_76)->((ord_less_eq_a_o C_31) A_138)))). % Axiom fact_333_ord__le__eq__trans:(forall (C_30:(int->Prop)) (A_137:(int->Prop)) (B_75:(int->Prop)), (((ord_less_eq_int_o A_137) B_75)->((((eq (int->Prop)) B_75) C_30)->((ord_less_eq_int_o A_137) C_30)))). % Axiom fact_334_ord__le__eq__trans:(forall (C_30:(nat->Prop)) (A_137:(nat->Prop)) (B_75:(nat->Prop)), (((ord_less_eq_nat_o A_137) B_75)->((((eq (nat->Prop)) B_75) C_30)->((ord_less_eq_nat_o A_137) C_30)))). % Axiom fact_335_ord__le__eq__trans:(forall (C_30:int) (A_137:int) (B_75:int), (((ord_less_eq_int A_137) B_75)->((((eq int) B_75) C_30)->((ord_less_eq_int A_137) C_30)))). % Axiom fact_336_ord__le__eq__trans:(forall (C_30:nat) (A_137:nat) (B_75:nat), (((ord_less_eq_nat A_137) B_75)->((((eq nat) B_75) C_30)->((ord_less_eq_nat A_137) C_30)))). % Axiom fact_337_ord__le__eq__trans:(forall (C_30:(x_a->Prop)) (A_137:(x_a->Prop)) (B_75:(x_a->Prop)), (((ord_less_eq_a_o A_137) B_75)->((((eq (x_a->Prop)) B_75) C_30)->((ord_less_eq_a_o A_137) C_30)))). % Axiom fact_338_xt1_I4_J:(forall (C_29:(int->Prop)) (B_74:(int->Prop)) (A_136:(int->Prop)), (((ord_less_eq_int_o B_74) A_136)->((((eq (int->Prop)) B_74) C_29)->((ord_less_eq_int_o C_29) A_136)))). % Axiom fact_339_xt1_I4_J:(forall (C_29:(nat->Prop)) (B_74:(nat->Prop)) (A_136:(nat->Prop)), (((ord_less_eq_nat_o B_74) A_136)->((((eq (nat->Prop)) B_74) C_29)->((ord_less_eq_nat_o C_29) A_136)))). % Axiom fact_340_xt1_I4_J:(forall (C_29:int) (B_74:int) (A_136:int), (((ord_less_eq_int B_74) A_136)->((((eq int) B_74) C_29)->((ord_less_eq_int C_29) A_136)))). % Axiom fact_341_xt1_I4_J:(forall (C_29:nat) (B_74:nat) (A_136:nat), (((ord_less_eq_nat B_74) A_136)->((((eq nat) B_74) C_29)->((ord_less_eq_nat C_29) A_136)))). % Axiom fact_342_xt1_I4_J:(forall (C_29:(x_a->Prop)) (B_74:(x_a->Prop)) (A_136:(x_a->Prop)), (((ord_less_eq_a_o B_74) A_136)->((((eq (x_a->Prop)) B_74) C_29)->((ord_less_eq_a_o C_29) A_136)))). % Axiom fact_343_order__antisym:(forall (X_44:(int->Prop)) (Y_8:(int->Prop)), (((ord_less_eq_int_o X_44) Y_8)->(((ord_less_eq_int_o Y_8) X_44)->(((eq (int->Prop)) X_44) Y_8)))). % Axiom fact_344_order__antisym:(forall (X_44:(nat->Prop)) (Y_8:(nat->Prop)), (((ord_less_eq_nat_o X_44) Y_8)->(((ord_less_eq_nat_o Y_8) X_44)->(((eq (nat->Prop)) X_44) Y_8)))). % Axiom fact_345_order__antisym:(forall (X_44:int) (Y_8:int), (((ord_less_eq_int X_44) Y_8)->(((ord_less_eq_int Y_8) X_44)->(((eq int) X_44) Y_8)))). % Axiom fact_346_order__antisym:(forall (X_44:nat) (Y_8:nat), (((ord_less_eq_nat X_44) Y_8)->(((ord_less_eq_nat Y_8) X_44)->(((eq nat) X_44) Y_8)))). % Axiom fact_347_order__antisym:(forall (X_44:(x_a->Prop)) (Y_8:(x_a->Prop)), (((ord_less_eq_a_o X_44) Y_8)->(((ord_less_eq_a_o Y_8) X_44)->(((eq (x_a->Prop)) X_44) Y_8)))). % Axiom fact_348_order__trans:(forall (Z_6:(int->Prop)) (X_43:(int->Prop)) (Y_7:(int->Prop)), (((ord_less_eq_int_o X_43) Y_7)->(((ord_less_eq_int_o Y_7) Z_6)->((ord_less_eq_int_o X_43) Z_6)))). % Axiom fact_349_order__trans:(forall (Z_6:(nat->Prop)) (X_43:(nat->Prop)) (Y_7:(nat->Prop)), (((ord_less_eq_nat_o X_43) Y_7)->(((ord_less_eq_nat_o Y_7) Z_6)->((ord_less_eq_nat_o X_43) Z_6)))). % Axiom fact_350_order__trans:(forall (Z_6:int) (X_43:int) (Y_7:int), (((ord_less_eq_int X_43) Y_7)->(((ord_less_eq_int Y_7) Z_6)->((ord_less_eq_int X_43) Z_6)))). % Axiom fact_351_order__trans:(forall (Z_6:nat) (X_43:nat) (Y_7:nat), (((ord_less_eq_nat X_43) Y_7)->(((ord_less_eq_nat Y_7) Z_6)->((ord_less_eq_nat X_43) Z_6)))). % Axiom fact_352_order__trans:(forall (Z_6:(x_a->Prop)) (X_43:(x_a->Prop)) (Y_7:(x_a->Prop)), (((ord_less_eq_a_o X_43) Y_7)->(((ord_less_eq_a_o Y_7) Z_6)->((ord_less_eq_a_o X_43) Z_6)))). % Axiom fact_353_xt1_I5_J:(forall (Y_6:(int->Prop)) (X_42:(int->Prop)), (((ord_less_eq_int_o Y_6) X_42)->(((ord_less_eq_int_o X_42) Y_6)->(((eq (int->Prop)) X_42) Y_6)))). % Axiom fact_354_xt1_I5_J:(forall (Y_6:(nat->Prop)) (X_42:(nat->Prop)), (((ord_less_eq_nat_o Y_6) X_42)->(((ord_less_eq_nat_o X_42) Y_6)->(((eq (nat->Prop)) X_42) Y_6)))). % Axiom fact_355_xt1_I5_J:(forall (Y_6:int) (X_42:int), (((ord_less_eq_int Y_6) X_42)->(((ord_less_eq_int X_42) Y_6)->(((eq int) X_42) Y_6)))). % Axiom fact_356_xt1_I5_J:(forall (Y_6:nat) (X_42:nat), (((ord_less_eq_nat Y_6) X_42)->(((ord_less_eq_nat X_42) Y_6)->(((eq nat) X_42) Y_6)))). % Axiom fact_357_xt1_I5_J:(forall (Y_6:(x_a->Prop)) (X_42:(x_a->Prop)), (((ord_less_eq_a_o Y_6) X_42)->(((ord_less_eq_a_o X_42) Y_6)->(((eq (x_a->Prop)) X_42) Y_6)))). % Axiom fact_358_xt1_I6_J:(forall (Z_5:(int->Prop)) (Y_5:(int->Prop)) (X_41:(int->Prop)), (((ord_less_eq_int_o Y_5) X_41)->(((ord_less_eq_int_o Z_5) Y_5)->((ord_less_eq_int_o Z_5) X_41)))). % Axiom fact_359_xt1_I6_J:(forall (Z_5:(nat->Prop)) (Y_5:(nat->Prop)) (X_41:(nat->Prop)), (((ord_less_eq_nat_o Y_5) X_41)->(((ord_less_eq_nat_o Z_5) Y_5)->((ord_less_eq_nat_o Z_5) X_41)))). % Axiom fact_360_xt1_I6_J:(forall (Z_5:int) (Y_5:int) (X_41:int), (((ord_less_eq_int Y_5) X_41)->(((ord_less_eq_int Z_5) Y_5)->((ord_less_eq_int Z_5) X_41)))). % Axiom fact_361_xt1_I6_J:(forall (Z_5:nat) (Y_5:nat) (X_41:nat), (((ord_less_eq_nat Y_5) X_41)->(((ord_less_eq_nat Z_5) Y_5)->((ord_less_eq_nat Z_5) X_41)))). % Axiom fact_362_xt1_I6_J:(forall (Z_5:(x_a->Prop)) (Y_5:(x_a->Prop)) (X_41:(x_a->Prop)), (((ord_less_eq_a_o Y_5) X_41)->(((ord_less_eq_a_o Z_5) Y_5)->((ord_less_eq_a_o Z_5) X_41)))). % Axiom fact_363_linorder__le__cases:(forall (X_40:int) (Y_4:int), ((((ord_less_eq_int X_40) Y_4)->False)->((ord_less_eq_int Y_4) X_40))). % Axiom fact_364_linorder__le__cases:(forall (X_40:nat) (Y_4:nat), ((((ord_less_eq_nat X_40) Y_4)->False)->((ord_less_eq_nat Y_4) X_40))). % Axiom fact_365_insertI1:(forall (A_135:x_a) (B_73:(x_a->Prop)), ((member_a A_135) ((insert_a A_135) B_73))). % Axiom fact_366_insertI1:(forall (A_135:int) (B_73:(int->Prop)), ((member_int A_135) ((insert_int A_135) B_73))). % Axiom fact_367_insertI1:(forall (A_135:nat) (B_73:(nat->Prop)), ((member_nat A_135) ((insert_nat A_135) B_73))). % Axiom fact_368_insertI1:(forall (A_135:pname) (B_73:(pname->Prop)), ((member_pname A_135) ((insert_pname A_135) B_73))). % Axiom fact_369_insert__compr:(forall (A_134:x_a) (B_72:(x_a->Prop)), (((eq (x_a->Prop)) ((insert_a A_134) B_72)) (collect_a (fun (X_1:x_a)=> ((or (((eq x_a) X_1) A_134)) ((member_a X_1) B_72)))))). % Axiom fact_370_insert__compr:(forall (A_134:int) (B_72:(int->Prop)), (((eq (int->Prop)) ((insert_int A_134) B_72)) (collect_int (fun (X_1:int)=> ((or (((eq int) X_1) A_134)) ((member_int X_1) B_72)))))). % Axiom fact_371_insert__compr:(forall (A_134:nat) (B_72:(nat->Prop)), (((eq (nat->Prop)) ((insert_nat A_134) B_72)) (collect_nat (fun (X_1:nat)=> ((or (((eq nat) X_1) A_134)) ((member_nat X_1) B_72)))))). % Axiom fact_372_insert__compr:(forall (A_134:pname) (B_72:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname A_134) B_72)) (collect_pname (fun (X_1:pname)=> ((or (((eq pname) X_1) A_134)) ((member_pname X_1) B_72)))))). % Axiom fact_373_insert__Collect:(forall (A_133:x_a) (P_11:(x_a->Prop)), (((eq (x_a->Prop)) ((insert_a A_133) (collect_a P_11))) (collect_a (fun (U_1:x_a)=> (((fun (X:Prop) (Y:Prop)=> (X->Y)) (not (((eq x_a) U_1) A_133))) (P_11 U_1)))))). % Axiom fact_374_insert__Collect:(forall (A_133:int) (P_11:(int->Prop)), (((eq (int->Prop)) ((insert_int A_133) (collect_int P_11))) (collect_int (fun (U_1:int)=> (((fun (X:Prop) (Y:Prop)=> (X->Y)) (not (((eq int) U_1) A_133))) (P_11 U_1)))))). % Axiom fact_375_insert__Collect:(forall (A_133:nat) (P_11:(nat->Prop)), (((eq (nat->Prop)) ((insert_nat A_133) (collect_nat P_11))) (collect_nat (fun (U_1:nat)=> (((fun (X:Prop) (Y:Prop)=> (X->Y)) (not (((eq nat) U_1) A_133))) (P_11 U_1)))))). % Axiom fact_376_mem__def:(forall (X_39:int) (A_132:(int->Prop)), ((iff ((member_int X_39) A_132)) (A_132 X_39))). % Axiom fact_377_mem__def:(forall (X_39:nat) (A_132:(nat->Prop)), ((iff ((member_nat X_39) A_132)) (A_132 X_39))). % Axiom fact_378_mem__def:(forall (X_39:x_a) (A_132:(x_a->Prop)), ((iff ((member_a X_39) A_132)) (A_132 X_39))). % Axiom fact_379_mem__def:(forall (X_39:pname) (A_132:(pname->Prop)), ((iff ((member_pname X_39) A_132)) (A_132 X_39))). % Axiom fact_380_Collect__def:(forall (P_10:(int->Prop)), (((eq (int->Prop)) (collect_int P_10)) P_10)). % Axiom fact_381_Collect__def:(forall (P_10:(nat->Prop)), (((eq (nat->Prop)) (collect_nat P_10)) P_10)). % Axiom fact_382_insert__absorb2:(forall (X_38:x_a) (A_131:(x_a->Prop)), (((eq (x_a->Prop)) ((insert_a X_38) ((insert_a X_38) A_131))) ((insert_a X_38) A_131))). % Axiom fact_383_insert__commute:(forall (X_37:x_a) (Y_3:x_a) (A_130:(x_a->Prop)), (((eq (x_a->Prop)) ((insert_a X_37) ((insert_a Y_3) A_130))) ((insert_a Y_3) ((insert_a X_37) A_130)))). % Axiom fact_384_insert__iff:(forall (A_129:x_a) (B_71:x_a) (A_128:(x_a->Prop)), ((iff ((member_a A_129) ((insert_a B_71) A_128))) ((or (((eq x_a) A_129) B_71)) ((member_a A_129) A_128)))). % Axiom fact_385_insert__iff:(forall (A_129:int) (B_71:int) (A_128:(int->Prop)), ((iff ((member_int A_129) ((insert_int B_71) A_128))) ((or (((eq int) A_129) B_71)) ((member_int A_129) A_128)))). % Axiom fact_386_insert__iff:(forall (A_129:nat) (B_71:nat) (A_128:(nat->Prop)), ((iff ((member_nat A_129) ((insert_nat B_71) A_128))) ((or (((eq nat) A_129) B_71)) ((member_nat A_129) A_128)))). % Axiom fact_387_insert__iff:(forall (A_129:pname) (B_71:pname) (A_128:(pname->Prop)), ((iff ((member_pname A_129) ((insert_pname B_71) A_128))) ((or (((eq pname) A_129) B_71)) ((member_pname A_129) A_128)))). % Axiom fact_388_insert__code:(forall (Y_2:x_a) (A_127:(x_a->Prop)) (X_36:x_a), ((iff (((insert_a Y_2) A_127) X_36)) ((or (((eq x_a) Y_2) X_36)) (A_127 X_36)))). % Axiom fact_389_insert__ident:(forall (B_70:(x_a->Prop)) (X_35:x_a) (A_126:(x_a->Prop)), ((((member_a X_35) A_126)->False)->((((member_a X_35) B_70)->False)->((iff (((eq (x_a->Prop)) ((insert_a X_35) A_126)) ((insert_a X_35) B_70))) (((eq (x_a->Prop)) A_126) B_70))))). % Axiom fact_390_insert__ident:(forall (B_70:(int->Prop)) (X_35:int) (A_126:(int->Prop)), ((((member_int X_35) A_126)->False)->((((member_int X_35) B_70)->False)->((iff (((eq (int->Prop)) ((insert_int X_35) A_126)) ((insert_int X_35) B_70))) (((eq (int->Prop)) A_126) B_70))))). % Axiom fact_391_insert__ident:(forall (B_70:(nat->Prop)) (X_35:nat) (A_126:(nat->Prop)), ((((member_nat X_35) A_126)->False)->((((member_nat X_35) B_70)->False)->((iff (((eq (nat->Prop)) ((insert_nat X_35) A_126)) ((insert_nat X_35) B_70))) (((eq (nat->Prop)) A_126) B_70))))). % Axiom fact_392_insert__ident:(forall (B_70:(pname->Prop)) (X_35:pname) (A_126:(pname->Prop)), ((((member_pname X_35) A_126)->False)->((((member_pname X_35) B_70)->False)->((iff (((eq (pname->Prop)) ((insert_pname X_35) A_126)) ((insert_pname X_35) B_70))) (((eq (pname->Prop)) A_126) B_70))))). % Axiom fact_393_insertI2:(forall (B_69:x_a) (A_125:x_a) (B_68:(x_a->Prop)), (((member_a A_125) B_68)->((member_a A_125) ((insert_a B_69) B_68)))). % Axiom fact_394_insertI2:(forall (B_69:int) (A_125:int) (B_68:(int->Prop)), (((member_int A_125) B_68)->((member_int A_125) ((insert_int B_69) B_68)))). % Axiom fact_395_insertI2:(forall (B_69:nat) (A_125:nat) (B_68:(nat->Prop)), (((member_nat A_125) B_68)->((member_nat A_125) ((insert_nat B_69) B_68)))). % Axiom fact_396_insertI2:(forall (B_69:pname) (A_125:pname) (B_68:(pname->Prop)), (((member_pname A_125) B_68)->((member_pname A_125) ((insert_pname B_69) B_68)))). % Axiom fact_397_insert__absorb:(forall (A_124:x_a) (A_123:(x_a->Prop)), (((member_a A_124) A_123)->(((eq (x_a->Prop)) ((insert_a A_124) A_123)) A_123))). % Axiom fact_398_insert__absorb:(forall (A_124:int) (A_123:(int->Prop)), (((member_int A_124) A_123)->(((eq (int->Prop)) ((insert_int A_124) A_123)) A_123))). % Axiom fact_399_insert__absorb:(forall (A_124:nat) (A_123:(nat->Prop)), (((member_nat A_124) A_123)->(((eq (nat->Prop)) ((insert_nat A_124) A_123)) A_123))). % Axiom fact_400_insert__absorb:(forall (A_124:pname) (A_123:(pname->Prop)), (((member_pname A_124) A_123)->(((eq (pname->Prop)) ((insert_pname A_124) A_123)) A_123))). % Axiom fact_401_subset__refl:(forall (A_122:(int->Prop)), ((ord_less_eq_int_o A_122) A_122)). % Axiom fact_402_subset__refl:(forall (A_122:(nat->Prop)), ((ord_less_eq_nat_o A_122) A_122)). % Axiom fact_403_subset__refl:(forall (A_122:(x_a->Prop)), ((ord_less_eq_a_o A_122) A_122)). % Axiom fact_404_set__eq__subset:(forall (A_121:(int->Prop)) (B_67:(int->Prop)), ((iff (((eq (int->Prop)) A_121) B_67)) ((and ((ord_less_eq_int_o A_121) B_67)) ((ord_less_eq_int_o B_67) A_121)))). % Axiom fact_405_set__eq__subset:(forall (A_121:(nat->Prop)) (B_67:(nat->Prop)), ((iff (((eq (nat->Prop)) A_121) B_67)) ((and ((ord_less_eq_nat_o A_121) B_67)) ((ord_less_eq_nat_o B_67) A_121)))). % Axiom fact_406_set__eq__subset:(forall (A_121:(x_a->Prop)) (B_67:(x_a->Prop)), ((iff (((eq (x_a->Prop)) A_121) B_67)) ((and ((ord_less_eq_a_o A_121) B_67)) ((ord_less_eq_a_o B_67) A_121)))). % Axiom fact_407_equalityD1:(forall (A_120:(int->Prop)) (B_66:(int->Prop)), ((((eq (int->Prop)) A_120) B_66)->((ord_less_eq_int_o A_120) B_66))). % Axiom fact_408_equalityD1:(forall (A_120:(nat->Prop)) (B_66:(nat->Prop)), ((((eq (nat->Prop)) A_120) B_66)->((ord_less_eq_nat_o A_120) B_66))). % Axiom fact_409_equalityD1:(forall (A_120:(x_a->Prop)) (B_66:(x_a->Prop)), ((((eq (x_a->Prop)) A_120) B_66)->((ord_less_eq_a_o A_120) B_66))). % Axiom fact_410_equalityD2:(forall (A_119:(int->Prop)) (B_65:(int->Prop)), ((((eq (int->Prop)) A_119) B_65)->((ord_less_eq_int_o B_65) A_119))). % Axiom fact_411_equalityD2:(forall (A_119:(nat->Prop)) (B_65:(nat->Prop)), ((((eq (nat->Prop)) A_119) B_65)->((ord_less_eq_nat_o B_65) A_119))). % Axiom fact_412_equalityD2:(forall (A_119:(x_a->Prop)) (B_65:(x_a->Prop)), ((((eq (x_a->Prop)) A_119) B_65)->((ord_less_eq_a_o B_65) A_119))). % Axiom fact_413_in__mono:(forall (X_34:int) (A_118:(int->Prop)) (B_64:(int->Prop)), (((ord_less_eq_int_o A_118) B_64)->(((member_int X_34) A_118)->((member_int X_34) B_64)))). % Axiom fact_414_in__mono:(forall (X_34:nat) (A_118:(nat->Prop)) (B_64:(nat->Prop)), (((ord_less_eq_nat_o A_118) B_64)->(((member_nat X_34) A_118)->((member_nat X_34) B_64)))). % Axiom fact_415_in__mono:(forall (X_34:x_a) (A_118:(x_a->Prop)) (B_64:(x_a->Prop)), (((ord_less_eq_a_o A_118) B_64)->(((member_a X_34) A_118)->((member_a X_34) B_64)))). % Axiom fact_416_in__mono:(forall (X_34:pname) (A_118:(pname->Prop)) (B_64:(pname->Prop)), (((ord_less_eq_pname_o A_118) B_64)->(((member_pname X_34) A_118)->((member_pname X_34) B_64)))). % Axiom fact_417_set__rev__mp:(forall (B_63:(int->Prop)) (X_33:int) (A_117:(int->Prop)), (((member_int X_33) A_117)->(((ord_less_eq_int_o A_117) B_63)->((member_int X_33) B_63)))). % Axiom fact_418_set__rev__mp:(forall (B_63:(nat->Prop)) (X_33:nat) (A_117:(nat->Prop)), (((member_nat X_33) A_117)->(((ord_less_eq_nat_o A_117) B_63)->((member_nat X_33) B_63)))). % Axiom fact_419_set__rev__mp:(forall (B_63:(x_a->Prop)) (X_33:x_a) (A_117:(x_a->Prop)), (((member_a X_33) A_117)->(((ord_less_eq_a_o A_117) B_63)->((member_a X_33) B_63)))). % Axiom fact_420_set__rev__mp:(forall (B_63:(pname->Prop)) (X_33:pname) (A_117:(pname->Prop)), (((member_pname X_33) A_117)->(((ord_less_eq_pname_o A_117) B_63)->((member_pname X_33) B_63)))). % Axiom fact_421_set__mp:(forall (X_32:int) (A_116:(int->Prop)) (B_62:(int->Prop)), (((ord_less_eq_int_o A_116) B_62)->(((member_int X_32) A_116)->((member_int X_32) B_62)))). % Axiom fact_422_set__mp:(forall (X_32:nat) (A_116:(nat->Prop)) (B_62:(nat->Prop)), (((ord_less_eq_nat_o A_116) B_62)->(((member_nat X_32) A_116)->((member_nat X_32) B_62)))). % Axiom fact_423_set__mp:(forall (X_32:x_a) (A_116:(x_a->Prop)) (B_62:(x_a->Prop)), (((ord_less_eq_a_o A_116) B_62)->(((member_a X_32) A_116)->((member_a X_32) B_62)))). % Axiom fact_424_set__mp:(forall (X_32:pname) (A_116:(pname->Prop)) (B_62:(pname->Prop)), (((ord_less_eq_pname_o A_116) B_62)->(((member_pname X_32) A_116)->((member_pname X_32) B_62)))). % Axiom fact_425_subset__trans:(forall (C_28:(int->Prop)) (A_115:(int->Prop)) (B_61:(int->Prop)), (((ord_less_eq_int_o A_115) B_61)->(((ord_less_eq_int_o B_61) C_28)->((ord_less_eq_int_o A_115) C_28)))). % Axiom fact_426_subset__trans:(forall (C_28:(nat->Prop)) (A_115:(nat->Prop)) (B_61:(nat->Prop)), (((ord_less_eq_nat_o A_115) B_61)->(((ord_less_eq_nat_o B_61) C_28)->((ord_less_eq_nat_o A_115) C_28)))). % Axiom fact_427_subset__trans:(forall (C_28:(x_a->Prop)) (A_115:(x_a->Prop)) (B_61:(x_a->Prop)), (((ord_less_eq_a_o A_115) B_61)->(((ord_less_eq_a_o B_61) C_28)->((ord_less_eq_a_o A_115) C_28)))). % Axiom fact_428_equalityE:(forall (A_114:(int->Prop)) (B_60:(int->Prop)), ((((eq (int->Prop)) A_114) B_60)->((((ord_less_eq_int_o A_114) B_60)->(((ord_less_eq_int_o B_60) A_114)->False))->False))). % Axiom fact_429_equalityE:(forall (A_114:(nat->Prop)) (B_60:(nat->Prop)), ((((eq (nat->Prop)) A_114) B_60)->((((ord_less_eq_nat_o A_114) B_60)->(((ord_less_eq_nat_o B_60) A_114)->False))->False))). % Axiom fact_430_equalityE:(forall (A_114:(x_a->Prop)) (B_60:(x_a->Prop)), ((((eq (x_a->Prop)) A_114) B_60)->((((ord_less_eq_a_o A_114) B_60)->(((ord_less_eq_a_o B_60) A_114)->False))->False))). % Axiom fact_431_image__iff:(forall (Z_4:int) (F_35:(nat->int)) (A_113:(nat->Prop)), ((iff ((member_int Z_4) ((image_nat_int F_35) A_113))) ((ex nat) (fun (X_1:nat)=> ((and ((member_nat X_1) A_113)) (((eq int) Z_4) (F_35 X_1))))))). % Axiom fact_432_image__iff:(forall (Z_4:x_a) (F_35:(pname->x_a)) (A_113:(pname->Prop)), ((iff ((member_a Z_4) ((image_pname_a F_35) A_113))) ((ex pname) (fun (X_1:pname)=> ((and ((member_pname X_1) A_113)) (((eq x_a) Z_4) (F_35 X_1))))))). % Axiom fact_433_imageI:(forall (F_34:(nat->int)) (X_31:nat) (A_112:(nat->Prop)), (((member_nat X_31) A_112)->((member_int (F_34 X_31)) ((image_nat_int F_34) A_112)))). % Axiom fact_434_imageI:(forall (F_34:(pname->x_a)) (X_31:pname) (A_112:(pname->Prop)), (((member_pname X_31) A_112)->((member_a (F_34 X_31)) ((image_pname_a F_34) A_112)))). % Axiom fact_435_rev__image__eqI:(forall (B_59:int) (F_33:(nat->int)) (X_30:nat) (A_111:(nat->Prop)), (((member_nat X_30) A_111)->((((eq int) B_59) (F_33 X_30))->((member_int B_59) ((image_nat_int F_33) A_111))))). % Axiom fact_436_rev__image__eqI:(forall (B_59:x_a) (F_33:(pname->x_a)) (X_30:pname) (A_111:(pname->Prop)), (((member_pname X_30) A_111)->((((eq x_a) B_59) (F_33 X_30))->((member_a B_59) ((image_pname_a F_33) A_111))))). % Axiom fact_437_insert__compr__raw:(forall (X_1:x_a) (Xa:(x_a->Prop)), (((eq (x_a->Prop)) ((insert_a X_1) Xa)) (collect_a (fun (Y_1:x_a)=> ((or (((eq x_a) Y_1) X_1)) ((member_a Y_1) Xa)))))). % Axiom fact_438_insert__compr__raw:(forall (X_1:int) (Xa:(int->Prop)), (((eq (int->Prop)) ((insert_int X_1) Xa)) (collect_int (fun (Y_1:int)=> ((or (((eq int) Y_1) X_1)) ((member_int Y_1) Xa)))))). % Axiom fact_439_insert__compr__raw:(forall (X_1:nat) (Xa:(nat->Prop)), (((eq (nat->Prop)) ((insert_nat X_1) Xa)) (collect_nat (fun (Y_1:nat)=> ((or (((eq nat) Y_1) X_1)) ((member_nat Y_1) Xa)))))). % Axiom fact_440_insert__compr__raw:(forall (X_1:pname) (Xa:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname X_1) Xa)) (collect_pname (fun (Y_1:pname)=> ((or (((eq pname) Y_1) X_1)) ((member_pname Y_1) Xa)))))). % Axiom fact_441_le__fun__def:(forall (F_32:(int->Prop)) (G_4:(int->Prop)), ((iff ((ord_less_eq_int_o F_32) G_4)) (forall (X_1:int), ((ord_less_eq_o (F_32 X_1)) (G_4 X_1))))). % Axiom fact_442_le__fun__def:(forall (F_32:(nat->Prop)) (G_4:(nat->Prop)), ((iff ((ord_less_eq_nat_o F_32) G_4)) (forall (X_1:nat), ((ord_less_eq_o (F_32 X_1)) (G_4 X_1))))). % Axiom fact_443_le__fun__def:(forall (F_32:(x_a->Prop)) (G_4:(x_a->Prop)), ((iff ((ord_less_eq_a_o F_32) G_4)) (forall (X_1:x_a), ((ord_less_eq_o (F_32 X_1)) (G_4 X_1))))). % Axiom fact_444_le__funD:(forall (X_29:int) (F_31:(int->Prop)) (G_3:(int->Prop)), (((ord_less_eq_int_o F_31) G_3)->((ord_less_eq_o (F_31 X_29)) (G_3 X_29)))). % Axiom fact_445_le__funD:(forall (X_29:nat) (F_31:(nat->Prop)) (G_3:(nat->Prop)), (((ord_less_eq_nat_o F_31) G_3)->((ord_less_eq_o (F_31 X_29)) (G_3 X_29)))). % Axiom fact_446_le__funD:(forall (X_29:x_a) (F_31:(x_a->Prop)) (G_3:(x_a->Prop)), (((ord_less_eq_a_o F_31) G_3)->((ord_less_eq_o (F_31 X_29)) (G_3 X_29)))). % Axiom fact_447_le__funE:(forall (X_28:int) (F_30:(int->Prop)) (G_2:(int->Prop)), (((ord_less_eq_int_o F_30) G_2)->((ord_less_eq_o (F_30 X_28)) (G_2 X_28)))). % Axiom fact_448_le__funE:(forall (X_28:nat) (F_30:(nat->Prop)) (G_2:(nat->Prop)), (((ord_less_eq_nat_o F_30) G_2)->((ord_less_eq_o (F_30 X_28)) (G_2 X_28)))). % Axiom fact_449_le__funE:(forall (X_28:x_a) (F_30:(x_a->Prop)) (G_2:(x_a->Prop)), (((ord_less_eq_a_o F_30) G_2)->((ord_less_eq_o (F_30 X_28)) (G_2 X_28)))). % Axiom fact_450_subset__insertI:(forall (B_58:(x_a->Prop)) (A_110:x_a), ((ord_less_eq_a_o B_58) ((insert_a A_110) B_58))). % Axiom fact_451_subset__insertI:(forall (B_58:(int->Prop)) (A_110:int), ((ord_less_eq_int_o B_58) ((insert_int A_110) B_58))). % Axiom fact_452_subset__insertI:(forall (B_58:(nat->Prop)) (A_110:nat), ((ord_less_eq_nat_o B_58) ((insert_nat A_110) B_58))). % Axiom fact_453_insert__subset:(forall (X_27:x_a) (A_109:(x_a->Prop)) (B_57:(x_a->Prop)), ((iff ((ord_less_eq_a_o ((insert_a X_27) A_109)) B_57)) ((and ((member_a X_27) B_57)) ((ord_less_eq_a_o A_109) B_57)))). % Axiom fact_454_insert__subset:(forall (X_27:int) (A_109:(int->Prop)) (B_57:(int->Prop)), ((iff ((ord_less_eq_int_o ((insert_int X_27) A_109)) B_57)) ((and ((member_int X_27) B_57)) ((ord_less_eq_int_o A_109) B_57)))). % Axiom fact_455_insert__subset:(forall (X_27:nat) (A_109:(nat->Prop)) (B_57:(nat->Prop)), ((iff ((ord_less_eq_nat_o ((insert_nat X_27) A_109)) B_57)) ((and ((member_nat X_27) B_57)) ((ord_less_eq_nat_o A_109) B_57)))). % Axiom fact_456_insert__subset:(forall (X_27:pname) (A_109:(pname->Prop)) (B_57:(pname->Prop)), ((iff ((ord_less_eq_pname_o ((insert_pname X_27) A_109)) B_57)) ((and ((member_pname X_27) B_57)) ((ord_less_eq_pname_o A_109) B_57)))). % Axiom fact_457_subset__insert:(forall (B_56:(x_a->Prop)) (X_26:x_a) (A_108:(x_a->Prop)), ((((member_a X_26) A_108)->False)->((iff ((ord_less_eq_a_o A_108) ((insert_a X_26) B_56))) ((ord_less_eq_a_o A_108) B_56)))). % Axiom fact_458_subset__insert:(forall (B_56:(int->Prop)) (X_26:int) (A_108:(int->Prop)), ((((member_int X_26) A_108)->False)->((iff ((ord_less_eq_int_o A_108) ((insert_int X_26) B_56))) ((ord_less_eq_int_o A_108) B_56)))). % Axiom fact_459_subset__insert:(forall (B_56:(nat->Prop)) (X_26:nat) (A_108:(nat->Prop)), ((((member_nat X_26) A_108)->False)->((iff ((ord_less_eq_nat_o A_108) ((insert_nat X_26) B_56))) ((ord_less_eq_nat_o A_108) B_56)))). % Axiom fact_460_subset__insert:(forall (B_56:(pname->Prop)) (X_26:pname) (A_108:(pname->Prop)), ((((member_pname X_26) A_108)->False)->((iff ((ord_less_eq_pname_o A_108) ((insert_pname X_26) B_56))) ((ord_less_eq_pname_o A_108) B_56)))). % Axiom fact_461_subset__insertI2:(forall (B_55:x_a) (A_107:(x_a->Prop)) (B_54:(x_a->Prop)), (((ord_less_eq_a_o A_107) B_54)->((ord_less_eq_a_o A_107) ((insert_a B_55) B_54)))). % Axiom fact_462_subset__insertI2:(forall (B_55:int) (A_107:(int->Prop)) (B_54:(int->Prop)), (((ord_less_eq_int_o A_107) B_54)->((ord_less_eq_int_o A_107) ((insert_int B_55) B_54)))). % Axiom fact_463_subset__insertI2:(forall (B_55:nat) (A_107:(nat->Prop)) (B_54:(nat->Prop)), (((ord_less_eq_nat_o A_107) B_54)->((ord_less_eq_nat_o A_107) ((insert_nat B_55) B_54)))). % Axiom fact_464_insert__mono:(forall (A_106:x_a) (C_27:(x_a->Prop)) (D_7:(x_a->Prop)), (((ord_less_eq_a_o C_27) D_7)->((ord_less_eq_a_o ((insert_a A_106) C_27)) ((insert_a A_106) D_7)))). % Axiom fact_465_insert__mono:(forall (A_106:int) (C_27:(int->Prop)) (D_7:(int->Prop)), (((ord_less_eq_int_o C_27) D_7)->((ord_less_eq_int_o ((insert_int A_106) C_27)) ((insert_int A_106) D_7)))). % Axiom fact_466_insert__mono:(forall (A_106:nat) (C_27:(nat->Prop)) (D_7:(nat->Prop)), (((ord_less_eq_nat_o C_27) D_7)->((ord_less_eq_nat_o ((insert_nat A_106) C_27)) ((insert_nat A_106) D_7)))). % Axiom fact_467_image__insert:(forall (F_29:(nat->int)) (A_105:nat) (B_53:(nat->Prop)), (((eq (int->Prop)) ((image_nat_int F_29) ((insert_nat A_105) B_53))) ((insert_int (F_29 A_105)) ((image_nat_int F_29) B_53)))). % Axiom fact_468_image__insert:(forall (F_29:(pname->x_a)) (A_105:pname) (B_53:(pname->Prop)), (((eq (x_a->Prop)) ((image_pname_a F_29) ((insert_pname A_105) B_53))) ((insert_a (F_29 A_105)) ((image_pname_a F_29) B_53)))). % Axiom fact_469_insert__image:(forall (F_28:(nat->int)) (X_25:nat) (A_104:(nat->Prop)), (((member_nat X_25) A_104)->(((eq (int->Prop)) ((insert_int (F_28 X_25)) ((image_nat_int F_28) A_104))) ((image_nat_int F_28) A_104)))). % Axiom fact_470_insert__image:(forall (F_28:(pname->x_a)) (X_25:pname) (A_104:(pname->Prop)), (((member_pname X_25) A_104)->(((eq (x_a->Prop)) ((insert_a (F_28 X_25)) ((image_pname_a F_28) A_104))) ((image_pname_a F_28) A_104)))). % Axiom fact_471_subset__image__iff:(forall (B_52:(int->Prop)) (F_27:(nat->int)) (A_103:(nat->Prop)), ((iff ((ord_less_eq_int_o B_52) ((image_nat_int F_27) A_103))) ((ex (nat->Prop)) (fun (AA:(nat->Prop))=> ((and ((ord_less_eq_nat_o AA) A_103)) (((eq (int->Prop)) B_52) ((image_nat_int F_27) AA))))))). % Axiom fact_472_subset__image__iff:(forall (B_52:(x_a->Prop)) (F_27:(pname->x_a)) (A_103:(pname->Prop)), ((iff ((ord_less_eq_a_o B_52) ((image_pname_a F_27) A_103))) ((ex (pname->Prop)) (fun (AA:(pname->Prop))=> ((and ((ord_less_eq_pname_o AA) A_103)) (((eq (x_a->Prop)) B_52) ((image_pname_a F_27) AA))))))). % Axiom fact_473_image__mono:(forall (F_26:(nat->int)) (A_102:(nat->Prop)) (B_51:(nat->Prop)), (((ord_less_eq_nat_o A_102) B_51)->((ord_less_eq_int_o ((image_nat_int F_26) A_102)) ((image_nat_int F_26) B_51)))). % Axiom fact_474_image__mono:(forall (F_26:(pname->x_a)) (A_102:(pname->Prop)) (B_51:(pname->Prop)), (((ord_less_eq_pname_o A_102) B_51)->((ord_less_eq_a_o ((image_pname_a F_26) A_102)) ((image_pname_a F_26) B_51)))). % Axiom fact_475_imageE:(forall (B_50:int) (F_25:(nat->int)) (A_101:(nat->Prop)), (((member_int B_50) ((image_nat_int F_25) A_101))->((forall (X_1:nat), ((((eq int) B_50) (F_25 X_1))->(((member_nat X_1) A_101)->False)))->False))). % Axiom fact_476_imageE:(forall (B_50:x_a) (F_25:(pname->x_a)) (A_101:(pname->Prop)), (((member_a B_50) ((image_pname_a F_25) A_101))->((forall (X_1:pname), ((((eq x_a) B_50) (F_25 X_1))->(((member_pname X_1) A_101)->False)))->False))). % Axiom fact_477_subsetI:(forall (B_49:(int->Prop)) (A_100:(int->Prop)), ((forall (X_1:int), (((member_int X_1) A_100)->((member_int X_1) B_49)))->((ord_less_eq_int_o A_100) B_49))). % Axiom fact_478_subsetI:(forall (B_49:(nat->Prop)) (A_100:(nat->Prop)), ((forall (X_1:nat), (((member_nat X_1) A_100)->((member_nat X_1) B_49)))->((ord_less_eq_nat_o A_100) B_49))). % Axiom fact_479_subsetI:(forall (B_49:(x_a->Prop)) (A_100:(x_a->Prop)), ((forall (X_1:x_a), (((member_a X_1) A_100)->((member_a X_1) B_49)))->((ord_less_eq_a_o A_100) B_49))). % Axiom fact_480_subsetI:(forall (B_49:(pname->Prop)) (A_100:(pname->Prop)), ((forall (X_1:pname), (((member_pname X_1) A_100)->((member_pname X_1) B_49)))->((ord_less_eq_pname_o A_100) B_49))). % Axiom fact_481_image__subsetI:(forall (F_24:(nat->int)) (B_48:(int->Prop)) (A_99:(nat->Prop)), ((forall (X_1:nat), (((member_nat X_1) A_99)->((member_int (F_24 X_1)) B_48)))->((ord_less_eq_int_o ((image_nat_int F_24) A_99)) B_48))). % Axiom fact_482_image__subsetI:(forall (F_24:(pname->x_a)) (B_48:(x_a->Prop)) (A_99:(pname->Prop)), ((forall (X_1:pname), (((member_pname X_1) A_99)->((member_a (F_24 X_1)) B_48)))->((ord_less_eq_a_o ((image_pname_a F_24) A_99)) B_48))). % Axiom fact_483_le__funI:(forall (F_23:(int->Prop)) (G_1:(int->Prop)), ((forall (X_1:int), ((ord_less_eq_o (F_23 X_1)) (G_1 X_1)))->((ord_less_eq_int_o F_23) G_1))). % Axiom fact_484_le__funI:(forall (F_23:(nat->Prop)) (G_1:(nat->Prop)), ((forall (X_1:nat), ((ord_less_eq_o (F_23 X_1)) (G_1 X_1)))->((ord_less_eq_nat_o F_23) G_1))). % Axiom fact_485_le__funI:(forall (F_23:(x_a->Prop)) (G_1:(x_a->Prop)), ((forall (X_1:x_a), ((ord_less_eq_o (F_23 X_1)) (G_1 X_1)))->((ord_less_eq_a_o F_23) G_1))). % Axiom fact_486_finite__nat__set__iff__bounded__le:(forall (N_2:(nat->Prop)), ((iff (finite_finite_nat N_2)) ((ex nat) (fun (M_1:nat)=> (forall (X_1:nat), (((member_nat X_1) N_2)->((ord_less_eq_nat X_1) M_1))))))). % Axiom fact_487_assms_I3_J:(forall (G:(x_a->Prop)) (C:com), ((wt C)->((forall (X_1:pname), (((member_pname X_1) u)->((p G) ((insert_a (mgt_call X_1)) bot_bot_a_o))))->((p G) ((insert_a (mgt C)) bot_bot_a_o))))). % Axiom fact_488_diff__eq__diff__less__eq:(forall (A_98:int) (B_47:int) (C_26:int) (D_6:int), ((((eq int) ((minus_minus_int A_98) B_47)) ((minus_minus_int C_26) D_6))->((iff ((ord_less_eq_int A_98) B_47)) ((ord_less_eq_int C_26) D_6)))). % Axiom fact_489_less__eq__nat_Osimps_I2_J:(forall (M:nat) (N:nat), ((iff ((ord_less_eq_nat (suc M)) N)) (((nat_case_o False) (ord_less_eq_nat M)) N))). % Axiom fact_490_emptyE:(forall (A_97:int), (((member_int A_97) bot_bot_int_o)->False)). % Axiom fact_491_emptyE:(forall (A_97:nat), (((member_nat A_97) bot_bot_nat_o)->False)). % Axiom fact_492_emptyE:(forall (A_97:x_a), (((member_a A_97) bot_bot_a_o)->False)). % Axiom fact_493_emptyE:(forall (A_97:pname), (((member_pname A_97) bot_bot_pname_o)->False)). % Axiom fact_494_finite__Diff:(forall (B_46:(int->Prop)) (A_96:(int->Prop)), ((finite_finite_int A_96)->(finite_finite_int ((minus_minus_int_o A_96) B_46)))). % Axiom fact_495_finite__Diff:(forall (B_46:(nat->Prop)) (A_96:(nat->Prop)), ((finite_finite_nat A_96)->(finite_finite_nat ((minus_minus_nat_o A_96) B_46)))). % Axiom fact_496_finite__Diff:(forall (B_46:(pname->Prop)) (A_96:(pname->Prop)), ((finite_finite_pname A_96)->(finite_finite_pname ((minus_minus_pname_o A_96) B_46)))). % Axiom fact_497_finite_OemptyI:(finite_finite_int bot_bot_int_o). % Axiom fact_498_finite_OemptyI:(finite_finite_nat bot_bot_nat_o). % Axiom fact_499_finite_OemptyI:(finite_finite_pname bot_bot_pname_o). % Axiom fact_500_finite_OemptyI:(finite_finite_a bot_bot_a_o). % Axiom fact_501_empty__subsetI:(forall (A_95:(nat->Prop)), ((ord_less_eq_nat_o bot_bot_nat_o) A_95)). % Axiom fact_502_empty__subsetI:(forall (A_95:(int->Prop)), ((ord_less_eq_int_o bot_bot_int_o) A_95)). % Axiom fact_503_empty__subsetI:(forall (A_95:(x_a->Prop)), ((ord_less_eq_a_o bot_bot_a_o) A_95)). % Axiom fact_504_equals0D:(forall (A_94:int) (A_93:(int->Prop)), ((((eq (int->Prop)) A_93) bot_bot_int_o)->(((member_int A_94) A_93)->False))). % Axiom fact_505_equals0D:(forall (A_94:nat) (A_93:(nat->Prop)), ((((eq (nat->Prop)) A_93) bot_bot_nat_o)->(((member_nat A_94) A_93)->False))). % Axiom fact_506_equals0D:(forall (A_94:x_a) (A_93:(x_a->Prop)), ((((eq (x_a->Prop)) A_93) bot_bot_a_o)->(((member_a A_94) A_93)->False))). % Axiom fact_507_equals0D:(forall (A_94:pname) (A_93:(pname->Prop)), ((((eq (pname->Prop)) A_93) bot_bot_pname_o)->(((member_pname A_94) A_93)->False))). % Axiom fact_508_Collect__empty__eq:(forall (P_9:(int->Prop)), ((iff (((eq (int->Prop)) (collect_int P_9)) bot_bot_int_o)) (forall (X_1:int), ((P_9 X_1)->False)))). % Axiom fact_509_Collect__empty__eq:(forall (P_9:(nat->Prop)), ((iff (((eq (nat->Prop)) (collect_nat P_9)) bot_bot_nat_o)) (forall (X_1:nat), ((P_9 X_1)->False)))). % Axiom fact_510_Collect__empty__eq:(forall (P_9:(x_a->Prop)), ((iff (((eq (x_a->Prop)) (collect_a P_9)) bot_bot_a_o)) (forall (X_1:x_a), ((P_9 X_1)->False)))). % Axiom fact_511_Diff__cancel:(forall (A_92:(nat->Prop)), (((eq (nat->Prop)) ((minus_minus_nat_o A_92) A_92)) bot_bot_nat_o)). % Axiom fact_512_Diff__cancel:(forall (A_92:(int->Prop)), (((eq (int->Prop)) ((minus_minus_int_o A_92) A_92)) bot_bot_int_o)). % Axiom fact_513_Diff__cancel:(forall (A_92:(x_a->Prop)), (((eq (x_a->Prop)) ((minus_minus_a_o A_92) A_92)) bot_bot_a_o)). % Axiom fact_514_Diff__empty:(forall (A_91:(nat->Prop)), (((eq (nat->Prop)) ((minus_minus_nat_o A_91) bot_bot_nat_o)) A_91)). % Axiom fact_515_Diff__empty:(forall (A_91:(int->Prop)), (((eq (int->Prop)) ((minus_minus_int_o A_91) bot_bot_int_o)) A_91)). % Axiom fact_516_Diff__empty:(forall (A_91:(x_a->Prop)), (((eq (x_a->Prop)) ((minus_minus_a_o A_91) bot_bot_a_o)) A_91)). % Axiom fact_517_empty__iff:(forall (C_25:int), (((member_int C_25) bot_bot_int_o)->False)). % Axiom fact_518_empty__iff:(forall (C_25:nat), (((member_nat C_25) bot_bot_nat_o)->False)). % Axiom fact_519_empty__iff:(forall (C_25:x_a), (((member_a C_25) bot_bot_a_o)->False)). % Axiom fact_520_empty__iff:(forall (C_25:pname), (((member_pname C_25) bot_bot_pname_o)->False)). % Axiom fact_521_empty__Collect__eq:(forall (P_8:(int->Prop)), ((iff (((eq (int->Prop)) bot_bot_int_o) (collect_int P_8))) (forall (X_1:int), ((P_8 X_1)->False)))). % Axiom fact_522_empty__Collect__eq:(forall (P_8:(nat->Prop)), ((iff (((eq (nat->Prop)) bot_bot_nat_o) (collect_nat P_8))) (forall (X_1:nat), ((P_8 X_1)->False)))). % Axiom fact_523_empty__Collect__eq:(forall (P_8:(x_a->Prop)), ((iff (((eq (x_a->Prop)) bot_bot_a_o) (collect_a P_8))) (forall (X_1:x_a), ((P_8 X_1)->False)))). % Axiom fact_524_empty__Diff:(forall (A_90:(nat->Prop)), (((eq (nat->Prop)) ((minus_minus_nat_o bot_bot_nat_o) A_90)) bot_bot_nat_o)). % Axiom fact_525_empty__Diff:(forall (A_90:(int->Prop)), (((eq (int->Prop)) ((minus_minus_int_o bot_bot_int_o) A_90)) bot_bot_int_o)). % Axiom fact_526_empty__Diff:(forall (A_90:(x_a->Prop)), (((eq (x_a->Prop)) ((minus_minus_a_o bot_bot_a_o) A_90)) bot_bot_a_o)). % Axiom fact_527_ex__in__conv:(forall (A_89:(int->Prop)), ((iff ((ex int) (fun (X_1:int)=> ((member_int X_1) A_89)))) (not (((eq (int->Prop)) A_89) bot_bot_int_o)))). % Axiom fact_528_ex__in__conv:(forall (A_89:(nat->Prop)), ((iff ((ex nat) (fun (X_1:nat)=> ((member_nat X_1) A_89)))) (not (((eq (nat->Prop)) A_89) bot_bot_nat_o)))). % Axiom fact_529_ex__in__conv:(forall (A_89:(x_a->Prop)), ((iff ((ex x_a) (fun (X_1:x_a)=> ((member_a X_1) A_89)))) (not (((eq (x_a->Prop)) A_89) bot_bot_a_o)))). % Axiom fact_530_ex__in__conv:(forall (A_89:(pname->Prop)), ((iff ((ex pname) (fun (X_1:pname)=> ((member_pname X_1) A_89)))) (not (((eq (pname->Prop)) A_89) bot_bot_pname_o)))). % Axiom fact_531_all__not__in__conv:(forall (A_88:(int->Prop)), ((iff (forall (X_1:int), (((member_int X_1) A_88)->False))) (((eq (int->Prop)) A_88) bot_bot_int_o))). % Axiom fact_532_all__not__in__conv:(forall (A_88:(nat->Prop)), ((iff (forall (X_1:nat), (((member_nat X_1) A_88)->False))) (((eq (nat->Prop)) A_88) bot_bot_nat_o))). % Axiom fact_533_all__not__in__conv:(forall (A_88:(x_a->Prop)), ((iff (forall (X_1:x_a), (((member_a X_1) A_88)->False))) (((eq (x_a->Prop)) A_88) bot_bot_a_o))). % Axiom fact_534_all__not__in__conv:(forall (A_88:(pname->Prop)), ((iff (forall (X_1:pname), (((member_pname X_1) A_88)->False))) (((eq (pname->Prop)) A_88) bot_bot_pname_o))). % Axiom fact_535_bot__apply:(forall (X_24:nat), ((iff (bot_bot_nat_o X_24)) bot_bot_o)). % Axiom fact_536_bot__apply:(forall (X_24:int), ((iff (bot_bot_int_o X_24)) bot_bot_o)). % Axiom fact_537_bot__apply:(forall (X_24:x_a), ((iff (bot_bot_a_o X_24)) bot_bot_o)). % Axiom fact_538_empty__def:(((eq (int->Prop)) bot_bot_int_o) (collect_int (fun (X_1:int)=> False))). % Axiom fact_539_empty__def:(((eq (nat->Prop)) bot_bot_nat_o) (collect_nat (fun (X_1:nat)=> False))). % Axiom fact_540_empty__def:(((eq (x_a->Prop)) bot_bot_a_o) (collect_a (fun (X_1:x_a)=> False))). % Axiom fact_541_bot__fun__def:(forall (X_1:nat), ((iff (bot_bot_nat_o X_1)) bot_bot_o)). % Axiom fact_542_bot__fun__def:(forall (X_1:int), ((iff (bot_bot_int_o X_1)) bot_bot_o)). % Axiom fact_543_bot__fun__def:(forall (X_1:x_a), ((iff (bot_bot_a_o X_1)) bot_bot_o)). % Axiom fact_544_insert__Diff:(forall (A_87:x_a) (A_86:(x_a->Prop)), (((member_a A_87) A_86)->(((eq (x_a->Prop)) ((insert_a A_87) ((minus_minus_a_o A_86) ((insert_a A_87) bot_bot_a_o)))) A_86))). % Axiom fact_545_insert__Diff:(forall (A_87:int) (A_86:(int->Prop)), (((member_int A_87) A_86)->(((eq (int->Prop)) ((insert_int A_87) ((minus_minus_int_o A_86) ((insert_int A_87) bot_bot_int_o)))) A_86))). % Axiom fact_546_insert__Diff:(forall (A_87:nat) (A_86:(nat->Prop)), (((member_nat A_87) A_86)->(((eq (nat->Prop)) ((insert_nat A_87) ((minus_minus_nat_o A_86) ((insert_nat A_87) bot_bot_nat_o)))) A_86))). % Axiom fact_547_insert__Diff:(forall (A_87:pname) (A_86:(pname->Prop)), (((member_pname A_87) A_86)->(((eq (pname->Prop)) ((insert_pname A_87) ((minus_minus_pname_o A_86) ((insert_pname A_87) bot_bot_pname_o)))) A_86))). % Axiom fact_548_Diff__insert__absorb:(forall (X_23:x_a) (A_85:(x_a->Prop)), ((((member_a X_23) A_85)->False)->(((eq (x_a->Prop)) ((minus_minus_a_o ((insert_a X_23) A_85)) ((insert_a X_23) bot_bot_a_o))) A_85))). % Axiom fact_549_Diff__insert__absorb:(forall (X_23:int) (A_85:(int->Prop)), ((((member_int X_23) A_85)->False)->(((eq (int->Prop)) ((minus_minus_int_o ((insert_int X_23) A_85)) ((insert_int X_23) bot_bot_int_o))) A_85))). % Axiom fact_550_Diff__insert__absorb:(forall (X_23:nat) (A_85:(nat->Prop)), ((((member_nat X_23) A_85)->False)->(((eq (nat->Prop)) ((minus_minus_nat_o ((insert_nat X_23) A_85)) ((insert_nat X_23) bot_bot_nat_o))) A_85))). % Axiom fact_551_Diff__insert__absorb:(forall (X_23:pname) (A_85:(pname->Prop)), ((((member_pname X_23) A_85)->False)->(((eq (pname->Prop)) ((minus_minus_pname_o ((insert_pname X_23) A_85)) ((insert_pname X_23) bot_bot_pname_o))) A_85))). % Axiom fact_552_insert__Diff__single:(forall (A_84:x_a) (A_83:(x_a->Prop)), (((eq (x_a->Prop)) ((insert_a A_84) ((minus_minus_a_o A_83) ((insert_a A_84) bot_bot_a_o)))) ((insert_a A_84) A_83))). % Axiom fact_553_insert__Diff__single:(forall (A_84:nat) (A_83:(nat->Prop)), (((eq (nat->Prop)) ((insert_nat A_84) ((minus_minus_nat_o A_83) ((insert_nat A_84) bot_bot_nat_o)))) ((insert_nat A_84) A_83))). % Axiom fact_554_insert__Diff__single:(forall (A_84:int) (A_83:(int->Prop)), (((eq (int->Prop)) ((insert_int A_84) ((minus_minus_int_o A_83) ((insert_int A_84) bot_bot_int_o)))) ((insert_int A_84) A_83))). % Axiom fact_555_Diff__insert2:(forall (A_82:(x_a->Prop)) (A_81:x_a) (B_45:(x_a->Prop)), (((eq (x_a->Prop)) ((minus_minus_a_o A_82) ((insert_a A_81) B_45))) ((minus_minus_a_o ((minus_minus_a_o A_82) ((insert_a A_81) bot_bot_a_o))) B_45))). % Axiom fact_556_Diff__insert2:(forall (A_82:(nat->Prop)) (A_81:nat) (B_45:(nat->Prop)), (((eq (nat->Prop)) ((minus_minus_nat_o A_82) ((insert_nat A_81) B_45))) ((minus_minus_nat_o ((minus_minus_nat_o A_82) ((insert_nat A_81) bot_bot_nat_o))) B_45))). % Axiom fact_557_Diff__insert2:(forall (A_82:(int->Prop)) (A_81:int) (B_45:(int->Prop)), (((eq (int->Prop)) ((minus_minus_int_o A_82) ((insert_int A_81) B_45))) ((minus_minus_int_o ((minus_minus_int_o A_82) ((insert_int A_81) bot_bot_int_o))) B_45))). % Axiom fact_558_Diff__insert:(forall (A_80:(x_a->Prop)) (A_79:x_a) (B_44:(x_a->Prop)), (((eq (x_a->Prop)) ((minus_minus_a_o A_80) ((insert_a A_79) B_44))) ((minus_minus_a_o ((minus_minus_a_o A_80) B_44)) ((insert_a A_79) bot_bot_a_o)))). % Axiom fact_559_Diff__insert:(forall (A_80:(nat->Prop)) (A_79:nat) (B_44:(nat->Prop)), (((eq (nat->Prop)) ((minus_minus_nat_o A_80) ((insert_nat A_79) B_44))) ((minus_minus_nat_o ((minus_minus_nat_o A_80) B_44)) ((insert_nat A_79) bot_bot_nat_o)))). % Axiom fact_560_Diff__insert:(forall (A_80:(int->Prop)) (A_79:int) (B_44:(int->Prop)), (((eq (int->Prop)) ((minus_minus_int_o A_80) ((insert_int A_79) B_44))) ((minus_minus_int_o ((minus_minus_int_o A_80) B_44)) ((insert_int A_79) bot_bot_int_o)))). % Axiom fact_561_diff__single__insert:(forall (A_78:(x_a->Prop)) (X_22:x_a) (B_43:(x_a->Prop)), (((ord_less_eq_a_o ((minus_minus_a_o A_78) ((insert_a X_22) bot_bot_a_o))) B_43)->(((member_a X_22) A_78)->((ord_less_eq_a_o A_78) ((insert_a X_22) B_43))))). % Axiom fact_562_diff__single__insert:(forall (A_78:(int->Prop)) (X_22:int) (B_43:(int->Prop)), (((ord_less_eq_int_o ((minus_minus_int_o A_78) ((insert_int X_22) bot_bot_int_o))) B_43)->(((member_int X_22) A_78)->((ord_less_eq_int_o A_78) ((insert_int X_22) B_43))))). % Axiom fact_563_diff__single__insert:(forall (A_78:(nat->Prop)) (X_22:nat) (B_43:(nat->Prop)), (((ord_less_eq_nat_o ((minus_minus_nat_o A_78) ((insert_nat X_22) bot_bot_nat_o))) B_43)->(((member_nat X_22) A_78)->((ord_less_eq_nat_o A_78) ((insert_nat X_22) B_43))))). % Axiom fact_564_diff__single__insert:(forall (A_78:(pname->Prop)) (X_22:pname) (B_43:(pname->Prop)), (((ord_less_eq_pname_o ((minus_minus_pname_o A_78) ((insert_pname X_22) bot_bot_pname_o))) B_43)->(((member_pname X_22) A_78)->((ord_less_eq_pname_o A_78) ((insert_pname X_22) B_43))))). % Axiom fact_565_subset__insert__iff:(forall (A_77:(x_a->Prop)) (X_21:x_a) (B_42:(x_a->Prop)), ((iff ((ord_less_eq_a_o A_77) ((insert_a X_21) B_42))) ((and (((member_a X_21) A_77)->((ord_less_eq_a_o ((minus_minus_a_o A_77) ((insert_a X_21) bot_bot_a_o))) B_42))) ((((member_a X_21) A_77)->False)->((ord_less_eq_a_o A_77) B_42))))). % Axiom fact_566_subset__insert__iff:(forall (A_77:(int->Prop)) (X_21:int) (B_42:(int->Prop)), ((iff ((ord_less_eq_int_o A_77) ((insert_int X_21) B_42))) ((and (((member_int X_21) A_77)->((ord_less_eq_int_o ((minus_minus_int_o A_77) ((insert_int X_21) bot_bot_int_o))) B_42))) ((((member_int X_21) A_77)->False)->((ord_less_eq_int_o A_77) B_42))))). % Axiom fact_567_subset__insert__iff:(forall (A_77:(nat->Prop)) (X_21:nat) (B_42:(nat->Prop)), ((iff ((ord_less_eq_nat_o A_77) ((insert_nat X_21) B_42))) ((and (((member_nat X_21) A_77)->((ord_less_eq_nat_o ((minus_minus_nat_o A_77) ((insert_nat X_21) bot_bot_nat_o))) B_42))) ((((member_nat X_21) A_77)->False)->((ord_less_eq_nat_o A_77) B_42))))). % Axiom fact_568_subset__insert__iff:(forall (A_77:(pname->Prop)) (X_21:pname) (B_42:(pname->Prop)), ((iff ((ord_less_eq_pname_o A_77) ((insert_pname X_21) B_42))) ((and (((member_pname X_21) A_77)->((ord_less_eq_pname_o ((minus_minus_pname_o A_77) ((insert_pname X_21) bot_bot_pname_o))) B_42))) ((((member_pname X_21) A_77)->False)->((ord_less_eq_pname_o A_77) B_42))))). % Axiom fact_569_finite__Diff2:(forall (A_76:(int->Prop)) (B_41:(int->Prop)), ((finite_finite_int B_41)->((iff (finite_finite_int ((minus_minus_int_o A_76) B_41))) (finite_finite_int A_76)))). % Axiom fact_570_finite__Diff2:(forall (A_76:(nat->Prop)) (B_41:(nat->Prop)), ((finite_finite_nat B_41)->((iff (finite_finite_nat ((minus_minus_nat_o A_76) B_41))) (finite_finite_nat A_76)))). % Axiom fact_571_finite__Diff2:(forall (A_76:(pname->Prop)) (B_41:(pname->Prop)), ((finite_finite_pname B_41)->((iff (finite_finite_pname ((minus_minus_pname_o A_76) B_41))) (finite_finite_pname A_76)))). % Axiom fact_572_insert__Diff1:(forall (A_75:(x_a->Prop)) (X_20:x_a) (B_40:(x_a->Prop)), (((member_a X_20) B_40)->(((eq (x_a->Prop)) ((minus_minus_a_o ((insert_a X_20) A_75)) B_40)) ((minus_minus_a_o A_75) B_40)))). % Axiom fact_573_insert__Diff1:(forall (A_75:(int->Prop)) (X_20:int) (B_40:(int->Prop)), (((member_int X_20) B_40)->(((eq (int->Prop)) ((minus_minus_int_o ((insert_int X_20) A_75)) B_40)) ((minus_minus_int_o A_75) B_40)))). % Axiom fact_574_insert__Diff1:(forall (A_75:(nat->Prop)) (X_20:nat) (B_40:(nat->Prop)), (((member_nat X_20) B_40)->(((eq (nat->Prop)) ((minus_minus_nat_o ((insert_nat X_20) A_75)) B_40)) ((minus_minus_nat_o A_75) B_40)))). % Axiom fact_575_insert__Diff1:(forall (A_75:(pname->Prop)) (X_20:pname) (B_40:(pname->Prop)), (((member_pname X_20) B_40)->(((eq (pname->Prop)) ((minus_minus_pname_o ((insert_pname X_20) A_75)) B_40)) ((minus_minus_pname_o A_75) B_40)))). % Axiom fact_576_insert__Diff__if:(forall (A_74:(x_a->Prop)) (X_19:x_a) (B_39:(x_a->Prop)), ((and (((member_a X_19) B_39)->(((eq (x_a->Prop)) ((minus_minus_a_o ((insert_a X_19) A_74)) B_39)) ((minus_minus_a_o A_74) B_39)))) ((((member_a X_19) B_39)->False)->(((eq (x_a->Prop)) ((minus_minus_a_o ((insert_a X_19) A_74)) B_39)) ((insert_a X_19) ((minus_minus_a_o A_74) B_39)))))). % Axiom fact_577_insert__Diff__if:(forall (A_74:(int->Prop)) (X_19:int) (B_39:(int->Prop)), ((and (((member_int X_19) B_39)->(((eq (int->Prop)) ((minus_minus_int_o ((insert_int X_19) A_74)) B_39)) ((minus_minus_int_o A_74) B_39)))) ((((member_int X_19) B_39)->False)->(((eq (int->Prop)) ((minus_minus_int_o ((insert_int X_19) A_74)) B_39)) ((insert_int X_19) ((minus_minus_int_o A_74) B_39)))))). % Axiom fact_578_insert__Diff__if:(forall (A_74:(nat->Prop)) (X_19:nat) (B_39:(nat->Prop)), ((and (((member_nat X_19) B_39)->(((eq (nat->Prop)) ((minus_minus_nat_o ((insert_nat X_19) A_74)) B_39)) ((minus_minus_nat_o A_74) B_39)))) ((((member_nat X_19) B_39)->False)->(((eq (nat->Prop)) ((minus_minus_nat_o ((insert_nat X_19) A_74)) B_39)) ((insert_nat X_19) ((minus_minus_nat_o A_74) B_39)))))). % Axiom fact_579_insert__Diff__if:(forall (A_74:(pname->Prop)) (X_19:pname) (B_39:(pname->Prop)), ((and (((member_pname X_19) B_39)->(((eq (pname->Prop)) ((minus_minus_pname_o ((insert_pname X_19) A_74)) B_39)) ((minus_minus_pname_o A_74) B_39)))) ((((member_pname X_19) B_39)->False)->(((eq (pname->Prop)) ((minus_minus_pname_o ((insert_pname X_19) A_74)) B_39)) ((insert_pname X_19) ((minus_minus_pname_o A_74) B_39)))))). % Axiom fact_580_double__diff:(forall (C_24:(int->Prop)) (A_73:(int->Prop)) (B_38:(int->Prop)), (((ord_less_eq_int_o A_73) B_38)->(((ord_less_eq_int_o B_38) C_24)->(((eq (int->Prop)) ((minus_minus_int_o B_38) ((minus_minus_int_o C_24) A_73))) A_73)))). % Axiom fact_581_double__diff:(forall (C_24:(nat->Prop)) (A_73:(nat->Prop)) (B_38:(nat->Prop)), (((ord_less_eq_nat_o A_73) B_38)->(((ord_less_eq_nat_o B_38) C_24)->(((eq (nat->Prop)) ((minus_minus_nat_o B_38) ((minus_minus_nat_o C_24) A_73))) A_73)))). % Axiom fact_582_double__diff:(forall (C_24:(x_a->Prop)) (A_73:(x_a->Prop)) (B_38:(x_a->Prop)), (((ord_less_eq_a_o A_73) B_38)->(((ord_less_eq_a_o B_38) C_24)->(((eq (x_a->Prop)) ((minus_minus_a_o B_38) ((minus_minus_a_o C_24) A_73))) A_73)))). % Axiom fact_583_Diff__mono:(forall (D_5:(int->Prop)) (B_37:(int->Prop)) (A_72:(int->Prop)) (C_23:(int->Prop)), (((ord_less_eq_int_o A_72) C_23)->(((ord_less_eq_int_o D_5) B_37)->((ord_less_eq_int_o ((minus_minus_int_o A_72) B_37)) ((minus_minus_int_o C_23) D_5))))). % Axiom fact_584_Diff__mono:(forall (D_5:(nat->Prop)) (B_37:(nat->Prop)) (A_72:(nat->Prop)) (C_23:(nat->Prop)), (((ord_less_eq_nat_o A_72) C_23)->(((ord_less_eq_nat_o D_5) B_37)->((ord_less_eq_nat_o ((minus_minus_nat_o A_72) B_37)) ((minus_minus_nat_o C_23) D_5))))). % Axiom fact_585_Diff__mono:(forall (D_5:(x_a->Prop)) (B_37:(x_a->Prop)) (A_72:(x_a->Prop)) (C_23:(x_a->Prop)), (((ord_less_eq_a_o A_72) C_23)->(((ord_less_eq_a_o D_5) B_37)->((ord_less_eq_a_o ((minus_minus_a_o A_72) B_37)) ((minus_minus_a_o C_23) D_5))))). % Axiom fact_586_Diff__subset:(forall (A_71:(int->Prop)) (B_36:(int->Prop)), ((ord_less_eq_int_o ((minus_minus_int_o A_71) B_36)) A_71)). % Axiom fact_587_Diff__subset:(forall (A_71:(nat->Prop)) (B_36:(nat->Prop)), ((ord_less_eq_nat_o ((minus_minus_nat_o A_71) B_36)) A_71)). % Axiom fact_588_Diff__subset:(forall (A_71:(x_a->Prop)) (B_36:(x_a->Prop)), ((ord_less_eq_a_o ((minus_minus_a_o A_71) B_36)) A_71)). % Axiom fact_589_singleton__inject:(forall (A_70:x_a) (B_35:x_a), ((((eq (x_a->Prop)) ((insert_a A_70) bot_bot_a_o)) ((insert_a B_35) bot_bot_a_o))->(((eq x_a) A_70) B_35))). % Axiom fact_590_singleton__inject:(forall (A_70:nat) (B_35:nat), ((((eq (nat->Prop)) ((insert_nat A_70) bot_bot_nat_o)) ((insert_nat B_35) bot_bot_nat_o))->(((eq nat) A_70) B_35))). % Axiom fact_591_singleton__inject:(forall (A_70:int) (B_35:int), ((((eq (int->Prop)) ((insert_int A_70) bot_bot_int_o)) ((insert_int B_35) bot_bot_int_o))->(((eq int) A_70) B_35))). % Axiom fact_592_singletonE:(forall (B_34:x_a) (A_69:x_a), (((member_a B_34) ((insert_a A_69) bot_bot_a_o))->(((eq x_a) B_34) A_69))). % Axiom fact_593_singletonE:(forall (B_34:int) (A_69:int), (((member_int B_34) ((insert_int A_69) bot_bot_int_o))->(((eq int) B_34) A_69))). % Axiom fact_594_singletonE:(forall (B_34:nat) (A_69:nat), (((member_nat B_34) ((insert_nat A_69) bot_bot_nat_o))->(((eq nat) B_34) A_69))). % Axiom fact_595_singletonE:(forall (B_34:pname) (A_69:pname), (((member_pname B_34) ((insert_pname A_69) bot_bot_pname_o))->(((eq pname) B_34) A_69))). % Axiom fact_596_doubleton__eq__iff:(forall (A_68:x_a) (B_33:x_a) (C_22:x_a) (D_4:x_a), ((iff (((eq (x_a->Prop)) ((insert_a A_68) ((insert_a B_33) bot_bot_a_o))) ((insert_a C_22) ((insert_a D_4) bot_bot_a_o)))) ((or ((and (((eq x_a) A_68) C_22)) (((eq x_a) B_33) D_4))) ((and (((eq x_a) A_68) D_4)) (((eq x_a) B_33) C_22))))). % Axiom fact_597_doubleton__eq__iff:(forall (A_68:nat) (B_33:nat) (C_22:nat) (D_4:nat), ((iff (((eq (nat->Prop)) ((insert_nat A_68) ((insert_nat B_33) bot_bot_nat_o))) ((insert_nat C_22) ((insert_nat D_4) bot_bot_nat_o)))) ((or ((and (((eq nat) A_68) C_22)) (((eq nat) B_33) D_4))) ((and (((eq nat) A_68) D_4)) (((eq nat) B_33) C_22))))). % Axiom fact_598_doubleton__eq__iff:(forall (A_68:int) (B_33:int) (C_22:int) (D_4:int), ((iff (((eq (int->Prop)) ((insert_int A_68) ((insert_int B_33) bot_bot_int_o))) ((insert_int C_22) ((insert_int D_4) bot_bot_int_o)))) ((or ((and (((eq int) A_68) C_22)) (((eq int) B_33) D_4))) ((and (((eq int) A_68) D_4)) (((eq int) B_33) C_22))))). % Axiom fact_599_singleton__iff:(forall (B_32:x_a) (A_67:x_a), ((iff ((member_a B_32) ((insert_a A_67) bot_bot_a_o))) (((eq x_a) B_32) A_67))). % Axiom fact_600_singleton__iff:(forall (B_32:int) (A_67:int), ((iff ((member_int B_32) ((insert_int A_67) bot_bot_int_o))) (((eq int) B_32) A_67))). % Axiom fact_601_singleton__iff:(forall (B_32:nat) (A_67:nat), ((iff ((member_nat B_32) ((insert_nat A_67) bot_bot_nat_o))) (((eq nat) B_32) A_67))). % Axiom fact_602_singleton__iff:(forall (B_32:pname) (A_67:pname), ((iff ((member_pname B_32) ((insert_pname A_67) bot_bot_pname_o))) (((eq pname) B_32) A_67))). % Axiom fact_603_insert__not__empty:(forall (A_66:x_a) (A_65:(x_a->Prop)), (not (((eq (x_a->Prop)) ((insert_a A_66) A_65)) bot_bot_a_o))). % Axiom fact_604_insert__not__empty:(forall (A_66:nat) (A_65:(nat->Prop)), (not (((eq (nat->Prop)) ((insert_nat A_66) A_65)) bot_bot_nat_o))). % Axiom fact_605_insert__not__empty:(forall (A_66:int) (A_65:(int->Prop)), (not (((eq (int->Prop)) ((insert_int A_66) A_65)) bot_bot_int_o))). % Axiom fact_606_empty__not__insert:(forall (A_64:x_a) (A_63:(x_a->Prop)), (not (((eq (x_a->Prop)) bot_bot_a_o) ((insert_a A_64) A_63)))). % Axiom fact_607_empty__not__insert:(forall (A_64:nat) (A_63:(nat->Prop)), (not (((eq (nat->Prop)) bot_bot_nat_o) ((insert_nat A_64) A_63)))). % Axiom fact_608_empty__not__insert:(forall (A_64:int) (A_63:(int->Prop)), (not (((eq (int->Prop)) bot_bot_int_o) ((insert_int A_64) A_63)))). % Axiom fact_609_subset__empty:(forall (A_62:(nat->Prop)), ((iff ((ord_less_eq_nat_o A_62) bot_bot_nat_o)) (((eq (nat->Prop)) A_62) bot_bot_nat_o))). % Axiom fact_610_subset__empty:(forall (A_62:(int->Prop)), ((iff ((ord_less_eq_int_o A_62) bot_bot_int_o)) (((eq (int->Prop)) A_62) bot_bot_int_o))). % Axiom fact_611_subset__empty:(forall (A_62:(x_a->Prop)), ((iff ((ord_less_eq_a_o A_62) bot_bot_a_o)) (((eq (x_a->Prop)) A_62) bot_bot_a_o))). % Axiom fact_612_image__is__empty:(forall (F_22:(nat->int)) (A_61:(nat->Prop)), ((iff (((eq (int->Prop)) ((image_nat_int F_22) A_61)) bot_bot_int_o)) (((eq (nat->Prop)) A_61) bot_bot_nat_o))). % Axiom fact_613_image__is__empty:(forall (F_22:(pname->x_a)) (A_61:(pname->Prop)), ((iff (((eq (x_a->Prop)) ((image_pname_a F_22) A_61)) bot_bot_a_o)) (((eq (pname->Prop)) A_61) bot_bot_pname_o))). % Axiom fact_614_image__empty:(forall (F_21:(nat->int)), (((eq (int->Prop)) ((image_nat_int F_21) bot_bot_nat_o)) bot_bot_int_o)). % Axiom fact_615_image__empty:(forall (F_21:(pname->x_a)), (((eq (x_a->Prop)) ((image_pname_a F_21) bot_bot_pname_o)) bot_bot_a_o)). % Axiom fact_616_empty__is__image:(forall (F_20:(nat->int)) (A_60:(nat->Prop)), ((iff (((eq (int->Prop)) bot_bot_int_o) ((image_nat_int F_20) A_60))) (((eq (nat->Prop)) A_60) bot_bot_nat_o))). % Axiom fact_617_empty__is__image:(forall (F_20:(pname->x_a)) (A_60:(pname->Prop)), ((iff (((eq (x_a->Prop)) bot_bot_a_o) ((image_pname_a F_20) A_60))) (((eq (pname->Prop)) A_60) bot_bot_pname_o))). % Axiom fact_618_le__bot:(forall (A_59:(nat->Prop)), (((ord_less_eq_nat_o A_59) bot_bot_nat_o)->(((eq (nat->Prop)) A_59) bot_bot_nat_o))). % Axiom fact_619_le__bot:(forall (A_59:(int->Prop)), (((ord_less_eq_int_o A_59) bot_bot_int_o)->(((eq (int->Prop)) A_59) bot_bot_int_o))). % Axiom fact_620_le__bot:(forall (A_59:nat), (((ord_less_eq_nat A_59) bot_bot_nat)->(((eq nat) A_59) bot_bot_nat))). % Axiom fact_621_le__bot:(forall (A_59:(x_a->Prop)), (((ord_less_eq_a_o A_59) bot_bot_a_o)->(((eq (x_a->Prop)) A_59) bot_bot_a_o))). % Axiom fact_622_bot__unique:(forall (A_58:(nat->Prop)), ((iff ((ord_less_eq_nat_o A_58) bot_bot_nat_o)) (((eq (nat->Prop)) A_58) bot_bot_nat_o))). % Axiom fact_623_bot__unique:(forall (A_58:(int->Prop)), ((iff ((ord_less_eq_int_o A_58) bot_bot_int_o)) (((eq (int->Prop)) A_58) bot_bot_int_o))). % Axiom fact_624_bot__unique:(forall (A_58:nat), ((iff ((ord_less_eq_nat A_58) bot_bot_nat)) (((eq nat) A_58) bot_bot_nat))). % Axiom fact_625_bot__unique:(forall (A_58:(x_a->Prop)), ((iff ((ord_less_eq_a_o A_58) bot_bot_a_o)) (((eq (x_a->Prop)) A_58) bot_bot_a_o))). % Axiom fact_626_bot__least:(forall (A_57:(nat->Prop)), ((ord_less_eq_nat_o bot_bot_nat_o) A_57)). % Axiom fact_627_bot__least:(forall (A_57:(int->Prop)), ((ord_less_eq_int_o bot_bot_int_o) A_57)). % Axiom fact_628_bot__least:(forall (A_57:nat), ((ord_less_eq_nat bot_bot_nat) A_57)). % Axiom fact_629_bot__least:(forall (A_57:(x_a->Prop)), ((ord_less_eq_a_o bot_bot_a_o) A_57)). % Axiom fact_630_Collect__conv__if:(forall (P_7:(x_a->Prop)) (A_56:x_a), ((and ((P_7 A_56)->(((eq (x_a->Prop)) (collect_a (fun (X_1:x_a)=> ((and (((eq x_a) X_1) A_56)) (P_7 X_1))))) ((insert_a A_56) bot_bot_a_o)))) (((P_7 A_56)->False)->(((eq (x_a->Prop)) (collect_a (fun (X_1:x_a)=> ((and (((eq x_a) X_1) A_56)) (P_7 X_1))))) bot_bot_a_o)))). % Axiom fact_631_Collect__conv__if:(forall (P_7:(int->Prop)) (A_56:int), ((and ((P_7 A_56)->(((eq (int->Prop)) (collect_int (fun (X_1:int)=> ((and (((eq int) X_1) A_56)) (P_7 X_1))))) ((insert_int A_56) bot_bot_int_o)))) (((P_7 A_56)->False)->(((eq (int->Prop)) (collect_int (fun (X_1:int)=> ((and (((eq int) X_1) A_56)) (P_7 X_1))))) bot_bot_int_o)))). % Axiom fact_632_Collect__conv__if:(forall (P_7:(nat->Prop)) (A_56:nat), ((and ((P_7 A_56)->(((eq (nat->Prop)) (collect_nat (fun (X_1:nat)=> ((and (((eq nat) X_1) A_56)) (P_7 X_1))))) ((insert_nat A_56) bot_bot_nat_o)))) (((P_7 A_56)->False)->(((eq (nat->Prop)) (collect_nat (fun (X_1:nat)=> ((and (((eq nat) X_1) A_56)) (P_7 X_1))))) bot_bot_nat_o)))). % Axiom fact_633_Collect__conv__if2:(forall (P_6:(x_a->Prop)) (A_55:x_a), ((and ((P_6 A_55)->(((eq (x_a->Prop)) (collect_a (fun (X_1:x_a)=> ((and (((eq x_a) A_55) X_1)) (P_6 X_1))))) ((insert_a A_55) bot_bot_a_o)))) (((P_6 A_55)->False)->(((eq (x_a->Prop)) (collect_a (fun (X_1:x_a)=> ((and (((eq x_a) A_55) X_1)) (P_6 X_1))))) bot_bot_a_o)))). % Axiom fact_634_Collect__conv__if2:(forall (P_6:(int->Prop)) (A_55:int), ((and ((P_6 A_55)->(((eq (int->Prop)) (collect_int (fun (X_1:int)=> ((and (((eq int) A_55) X_1)) (P_6 X_1))))) ((insert_int A_55) bot_bot_int_o)))) (((P_6 A_55)->False)->(((eq (int->Prop)) (collect_int (fun (X_1:int)=> ((and (((eq int) A_55) X_1)) (P_6 X_1))))) bot_bot_int_o)))). % Axiom fact_635_Collect__conv__if2:(forall (P_6:(nat->Prop)) (A_55:nat), ((and ((P_6 A_55)->(((eq (nat->Prop)) (collect_nat (fun (X_1:nat)=> ((and (((eq nat) A_55) X_1)) (P_6 X_1))))) ((insert_nat A_55) bot_bot_nat_o)))) (((P_6 A_55)->False)->(((eq (nat->Prop)) (collect_nat (fun (X_1:nat)=> ((and (((eq nat) A_55) X_1)) (P_6 X_1))))) bot_bot_nat_o)))). % Axiom fact_636_singleton__conv:(forall (A_54:x_a), (((eq (x_a->Prop)) (collect_a (fun (X_1:x_a)=> (((eq x_a) X_1) A_54)))) ((insert_a A_54) bot_bot_a_o))). % Axiom fact_637_singleton__conv:(forall (A_54:int), (((eq (int->Prop)) (collect_int (fun (X_1:int)=> (((eq int) X_1) A_54)))) ((insert_int A_54) bot_bot_int_o))). % Axiom fact_638_singleton__conv:(forall (A_54:nat), (((eq (nat->Prop)) (collect_nat (fun (X_1:nat)=> (((eq nat) X_1) A_54)))) ((insert_nat A_54) bot_bot_nat_o))). % Axiom fact_639_singleton__conv2:(forall (A_53:x_a), (((eq (x_a->Prop)) (collect_a (fequal_a A_53))) ((insert_a A_53) bot_bot_a_o))). % Axiom fact_640_singleton__conv2:(forall (A_53:int), (((eq (int->Prop)) (collect_int (fequal_int A_53))) ((insert_int A_53) bot_bot_int_o))). % Axiom fact_641_singleton__conv2:(forall (A_53:nat), (((eq (nat->Prop)) (collect_nat (fequal_nat A_53))) ((insert_nat A_53) bot_bot_nat_o))). % Axiom fact_642_card__Suc__Diff1:(forall (X_18:x_a) (A_52:(x_a->Prop)), ((finite_finite_a A_52)->(((member_a X_18) A_52)->(((eq nat) (suc (finite_card_a ((minus_minus_a_o A_52) ((insert_a X_18) bot_bot_a_o))))) (finite_card_a A_52))))). % Axiom fact_643_card__Suc__Diff1:(forall (X_18:int) (A_52:(int->Prop)), ((finite_finite_int A_52)->(((member_int X_18) A_52)->(((eq nat) (suc (finite_card_int ((minus_minus_int_o A_52) ((insert_int X_18) bot_bot_int_o))))) (finite_card_int A_52))))). % Axiom fact_644_card__Suc__Diff1:(forall (X_18:nat) (A_52:(nat->Prop)), ((finite_finite_nat A_52)->(((member_nat X_18) A_52)->(((eq nat) (suc (finite_card_nat ((minus_minus_nat_o A_52) ((insert_nat X_18) bot_bot_nat_o))))) (finite_card_nat A_52))))). % Axiom fact_645_card__Suc__Diff1:(forall (X_18:pname) (A_52:(pname->Prop)), ((finite_finite_pname A_52)->(((member_pname X_18) A_52)->(((eq nat) (suc (finite_card_pname ((minus_minus_pname_o A_52) ((insert_pname X_18) bot_bot_pname_o))))) (finite_card_pname A_52))))). % Axiom fact_646_card__insert:(forall (X_17:x_a) (A_51:(x_a->Prop)), ((finite_finite_a A_51)->(((eq nat) (finite_card_a ((insert_a X_17) A_51))) (suc (finite_card_a ((minus_minus_a_o A_51) ((insert_a X_17) bot_bot_a_o))))))). % Axiom fact_647_card__insert:(forall (X_17:int) (A_51:(int->Prop)), ((finite_finite_int A_51)->(((eq nat) (finite_card_int ((insert_int X_17) A_51))) (suc (finite_card_int ((minus_minus_int_o A_51) ((insert_int X_17) bot_bot_int_o))))))). % Axiom fact_648_card__insert:(forall (X_17:nat) (A_51:(nat->Prop)), ((finite_finite_nat A_51)->(((eq nat) (finite_card_nat ((insert_nat X_17) A_51))) (suc (finite_card_nat ((minus_minus_nat_o A_51) ((insert_nat X_17) bot_bot_nat_o))))))). % Axiom fact_649_card__insert:(forall (X_17:pname) (A_51:(pname->Prop)), ((finite_finite_pname A_51)->(((eq nat) (finite_card_pname ((insert_pname X_17) A_51))) (suc (finite_card_pname ((minus_minus_pname_o A_51) ((insert_pname X_17) bot_bot_pname_o))))))). % Axiom fact_650_card__Diff1__le:(forall (X_16:x_a) (A_50:(x_a->Prop)), ((finite_finite_a A_50)->((ord_less_eq_nat (finite_card_a ((minus_minus_a_o A_50) ((insert_a X_16) bot_bot_a_o)))) (finite_card_a A_50)))). % Axiom fact_651_card__Diff1__le:(forall (X_16:int) (A_50:(int->Prop)), ((finite_finite_int A_50)->((ord_less_eq_nat (finite_card_int ((minus_minus_int_o A_50) ((insert_int X_16) bot_bot_int_o)))) (finite_card_int A_50)))). % Axiom fact_652_card__Diff1__le:(forall (X_16:nat) (A_50:(nat->Prop)), ((finite_finite_nat A_50)->((ord_less_eq_nat (finite_card_nat ((minus_minus_nat_o A_50) ((insert_nat X_16) bot_bot_nat_o)))) (finite_card_nat A_50)))). % Axiom fact_653_card__Diff1__le:(forall (X_16:pname) (A_50:(pname->Prop)), ((finite_finite_pname A_50)->((ord_less_eq_nat (finite_card_pname ((minus_minus_pname_o A_50) ((insert_pname X_16) bot_bot_pname_o)))) (finite_card_pname A_50)))). % Axiom fact_654_finite__Diff__insert:(forall (A_49:(x_a->Prop)) (A_48:x_a) (B_31:(x_a->Prop)), ((iff (finite_finite_a ((minus_minus_a_o A_49) ((insert_a A_48) B_31)))) (finite_finite_a ((minus_minus_a_o A_49) B_31)))). % Axiom fact_655_finite__Diff__insert:(forall (A_49:(int->Prop)) (A_48:int) (B_31:(int->Prop)), ((iff (finite_finite_int ((minus_minus_int_o A_49) ((insert_int A_48) B_31)))) (finite_finite_int ((minus_minus_int_o A_49) B_31)))). % Axiom fact_656_finite__Diff__insert:(forall (A_49:(nat->Prop)) (A_48:nat) (B_31:(nat->Prop)), ((iff (finite_finite_nat ((minus_minus_nat_o A_49) ((insert_nat A_48) B_31)))) (finite_finite_nat ((minus_minus_nat_o A_49) B_31)))). % Axiom fact_657_finite__Diff__insert:(forall (A_49:(pname->Prop)) (A_48:pname) (B_31:(pname->Prop)), ((iff (finite_finite_pname ((minus_minus_pname_o A_49) ((insert_pname A_48) B_31)))) (finite_finite_pname ((minus_minus_pname_o A_49) B_31)))). % Axiom fact_658_image__diff__subset:(forall (F_19:(nat->int)) (A_47:(nat->Prop)) (B_30:(nat->Prop)), ((ord_less_eq_int_o ((minus_minus_int_o ((image_nat_int F_19) A_47)) ((image_nat_int F_19) B_30))) ((image_nat_int F_19) ((minus_minus_nat_o A_47) B_30)))). % Axiom fact_659_image__diff__subset:(forall (F_19:(pname->x_a)) (A_47:(pname->Prop)) (B_30:(pname->Prop)), ((ord_less_eq_a_o ((minus_minus_a_o ((image_pname_a F_19) A_47)) ((image_pname_a F_19) B_30))) ((image_pname_a F_19) ((minus_minus_pname_o A_47) B_30)))). % Axiom fact_660_subset__singletonD:(forall (A_46:(x_a->Prop)) (X_15:x_a), (((ord_less_eq_a_o A_46) ((insert_a X_15) bot_bot_a_o))->((or (((eq (x_a->Prop)) A_46) bot_bot_a_o)) (((eq (x_a->Prop)) A_46) ((insert_a X_15) bot_bot_a_o))))). % Axiom fact_661_subset__singletonD:(forall (A_46:(nat->Prop)) (X_15:nat), (((ord_less_eq_nat_o A_46) ((insert_nat X_15) bot_bot_nat_o))->((or (((eq (nat->Prop)) A_46) bot_bot_nat_o)) (((eq (nat->Prop)) A_46) ((insert_nat X_15) bot_bot_nat_o))))). % Axiom fact_662_subset__singletonD:(forall (A_46:(int->Prop)) (X_15:int), (((ord_less_eq_int_o A_46) ((insert_int X_15) bot_bot_int_o))->((or (((eq (int->Prop)) A_46) bot_bot_int_o)) (((eq (int->Prop)) A_46) ((insert_int X_15) bot_bot_int_o))))). % Axiom fact_663_nat__case__Suc:(forall (F1:nat) (F2:(nat->nat)) (Nat_3:nat), (((eq nat) (((nat_case_nat F1) F2) (suc Nat_3))) (F2 Nat_3))). % Axiom fact_664_nat__case__Suc:(forall (F1:Prop) (F2:(nat->Prop)) (Nat_3:nat), ((iff (((nat_case_o F1) F2) (suc Nat_3))) (F2 Nat_3))). % Axiom fact_665_image__constant:(forall (C_21:int) (X_14:nat) (A_45:(nat->Prop)), (((member_nat X_14) A_45)->(((eq (int->Prop)) ((image_nat_int (fun (X_1:nat)=> C_21)) A_45)) ((insert_int C_21) bot_bot_int_o)))). % Axiom fact_666_image__constant:(forall (C_21:x_a) (X_14:pname) (A_45:(pname->Prop)), (((member_pname X_14) A_45)->(((eq (x_a->Prop)) ((image_pname_a (fun (X_1:pname)=> C_21)) A_45)) ((insert_a C_21) bot_bot_a_o)))). % Axiom fact_667_image__constant__conv:(forall (C_20:int) (A_44:(nat->Prop)), ((and ((((eq (nat->Prop)) A_44) bot_bot_nat_o)->(((eq (int->Prop)) ((image_nat_int (fun (X_1:nat)=> C_20)) A_44)) bot_bot_int_o))) ((not (((eq (nat->Prop)) A_44) bot_bot_nat_o))->(((eq (int->Prop)) ((image_nat_int (fun (X_1:nat)=> C_20)) A_44)) ((insert_int C_20) bot_bot_int_o))))). % Axiom fact_668_image__constant__conv:(forall (C_20:x_a) (A_44:(pname->Prop)), ((and ((((eq (pname->Prop)) A_44) bot_bot_pname_o)->(((eq (x_a->Prop)) ((image_pname_a (fun (X_1:pname)=> C_20)) A_44)) bot_bot_a_o))) ((not (((eq (pname->Prop)) A_44) bot_bot_pname_o))->(((eq (x_a->Prop)) ((image_pname_a (fun (X_1:pname)=> C_20)) A_44)) ((insert_a C_20) bot_bot_a_o))))). % Axiom fact_669_diff__eq__diff__eq:(forall (A_43:int) (B_29:int) (C_19:int) (D_3:int), ((((eq int) ((minus_minus_int A_43) B_29)) ((minus_minus_int C_19) D_3))->((iff (((eq int) A_43) B_29)) (((eq int) C_19) D_3)))). % Axiom fact_670_card__Diff__subset:(forall (A_42:(int->Prop)) (B_28:(int->Prop)), ((finite_finite_int B_28)->(((ord_less_eq_int_o B_28) A_42)->(((eq nat) (finite_card_int ((minus_minus_int_o A_42) B_28))) ((minus_minus_nat (finite_card_int A_42)) (finite_card_int B_28)))))). % Axiom fact_671_card__Diff__subset:(forall (A_42:(nat->Prop)) (B_28:(nat->Prop)), ((finite_finite_nat B_28)->(((ord_less_eq_nat_o B_28) A_42)->(((eq nat) (finite_card_nat ((minus_minus_nat_o A_42) B_28))) ((minus_minus_nat (finite_card_nat A_42)) (finite_card_nat B_28)))))). % Axiom fact_672_card__Diff__subset:(forall (A_42:(x_a->Prop)) (B_28:(x_a->Prop)), ((finite_finite_a B_28)->(((ord_less_eq_a_o B_28) A_42)->(((eq nat) (finite_card_a ((minus_minus_a_o A_42) B_28))) ((minus_minus_nat (finite_card_a A_42)) (finite_card_a B_28)))))). % Axiom fact_673_card__Diff__subset:(forall (A_42:(pname->Prop)) (B_28:(pname->Prop)), ((finite_finite_pname B_28)->(((ord_less_eq_pname_o B_28) A_42)->(((eq nat) (finite_card_pname ((minus_minus_pname_o A_42) B_28))) ((minus_minus_nat (finite_card_pname A_42)) (finite_card_pname B_28)))))). % Axiom fact_674_diff__card__le__card__Diff:(forall (A_41:(int->Prop)) (B_27:(int->Prop)), ((finite_finite_int B_27)->((ord_less_eq_nat ((minus_minus_nat (finite_card_int A_41)) (finite_card_int B_27))) (finite_card_int ((minus_minus_int_o A_41) B_27))))). % Axiom fact_675_diff__card__le__card__Diff:(forall (A_41:(nat->Prop)) (B_27:(nat->Prop)), ((finite_finite_nat B_27)->((ord_less_eq_nat ((minus_minus_nat (finite_card_nat A_41)) (finite_card_nat B_27))) (finite_card_nat ((minus_minus_nat_o A_41) B_27))))). % Axiom fact_676_diff__card__le__card__Diff:(forall (A_41:(x_a->Prop)) (B_27:(x_a->Prop)), ((finite_finite_a B_27)->((ord_less_eq_nat ((minus_minus_nat (finite_card_a A_41)) (finite_card_a B_27))) (finite_card_a ((minus_minus_a_o A_41) B_27))))). % Axiom fact_677_diff__card__le__card__Diff:(forall (A_41:(pname->Prop)) (B_27:(pname->Prop)), ((finite_finite_pname B_27)->((ord_less_eq_nat ((minus_minus_nat (finite_card_pname A_41)) (finite_card_pname B_27))) (finite_card_pname ((minus_minus_pname_o A_41) B_27))))). % Axiom fact_678_finite__subset__induct:(forall (P_5:((x_a->Prop)->Prop)) (A_40:(x_a->Prop)) (F_18:(x_a->Prop)), ((finite_finite_a F_18)->(((ord_less_eq_a_o F_18) A_40)->((P_5 bot_bot_a_o)->((forall (A_37:x_a) (F_2:(x_a->Prop)), ((finite_finite_a F_2)->(((member_a A_37) A_40)->((((member_a A_37) F_2)->False)->((P_5 F_2)->(P_5 ((insert_a A_37) F_2)))))))->(P_5 F_18)))))). % Axiom fact_679_finite__subset__induct:(forall (P_5:((int->Prop)->Prop)) (A_40:(int->Prop)) (F_18:(int->Prop)), ((finite_finite_int F_18)->(((ord_less_eq_int_o F_18) A_40)->((P_5 bot_bot_int_o)->((forall (A_37:int) (F_2:(int->Prop)), ((finite_finite_int F_2)->(((member_int A_37) A_40)->((((member_int A_37) F_2)->False)->((P_5 F_2)->(P_5 ((insert_int A_37) F_2)))))))->(P_5 F_18)))))). % Axiom fact_680_finite__subset__induct:(forall (P_5:((nat->Prop)->Prop)) (A_40:(nat->Prop)) (F_18:(nat->Prop)), ((finite_finite_nat F_18)->(((ord_less_eq_nat_o F_18) A_40)->((P_5 bot_bot_nat_o)->((forall (A_37:nat) (F_2:(nat->Prop)), ((finite_finite_nat F_2)->(((member_nat A_37) A_40)->((((member_nat A_37) F_2)->False)->((P_5 F_2)->(P_5 ((insert_nat A_37) F_2)))))))->(P_5 F_18)))))). % Axiom fact_681_finite__subset__induct:(forall (P_5:((pname->Prop)->Prop)) (A_40:(pname->Prop)) (F_18:(pname->Prop)), ((finite_finite_pname F_18)->(((ord_less_eq_pname_o F_18) A_40)->((P_5 bot_bot_pname_o)->((forall (A_37:pname) (F_2:(pname->Prop)), ((finite_finite_pname F_2)->(((member_pname A_37) A_40)->((((member_pname A_37) F_2)->False)->((P_5 F_2)->(P_5 ((insert_pname A_37) F_2)))))))->(P_5 F_18)))))). % Axiom fact_682_assms_I2_J:(forall (Pn:pname) (G:(x_a->Prop)), (((p ((insert_a (mgt_call Pn)) G)) ((insert_a (mgt (the_com (body Pn)))) bot_bot_a_o))->((p G) ((insert_a (mgt_call Pn)) bot_bot_a_o)))). % Axiom fact_683_finite__empty__induct:(forall (P_4:((x_a->Prop)->Prop)) (A_39:(x_a->Prop)), ((finite_finite_a A_39)->((P_4 A_39)->((forall (A_37:x_a) (A_38:(x_a->Prop)), ((finite_finite_a A_38)->(((member_a A_37) A_38)->((P_4 A_38)->(P_4 ((minus_minus_a_o A_38) ((insert_a A_37) bot_bot_a_o)))))))->(P_4 bot_bot_a_o))))). % Axiom fact_684_finite__empty__induct:(forall (P_4:((int->Prop)->Prop)) (A_39:(int->Prop)), ((finite_finite_int A_39)->((P_4 A_39)->((forall (A_37:int) (A_38:(int->Prop)), ((finite_finite_int A_38)->(((member_int A_37) A_38)->((P_4 A_38)->(P_4 ((minus_minus_int_o A_38) ((insert_int A_37) bot_bot_int_o)))))))->(P_4 bot_bot_int_o))))). % Axiom fact_685_finite__empty__induct:(forall (P_4:((nat->Prop)->Prop)) (A_39:(nat->Prop)), ((finite_finite_nat A_39)->((P_4 A_39)->((forall (A_37:nat) (A_38:(nat->Prop)), ((finite_finite_nat A_38)->(((member_nat A_37) A_38)->((P_4 A_38)->(P_4 ((minus_minus_nat_o A_38) ((insert_nat A_37) bot_bot_nat_o)))))))->(P_4 bot_bot_nat_o))))). % Axiom fact_686_finite__empty__induct:(forall (P_4:((pname->Prop)->Prop)) (A_39:(pname->Prop)), ((finite_finite_pname A_39)->((P_4 A_39)->((forall (A_37:pname) (A_38:(pname->Prop)), ((finite_finite_pname A_38)->(((member_pname A_37) A_38)->((P_4 A_38)->(P_4 ((minus_minus_pname_o A_38) ((insert_pname A_37) bot_bot_pname_o)))))))->(P_4 bot_bot_pname_o))))). % Axiom fact_687_finite__induct:(forall (P_3:((x_a->Prop)->Prop)) (F_17:(x_a->Prop)), ((finite_finite_a F_17)->((P_3 bot_bot_a_o)->((forall (X_1:x_a) (F_2:(x_a->Prop)), ((finite_finite_a F_2)->((((member_a X_1) F_2)->False)->((P_3 F_2)->(P_3 ((insert_a X_1) F_2))))))->(P_3 F_17))))). % Axiom fact_688_finite__induct:(forall (P_3:((int->Prop)->Prop)) (F_17:(int->Prop)), ((finite_finite_int F_17)->((P_3 bot_bot_int_o)->((forall (X_1:int) (F_2:(int->Prop)), ((finite_finite_int F_2)->((((member_int X_1) F_2)->False)->((P_3 F_2)->(P_3 ((insert_int X_1) F_2))))))->(P_3 F_17))))). % Axiom fact_689_finite__induct:(forall (P_3:((nat->Prop)->Prop)) (F_17:(nat->Prop)), ((finite_finite_nat F_17)->((P_3 bot_bot_nat_o)->((forall (X_1:nat) (F_2:(nat->Prop)), ((finite_finite_nat F_2)->((((member_nat X_1) F_2)->False)->((P_3 F_2)->(P_3 ((insert_nat X_1) F_2))))))->(P_3 F_17))))). % Axiom fact_690_finite__induct:(forall (P_3:((pname->Prop)->Prop)) (F_17:(pname->Prop)), ((finite_finite_pname F_17)->((P_3 bot_bot_pname_o)->((forall (X_1:pname) (F_2:(pname->Prop)), ((finite_finite_pname F_2)->((((member_pname X_1) F_2)->False)->((P_3 F_2)->(P_3 ((insert_pname X_1) F_2))))))->(P_3 F_17))))). % Axiom fact_691_finite_Osimps:(forall (A_36:(x_a->Prop)), ((iff (finite_finite_a A_36)) ((or (((eq (x_a->Prop)) A_36) bot_bot_a_o)) ((ex (x_a->Prop)) (fun (A_38:(x_a->Prop))=> ((ex x_a) (fun (A_37:x_a)=> ((and (((eq (x_a->Prop)) A_36) ((insert_a A_37) A_38))) (finite_finite_a A_38))))))))). % Axiom fact_692_finite_Osimps:(forall (A_36:(int->Prop)), ((iff (finite_finite_int A_36)) ((or (((eq (int->Prop)) A_36) bot_bot_int_o)) ((ex (int->Prop)) (fun (A_38:(int->Prop))=> ((ex int) (fun (A_37:int)=> ((and (((eq (int->Prop)) A_36) ((insert_int A_37) A_38))) (finite_finite_int A_38))))))))). % Axiom fact_693_finite_Osimps:(forall (A_36:(nat->Prop)), ((iff (finite_finite_nat A_36)) ((or (((eq (nat->Prop)) A_36) bot_bot_nat_o)) ((ex (nat->Prop)) (fun (A_38:(nat->Prop))=> ((ex nat) (fun (A_37:nat)=> ((and (((eq (nat->Prop)) A_36) ((insert_nat A_37) A_38))) (finite_finite_nat A_38))))))))). % Axiom fact_694_finite_Osimps:(forall (A_36:(pname->Prop)), ((iff (finite_finite_pname A_36)) ((or (((eq (pname->Prop)) A_36) bot_bot_pname_o)) ((ex (pname->Prop)) (fun (A_38:(pname->Prop))=> ((ex pname) (fun (A_37:pname)=> ((and (((eq (pname->Prop)) A_36) ((insert_pname A_37) A_38))) (finite_finite_pname A_38))))))))). % Axiom fact_695_finite__less__ub:(forall (U:nat) (F:(nat->nat)), ((forall (N_1:nat), ((ord_less_eq_nat N_1) (F N_1)))->(finite_finite_nat (collect_nat (fun (N_1:nat)=> ((ord_less_eq_nat (F N_1)) U)))))). % Axiom fact_696_the__elem__eq:(forall (X_13:x_a), (((eq x_a) (the_elem_a ((insert_a X_13) bot_bot_a_o))) X_13)). % Axiom fact_697_the__elem__eq:(forall (X_13:nat), (((eq nat) (the_elem_nat ((insert_nat X_13) bot_bot_nat_o))) X_13)). % Axiom fact_698_the__elem__eq:(forall (X_13:int), (((eq int) (the_elem_int ((insert_int X_13) bot_bot_int_o))) X_13)). % Axiom fact_699_nonempty__iff:(forall (A_35:(x_a->Prop)), ((iff (not (((eq (x_a->Prop)) A_35) bot_bot_a_o))) ((ex x_a) (fun (X_1:x_a)=> ((ex (x_a->Prop)) (fun (B_26:(x_a->Prop))=> ((and (((eq (x_a->Prop)) A_35) ((insert_a X_1) B_26))) (((member_a X_1) B_26)->False)))))))). % Axiom fact_700_nonempty__iff:(forall (A_35:(int->Prop)), ((iff (not (((eq (int->Prop)) A_35) bot_bot_int_o))) ((ex int) (fun (X_1:int)=> ((ex (int->Prop)) (fun (B_26:(int->Prop))=> ((and (((eq (int->Prop)) A_35) ((insert_int X_1) B_26))) (((member_int X_1) B_26)->False)))))))). % Axiom fact_701_nonempty__iff:(forall (A_35:(nat->Prop)), ((iff (not (((eq (nat->Prop)) A_35) bot_bot_nat_o))) ((ex nat) (fun (X_1:nat)=> ((ex (nat->Prop)) (fun (B_26:(nat->Prop))=> ((and (((eq (nat->Prop)) A_35) ((insert_nat X_1) B_26))) (((member_nat X_1) B_26)->False)))))))). % Axiom fact_702_nonempty__iff:(forall (A_35:(pname->Prop)), ((iff (not (((eq (pname->Prop)) A_35) bot_bot_pname_o))) ((ex pname) (fun (X_1:pname)=> ((ex (pname->Prop)) (fun (B_26:(pname->Prop))=> ((and (((eq (pname->Prop)) A_35) ((insert_pname X_1) B_26))) (((member_pname X_1) B_26)->False)))))))). % Axiom fact_703_assms_I4_J:(forall (Pn:pname), (((member_pname Pn) u)->(wt (the_com (body Pn))))). % Axiom fact_704_DiffE:(forall (C_18:int) (A_34:(int->Prop)) (B_25:(int->Prop)), (((member_int C_18) ((minus_minus_int_o A_34) B_25))->((((member_int C_18) A_34)->((member_int C_18) B_25))->False))). % Axiom fact_705_DiffE:(forall (C_18:nat) (A_34:(nat->Prop)) (B_25:(nat->Prop)), (((member_nat C_18) ((minus_minus_nat_o A_34) B_25))->((((member_nat C_18) A_34)->((member_nat C_18) B_25))->False))). % Axiom fact_706_DiffE:(forall (C_18:x_a) (A_34:(x_a->Prop)) (B_25:(x_a->Prop)), (((member_a C_18) ((minus_minus_a_o A_34) B_25))->((((member_a C_18) A_34)->((member_a C_18) B_25))->False))). % Axiom fact_707_DiffE:(forall (C_18:pname) (A_34:(pname->Prop)) (B_25:(pname->Prop)), (((member_pname C_18) ((minus_minus_pname_o A_34) B_25))->((((member_pname C_18) A_34)->((member_pname C_18) B_25))->False))). % Axiom fact_708_DiffI:(forall (B_24:(int->Prop)) (C_17:int) (A_33:(int->Prop)), (((member_int C_17) A_33)->((((member_int C_17) B_24)->False)->((member_int C_17) ((minus_minus_int_o A_33) B_24))))). % Axiom fact_709_DiffI:(forall (B_24:(nat->Prop)) (C_17:nat) (A_33:(nat->Prop)), (((member_nat C_17) A_33)->((((member_nat C_17) B_24)->False)->((member_nat C_17) ((minus_minus_nat_o A_33) B_24))))). % Axiom fact_710_DiffI:(forall (B_24:(x_a->Prop)) (C_17:x_a) (A_33:(x_a->Prop)), (((member_a C_17) A_33)->((((member_a C_17) B_24)->False)->((member_a C_17) ((minus_minus_a_o A_33) B_24))))). % Axiom fact_711_DiffI:(forall (B_24:(pname->Prop)) (C_17:pname) (A_33:(pname->Prop)), (((member_pname C_17) A_33)->((((member_pname C_17) B_24)->False)->((member_pname C_17) ((minus_minus_pname_o A_33) B_24))))). % Axiom fact_712_DiffD2:(forall (C_16:int) (A_32:(int->Prop)) (B_23:(int->Prop)), (((member_int C_16) ((minus_minus_int_o A_32) B_23))->(((member_int C_16) B_23)->False))). % Axiom fact_713_DiffD2:(forall (C_16:nat) (A_32:(nat->Prop)) (B_23:(nat->Prop)), (((member_nat C_16) ((minus_minus_nat_o A_32) B_23))->(((member_nat C_16) B_23)->False))). % Axiom fact_714_DiffD2:(forall (C_16:x_a) (A_32:(x_a->Prop)) (B_23:(x_a->Prop)), (((member_a C_16) ((minus_minus_a_o A_32) B_23))->(((member_a C_16) B_23)->False))). % Axiom fact_715_DiffD2:(forall (C_16:pname) (A_32:(pname->Prop)) (B_23:(pname->Prop)), (((member_pname C_16) ((minus_minus_pname_o A_32) B_23))->(((member_pname C_16) B_23)->False))). % Axiom fact_716_DiffD1:(forall (C_15:int) (A_31:(int->Prop)) (B_22:(int->Prop)), (((member_int C_15) ((minus_minus_int_o A_31) B_22))->((member_int C_15) A_31))). % Axiom fact_717_DiffD1:(forall (C_15:nat) (A_31:(nat->Prop)) (B_22:(nat->Prop)), (((member_nat C_15) ((minus_minus_nat_o A_31) B_22))->((member_nat C_15) A_31))). % Axiom fact_718_DiffD1:(forall (C_15:x_a) (A_31:(x_a->Prop)) (B_22:(x_a->Prop)), (((member_a C_15) ((minus_minus_a_o A_31) B_22))->((member_a C_15) A_31))). % Axiom fact_719_DiffD1:(forall (C_15:pname) (A_31:(pname->Prop)) (B_22:(pname->Prop)), (((member_pname C_15) ((minus_minus_pname_o A_31) B_22))->((member_pname C_15) A_31))). % Axiom fact_720_Diff__iff:(forall (C_14:int) (A_30:(int->Prop)) (B_21:(int->Prop)), ((iff ((member_int C_14) ((minus_minus_int_o A_30) B_21))) ((and ((member_int C_14) A_30)) (((member_int C_14) B_21)->False)))). % Axiom fact_721_Diff__iff:(forall (C_14:nat) (A_30:(nat->Prop)) (B_21:(nat->Prop)), ((iff ((member_nat C_14) ((minus_minus_nat_o A_30) B_21))) ((and ((member_nat C_14) A_30)) (((member_nat C_14) B_21)->False)))). % Axiom fact_722_Diff__iff:(forall (C_14:x_a) (A_30:(x_a->Prop)) (B_21:(x_a->Prop)), ((iff ((member_a C_14) ((minus_minus_a_o A_30) B_21))) ((and ((member_a C_14) A_30)) (((member_a C_14) B_21)->False)))). % Axiom fact_723_Diff__iff:(forall (C_14:pname) (A_30:(pname->Prop)) (B_21:(pname->Prop)), ((iff ((member_pname C_14) ((minus_minus_pname_o A_30) B_21))) ((and ((member_pname C_14) A_30)) (((member_pname C_14) B_21)->False)))). % Axiom fact_724_set__diff__eq:(forall (A_29:(int->Prop)) (B_20:(int->Prop)), (((eq (int->Prop)) ((minus_minus_int_o A_29) B_20)) (collect_int (fun (X_1:int)=> ((and ((member_int X_1) A_29)) (not ((member_int X_1) B_20))))))). % Axiom fact_725_set__diff__eq:(forall (A_29:(nat->Prop)) (B_20:(nat->Prop)), (((eq (nat->Prop)) ((minus_minus_nat_o A_29) B_20)) (collect_nat (fun (X_1:nat)=> ((and ((member_nat X_1) A_29)) (not ((member_nat X_1) B_20))))))). % Axiom fact_726_set__diff__eq:(forall (A_29:(x_a->Prop)) (B_20:(x_a->Prop)), (((eq (x_a->Prop)) ((minus_minus_a_o A_29) B_20)) (collect_a (fun (X_1:x_a)=> ((and ((member_a X_1) A_29)) (not ((member_a X_1) B_20))))))). % Axiom fact_727_set__diff__eq:(forall (A_29:(pname->Prop)) (B_20:(pname->Prop)), (((eq (pname->Prop)) ((minus_minus_pname_o A_29) B_20)) (collect_pname (fun (X_1:pname)=> ((and ((member_pname X_1) A_29)) (not ((member_pname X_1) B_20))))))). % Axiom fact_728_folding__one_Oinsert__remove:(forall (X_12:x_a) (A_28:(x_a->Prop)) (F_16:(x_a->(x_a->x_a))) (F_15:((x_a->Prop)->x_a)), (((finite_folding_one_a F_16) F_15)->((finite_finite_a A_28)->((and ((((eq (x_a->Prop)) ((minus_minus_a_o A_28) ((insert_a X_12) bot_bot_a_o))) bot_bot_a_o)->(((eq x_a) (F_15 ((insert_a X_12) A_28))) X_12))) ((not (((eq (x_a->Prop)) ((minus_minus_a_o A_28) ((insert_a X_12) bot_bot_a_o))) bot_bot_a_o))->(((eq x_a) (F_15 ((insert_a X_12) A_28))) ((F_16 X_12) (F_15 ((minus_minus_a_o A_28) ((insert_a X_12) bot_bot_a_o)))))))))). % Axiom fact_729_folding__one_Oinsert__remove:(forall (X_12:int) (A_28:(int->Prop)) (F_16:(int->(int->int))) (F_15:((int->Prop)->int)), (((finite1626084323ne_int F_16) F_15)->((finite_finite_int A_28)->((and ((((eq (int->Prop)) ((minus_minus_int_o A_28) ((insert_int X_12) bot_bot_int_o))) bot_bot_int_o)->(((eq int) (F_15 ((insert_int X_12) A_28))) X_12))) ((not (((eq (int->Prop)) ((minus_minus_int_o A_28) ((insert_int X_12) bot_bot_int_o))) bot_bot_int_o))->(((eq int) (F_15 ((insert_int X_12) A_28))) ((F_16 X_12) (F_15 ((minus_minus_int_o A_28) ((insert_int X_12) bot_bot_int_o)))))))))). % Axiom fact_730_folding__one_Oinsert__remove:(forall (X_12:nat) (A_28:(nat->Prop)) (F_16:(nat->(nat->nat))) (F_15:((nat->Prop)->nat)), (((finite988810631ne_nat F_16) F_15)->((finite_finite_nat A_28)->((and ((((eq (nat->Prop)) ((minus_minus_nat_o A_28) ((insert_nat X_12) bot_bot_nat_o))) bot_bot_nat_o)->(((eq nat) (F_15 ((insert_nat X_12) A_28))) X_12))) ((not (((eq (nat->Prop)) ((minus_minus_nat_o A_28) ((insert_nat X_12) bot_bot_nat_o))) bot_bot_nat_o))->(((eq nat) (F_15 ((insert_nat X_12) A_28))) ((F_16 X_12) (F_15 ((minus_minus_nat_o A_28) ((insert_nat X_12) bot_bot_nat_o)))))))))). % Axiom fact_731_folding__one_Oinsert__remove:(forall (X_12:pname) (A_28:(pname->Prop)) (F_16:(pname->(pname->pname))) (F_15:((pname->Prop)->pname)), (((finite1282449217_pname F_16) F_15)->((finite_finite_pname A_28)->((and ((((eq (pname->Prop)) ((minus_minus_pname_o A_28) ((insert_pname X_12) bot_bot_pname_o))) bot_bot_pname_o)->(((eq pname) (F_15 ((insert_pname X_12) A_28))) X_12))) ((not (((eq (pname->Prop)) ((minus_minus_pname_o A_28) ((insert_pname X_12) bot_bot_pname_o))) bot_bot_pname_o))->(((eq pname) (F_15 ((insert_pname X_12) A_28))) ((F_16 X_12) (F_15 ((minus_minus_pname_o A_28) ((insert_pname X_12) bot_bot_pname_o)))))))))). % Axiom fact_732_folding__one_Oremove:(forall (X_11:x_a) (A_27:(x_a->Prop)) (F_14:(x_a->(x_a->x_a))) (F_13:((x_a->Prop)->x_a)), (((finite_folding_one_a F_14) F_13)->((finite_finite_a A_27)->(((member_a X_11) A_27)->((and ((((eq (x_a->Prop)) ((minus_minus_a_o A_27) ((insert_a X_11) bot_bot_a_o))) bot_bot_a_o)->(((eq x_a) (F_13 A_27)) X_11))) ((not (((eq (x_a->Prop)) ((minus_minus_a_o A_27) ((insert_a X_11) bot_bot_a_o))) bot_bot_a_o))->(((eq x_a) (F_13 A_27)) ((F_14 X_11) (F_13 ((minus_minus_a_o A_27) ((insert_a X_11) bot_bot_a_o))))))))))). % Axiom fact_733_folding__one_Oremove:(forall (X_11:int) (A_27:(int->Prop)) (F_14:(int->(int->int))) (F_13:((int->Prop)->int)), (((finite1626084323ne_int F_14) F_13)->((finite_finite_int A_27)->(((member_int X_11) A_27)->((and ((((eq (int->Prop)) ((minus_minus_int_o A_27) ((insert_int X_11) bot_bot_int_o))) bot_bot_int_o)->(((eq int) (F_13 A_27)) X_11))) ((not (((eq (int->Prop)) ((minus_minus_int_o A_27) ((insert_int X_11) bot_bot_int_o))) bot_bot_int_o))->(((eq int) (F_13 A_27)) ((F_14 X_11) (F_13 ((minus_minus_int_o A_27) ((insert_int X_11) bot_bot_int_o))))))))))). % Axiom fact_734_folding__one_Oremove:(forall (X_11:nat) (A_27:(nat->Prop)) (F_14:(nat->(nat->nat))) (F_13:((nat->Prop)->nat)), (((finite988810631ne_nat F_14) F_13)->((finite_finite_nat A_27)->(((member_nat X_11) A_27)->((and ((((eq (nat->Prop)) ((minus_minus_nat_o A_27) ((insert_nat X_11) bot_bot_nat_o))) bot_bot_nat_o)->(((eq nat) (F_13 A_27)) X_11))) ((not (((eq (nat->Prop)) ((minus_minus_nat_o A_27) ((insert_nat X_11) bot_bot_nat_o))) bot_bot_nat_o))->(((eq nat) (F_13 A_27)) ((F_14 X_11) (F_13 ((minus_minus_nat_o A_27) ((insert_nat X_11) bot_bot_nat_o))))))))))). % Axiom fact_735_folding__one_Oremove:(forall (X_11:pname) (A_27:(pname->Prop)) (F_14:(pname->(pname->pname))) (F_13:((pname->Prop)->pname)), (((finite1282449217_pname F_14) F_13)->((finite_finite_pname A_27)->(((member_pname X_11) A_27)->((and ((((eq (pname->Prop)) ((minus_minus_pname_o A_27) ((insert_pname X_11) bot_bot_pname_o))) bot_bot_pname_o)->(((eq pname) (F_13 A_27)) X_11))) ((not (((eq (pname->Prop)) ((minus_minus_pname_o A_27) ((insert_pname X_11) bot_bot_pname_o))) bot_bot_pname_o))->(((eq pname) (F_13 A_27)) ((F_14 X_11) (F_13 ((minus_minus_pname_o A_27) ((insert_pname X_11) bot_bot_pname_o))))))))))). % Axiom fact_736_card__Diff__singleton__if:(forall (X_10:x_a) (A_26:(x_a->Prop)), ((finite_finite_a A_26)->((and (((member_a X_10) A_26)->(((eq nat) (finite_card_a ((minus_minus_a_o A_26) ((insert_a X_10) bot_bot_a_o)))) ((minus_minus_nat (finite_card_a A_26)) one_one_nat)))) ((((member_a X_10) A_26)->False)->(((eq nat) (finite_card_a ((minus_minus_a_o A_26) ((insert_a X_10) bot_bot_a_o)))) (finite_card_a A_26)))))). % Axiom fact_737_card__Diff__singleton__if:(forall (X_10:int) (A_26:(int->Prop)), ((finite_finite_int A_26)->((and (((member_int X_10) A_26)->(((eq nat) (finite_card_int ((minus_minus_int_o A_26) ((insert_int X_10) bot_bot_int_o)))) ((minus_minus_nat (finite_card_int A_26)) one_one_nat)))) ((((member_int X_10) A_26)->False)->(((eq nat) (finite_card_int ((minus_minus_int_o A_26) ((insert_int X_10) bot_bot_int_o)))) (finite_card_int A_26)))))). % Axiom fact_738_card__Diff__singleton__if:(forall (X_10:nat) (A_26:(nat->Prop)), ((finite_finite_nat A_26)->((and (((member_nat X_10) A_26)->(((eq nat) (finite_card_nat ((minus_minus_nat_o A_26) ((insert_nat X_10) bot_bot_nat_o)))) ((minus_minus_nat (finite_card_nat A_26)) one_one_nat)))) ((((member_nat X_10) A_26)->False)->(((eq nat) (finite_card_nat ((minus_minus_nat_o A_26) ((insert_nat X_10) bot_bot_nat_o)))) (finite_card_nat A_26)))))). % Axiom fact_739_card__Diff__singleton__if:(forall (X_10:pname) (A_26:(pname->Prop)), ((finite_finite_pname A_26)->((and (((member_pname X_10) A_26)->(((eq nat) (finite_card_pname ((minus_minus_pname_o A_26) ((insert_pname X_10) bot_bot_pname_o)))) ((minus_minus_nat (finite_card_pname A_26)) one_one_nat)))) ((((member_pname X_10) A_26)->False)->(((eq nat) (finite_card_pname ((minus_minus_pname_o A_26) ((insert_pname X_10) bot_bot_pname_o)))) (finite_card_pname A_26)))))). % Axiom fact_740_card__Diff__singleton:(forall (X_9:x_a) (A_25:(x_a->Prop)), ((finite_finite_a A_25)->(((member_a X_9) A_25)->(((eq nat) (finite_card_a ((minus_minus_a_o A_25) ((insert_a X_9) bot_bot_a_o)))) ((minus_minus_nat (finite_card_a A_25)) one_one_nat))))). % Axiom fact_741_card__Diff__singleton:(forall (X_9:int) (A_25:(int->Prop)), ((finite_finite_int A_25)->(((member_int X_9) A_25)->(((eq nat) (finite_card_int ((minus_minus_int_o A_25) ((insert_int X_9) bot_bot_int_o)))) ((minus_minus_nat (finite_card_int A_25)) one_one_nat))))). % Axiom fact_742_card__Diff__singleton:(forall (X_9:nat) (A_25:(nat->Prop)), ((finite_finite_nat A_25)->(((member_nat X_9) A_25)->(((eq nat) (finite_card_nat ((minus_minus_nat_o A_25) ((insert_nat X_9) bot_bot_nat_o)))) ((minus_minus_nat (finite_card_nat A_25)) one_one_nat))))). % Axiom fact_743_card__Diff__singleton:(forall (X_9:pname) (A_25:(pname->Prop)), ((finite_finite_pname A_25)->(((member_pname X_9) A_25)->(((eq nat) (finite_card_pname ((minus_minus_pname_o A_25) ((insert_pname X_9) bot_bot_pname_o)))) ((minus_minus_nat (finite_card_pname A_25)) one_one_nat))))). % Axiom fact_744_one__reorient:(forall (X_8:int), ((iff (((eq int) one_one_int) X_8)) (((eq int) X_8) one_one_int))). % Axiom fact_745_one__reorient:(forall (X_8:nat), ((iff (((eq nat) one_one_nat) X_8)) (((eq nat) X_8) one_one_nat))). % Axiom fact_746_diff__Suc__1:(forall (N:nat), (((eq nat) ((minus_minus_nat (suc N)) one_one_nat)) N)). % Axiom fact_747_diff__Suc__eq__diff__pred:(forall (M:nat) (N:nat), (((eq nat) ((minus_minus_nat M) (suc N))) ((minus_minus_nat ((minus_minus_nat M) one_one_nat)) N))). % Axiom fact_748_folding__one_Osingleton:(forall (X_7:x_a) (F_12:(x_a->(x_a->x_a))) (F_11:((x_a->Prop)->x_a)), (((finite_folding_one_a F_12) F_11)->(((eq x_a) (F_11 ((insert_a X_7) bot_bot_a_o))) X_7))). % Axiom fact_749_folding__one_Osingleton:(forall (X_7:nat) (F_12:(nat->(nat->nat))) (F_11:((nat->Prop)->nat)), (((finite988810631ne_nat F_12) F_11)->(((eq nat) (F_11 ((insert_nat X_7) bot_bot_nat_o))) X_7))). % Axiom fact_750_folding__one_Osingleton:(forall (X_7:int) (F_12:(int->(int->int))) (F_11:((int->Prop)->int)), (((finite1626084323ne_int F_12) F_11)->(((eq int) (F_11 ((insert_int X_7) bot_bot_int_o))) X_7))). % Axiom fact_751_card__Diff__insert:(forall (B_19:(x_a->Prop)) (A_24:x_a) (A_23:(x_a->Prop)), ((finite_finite_a A_23)->(((member_a A_24) A_23)->((((member_a A_24) B_19)->False)->(((eq nat) (finite_card_a ((minus_minus_a_o A_23) ((insert_a A_24) B_19)))) ((minus_minus_nat (finite_card_a ((minus_minus_a_o A_23) B_19))) one_one_nat)))))). % Axiom fact_752_card__Diff__insert:(forall (B_19:(int->Prop)) (A_24:int) (A_23:(int->Prop)), ((finite_finite_int A_23)->(((member_int A_24) A_23)->((((member_int A_24) B_19)->False)->(((eq nat) (finite_card_int ((minus_minus_int_o A_23) ((insert_int A_24) B_19)))) ((minus_minus_nat (finite_card_int ((minus_minus_int_o A_23) B_19))) one_one_nat)))))). % Axiom fact_753_card__Diff__insert:(forall (B_19:(nat->Prop)) (A_24:nat) (A_23:(nat->Prop)), ((finite_finite_nat A_23)->(((member_nat A_24) A_23)->((((member_nat A_24) B_19)->False)->(((eq nat) (finite_card_nat ((minus_minus_nat_o A_23) ((insert_nat A_24) B_19)))) ((minus_minus_nat (finite_card_nat ((minus_minus_nat_o A_23) B_19))) one_one_nat)))))). % Axiom fact_754_card__Diff__insert:(forall (B_19:(pname->Prop)) (A_24:pname) (A_23:(pname->Prop)), ((finite_finite_pname A_23)->(((member_pname A_24) A_23)->((((member_pname A_24) B_19)->False)->(((eq nat) (finite_card_pname ((minus_minus_pname_o A_23) ((insert_pname A_24) B_19)))) ((minus_minus_nat (finite_card_pname ((minus_minus_pname_o A_23) B_19))) one_one_nat)))))). % Axiom fact_755_folding__one_Oinsert:(forall (X_6:x_a) (A_22:(x_a->Prop)) (F_10:(x_a->(x_a->x_a))) (F_9:((x_a->Prop)->x_a)), (((finite_folding_one_a F_10) F_9)->((finite_finite_a A_22)->((((member_a X_6) A_22)->False)->((not (((eq (x_a->Prop)) A_22) bot_bot_a_o))->(((eq x_a) (F_9 ((insert_a X_6) A_22))) ((F_10 X_6) (F_9 A_22)))))))). % Axiom fact_756_folding__one_Oinsert:(forall (X_6:int) (A_22:(int->Prop)) (F_10:(int->(int->int))) (F_9:((int->Prop)->int)), (((finite1626084323ne_int F_10) F_9)->((finite_finite_int A_22)->((((member_int X_6) A_22)->False)->((not (((eq (int->Prop)) A_22) bot_bot_int_o))->(((eq int) (F_9 ((insert_int X_6) A_22))) ((F_10 X_6) (F_9 A_22)))))))). % Axiom fact_757_folding__one_Oinsert:(forall (X_6:nat) (A_22:(nat->Prop)) (F_10:(nat->(nat->nat))) (F_9:((nat->Prop)->nat)), (((finite988810631ne_nat F_10) F_9)->((finite_finite_nat A_22)->((((member_nat X_6) A_22)->False)->((not (((eq (nat->Prop)) A_22) bot_bot_nat_o))->(((eq nat) (F_9 ((insert_nat X_6) A_22))) ((F_10 X_6) (F_9 A_22)))))))). % Axiom fact_758_folding__one_Oinsert:(forall (X_6:pname) (A_22:(pname->Prop)) (F_10:(pname->(pname->pname))) (F_9:((pname->Prop)->pname)), (((finite1282449217_pname F_10) F_9)->((finite_finite_pname A_22)->((((member_pname X_6) A_22)->False)->((not (((eq (pname->Prop)) A_22) bot_bot_pname_o))->(((eq pname) (F_9 ((insert_pname X_6) A_22))) ((F_10 X_6) (F_9 A_22)))))))). % Axiom fact_759_folding__one_Oclosed:(forall (A_21:(x_a->Prop)) (F_8:(x_a->(x_a->x_a))) (F_7:((x_a->Prop)->x_a)), (((finite_folding_one_a F_8) F_7)->((finite_finite_a A_21)->((not (((eq (x_a->Prop)) A_21) bot_bot_a_o))->((forall (X_1:x_a) (Y_1:x_a), ((member_a ((F_8 X_1) Y_1)) ((insert_a X_1) ((insert_a Y_1) bot_bot_a_o))))->((member_a (F_7 A_21)) A_21)))))). % Axiom fact_760_folding__one_Oclosed:(forall (A_21:(int->Prop)) (F_8:(int->(int->int))) (F_7:((int->Prop)->int)), (((finite1626084323ne_int F_8) F_7)->((finite_finite_int A_21)->((not (((eq (int->Prop)) A_21) bot_bot_int_o))->((forall (X_1:int) (Y_1:int), ((member_int ((F_8 X_1) Y_1)) ((insert_int X_1) ((insert_int Y_1) bot_bot_int_o))))->((member_int (F_7 A_21)) A_21)))))). % Axiom fact_761_folding__one_Oclosed:(forall (A_21:(nat->Prop)) (F_8:(nat->(nat->nat))) (F_7:((nat->Prop)->nat)), (((finite988810631ne_nat F_8) F_7)->((finite_finite_nat A_21)->((not (((eq (nat->Prop)) A_21) bot_bot_nat_o))->((forall (X_1:nat) (Y_1:nat), ((member_nat ((F_8 X_1) Y_1)) ((insert_nat X_1) ((insert_nat Y_1) bot_bot_nat_o))))->((member_nat (F_7 A_21)) A_21)))))). % Axiom fact_762_folding__one_Oclosed:(forall (A_21:(pname->Prop)) (F_8:(pname->(pname->pname))) (F_7:((pname->Prop)->pname)), (((finite1282449217_pname F_8) F_7)->((finite_finite_pname A_21)->((not (((eq (pname->Prop)) A_21) bot_bot_pname_o))->((forall (X_1:pname) (Y_1:pname), ((member_pname ((F_8 X_1) Y_1)) ((insert_pname X_1) ((insert_pname Y_1) bot_bot_pname_o))))->((member_pname (F_7 A_21)) A_21)))))). % Axiom fact_763_card_Oremove:(forall (X_5:x_a) (A_20:(x_a->Prop)), ((finite_finite_a A_20)->(((member_a X_5) A_20)->(((eq nat) (finite_card_a A_20)) ((plus_plus_nat one_one_nat) (finite_card_a ((minus_minus_a_o A_20) ((insert_a X_5) bot_bot_a_o)))))))). % Axiom fact_764_card_Oremove:(forall (X_5:int) (A_20:(int->Prop)), ((finite_finite_int A_20)->(((member_int X_5) A_20)->(((eq nat) (finite_card_int A_20)) ((plus_plus_nat one_one_nat) (finite_card_int ((minus_minus_int_o A_20) ((insert_int X_5) bot_bot_int_o)))))))). % Axiom fact_765_card_Oremove:(forall (X_5:nat) (A_20:(nat->Prop)), ((finite_finite_nat A_20)->(((member_nat X_5) A_20)->(((eq nat) (finite_card_nat A_20)) ((plus_plus_nat one_one_nat) (finite_card_nat ((minus_minus_nat_o A_20) ((insert_nat X_5) bot_bot_nat_o)))))))). % Axiom fact_766_card_Oremove:(forall (X_5:pname) (A_20:(pname->Prop)), ((finite_finite_pname A_20)->(((member_pname X_5) A_20)->(((eq nat) (finite_card_pname A_20)) ((plus_plus_nat one_one_nat) (finite_card_pname ((minus_minus_pname_o A_20) ((insert_pname X_5) bot_bot_pname_o)))))))). % Axiom fact_767_card_Oinsert__remove:(forall (X_4:x_a) (A_19:(x_a->Prop)), ((finite_finite_a A_19)->(((eq nat) (finite_card_a ((insert_a X_4) A_19))) ((plus_plus_nat one_one_nat) (finite_card_a ((minus_minus_a_o A_19) ((insert_a X_4) bot_bot_a_o))))))). % Axiom fact_768_card_Oinsert__remove:(forall (X_4:int) (A_19:(int->Prop)), ((finite_finite_int A_19)->(((eq nat) (finite_card_int ((insert_int X_4) A_19))) ((plus_plus_nat one_one_nat) (finite_card_int ((minus_minus_int_o A_19) ((insert_int X_4) bot_bot_int_o))))))). % Axiom fact_769_card_Oinsert__remove:(forall (X_4:nat) (A_19:(nat->Prop)), ((finite_finite_nat A_19)->(((eq nat) (finite_card_nat ((insert_nat X_4) A_19))) ((plus_plus_nat one_one_nat) (finite_card_nat ((minus_minus_nat_o A_19) ((insert_nat X_4) bot_bot_nat_o))))))). % Axiom fact_770_card_Oinsert__remove:(forall (X_4:pname) (A_19:(pname->Prop)), ((finite_finite_pname A_19)->(((eq nat) (finite_card_pname ((insert_pname X_4) A_19))) ((plus_plus_nat one_one_nat) (finite_card_pname ((minus_minus_pname_o A_19) ((insert_pname X_4) bot_bot_pname_o))))))). % Axiom fact_771_folding__one__idem_Osubset__idem:(forall (B_18:(int->Prop)) (A_18:(int->Prop)) (F_6:(int->(int->int))) (F_5:((int->Prop)->int)), (((finite1432773856em_int F_6) F_5)->((finite_finite_int A_18)->((not (((eq (int->Prop)) B_18) bot_bot_int_o))->(((ord_less_eq_int_o B_18) A_18)->(((eq int) ((F_6 (F_5 B_18)) (F_5 A_18))) (F_5 A_18))))))). % Axiom fact_772_folding__one__idem_Osubset__idem:(forall (B_18:(nat->Prop)) (A_18:(nat->Prop)) (F_6:(nat->(nat->nat))) (F_5:((nat->Prop)->nat)), (((finite795500164em_nat F_6) F_5)->((finite_finite_nat A_18)->((not (((eq (nat->Prop)) B_18) bot_bot_nat_o))->(((ord_less_eq_nat_o B_18) A_18)->(((eq nat) ((F_6 (F_5 B_18)) (F_5 A_18))) (F_5 A_18))))))). % Axiom fact_773_folding__one__idem_Osubset__idem:(forall (B_18:(pname->Prop)) (A_18:(pname->Prop)) (F_6:(pname->(pname->pname))) (F_5:((pname->Prop)->pname)), (((finite89670078_pname F_6) F_5)->((finite_finite_pname A_18)->((not (((eq (pname->Prop)) B_18) bot_bot_pname_o))->(((ord_less_eq_pname_o B_18) A_18)->(((eq pname) ((F_6 (F_5 B_18)) (F_5 A_18))) (F_5 A_18))))))). % Axiom fact_774_folding__one__idem_Osubset__idem:(forall (B_18:(x_a->Prop)) (A_18:(x_a->Prop)) (F_6:(x_a->(x_a->x_a))) (F_5:((x_a->Prop)->x_a)), (((finite1819937229idem_a F_6) F_5)->((finite_finite_a A_18)->((not (((eq (x_a->Prop)) B_18) bot_bot_a_o))->(((ord_less_eq_a_o B_18) A_18)->(((eq x_a) ((F_6 (F_5 B_18)) (F_5 A_18))) (F_5 A_18))))))). % Axiom fact_775_folding__one__idem_Oinsert__idem:(forall (X_3:x_a) (A_17:(x_a->Prop)) (F_4:(x_a->(x_a->x_a))) (F_3:((x_a->Prop)->x_a)), (((finite1819937229idem_a F_4) F_3)->((finite_finite_a A_17)->((not (((eq (x_a->Prop)) A_17) bot_bot_a_o))->(((eq x_a) (F_3 ((insert_a X_3) A_17))) ((F_4 X_3) (F_3 A_17))))))). % Axiom fact_776_folding__one__idem_Oinsert__idem:(forall (X_3:int) (A_17:(int->Prop)) (F_4:(int->(int->int))) (F_3:((int->Prop)->int)), (((finite1432773856em_int F_4) F_3)->((finite_finite_int A_17)->((not (((eq (int->Prop)) A_17) bot_bot_int_o))->(((eq int) (F_3 ((insert_int X_3) A_17))) ((F_4 X_3) (F_3 A_17))))))). % Axiom fact_777_folding__one__idem_Oinsert__idem:(forall (X_3:nat) (A_17:(nat->Prop)) (F_4:(nat->(nat->nat))) (F_3:((nat->Prop)->nat)), (((finite795500164em_nat F_4) F_3)->((finite_finite_nat A_17)->((not (((eq (nat->Prop)) A_17) bot_bot_nat_o))->(((eq nat) (F_3 ((insert_nat X_3) A_17))) ((F_4 X_3) (F_3 A_17))))))). % Axiom fact_778_folding__one__idem_Oinsert__idem:(forall (X_3:pname) (A_17:(pname->Prop)) (F_4:(pname->(pname->pname))) (F_3:((pname->Prop)->pname)), (((finite89670078_pname F_4) F_3)->((finite_finite_pname A_17)->((not (((eq (pname->Prop)) A_17) bot_bot_pname_o))->(((eq pname) (F_3 ((insert_pname X_3) A_17))) ((F_4 X_3) (F_3 A_17))))))). % Axiom fact_779_finite__ne__induct:(forall (P_2:((x_a->Prop)->Prop)) (F_1:(x_a->Prop)), ((finite_finite_a F_1)->((not (((eq (x_a->Prop)) F_1) bot_bot_a_o))->((forall (X_1:x_a), (P_2 ((insert_a X_1) bot_bot_a_o)))->((forall (X_1:x_a) (F_2:(x_a->Prop)), ((finite_finite_a F_2)->((not (((eq (x_a->Prop)) F_2) bot_bot_a_o))->((((member_a X_1) F_2)->False)->((P_2 F_2)->(P_2 ((insert_a X_1) F_2)))))))->(P_2 F_1)))))). % Axiom fact_780_finite__ne__induct:(forall (P_2:((int->Prop)->Prop)) (F_1:(int->Prop)), ((finite_finite_int F_1)->((not (((eq (int->Prop)) F_1) bot_bot_int_o))->((forall (X_1:int), (P_2 ((insert_int X_1) bot_bot_int_o)))->((forall (X_1:int) (F_2:(int->Prop)), ((finite_finite_int F_2)->((not (((eq (int->Prop)) F_2) bot_bot_int_o))->((((member_int X_1) F_2)->False)->((P_2 F_2)->(P_2 ((insert_int X_1) F_2)))))))->(P_2 F_1)))))). % Axiom fact_781_finite__ne__induct:(forall (P_2:((nat->Prop)->Prop)) (F_1:(nat->Prop)), ((finite_finite_nat F_1)->((not (((eq (nat->Prop)) F_1) bot_bot_nat_o))->((forall (X_1:nat), (P_2 ((insert_nat X_1) bot_bot_nat_o)))->((forall (X_1:nat) (F_2:(nat->Prop)), ((finite_finite_nat F_2)->((not (((eq (nat->Prop)) F_2) bot_bot_nat_o))->((((member_nat X_1) F_2)->False)->((P_2 F_2)->(P_2 ((insert_nat X_1) F_2)))))))->(P_2 F_1)))))). % Axiom fact_782_finite__ne__induct:(forall (P_2:((pname->Prop)->Prop)) (F_1:(pname->Prop)), ((finite_finite_pname F_1)->((not (((eq (pname->Prop)) F_1) bot_bot_pname_o))->((forall (X_1:pname), (P_2 ((insert_pname X_1) bot_bot_pname_o)))->((forall (X_1:pname) (F_2:(pname->Prop)), ((finite_finite_pname F_2)->((not (((eq (pname->Prop)) F_2) bot_bot_pname_o))->((((member_pname X_1) F_2)->False)->((P_2 F_2)->(P_2 ((insert_pname X_1) F_2)))))))->(P_2 F_1)))))). % Axiom fact_783_the__elem__def:(forall (X_2:(x_a->Prop)), (((eq x_a) (the_elem_a X_2)) (the_a (fun (X_1:x_a)=> (((eq (x_a->Prop)) X_2) ((insert_a X_1) bot_bot_a_o)))))). % Axiom fact_784_the__elem__def:(forall (X_2:(nat->Prop)), (((eq nat) (the_elem_nat X_2)) (the_nat (fun (X_1:nat)=> (((eq (nat->Prop)) X_2) ((insert_nat X_1) bot_bot_nat_o)))))). % Axiom fact_785_the__elem__def:(forall (X_2:(int->Prop)), (((eq int) (the_elem_int X_2)) (the_int (fun (X_1:int)=> (((eq (int->Prop)) X_2) ((insert_int X_1) bot_bot_int_o)))))). % Axiom fact_786_ab__semigroup__add__class_Oadd__ac_I1_J:(forall (A_16:int) (B_17:int) (C_13:int), (((eq int) ((plus_plus_int ((plus_plus_int A_16) B_17)) C_13)) ((plus_plus_int A_16) ((plus_plus_int B_17) C_13)))). % Axiom fact_787_ab__semigroup__add__class_Oadd__ac_I1_J:(forall (A_16:nat) (B_17:nat) (C_13:nat), (((eq nat) ((plus_plus_nat ((plus_plus_nat A_16) B_17)) C_13)) ((plus_plus_nat A_16) ((plus_plus_nat B_17) C_13)))). % Axiom fact_788_add__left__cancel:(forall (A_15:int) (B_16:int) (C_12:int), ((iff (((eq int) ((plus_plus_int A_15) B_16)) ((plus_plus_int A_15) C_12))) (((eq int) B_16) C_12))). % Axiom fact_789_add__left__cancel:(forall (A_15:nat) (B_16:nat) (C_12:nat), ((iff (((eq nat) ((plus_plus_nat A_15) B_16)) ((plus_plus_nat A_15) C_12))) (((eq nat) B_16) C_12))). % Axiom fact_790_add__right__cancel:(forall (B_15:int) (A_14:int) (C_11:int), ((iff (((eq int) ((plus_plus_int B_15) A_14)) ((plus_plus_int C_11) A_14))) (((eq int) B_15) C_11))). % Axiom fact_791_add__right__cancel:(forall (B_15:nat) (A_14:nat) (C_11:nat), ((iff (((eq nat) ((plus_plus_nat B_15) A_14)) ((plus_plus_nat C_11) A_14))) (((eq nat) B_15) C_11))). % Axiom fact_792_add__left__imp__eq:(forall (A_13:int) (B_14:int) (C_10:int), ((((eq int) ((plus_plus_int A_13) B_14)) ((plus_plus_int A_13) C_10))->(((eq int) B_14) C_10))). % Axiom fact_793_add__left__imp__eq:(forall (A_13:nat) (B_14:nat) (C_10:nat), ((((eq nat) ((plus_plus_nat A_13) B_14)) ((plus_plus_nat A_13) C_10))->(((eq nat) B_14) C_10))). % Axiom fact_794_add__imp__eq:(forall (A_12:int) (B_13:int) (C_9:int), ((((eq int) ((plus_plus_int A_12) B_13)) ((plus_plus_int A_12) C_9))->(((eq int) B_13) C_9))). % Axiom fact_795_add__imp__eq:(forall (A_12:nat) (B_13:nat) (C_9:nat), ((((eq nat) ((plus_plus_nat A_12) B_13)) ((plus_plus_nat A_12) C_9))->(((eq nat) B_13) C_9))). % Axiom fact_796_add__right__imp__eq:(forall (B_12:int) (A_11:int) (C_8:int), ((((eq int) ((plus_plus_int B_12) A_11)) ((plus_plus_int C_8) A_11))->(((eq int) B_12) C_8))). % Axiom fact_797_add__right__imp__eq:(forall (B_12:nat) (A_11:nat) (C_8:nat), ((((eq nat) ((plus_plus_nat B_12) A_11)) ((plus_plus_nat C_8) A_11))->(((eq nat) B_12) C_8))). % Axiom fact_798_nat__add__commute:(forall (M:nat) (N:nat), (((eq nat) ((plus_plus_nat M) N)) ((plus_plus_nat N) M))). % Axiom fact_799_nat__add__left__commute:(forall (X:nat) (Y:nat) (Z:nat), (((eq nat) ((plus_plus_nat X) ((plus_plus_nat Y) Z))) ((plus_plus_nat Y) ((plus_plus_nat X) Z)))). % Axiom fact_800_nat__add__assoc:(forall (M:nat) (N:nat) (K:nat), (((eq nat) ((plus_plus_nat ((plus_plus_nat M) N)) K)) ((plus_plus_nat M) ((plus_plus_nat N) K)))). % Axiom fact_801_nat__add__left__cancel:(forall (K:nat) (M:nat) (N:nat), ((iff (((eq nat) ((plus_plus_nat K) M)) ((plus_plus_nat K) N))) (((eq nat) M) N))). % Axiom fact_802_nat__add__right__cancel:(forall (M:nat) (K:nat) (N:nat), ((iff (((eq nat) ((plus_plus_nat M) K)) ((plus_plus_nat N) K))) (((eq nat) M) N))). % Axiom fact_803_add__le__cancel__right:(forall (A_10:int) (C_7:int) (B_11:int), ((iff ((ord_less_eq_int ((plus_plus_int A_10) C_7)) ((plus_plus_int B_11) C_7))) ((ord_less_eq_int A_10) B_11))). % Axiom fact_804_add__le__cancel__right:(forall (A_10:nat) (C_7:nat) (B_11:nat), ((iff ((ord_less_eq_nat ((plus_plus_nat A_10) C_7)) ((plus_plus_nat B_11) C_7))) ((ord_less_eq_nat A_10) B_11))). % Axiom fact_805_add__le__cancel__left:(forall (C_6:int) (A_9:int) (B_10:int), ((iff ((ord_less_eq_int ((plus_plus_int C_6) A_9)) ((plus_plus_int C_6) B_10))) ((ord_less_eq_int A_9) B_10))). % Axiom fact_806_add__le__cancel__left:(forall (C_6:nat) (A_9:nat) (B_10:nat), ((iff ((ord_less_eq_nat ((plus_plus_nat C_6) A_9)) ((plus_plus_nat C_6) B_10))) ((ord_less_eq_nat A_9) B_10))). % Axiom fact_807_add__right__mono:(forall (C_5:int) (A_8:int) (B_9:int), (((ord_less_eq_int A_8) B_9)->((ord_less_eq_int ((plus_plus_int A_8) C_5)) ((plus_plus_int B_9) C_5)))). % Axiom fact_808_add__right__mono:(forall (C_5:nat) (A_8:nat) (B_9:nat), (((ord_less_eq_nat A_8) B_9)->((ord_less_eq_nat ((plus_plus_nat A_8) C_5)) ((plus_plus_nat B_9) C_5)))). % Axiom fact_809_add__left__mono:(forall (C_4:int) (A_7:int) (B_8:int), (((ord_less_eq_int A_7) B_8)->((ord_less_eq_int ((plus_plus_int C_4) A_7)) ((plus_plus_int C_4) B_8)))). % Axiom fact_810_add__left__mono:(forall (C_4:nat) (A_7:nat) (B_8:nat), (((ord_less_eq_nat A_7) B_8)->((ord_less_eq_nat ((plus_plus_nat C_4) A_7)) ((plus_plus_nat C_4) B_8)))). % Axiom fact_811_add__mono:(forall (C_3:int) (D_2:int) (A_6:int) (B_7:int), (((ord_less_eq_int A_6) B_7)->(((ord_less_eq_int C_3) D_2)->((ord_less_eq_int ((plus_plus_int A_6) C_3)) ((plus_plus_int B_7) D_2))))). % Axiom fact_812_add__mono:(forall (C_3:nat) (D_2:nat) (A_6:nat) (B_7:nat), (((ord_less_eq_nat A_6) B_7)->(((ord_less_eq_nat C_3) D_2)->((ord_less_eq_nat ((plus_plus_nat A_6) C_3)) ((plus_plus_nat B_7) D_2))))). % Axiom fact_813_add__le__imp__le__right:(forall (A_5:int) (C_2:int) (B_6:int), (((ord_less_eq_int ((plus_plus_int A_5) C_2)) ((plus_plus_int B_6) C_2))->((ord_less_eq_int A_5) B_6))). % Axiom fact_814_add__le__imp__le__right:(forall (A_5:nat) (C_2:nat) (B_6:nat), (((ord_less_eq_nat ((plus_plus_nat A_5) C_2)) ((plus_plus_nat B_6) C_2))->((ord_less_eq_nat A_5) B_6))). % Axiom fact_815_add__le__imp__le__left:(forall (C_1:int) (A_4:int) (B_5:int), (((ord_less_eq_int ((plus_plus_int C_1) A_4)) ((plus_plus_int C_1) B_5))->((ord_less_eq_int A_4) B_5))). % Axiom fact_816_add__le__imp__le__left:(forall (C_1:nat) (A_4:nat) (B_5:nat), (((ord_less_eq_nat ((plus_plus_nat C_1) A_4)) ((plus_plus_nat C_1) B_5))->((ord_less_eq_nat A_4) B_5))). % Axiom fact_817_diff__add__cancel:(forall (A_3:int) (B_4:int), (((eq int) ((plus_plus_int ((minus_minus_int A_3) B_4)) B_4)) A_3)). % Axiom fact_818_add__diff__cancel:(forall (A_2:int) (B_3:int), (((eq int) ((minus_minus_int ((plus_plus_int A_2) B_3)) B_3)) A_2)). % Axiom fact_819_add__Suc__right:(forall (M:nat) (N:nat), (((eq nat) ((plus_plus_nat M) (suc N))) (suc ((plus_plus_nat M) N)))). % Axiom fact_820_add__Suc:(forall (M:nat) (N:nat), (((eq nat) ((plus_plus_nat (suc M)) N)) (suc ((plus_plus_nat M) N)))). % Axiom fact_821_add__Suc__shift:(forall (M:nat) (N:nat), (((eq nat) ((plus_plus_nat (suc M)) N)) ((plus_plus_nat M) (suc N)))). % Axiom fact_822_le__add2:(forall (N:nat) (M:nat), ((ord_less_eq_nat N) ((plus_plus_nat M) N))). % Axiom fact_823_le__add1:(forall (N:nat) (M:nat), ((ord_less_eq_nat N) ((plus_plus_nat N) M))). % Axiom fact_824_le__iff__add:(forall (M:nat) (N:nat), ((iff ((ord_less_eq_nat M) N)) ((ex nat) (fun (K_1:nat)=> (((eq nat) N) ((plus_plus_nat M) K_1)))))). % Axiom fact_825_nat__add__left__cancel__le:(forall (K:nat) (M:nat) (N:nat), ((iff ((ord_less_eq_nat ((plus_plus_nat K) M)) ((plus_plus_nat K) N))) ((ord_less_eq_nat M) N))). % Axiom fact_826_trans__le__add1:(forall (M:nat) (I_1:nat) (J:nat), (((ord_less_eq_nat I_1) J)->((ord_less_eq_nat I_1) ((plus_plus_nat J) M)))). % Axiom fact_827_trans__le__add2:(forall (M:nat) (I_1:nat) (J:nat), (((ord_less_eq_nat I_1) J)->((ord_less_eq_nat I_1) ((plus_plus_nat M) J)))). % Axiom fact_828_add__le__mono1:(forall (K:nat) (I_1:nat) (J:nat), (((ord_less_eq_nat I_1) J)->((ord_less_eq_nat ((plus_plus_nat I_1) K)) ((plus_plus_nat J) K)))). % Axiom fact_829_add__le__mono:(forall (K:nat) (L:nat) (I_1:nat) (J:nat), (((ord_less_eq_nat I_1) J)->(((ord_less_eq_nat K) L)->((ord_less_eq_nat ((plus_plus_nat I_1) K)) ((plus_plus_nat J) L))))). % Axiom fact_830_add__leD2:(forall (M:nat) (K:nat) (N:nat), (((ord_less_eq_nat ((plus_plus_nat M) K)) N)->((ord_less_eq_nat K) N))). % Axiom fact_831_add__leD1:(forall (M:nat) (K:nat) (N:nat), (((ord_less_eq_nat ((plus_plus_nat M) K)) N)->((ord_less_eq_nat M) N))). % Axiom fact_832_add__leE:(forall (M:nat) (K:nat) (N:nat), (((ord_less_eq_nat ((plus_plus_nat M) K)) N)->((((ord_less_eq_nat M) N)->(((ord_less_eq_nat K) N)->False))->False))). % Axiom fact_833_diff__add__inverse2:(forall (M:nat) (N:nat), (((eq nat) ((minus_minus_nat ((plus_plus_nat M) N)) N)) M)). % Axiom fact_834_diff__add__inverse:(forall (N:nat) (M:nat), (((eq nat) ((minus_minus_nat ((plus_plus_nat N) M)) N)) M)). % Axiom fact_835_diff__diff__left:(forall (I_1:nat) (J:nat) (K:nat), (((eq nat) ((minus_minus_nat ((minus_minus_nat I_1) J)) K)) ((minus_minus_nat I_1) ((plus_plus_nat J) K)))). % Axiom fact_836_diff__cancel:(forall (K:nat) (M:nat) (N:nat), (((eq nat) ((minus_minus_nat ((plus_plus_nat K) M)) ((plus_plus_nat K) N))) ((minus_minus_nat M) N))). % Axiom fact_837_diff__cancel2:(forall (M:nat) (K:nat) (N:nat), (((eq nat) ((minus_minus_nat ((plus_plus_nat M) K)) ((plus_plus_nat N) K))) ((minus_minus_nat M) N))). % Axiom fact_838_diff__diff__right:(forall (I_1:nat) (K:nat) (J:nat), (((ord_less_eq_nat K) J)->(((eq nat) ((minus_minus_nat I_1) ((minus_minus_nat J) K))) ((minus_minus_nat ((plus_plus_nat I_1) K)) J)))). % Axiom fact_839_le__diff__conv:(forall (J:nat) (K:nat) (I_1:nat), ((iff ((ord_less_eq_nat ((minus_minus_nat J) K)) I_1)) ((ord_less_eq_nat J) ((plus_plus_nat I_1) K)))). % Axiom fact_840_le__add__diff:(forall (M:nat) (K:nat) (N:nat), (((ord_less_eq_nat K) N)->((ord_less_eq_nat M) ((minus_minus_nat ((plus_plus_nat N) M)) K)))). % Axiom fact_841_le__add__diff__inverse:(forall (N:nat) (M:nat), (((ord_less_eq_nat N) M)->(((eq nat) ((plus_plus_nat N) ((minus_minus_nat M) N))) M))). % Axiom fact_842_add__diff__assoc:(forall (I_1:nat) (K:nat) (J:nat), (((ord_less_eq_nat K) J)->(((eq nat) ((plus_plus_nat I_1) ((minus_minus_nat J) K))) ((minus_minus_nat ((plus_plus_nat I_1) J)) K)))). % Axiom fact_843_le__diff__conv2:(forall (I_1:nat) (K:nat) (J:nat), (((ord_less_eq_nat K) J)->((iff ((ord_less_eq_nat I_1) ((minus_minus_nat J) K))) ((ord_less_eq_nat ((plus_plus_nat I_1) K)) J)))). % Axiom fact_844_le__add__diff__inverse2:(forall (N:nat) (M:nat), (((ord_less_eq_nat N) M)->(((eq nat) ((plus_plus_nat ((minus_minus_nat M) N)) N)) M))). % Axiom fact_845_le__imp__diff__is__add:(forall (K:nat) (I_1:nat) (J:nat), (((ord_less_eq_nat I_1) J)->((iff (((eq nat) ((minus_minus_nat J) I_1)) K)) (((eq nat) J) ((plus_plus_nat K) I_1))))). % Axiom fact_846_diff__add__assoc:(forall (I_1:nat) (K:nat) (J:nat), (((ord_less_eq_nat K) J)->(((eq nat) ((minus_minus_nat ((plus_plus_nat I_1) J)) K)) ((plus_plus_nat I_1) ((minus_minus_nat J) K))))). % Axiom fact_847_add__diff__assoc2:(forall (I_1:nat) (K:nat) (J:nat), (((ord_less_eq_nat K) J)->(((eq nat) ((plus_plus_nat ((minus_minus_nat J) K)) I_1)) ((minus_minus_nat ((plus_plus_nat J) I_1)) K)))). % Axiom fact_848_diff__add__assoc2:(forall (I_1:nat) (K:nat) (J:nat), (((ord_less_eq_nat K) J)->(((eq nat) ((minus_minus_nat ((plus_plus_nat J) I_1)) K)) ((plus_plus_nat ((minus_minus_nat J) K)) I_1)))). % Axiom fact_849_Suc__eq__plus1__left:(forall (N:nat), (((eq nat) (suc N)) ((plus_plus_nat one_one_nat) N))). % Axiom fact_850_Suc__eq__plus1:(forall (N:nat), (((eq nat) (suc N)) ((plus_plus_nat N) one_one_nat))). % Axiom fact_851_diff__Suc__diff__eq1:(forall (M:nat) (K:nat) (J:nat), (((ord_less_eq_nat K) J)->(((eq nat) ((minus_minus_nat M) (suc ((minus_minus_nat J) K)))) ((minus_minus_nat ((plus_plus_nat M) K)) (suc J))))). % Axiom fact_852_diff__Suc__diff__eq2:(forall (M:nat) (K:nat) (J:nat), (((ord_less_eq_nat K) J)->(((eq nat) ((minus_minus_nat (suc ((minus_minus_nat J) K))) M)) ((minus_minus_nat (suc J)) ((plus_plus_nat K) M))))). % Axiom fact_853_termination__basic__simps_I4_J:(forall (Y:nat) (X:nat) (Z:nat), (((ord_less_eq_nat X) Z)->((ord_less_eq_nat X) ((plus_plus_nat Y) Z)))). % Axiom fact_854_termination__basic__simps_I3_J:(forall (Z:nat) (X:nat) (Y:nat), (((ord_less_eq_nat X) Y)->((ord_less_eq_nat X) ((plus_plus_nat Y) Z)))). % Axiom fact_855_lessI:(forall (N:nat), ((ord_less_nat N) (suc N))). % Axiom fact_856_Suc__mono:(forall (M:nat) (N:nat), (((ord_less_nat M) N)->((ord_less_nat (suc M)) (suc N)))). % Axiom fact_857_finite__Collect__less__nat:(forall (K:nat), (finite_finite_nat (collect_nat (fun (N_1:nat)=> ((ord_less_nat N_1) K))))). % Axiom fact_858_less__not__refl:(forall (N:nat), (((ord_less_nat N) N)->False)). % Axiom fact_859_nat__neq__iff:(forall (M:nat) (N:nat), ((iff (not (((eq nat) M) N))) ((or ((ord_less_nat M) N)) ((ord_less_nat N) M)))). % Axiom fact_860_linorder__neqE__nat:(forall (X:nat) (Y:nat), ((not (((eq nat) X) Y))->((((ord_less_nat X) Y)->False)->((ord_less_nat Y) X)))). % Axiom fact_861_less__irrefl__nat:(forall (N:nat), (((ord_less_nat N) N)->False)). % Axiom fact_862_less__not__refl2:(forall (N:nat) (M:nat), (((ord_less_nat N) M)->(not (((eq nat) M) N)))). % Axiom fact_863_less__not__refl3:(forall (S:nat) (T:nat), (((ord_less_nat S) T)->(not (((eq nat) S) T)))). % Axiom fact_864_nat__less__cases:(forall (P:(nat->(nat->Prop))) (M:nat) (N:nat), ((((ord_less_nat M) N)->((P N) M))->(((((eq nat) M) N)->((P N) M))->((((ord_less_nat N) M)->((P N) M))->((P N) M))))). % Axiom fact_865_not__less__eq:(forall (M:nat) (N:nat), ((iff (((ord_less_nat M) N)->False)) ((ord_less_nat N) (suc M)))). % Axiom fact_866_less__Suc__eq:(forall (M:nat) (N:nat), ((iff ((ord_less_nat M) (suc N))) ((or ((ord_less_nat M) N)) (((eq nat) M) N)))). % Axiom fact_867_Suc__less__eq:(forall (M:nat) (N:nat), ((iff ((ord_less_nat (suc M)) (suc N))) ((ord_less_nat M) N))). % Axiom fact_868_not__less__less__Suc__eq:(forall (N:nat) (M:nat), ((((ord_less_nat N) M)->False)->((iff ((ord_less_nat N) (suc M))) (((eq nat) N) M)))). % Axiom fact_869_less__antisym:(forall (N:nat) (M:nat), ((((ord_less_nat N) M)->False)->(((ord_less_nat N) (suc M))->(((eq nat) M) N)))). % Axiom fact_870_less__SucI:(forall (M:nat) (N:nat), (((ord_less_nat M) N)->((ord_less_nat M) (suc N)))). % Axiom fact_871_Suc__lessI:(forall (M:nat) (N:nat), (((ord_less_nat M) N)->((not (((eq nat) (suc M)) N))->((ord_less_nat (suc M)) N)))). % Axiom fact_872_less__trans__Suc:(forall (K:nat) (I_1:nat) (J:nat), (((ord_less_nat I_1) J)->(((ord_less_nat J) K)->((ord_less_nat (suc I_1)) K)))). % Axiom fact_873_less__SucE:(forall (M:nat) (N:nat), (((ord_less_nat M) (suc N))->((((ord_less_nat M) N)->False)->(((eq nat) M) N)))). % Axiom fact_874_Suc__lessD:(forall (M:nat) (N:nat), (((ord_less_nat (suc M)) N)->((ord_less_nat M) N))). % Axiom fact_875_Suc__less__SucD:(forall (M:nat) (N:nat), (((ord_less_nat (suc M)) (suc N))->((ord_less_nat M) N))). % Axiom fact_876_not__add__less1:(forall (I_1:nat) (J:nat), (((ord_less_nat ((plus_plus_nat I_1) J)) I_1)->False)). % Axiom fact_877_not__add__less2:(forall (J:nat) (I_1:nat), (((ord_less_nat ((plus_plus_nat J) I_1)) I_1)->False)). % Axiom fact_878_nat__add__left__cancel__less:(forall (K:nat) (M:nat) (N:nat), ((iff ((ord_less_nat ((plus_plus_nat K) M)) ((plus_plus_nat K) N))) ((ord_less_nat M) N))). % Axiom fact_879_trans__less__add1:(forall (M:nat) (I_1:nat) (J:nat), (((ord_less_nat I_1) J)->((ord_less_nat I_1) ((plus_plus_nat J) M)))). % Axiom fact_880_trans__less__add2:(forall (M:nat) (I_1:nat) (J:nat), (((ord_less_nat I_1) J)->((ord_less_nat I_1) ((plus_plus_nat M) J)))). % Axiom fact_881_add__less__mono1:(forall (K:nat) (I_1:nat) (J:nat), (((ord_less_nat I_1) J)->((ord_less_nat ((plus_plus_nat I_1) K)) ((plus_plus_nat J) K)))). % Axiom fact_882_add__less__mono:(forall (K:nat) (L:nat) (I_1:nat) (J:nat), (((ord_less_nat I_1) J)->(((ord_less_nat K) L)->((ord_less_nat ((plus_plus_nat I_1) K)) ((plus_plus_nat J) L))))). % Axiom fact_883_less__add__eq__less:(forall (M:nat) (N:nat) (K:nat) (L:nat), (((ord_less_nat K) L)->((((eq nat) ((plus_plus_nat M) L)) ((plus_plus_nat K) N))->((ord_less_nat M) N)))). % Axiom fact_884_add__lessD1:(forall (I_1:nat) (J:nat) (K:nat), (((ord_less_nat ((plus_plus_nat I_1) J)) K)->((ord_less_nat I_1) K))). % Axiom fact_885_termination__basic__simps_I1_J:(forall (Z:nat) (X:nat) (Y:nat), (((ord_less_nat X) Y)->((ord_less_nat X) ((plus_plus_nat Y) Z)))). % Axiom fact_886_termination__basic__simps_I2_J:(forall (Y:nat) (X:nat) (Z:nat), (((ord_less_nat X) Z)->((ord_less_nat X) ((plus_plus_nat Y) Z)))). % Axiom fact_887_nat__less__le:(forall (M:nat) (N:nat), ((iff ((ord_less_nat M) N)) ((and ((ord_less_eq_nat M) N)) (not (((eq nat) M) N))))). % Axiom fact_888_le__eq__less__or__eq:(forall (M:nat) (N:nat), ((iff ((ord_less_eq_nat M) N)) ((or ((ord_less_nat M) N)) (((eq nat) M) N)))). % Axiom fact_889_less__imp__le__nat:(forall (M:nat) (N:nat), (((ord_less_nat M) N)->((ord_less_eq_nat M) N))). % Axiom fact_890_le__neq__implies__less:(forall (M:nat) (N:nat), (((ord_less_eq_nat M) N)->((not (((eq nat) M) N))->((ord_less_nat M) N)))). % Axiom fact_891_less__or__eq__imp__le:(forall (M:nat) (N:nat), (((or ((ord_less_nat M) N)) (((eq nat) M) N))->((ord_less_eq_nat M) N))). % Axiom fact_892_termination__basic__simps_I5_J:(forall (X:nat) (Y:nat), (((ord_less_nat X) Y)->((ord_less_eq_nat X) Y))). % Axiom fact_893_less__imp__diff__less:(forall (N:nat) (J:nat) (K:nat), (((ord_less_nat J) K)->((ord_less_nat ((minus_minus_nat J) N)) K))). % Axiom fact_894_diff__less__mono2:(forall (L:nat) (M:nat) (N:nat), (((ord_less_nat M) N)->(((ord_less_nat M) L)->((ord_less_nat ((minus_minus_nat L) N)) ((minus_minus_nat L) M))))). % Axiom fact_895_finite__nat__set__iff__bounded:(forall (N_2:(nat->Prop)), ((iff (finite_finite_nat N_2)) ((ex nat) (fun (M_1:nat)=> (forall (X_1:nat), (((member_nat X_1) N_2)->((ord_less_nat X_1) M_1))))))). % Axiom fact_896_card__Collect__less__nat:(forall (N:nat), (((eq nat) (finite_card_nat (collect_nat (fun (_TPTP_I:nat)=> ((ord_less_nat _TPTP_I) N))))) N)). % Axiom fact_897_finite__M__bounded__by__nat:(forall (P:(nat->Prop)) (I_1:nat), (finite_finite_nat (collect_nat (fun (K_1:nat)=> ((and (P K_1)) ((ord_less_nat K_1) I_1)))))). % Axiom fact_898_less__add__Suc1:(forall (I_1:nat) (M:nat), ((ord_less_nat I_1) (suc ((plus_plus_nat I_1) M)))). % Axiom fact_899_less__add__Suc2:(forall (I_1:nat) (M:nat), ((ord_less_nat I_1) (suc ((plus_plus_nat M) I_1)))). % Axiom fact_900_less__iff__Suc__add:(forall (M:nat) (N:nat), ((iff ((ord_less_nat M) N)) ((ex nat) (fun (K_1:nat)=> (((eq nat) N) (suc ((plus_plus_nat M) K_1))))))). % Axiom fact_901_less__eq__Suc__le:(forall (N:nat) (M:nat), ((iff ((ord_less_nat N) M)) ((ord_less_eq_nat (suc N)) M))). % Axiom fact_902_less__Suc__eq__le:(forall (M:nat) (N:nat), ((iff ((ord_less_nat M) (suc N))) ((ord_less_eq_nat M) N))). % Axiom fact_903_Suc__le__eq:(forall (M:nat) (N:nat), ((iff ((ord_less_eq_nat (suc M)) N)) ((ord_less_nat M) N))). % Axiom fact_904_le__imp__less__Suc:(forall (M:nat) (N:nat), (((ord_less_eq_nat M) N)->((ord_less_nat M) (suc N)))). % Axiom fact_905_Suc__leI:(forall (M:nat) (N:nat), (((ord_less_nat M) N)->((ord_less_eq_nat (suc M)) N))). % Axiom fact_906_le__less__Suc__eq:(forall (M:nat) (N:nat), (((ord_less_eq_nat M) N)->((iff ((ord_less_nat N) (suc M))) (((eq nat) N) M)))). % Axiom fact_907_Suc__le__lessD:(forall (M:nat) (N:nat), (((ord_less_eq_nat (suc M)) N)->((ord_less_nat M) N))). % Axiom fact_908_diff__less__Suc:(forall (M:nat) (N:nat), ((ord_less_nat ((minus_minus_nat M) N)) (suc M))). % Axiom fact_909_less__diff__conv:(forall (I_1:nat) (J:nat) (K:nat), ((iff ((ord_less_nat I_1) ((minus_minus_nat J) K))) ((ord_less_nat ((plus_plus_nat I_1) K)) J))). % Axiom fact_910_add__diff__inverse:(forall (M:nat) (N:nat), ((((ord_less_nat M) N)->False)->(((eq nat) ((plus_plus_nat N) ((minus_minus_nat M) N))) M))). % Axiom fact_911_diff__less__mono:(forall (C:nat) (A_1:nat) (B_2:nat), (((ord_less_nat A_1) B_2)->(((ord_less_eq_nat C) A_1)->((ord_less_nat ((minus_minus_nat A_1) C)) ((minus_minus_nat B_2) C))))). % Axiom fact_912_less__diff__iff:(forall (N:nat) (K:nat) (M:nat), (((ord_less_eq_nat K) M)->(((ord_less_eq_nat K) N)->((iff ((ord_less_nat ((minus_minus_nat M) K)) ((minus_minus_nat N) K))) ((ord_less_nat M) N))))). % Axiom fact_913_less__eq__Suc__le__raw:(forall (X_1:nat), (((eq (nat->Prop)) (ord_less_nat X_1)) (ord_less_eq_nat (suc X_1)))). % Axiom fact_914_mono__nat__linear__lb:(forall (M:nat) (K:nat) (F:(nat->nat)), ((forall (M_1:nat) (N_1:nat), (((ord_less_nat M_1) N_1)->((ord_less_nat (F M_1)) (F N_1))))->((ord_less_eq_nat ((plus_plus_nat (F M)) K)) (F ((plus_plus_nat M) K))))). % Axiom fact_915_inc__induct:(forall (P:(nat->Prop)) (I_1:nat) (J:nat), (((ord_less_eq_nat I_1) J)->((P J)->((forall (_TPTP_I:nat), (((ord_less_nat _TPTP_I) J)->((P (suc _TPTP_I))->(P _TPTP_I))))->(P I_1))))). % Axiom fact_916_less__imp__Suc__add:(forall (M:nat) (N:nat), (((ord_less_nat M) N)->((ex nat) (fun (K_1:nat)=> (((eq nat) N) (suc ((plus_plus_nat M) K_1))))))). % Axiom fact_917_bounded__nat__set__is__finite:(forall (N:nat) (N_2:(nat->Prop)), ((forall (X_1:nat), (((member_nat X_1) N_2)->((ord_less_nat X_1) N)))->(finite_finite_nat N_2))). % Axiom fact_918_less__mono__imp__le__mono:(forall (I_1:nat) (J:nat) (F:(nat->nat)), ((forall (_TPTP_I:nat) (J_1:nat), (((ord_less_nat _TPTP_I) J_1)->((ord_less_nat (F _TPTP_I)) (F J_1))))->(((ord_less_eq_nat I_1) J)->((ord_less_eq_nat (F I_1)) (F J))))). % Axiom fact_919_lessE:(forall (I_1:nat) (K:nat), (((ord_less_nat I_1) K)->((not (((eq nat) K) (suc I_1)))->((forall (J_1:nat), (((ord_less_nat I_1) J_1)->(not (((eq nat) K) (suc J_1)))))->False)))). % Axiom fact_920_Suc__lessE:(forall (I_1:nat) (K:nat), (((ord_less_nat (suc I_1)) K)->((forall (J_1:nat), (((ord_less_nat I_1) J_1)->(not (((eq nat) K) (suc J_1)))))->False))). % Axiom fact_921_less__zeroE:(forall (N:nat), (((ord_less_nat N) zero_zero_nat)->False)). % Axiom fact_922_le0:(forall (N:nat), ((ord_less_eq_nat zero_zero_nat) N)). % Axiom fact_923_zero__less__Suc:(forall (N:nat), ((ord_less_nat zero_zero_nat) (suc N))). % Axiom fact_924_le__0__eq:(forall (N:nat), ((iff ((ord_less_eq_nat N) zero_zero_nat)) (((eq nat) N) zero_zero_nat))). % Axiom fact_925_less__eq__nat_Osimps_I1_J:(forall (N:nat), ((ord_less_eq_nat zero_zero_nat) N)). % Axiom fact_926_diffs0__imp__equal:(forall (M:nat) (N:nat), ((((eq nat) ((minus_minus_nat M) N)) zero_zero_nat)->((((eq nat) ((minus_minus_nat N) M)) zero_zero_nat)->(((eq nat) M) N)))). % Axiom fact_927_diff__self__eq__0:(forall (M:nat), (((eq nat) ((minus_minus_nat M) M)) zero_zero_nat)). % Axiom fact_928_minus__nat_Odiff__0:(forall (M:nat), (((eq nat) ((minus_minus_nat M) zero_zero_nat)) M)). % Axiom fact_929_diff__0__eq__0:(forall (N:nat), (((eq nat) ((minus_minus_nat zero_zero_nat) N)) zero_zero_nat)). % Axiom fact_930_bot__nat__def:(((eq nat) bot_bot_nat) zero_zero_nat). % Axiom fact_931_add__eq__self__zero:(forall (M:nat) (N:nat), ((((eq nat) ((plus_plus_nat M) N)) M)->(((eq nat) N) zero_zero_nat))). % Axiom fact_932_add__is__0:(forall (M:nat) (N:nat), ((iff (((eq nat) ((plus_plus_nat M) N)) zero_zero_nat)) ((and (((eq nat) M) zero_zero_nat)) (((eq nat) N) zero_zero_nat)))). % Axiom fact_933_Nat_Oadd__0__right:(forall (M:nat), (((eq nat) ((plus_plus_nat M) zero_zero_nat)) M)). % Axiom fact_934_plus__nat_Oadd__0:(forall (N:nat), (((eq nat) ((plus_plus_nat zero_zero_nat) N)) N)). % Axiom fact_935_gr0I:(forall (N:nat), ((not (((eq nat) N) zero_zero_nat))->((ord_less_nat zero_zero_nat) N))). % Axiom fact_936_gr__implies__not0:(forall (M:nat) (N:nat), (((ord_less_nat M) N)->(not (((eq nat) N) zero_zero_nat)))). % Axiom fact_937_less__nat__zero__code:(forall (N:nat), (((ord_less_nat N) zero_zero_nat)->False)). % Axiom fact_938_neq0__conv:(forall (N:nat), ((iff (not (((eq nat) N) zero_zero_nat))) ((ord_less_nat zero_zero_nat) N))). % Axiom fact_939_not__less0:(forall (N:nat), (((ord_less_nat N) zero_zero_nat)->False)). % Axiom fact_940_Suc__neq__Zero:(forall (M:nat), (not (((eq nat) (suc M)) zero_zero_nat))). % Axiom fact_941_Zero__neq__Suc:(forall (M:nat), (not (((eq nat) zero_zero_nat) (suc M)))). % Axiom fact_942_nat_Osimps_I3_J:(forall (Nat_2:nat), (not (((eq nat) (suc Nat_2)) zero_zero_nat))). % Axiom fact_943_Suc__not__Zero:(forall (M:nat), (not (((eq nat) (suc M)) zero_zero_nat))). % Axiom fact_944_nat_Osimps_I2_J:(forall (Nat_1:nat), (not (((eq nat) zero_zero_nat) (suc Nat_1)))). % Axiom fact_945_Zero__not__Suc:(forall (M:nat), (not (((eq nat) zero_zero_nat) (suc M)))). % Axiom fact_946_gr0__conv__Suc:(forall (N:nat), ((iff ((ord_less_nat zero_zero_nat) N)) ((ex nat) (fun (M_1:nat)=> (((eq nat) N) (suc M_1)))))). % Axiom fact_947_less__Suc0:(forall (N:nat), ((iff ((ord_less_nat N) (suc zero_zero_nat))) (((eq nat) N) zero_zero_nat))). % Axiom fact_948_less__Suc__eq__0__disj:(forall (M:nat) (N:nat), ((iff ((ord_less_nat M) (suc N))) ((or (((eq nat) M) zero_zero_nat)) ((ex nat) (fun (J_1:nat)=> ((and (((eq nat) M) (suc J_1))) ((ord_less_nat J_1) N))))))). % Axiom fact_949_one__is__add:(forall (M:nat) (N:nat), ((iff (((eq nat) (suc zero_zero_nat)) ((plus_plus_nat M) N))) ((or ((and (((eq nat) M) (suc zero_zero_nat))) (((eq nat) N) zero_zero_nat))) ((and (((eq nat) M) zero_zero_nat)) (((eq nat) N) (suc zero_zero_nat)))))). % Axiom fact_950_add__is__1:(forall (M:nat) (N:nat), ((iff (((eq nat) ((plus_plus_nat M) N)) (suc zero_zero_nat))) ((or ((and (((eq nat) M) (suc zero_zero_nat))) (((eq nat) N) zero_zero_nat))) ((and (((eq nat) M) zero_zero_nat)) (((eq nat) N) (suc zero_zero_nat)))))). % Axiom fact_951_add__gr__0:(forall (M:nat) (N:nat), ((iff ((ord_less_nat zero_zero_nat) ((plus_plus_nat M) N))) ((or ((ord_less_nat zero_zero_nat) M)) ((ord_less_nat zero_zero_nat) N)))). % Axiom fact_952_zero__less__diff:(forall (N:nat) (M:nat), ((iff ((ord_less_nat zero_zero_nat) ((minus_minus_nat N) M))) ((ord_less_nat M) N))). % Axiom fact_953_diff__less:(forall (M:nat) (N:nat), (((ord_less_nat zero_zero_nat) N)->(((ord_less_nat zero_zero_nat) M)->((ord_less_nat ((minus_minus_nat M) N)) M)))). % Axiom fact_954_diff__add__0:(forall (N:nat) (M:nat), (((eq nat) ((minus_minus_nat N) ((plus_plus_nat N) M))) zero_zero_nat)). % Axiom fact_955_diff__is__0__eq:(forall (M:nat) (N:nat), ((iff (((eq nat) ((minus_minus_nat M) N)) zero_zero_nat)) ((ord_less_eq_nat M) N))). % Axiom fact_956_diff__is__0__eq_H:(forall (M:nat) (N:nat), (((ord_less_eq_nat M) N)->(((eq nat) ((minus_minus_nat M) N)) zero_zero_nat))). % Axiom fact_957_One__nat__def:(((eq nat) one_one_nat) (suc zero_zero_nat)). % Axiom fact_958_diff__Suc:(forall (M:nat) (N:nat), (((eq nat) ((minus_minus_nat M) (suc N))) (((nat_case_nat zero_zero_nat) (fun (K_1:nat)=> K_1)) ((minus_minus_nat M) N)))). % Axiom fact_959_Suc__pred:(forall (N:nat), (((ord_less_nat zero_zero_nat) N)->(((eq nat) (suc ((minus_minus_nat N) (suc zero_zero_nat)))) N))). % Axiom fact_960_diff__Suc__less:(forall (I_1:nat) (N:nat), (((ord_less_nat zero_zero_nat) N)->((ord_less_nat ((minus_minus_nat N) (suc I_1))) N))). % Axiom fact_961_nat__diff__split:(forall (P:(nat->Prop)) (A_1:nat) (B_2:nat), ((iff (P ((minus_minus_nat A_1) B_2))) ((and (((ord_less_nat A_1) B_2)->(P zero_zero_nat))) (forall (D_1:nat), ((((eq nat) A_1) ((plus_plus_nat B_2) D_1))->(P D_1)))))). % Axiom fact_962_nat__diff__split__asm:(forall (P:(nat->Prop)) (A_1:nat) (B_2:nat), ((iff (P ((minus_minus_nat A_1) B_2))) (((or ((and ((ord_less_nat A_1) B_2)) ((P zero_zero_nat)->False))) ((ex nat) (fun (D_1:nat)=> ((and (((eq nat) A_1) ((plus_plus_nat B_2) D_1))) ((P D_1)->False)))))->False))). % Axiom fact_963_card__less__Suc:(forall (I_1:nat) (M_2:(nat->Prop)), (((member_nat zero_zero_nat) M_2)->(((eq nat) (suc (finite_card_nat (collect_nat (fun (K_1:nat)=> ((and ((member_nat (suc K_1)) M_2)) ((ord_less_nat K_1) I_1))))))) (finite_card_nat (collect_nat (fun (K_1:nat)=> ((and ((member_nat K_1) M_2)) ((ord_less_nat K_1) (suc I_1))))))))). % Axiom fact_964_card__less:(forall (I_1:nat) (M_2:(nat->Prop)), (((member_nat zero_zero_nat) M_2)->(not (((eq nat) (finite_card_nat (collect_nat (fun (K_1:nat)=> ((and ((member_nat K_1) M_2)) ((ord_less_nat K_1) (suc I_1))))))) zero_zero_nat)))). % Axiom fact_965_card__less__Suc2:(forall (I_1:nat) (M_2:(nat->Prop)), ((((member_nat zero_zero_nat) M_2)->False)->(((eq nat) (finite_card_nat (collect_nat (fun (K_1:nat)=> ((and ((member_nat (suc K_1)) M_2)) ((ord_less_nat K_1) I_1)))))) (finite_card_nat (collect_nat (fun (K_1:nat)=> ((and ((member_nat K_1) M_2)) ((ord_less_nat K_1) (suc I_1))))))))). % Axiom fact_966_Suc__diff__1:(forall (N:nat), (((ord_less_nat zero_zero_nat) N)->(((eq nat) (suc ((minus_minus_nat N) one_one_nat))) N))). % Axiom fact_967_Suc__pred_H:(forall (N:nat), (((ord_less_nat zero_zero_nat) N)->(((eq nat) N) (suc ((minus_minus_nat N) one_one_nat))))). % Axiom fact_968_add__eq__if:(forall (N:nat) (M:nat), ((and ((((eq nat) M) zero_zero_nat)->(((eq nat) ((plus_plus_nat M) N)) N))) ((not (((eq nat) M) zero_zero_nat))->(((eq nat) ((plus_plus_nat M) N)) (suc ((plus_plus_nat ((minus_minus_nat M) one_one_nat)) N)))))). % Axiom fact_969_ex__least__nat__less:(forall (N:nat) (P:(nat->Prop)), (((P zero_zero_nat)->False)->((P N)->((ex nat) (fun (K_1:nat)=> ((and ((and ((ord_less_nat K_1) N)) (forall (_TPTP_I:nat), (((ord_less_eq_nat _TPTP_I) K_1)->((P _TPTP_I)->False))))) (P ((plus_plus_nat K_1) one_one_nat)))))))). % Axiom fact_970_ex__least__nat__le:(forall (N:nat) (P:(nat->Prop)), (((P zero_zero_nat)->False)->((P N)->((ex nat) (fun (K_1:nat)=> ((and ((and ((ord_less_eq_nat K_1) N)) (forall (_TPTP_I:nat), (((ord_less_nat _TPTP_I) K_1)->((P _TPTP_I)->False))))) (P K_1))))))). % Axiom fact_971_less__imp__add__positive:(forall (I_1:nat) (J:nat), (((ord_less_nat I_1) J)->((ex nat) (fun (K_1:nat)=> ((and ((ord_less_nat zero_zero_nat) K_1)) (((eq nat) ((plus_plus_nat I_1) K_1)) J)))))). % Axiom fact_972_gr0__implies__Suc:(forall (N:nat), (((ord_less_nat zero_zero_nat) N)->((ex nat) (fun (M_1:nat)=> (((eq nat) N) (suc M_1)))))). % Axiom fact_973_nat_Oexhaust:(forall (Y:nat), ((not (((eq nat) Y) zero_zero_nat))->((forall (Nat:nat), (not (((eq nat) Y) (suc Nat))))->False))). % Axiom fact_974_zero__induct:(forall (P:(nat->Prop)) (K:nat), ((P K)->((forall (N_1:nat), ((P (suc N_1))->(P N_1)))->(P zero_zero_nat)))). % Axiom fact_975_not0__implies__Suc:(forall (N:nat), ((not (((eq nat) N) zero_zero_nat))->((ex nat) (fun (M_1:nat)=> (((eq nat) N) (suc M_1)))))). % Axiom fact_976_nat__induct:(forall (N:nat) (P:(nat->Prop)), ((P zero_zero_nat)->((forall (N_1:nat), ((P N_1)->(P (suc N_1))))->(P N)))). % Axiom fact_977_expand__Suc:(forall (V:int), (((ord_less_nat zero_zero_nat) (number_number_of_nat V))->(((eq nat) (number_number_of_nat V)) (suc ((minus_minus_nat (number_number_of_nat V)) one_one_nat))))). % Axiom fact_978_mult__0:(forall (N:nat), (((eq nat) ((times_times_nat zero_zero_nat) N)) zero_zero_nat)). % Axiom fact_979_mult__0__right:(forall (M:nat), (((eq nat) ((times_times_nat M) zero_zero_nat)) zero_zero_nat)). % Axiom fact_980_mult__is__0:(forall (M:nat) (N:nat), ((iff (((eq nat) ((times_times_nat M) N)) zero_zero_nat)) ((or (((eq nat) M) zero_zero_nat)) (((eq nat) N) zero_zero_nat)))). % Axiom fact_981_mult__cancel1:(forall (K:nat) (M:nat) (N:nat), ((iff (((eq nat) ((times_times_nat K) M)) ((times_times_nat K) N))) ((or (((eq nat) M) N)) (((eq nat) K) zero_zero_nat)))). % Axiom fact_982_mult__cancel2:(forall (M:nat) (K:nat) (N:nat), ((iff (((eq nat) ((times_times_nat M) K)) ((times_times_nat N) K))) ((or (((eq nat) M) N)) (((eq nat) K) zero_zero_nat)))). % Axiom fact_983_Suc__mult__cancel1:(forall (K:nat) (M:nat) (N:nat), ((iff (((eq nat) ((times_times_nat (suc K)) M)) ((times_times_nat (suc K)) N))) (((eq nat) M) N))). % Axiom fact_984_add__mult__distrib:(forall (M:nat) (N:nat) (K:nat), (((eq nat) ((times_times_nat ((plus_plus_nat M) N)) K)) ((plus_plus_nat ((times_times_nat M) K)) ((times_times_nat N) K)))). % Axiom fact_985_add__mult__distrib2:(forall (K:nat) (M:nat) (N:nat), (((eq nat) ((times_times_nat K) ((plus_plus_nat M) N))) ((plus_plus_nat ((times_times_nat K) M)) ((times_times_nat K) N)))). % Axiom fact_986_mult__le__mono:(forall (K:nat) (L:nat) (I_1:nat) (J:nat), (((ord_less_eq_nat I_1) J)->(((ord_less_eq_nat K) L)->((ord_less_eq_nat ((times_times_nat I_1) K)) ((times_times_nat J) L))))). % Axiom fact_987_mult__le__mono2:(forall (K:nat) (I_1:nat) (J:nat), (((ord_less_eq_nat I_1) J)->((ord_less_eq_nat ((times_times_nat K) I_1)) ((times_times_nat K) J)))). % Axiom fact_988_mult__le__mono1:(forall (K:nat) (I_1:nat) (J:nat), (((ord_less_eq_nat I_1) J)->((ord_less_eq_nat ((times_times_nat I_1) K)) ((times_times_nat J) K)))). % Axiom fact_989_le__cube:(forall (M:nat), ((ord_less_eq_nat M) ((times_times_nat M) ((times_times_nat M) M)))). % Axiom fact_990_le__square:(forall (M:nat), ((ord_less_eq_nat M) ((times_times_nat M) M))). % Axiom fact_991_diff__mult__distrib:(forall (M:nat) (N:nat) (K:nat), (((eq nat) ((times_times_nat ((minus_minus_nat M) N)) K)) ((minus_minus_nat ((times_times_nat M) K)) ((times_times_nat N) K)))). % Axiom fact_992_diff__mult__distrib2:(forall (K:nat) (M:nat) (N:nat), (((eq nat) ((times_times_nat K) ((minus_minus_nat M) N))) ((minus_minus_nat ((times_times_nat K) M)) ((times_times_nat K) N)))). % Axiom fact_993_nat__mult__eq__1__iff:(forall (M:nat) (N:nat), ((iff (((eq nat) ((times_times_nat M) N)) one_one_nat)) ((and (((eq nat) M) one_one_nat)) (((eq nat) N) one_one_nat)))). % Axiom fact_994_nat__mult__1__right:(forall (N:nat), (((eq nat) ((times_times_nat N) one_one_nat)) N)). % Axiom fact_995_nat__1__eq__mult__iff:(forall (M:nat) (N:nat), ((iff (((eq nat) one_one_nat) ((times_times_nat M) N))) ((and (((eq nat) M) one_one_nat)) (((eq nat) N) one_one_nat)))). % Axiom fact_996_nat__mult__1:(forall (N:nat), (((eq nat) ((times_times_nat one_one_nat) N)) N)). % Axiom fact_997_mult__eq__1__iff:(forall (M:nat) (N:nat), ((iff (((eq nat) ((times_times_nat M) N)) (suc zero_zero_nat))) ((and (((eq nat) M) (suc zero_zero_nat))) (((eq nat) N) (suc zero_zero_nat))))). % Axiom fact_998_mult__less__mono2:(forall (K:nat) (I_1:nat) (J:nat), (((ord_less_nat I_1) J)->(((ord_less_nat zero_zero_nat) K)->((ord_less_nat ((times_times_nat K) I_1)) ((times_times_nat K) J))))). % Axiom fact_999_mult__less__mono1:(forall (K:nat) (I_1:nat) (J:nat), (((ord_less_nat I_1) J)->(((ord_less_nat zero_zero_nat) K)->((ord_less_nat ((times_times_nat I_1) K)) ((times_times_nat J) K))))). % Axiom fact_1000_mult__less__cancel2:(forall (M:nat) (K:nat) (N:nat), ((iff ((ord_less_nat ((times_times_nat M) K)) ((times_times_nat N) K))) ((and ((ord_less_nat zero_zero_nat) K)) ((ord_less_nat M) N)))). % Axiom fact_1001_mult__less__cancel1:(forall (K:nat) (M:nat) (N:nat), ((iff ((ord_less_nat ((times_times_nat K) M)) ((times_times_nat K) N))) ((and ((ord_less_nat zero_zero_nat) K)) ((ord_less_nat M) N)))). % Axiom fact_1002_nat__0__less__mult__iff:(forall (M:nat) (N:nat), ((iff ((ord_less_nat zero_zero_nat) ((times_times_nat M) N))) ((and ((ord_less_nat zero_zero_nat) M)) ((ord_less_nat zero_zero_nat) N)))). % Axiom fact_1003_Suc__mult__less__cancel1:(forall (K:nat) (M:nat) (N:nat), ((iff ((ord_less_nat ((times_times_nat (suc K)) M)) ((times_times_nat (suc K)) N))) ((ord_less_nat M) N))). % Axiom fact_1004_mult__Suc__right:(forall (M:nat) (N:nat), (((eq nat) ((times_times_nat M) (suc N))) ((plus_plus_nat M) ((times_times_nat M) N)))). % Axiom fact_1005_mult__Suc:(forall (M:nat) (N:nat), (((eq nat) ((times_times_nat (suc M)) N)) ((plus_plus_nat N) ((times_times_nat M) N)))). % Axiom fact_1006_Suc__mult__le__cancel1:(forall (K:nat) (M:nat) (N:nat), ((iff ((ord_less_eq_nat ((times_times_nat (suc K)) M)) ((times_times_nat (suc K)) N))) ((ord_less_eq_nat M) N))). % Axiom fact_1007_mult__eq__self__implies__10:(forall (M:nat) (N:nat), ((((eq nat) M) ((times_times_nat M) N))->((or (((eq nat) N) one_one_nat)) (((eq nat) M) zero_zero_nat)))). % Axiom fact_1008_n__less__m__mult__n:(forall (M:nat) (N:nat), (((ord_less_nat (suc zero_zero_nat)) N)->(((ord_less_nat (suc zero_zero_nat)) M)->((ord_less_nat N) ((times_times_nat M) N))))). % Axiom fact_1009_n__less__n__mult__m:(forall (M:nat) (N:nat), (((ord_less_nat (suc zero_zero_nat)) N)->(((ord_less_nat (suc zero_zero_nat)) M)->((ord_less_nat N) ((times_times_nat N) M))))). % Axiom fact_1010_one__less__mult:(forall (M:nat) (N:nat), (((ord_less_nat (suc zero_zero_nat)) N)->(((ord_less_nat (suc zero_zero_nat)) M)->((ord_less_nat (suc zero_zero_nat)) ((times_times_nat M) N))))). % Axiom fact_1011_one__le__mult__iff:(forall (M:nat) (N:nat), ((iff ((ord_less_eq_nat (suc zero_zero_nat)) ((times_times_nat M) N))) ((and ((ord_less_eq_nat (suc zero_zero_nat)) M)) ((ord_less_eq_nat (suc zero_zero_nat)) N)))). % Axiom fact_1012_mult__le__cancel1:(forall (K:nat) (M:nat) (N:nat), ((iff ((ord_less_eq_nat ((times_times_nat K) M)) ((times_times_nat K) N))) (((ord_less_nat zero_zero_nat) K)->((ord_less_eq_nat M) N)))). % Axiom fact_1013_mult__le__cancel2:(forall (M:nat) (K:nat) (N:nat), ((iff ((ord_less_eq_nat ((times_times_nat M) K)) ((times_times_nat N) K))) (((ord_less_nat zero_zero_nat) K)->((ord_less_eq_nat M) N)))). % Axiom fact_1014_mult__eq__if:(forall (N:nat) (M:nat), ((and ((((eq nat) M) zero_zero_nat)->(((eq nat) ((times_times_nat M) N)) zero_zero_nat))) ((not (((eq nat) M) zero_zero_nat))->(((eq nat) ((times_times_nat M) N)) ((plus_plus_nat N) ((times_times_nat ((minus_minus_nat M) one_one_nat)) N)))))). % Axiom fact_1015_nat__less__add__iff2:(forall (U:nat) (M:nat) (N:nat) (I_1:nat) (J:nat), (((ord_less_eq_nat I_1) J)->((iff ((ord_less_nat ((plus_plus_nat ((times_times_nat I_1) U)) M)) ((plus_plus_nat ((times_times_nat J) U)) N))) ((ord_less_nat M) ((plus_plus_nat ((times_times_nat ((minus_minus_nat J) I_1)) U)) N))))). % Axiom fact_1016_nat__mult__commute:(forall (M:nat) (N:nat), (((eq nat) ((times_times_nat M) N)) ((times_times_nat N) M))). % Axiom fact_1017_nat__mult__assoc:(forall (M:nat) (N:nat) (K:nat), (((eq nat) ((times_times_nat ((times_times_nat M) N)) K)) ((times_times_nat M) ((times_times_nat N) K)))). % Axiom fact_1018_less__number__of__int__code:(forall (K:int) (L:int), ((iff ((ord_less_int (number_number_of_int K)) (number_number_of_int L))) ((ord_less_int K) L))). % Axiom fact_1019_zmult__1:(forall (Z:int), (((eq int) ((times_times_int one_one_int) Z)) Z)). % Axiom fact_1020_zmult__1__right:(forall (Z:int), (((eq int) ((times_times_int Z) one_one_int)) Z)). % Axiom fact_1021_zmult__commute:(forall (Z:int) (W:int), (((eq int) ((times_times_int Z) W)) ((times_times_int W) Z))). % Axiom fact_1022_times__numeral__code_I5_J:(forall (V:int) (W:int), (((eq int) ((times_times_int (number_number_of_int V)) (number_number_of_int W))) (number_number_of_int ((times_times_int V) W)))). % Axiom fact_1023_zmult__assoc:(forall (Z1:int) (Z2:int) (Z3:int), (((eq int) ((times_times_int ((times_times_int Z1) Z2)) Z3)) ((times_times_int Z1) ((times_times_int Z2) Z3)))). % Axiom fact_1024_less__eq__number__of__int__code:(forall (K:int) (L:int), ((iff ((ord_less_eq_int (number_number_of_int K)) (number_number_of_int L))) ((ord_less_eq_int K) L))). % Axiom fact_1025_zdiff__zmult__distrib:(forall (Z1:int) (Z2:int) (W:int), (((eq int) ((times_times_int ((minus_minus_int Z1) Z2)) W)) ((minus_minus_int ((times_times_int Z1) W)) ((times_times_int Z2) W)))). % Axiom fact_1026_zdiff__zmult__distrib2:(forall (W:int) (Z1:int) (Z2:int), (((eq int) ((times_times_int W) ((minus_minus_int Z1) Z2))) ((minus_minus_int ((times_times_int W) Z1)) ((times_times_int W) Z2)))). % Axiom fact_1027_zadd__zmult__distrib2:(forall (W:int) (Z1:int) (Z2:int), (((eq int) ((times_times_int W) ((plus_plus_int Z1) Z2))) ((plus_plus_int ((times_times_int W) Z1)) ((times_times_int W) Z2)))). % Axiom fact_1028_plus__numeral__code_I9_J:(forall (V:int) (W:int), (((eq int) ((plus_plus_int (number_number_of_int V)) (number_number_of_int W))) (number_number_of_int ((plus_plus_int V) W)))). % Axiom fact_1029_zadd__zmult__distrib:(forall (Z1:int) (Z2:int) (W:int), (((eq int) ((times_times_int ((plus_plus_int Z1) Z2)) W)) ((plus_plus_int ((times_times_int Z1) W)) ((times_times_int Z2) W)))). % Axiom fact_1030_zmult__zless__mono2:(forall (K:int) (I_1:int) (J:int), (((ord_less_int I_1) J)->(((ord_less_int zero_zero_int) K)->((ord_less_int ((times_times_int K) I_1)) ((times_times_int K) J))))). % Axiom fact_1031_pos__zmult__eq__1__iff:(forall (N:int) (M:int), (((ord_less_int zero_zero_int) M)->((iff (((eq int) ((times_times_int M) N)) one_one_int)) ((and (((eq int) M) one_one_int)) (((eq int) N) one_one_int))))). % Axiom fact_1032_odd__nonzero:(forall (Z:int), (not (((eq int) ((plus_plus_int ((plus_plus_int one_one_int) Z)) Z)) zero_zero_int))). % Axiom fact_1033_zadd__0__right:(forall (Z:int), (((eq int) ((plus_plus_int Z) zero_zero_int)) Z)). % Axiom fact_1034_zadd__0:(forall (Z:int), (((eq int) ((plus_plus_int zero_zero_int) Z)) Z)). % Axiom fact_1035_int__0__less__1:((ord_less_int zero_zero_int) one_one_int). % Axiom fact_1036_int__one__le__iff__zero__less:(forall (Z:int), ((iff ((ord_less_eq_int one_one_int) Z)) ((ord_less_int zero_zero_int) Z))). % Axiom fact_1037_less__bin__lemma:(forall (K:int) (L:int), ((iff ((ord_less_int K) L)) ((ord_less_int ((minus_minus_int K) L)) zero_zero_int))). % Axiom fact_1038_le__imp__0__less:(forall (Z:int), (((ord_less_eq_int zero_zero_int) Z)->((ord_less_int zero_zero_int) ((plus_plus_int one_one_int) Z)))). % Axiom fact_1039_odd__less__0:(forall (Z:int), ((iff ((ord_less_int ((plus_plus_int ((plus_plus_int one_one_int) Z)) Z)) zero_zero_int)) ((ord_less_int Z) zero_zero_int))). % Axiom fact_1040_zadd__left__mono:(forall (K:int) (I_1:int) (J:int), (((ord_less_eq_int I_1) J)->((ord_less_eq_int ((plus_plus_int K) I_1)) ((plus_plus_int K) J)))). % Axiom fact_1041_zadd__assoc:(forall (Z1:int) (Z2:int) (Z3:int), (((eq int) ((plus_plus_int ((plus_plus_int Z1) Z2)) Z3)) ((plus_plus_int Z1) ((plus_plus_int Z2) Z3)))). % Axiom fact_1042_zadd__left__commute:(forall (X:int) (Y:int) (Z:int), (((eq int) ((plus_plus_int X) ((plus_plus_int Y) Z))) ((plus_plus_int Y) ((plus_plus_int X) Z)))). % Axiom fact_1043_zadd__commute:(forall (Z:int) (W:int), (((eq int) ((plus_plus_int Z) W)) ((plus_plus_int W) Z))). % Axiom fact_1044_zle__refl:(forall (W:int), ((ord_less_eq_int W) W)). % Axiom fact_1045_zle__linear:(forall (Z:int) (W:int), ((or ((ord_less_eq_int Z) W)) ((ord_less_eq_int W) Z))). % Axiom fact_1046_zle__trans:(forall (K:int) (I_1:int) (J:int), (((ord_less_eq_int I_1) J)->(((ord_less_eq_int J) K)->((ord_less_eq_int I_1) K)))). % Axiom fact_1047_zle__antisym:(forall (Z:int) (W:int), (((ord_less_eq_int Z) W)->(((ord_less_eq_int W) Z)->(((eq int) Z) W)))). % Axiom fact_1048_zle__diff1__eq:(forall (W:int) (Z:int), ((iff ((ord_less_eq_int W) ((minus_minus_int Z) one_one_int))) ((ord_less_int W) Z))). % Axiom fact_1049_zless__linear:(forall (X:int) (Y:int), ((or ((or ((ord_less_int X) Y)) (((eq int) X) Y))) ((ord_less_int Y) X))). % Axiom fact_1050_zless__le:(forall (Z:int) (W:int), ((iff ((ord_less_int Z) W)) ((and ((ord_less_eq_int Z) W)) (not (((eq int) Z) W))))). % Axiom fact_1051_zadd__strict__right__mono:(forall (K:int) (I_1:int) (J:int), (((ord_less_int I_1) J)->((ord_less_int ((plus_plus_int I_1) K)) ((plus_plus_int J) K)))). % Axiom fact_1052_zadd__zless__mono:(forall (Z_3:int) (Z:int) (W_1:int) (W:int), (((ord_less_int W_1) W)->(((ord_less_eq_int Z_3) Z)->((ord_less_int ((plus_plus_int W_1) Z_3)) ((plus_plus_int W) Z))))). % Axiom fact_1053_zle__add1__eq__le:(forall (W:int) (Z:int), ((iff ((ord_less_int W) ((plus_plus_int Z) one_one_int))) ((ord_less_eq_int W) Z))). % Axiom fact_1054_add1__zle__eq:(forall (W:int) (Z:int), ((iff ((ord_less_eq_int ((plus_plus_int W) one_one_int)) Z)) ((ord_less_int W) Z))). % Axiom fact_1055_zless__imp__add1__zle:(forall (W:int) (Z:int), (((ord_less_int W) Z)->((ord_less_eq_int ((plus_plus_int W) one_one_int)) Z))). % Axiom fact_1056_zless__add1__eq:(forall (W:int) (Z:int), ((iff ((ord_less_int W) ((plus_plus_int Z) one_one_int))) ((or ((ord_less_int W) Z)) (((eq int) W) Z)))). % Axiom fact_1057_nat__mult__eq__cancel__disj:(forall (K:nat) (M:nat) (N:nat), ((iff (((eq nat) ((times_times_nat K) M)) ((times_times_nat K) N))) ((or (((eq nat) K) zero_zero_nat)) (((eq nat) M) N)))). % Axiom fact_1058_left__add__mult__distrib:(forall (I_1:nat) (U:nat) (J:nat) (K:nat), (((eq nat) ((plus_plus_nat ((times_times_nat I_1) U)) ((plus_plus_nat ((times_times_nat J) U)) K))) ((plus_plus_nat ((times_times_nat ((plus_plus_nat I_1) J)) U)) K))). % Axiom fact_1059_nat__mult__eq__cancel1:(forall (M:nat) (N:nat) (K:nat), (((ord_less_nat zero_zero_nat) K)->((iff (((eq nat) ((times_times_nat K) M)) ((times_times_nat K) N))) (((eq nat) M) N)))). % Axiom fact_1060_nat__mult__less__cancel1:(forall (M:nat) (N:nat) (K:nat), (((ord_less_nat zero_zero_nat) K)->((iff ((ord_less_nat ((times_times_nat K) M)) ((times_times_nat K) N))) ((ord_less_nat M) N)))). % Axiom fact_1061_nat__mult__le__cancel1:(forall (M:nat) (N:nat) (K:nat), (((ord_less_nat zero_zero_nat) K)->((iff ((ord_less_eq_nat ((times_times_nat K) M)) ((times_times_nat K) N))) ((ord_less_eq_nat M) N)))). % Axiom fact_1062_nat__le__add__iff1:(forall (U:nat) (M:nat) (N:nat) (J:nat) (I_1:nat), (((ord_less_eq_nat J) I_1)->((iff ((ord_less_eq_nat ((plus_plus_nat ((times_times_nat I_1) U)) M)) ((plus_plus_nat ((times_times_nat J) U)) N))) ((ord_less_eq_nat ((plus_plus_nat ((times_times_nat ((minus_minus_nat I_1) J)) U)) M)) N)))). % Axiom fact_1063_nat__diff__add__eq1:(forall (U:nat) (M:nat) (N:nat) (J:nat) (I_1:nat), (((ord_less_eq_nat J) I_1)->(((eq nat) ((minus_minus_nat ((plus_plus_nat ((times_times_nat I_1) U)) M)) ((plus_plus_nat ((times_times_nat J) U)) N))) ((minus_minus_nat ((plus_plus_nat ((times_times_nat ((minus_minus_nat I_1) J)) U)) M)) N)))). % Axiom fact_1064_nat__eq__add__iff1:(forall (U:nat) (M:nat) (N:nat) (J:nat) (I_1:nat), (((ord_less_eq_nat J) I_1)->((iff (((eq nat) ((plus_plus_nat ((times_times_nat I_1) U)) M)) ((plus_plus_nat ((times_times_nat J) U)) N))) (((eq nat) ((plus_plus_nat ((times_times_nat ((minus_minus_nat I_1) J)) U)) M)) N)))). % Axiom fact_1065_nat__le__add__iff2:(forall (U:nat) (M:nat) (N:nat) (I_1:nat) (J:nat), (((ord_less_eq_nat I_1) J)->((iff ((ord_less_eq_nat ((plus_plus_nat ((times_times_nat I_1) U)) M)) ((plus_plus_nat ((times_times_nat J) U)) N))) ((ord_less_eq_nat M) ((plus_plus_nat ((times_times_nat ((minus_minus_nat J) I_1)) U)) N))))). % Axiom fact_1066_nat__diff__add__eq2:(forall (U:nat) (M:nat) (N:nat) (I_1:nat) (J:nat), (((ord_less_eq_nat I_1) J)->(((eq nat) ((minus_minus_nat ((plus_plus_nat ((times_times_nat I_1) U)) M)) ((plus_plus_nat ((times_times_nat J) U)) N))) ((minus_minus_nat M) ((plus_plus_nat ((times_times_nat ((minus_minus_nat J) I_1)) U)) N))))). % Axiom fact_1067_nat__eq__add__iff2:(forall (U:nat) (M:nat) (N:nat) (I_1:nat) (J:nat), (((ord_less_eq_nat I_1) J)->((iff (((eq nat) ((plus_plus_nat ((times_times_nat I_1) U)) M)) ((plus_plus_nat ((times_times_nat J) U)) N))) (((eq nat) M) ((plus_plus_nat ((times_times_nat ((minus_minus_nat J) I_1)) U)) N))))). % Axiom fact_1068_nat__less__add__iff1:(forall (U:nat) (M:nat) (N:nat) (J:nat) (I_1:nat), (((ord_less_eq_nat J) I_1)->((iff ((ord_less_nat ((plus_plus_nat ((times_times_nat I_1) U)) M)) ((plus_plus_nat ((times_times_nat J) U)) N))) ((ord_less_nat ((plus_plus_nat ((times_times_nat ((minus_minus_nat I_1) J)) U)) M)) N)))). % Axiom fact_1069_zdiv__mono2__neg__lemma:(forall (B_2:int) (Q_1:int) (R_1:int) (B_1:int) (Q:int) (R:int), ((((eq int) ((plus_plus_int ((times_times_int B_2) Q_1)) R_1)) ((plus_plus_int ((times_times_int B_1) Q)) R))->(((ord_less_int ((plus_plus_int ((times_times_int B_1) Q)) R)) zero_zero_int)->(((ord_less_int R_1) B_2)->(((ord_less_eq_int zero_zero_int) R)->(((ord_less_int zero_zero_int) B_1)->(((ord_less_eq_int B_1) B_2)->((ord_less_eq_int Q) Q_1)))))))). % Axiom fact_1070_unique__quotient__lemma__neg:(forall (B_2:int) (Q:int) (R:int) (Q_1:int) (R_1:int), (((ord_less_eq_int ((plus_plus_int ((times_times_int B_2) Q)) R)) ((plus_plus_int ((times_times_int B_2) Q_1)) R_1))->(((ord_less_eq_int R_1) zero_zero_int)->(((ord_less_int B_2) R_1)->(((ord_less_int B_2) R)->((ord_less_eq_int Q_1) Q)))))). % Axiom fact_1071_number__of__is__id:(forall (K:int), (((eq int) (number_number_of_int K)) K)). % Axiom fact_1072_int__0__neq__1:(not (((eq int) zero_zero_int) one_one_int)). % Axiom fact_1073_self__quotient__aux1:(forall (R_1:int) (Q_1:int) (A_1:int), (((ord_less_int zero_zero_int) A_1)->((((eq int) A_1) ((plus_plus_int R_1) ((times_times_int A_1) Q_1)))->(((ord_less_int R_1) A_1)->((ord_less_eq_int one_one_int) Q_1))))). % Axiom fact_1074_self__quotient__aux2:(forall (R_1:int) (Q_1:int) (A_1:int), (((ord_less_int zero_zero_int) A_1)->((((eq int) A_1) ((plus_plus_int R_1) ((times_times_int A_1) Q_1)))->(((ord_less_eq_int zero_zero_int) R_1)->((ord_less_eq_int Q_1) one_one_int))))). % Axiom fact_1075_q__pos__lemma:(forall (B_1:int) (Q:int) (R:int), (((ord_less_eq_int zero_zero_int) ((plus_plus_int ((times_times_int B_1) Q)) R))->(((ord_less_int R) B_1)->(((ord_less_int zero_zero_int) B_1)->((ord_less_eq_int zero_zero_int) Q))))). % Axiom fact_1076_q__neg__lemma:(forall (B_1:int) (Q:int) (R:int), (((ord_less_int ((plus_plus_int ((times_times_int B_1) Q)) R)) zero_zero_int)->(((ord_less_eq_int zero_zero_int) R)->(((ord_less_int zero_zero_int) B_1)->((ord_less_eq_int Q) zero_zero_int))))). % Axiom fact_1077_unique__quotient__lemma:(forall (B_2:int) (Q:int) (R:int) (Q_1:int) (R_1:int), (((ord_less_eq_int ((plus_plus_int ((times_times_int B_2) Q)) R)) ((plus_plus_int ((times_times_int B_2) Q_1)) R_1))->(((ord_less_eq_int zero_zero_int) R)->(((ord_less_int R) B_2)->(((ord_less_int R_1) B_2)->((ord_less_eq_int Q) Q_1)))))). % Axiom fact_1078_zdiv__mono2__lemma:(forall (B_2:int) (Q_1:int) (R_1:int) (B_1:int) (Q:int) (R:int), ((((eq int) ((plus_plus_int ((times_times_int B_2) Q_1)) R_1)) ((plus_plus_int ((times_times_int B_1) Q)) R))->(((ord_less_eq_int zero_zero_int) ((plus_plus_int ((times_times_int B_1) Q)) R))->(((ord_less_int R) B_1)->(((ord_less_eq_int zero_zero_int) R_1)->(((ord_less_int zero_zero_int) B_1)->(((ord_less_eq_int B_1) B_2)->((ord_less_eq_int Q_1) Q)))))))). % Axiom fact_1079_int__less__induct:(forall (P:(int->Prop)) (I_1:int) (K:int), (((ord_less_int I_1) K)->((P ((minus_minus_int K) one_one_int))->((forall (_TPTP_I:int), (((ord_less_int _TPTP_I) K)->((P _TPTP_I)->(P ((minus_minus_int _TPTP_I) one_one_int)))))->(P I_1))))). % Axiom fact_1080_int__le__induct:(forall (P:(int->Prop)) (I_1:int) (K:int), (((ord_less_eq_int I_1) K)->((P K)->((forall (_TPTP_I:int), (((ord_less_eq_int _TPTP_I) K)->((P _TPTP_I)->(P ((minus_minus_int _TPTP_I) one_one_int)))))->(P I_1))))). % Axiom fact_1081_int__gr__induct:(forall (P:(int->Prop)) (K:int) (I_1:int), (((ord_less_int K) I_1)->((P ((plus_plus_int K) one_one_int))->((forall (_TPTP_I:int), (((ord_less_int K) _TPTP_I)->((P _TPTP_I)->(P ((plus_plus_int _TPTP_I) one_one_int)))))->(P I_1))))). % Axiom fact_1082_int__ge__induct:(forall (P:(int->Prop)) (K:int) (I_1:int), (((ord_less_eq_int K) I_1)->((P K)->((forall (_TPTP_I:int), (((ord_less_eq_int K) _TPTP_I)->((P _TPTP_I)->(P ((plus_plus_int _TPTP_I) one_one_int)))))->(P I_1))))). % Axiom fact_1083_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J:(forall (Y:int) (X:int), (((ord_less_eq_int zero_zero_int) X)->(((ord_less_eq_int zero_zero_int) Y)->((ord_less_eq_int zero_zero_int) ((times_times_int X) Y))))). % Axiom fact_1084_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J:((ord_less_eq_int zero_zero_int) zero_zero_int). % Axiom fact_1085_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J:(forall (Y:int) (X:int), (((ord_less_eq_int zero_zero_int) X)->(((ord_less_eq_int zero_zero_int) Y)->((ord_less_eq_int zero_zero_int) ((plus_plus_int X) Y))))). % Axiom fact_1086_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J:((ord_less_eq_int zero_zero_int) one_one_int). % Axiom fact_1087_transfer__nat__int__set__cong:(forall (P_1:(int->Prop)) (P:(int->Prop)), ((forall (X_1:int), (((ord_less_eq_int zero_zero_int) X_1)->((iff (P X_1)) (P_1 X_1))))->(((eq (int->Prop)) (collect_int (fun (X_1:int)=> ((and ((ord_less_eq_int zero_zero_int) X_1)) (P X_1))))) (collect_int (fun (X_1:int)=> ((and ((ord_less_eq_int zero_zero_int) X_1)) (P_1 X_1))))))). % Axiom fact_1088_decr__mult__lemma:(forall (K:int) (P:(int->Prop)) (D:int), (((ord_less_int zero_zero_int) D)->((forall (X_1:int), ((P X_1)->(P ((minus_minus_int X_1) D))))->(((ord_less_eq_int zero_zero_int) K)->(forall (X_1:int), ((P X_1)->(P ((minus_minus_int X_1) ((times_times_int K) D))))))))). % Axiom fact_1089_conj__le__cong:(forall (P_1:Prop) (P:Prop) (X:int), ((((ord_less_eq_int zero_zero_int) X)->((iff P) P_1))->((iff ((and ((ord_less_eq_int zero_zero_int) X)) P)) ((and ((ord_less_eq_int zero_zero_int) X)) P_1)))). % Axiom fact_1090_imp__le__cong:(forall (P_1:Prop) (P:Prop) (X:int), ((((ord_less_eq_int zero_zero_int) X)->((iff P) P_1))->((iff (((ord_less_eq_int zero_zero_int) X)->P)) (((ord_less_eq_int zero_zero_int) X)->P_1)))). % Axiom fact_1091_incr__mult__lemma:(forall (K:int) (P:(int->Prop)) (D:int), (((ord_less_int zero_zero_int) D)->((forall (X_1:int), ((P X_1)->(P ((plus_plus_int X_1) D))))->(((ord_less_eq_int zero_zero_int) K)->(forall (X_1:int), ((P X_1)->(P ((plus_plus_int X_1) ((times_times_int K) D))))))))). % Axiom fact_1092_int__induct:(forall (I_1:int) (P:(int->Prop)) (K:int), ((P K)->((forall (_TPTP_I:int), (((ord_less_eq_int K) _TPTP_I)->((P _TPTP_I)->(P ((plus_plus_int _TPTP_I) one_one_int)))))->((forall (_TPTP_I:int), (((ord_less_eq_int _TPTP_I) K)->((P _TPTP_I)->(P ((minus_minus_int _TPTP_I) one_one_int)))))->(P I_1))))). % Axiom fact_1093_minusinfinity:(forall (P:(int->Prop)) (P1:(int->Prop)) (D:int), (((ord_less_int zero_zero_int) D)->((forall (X_1:int) (K_1:int), ((iff (P1 X_1)) (P1 ((minus_minus_int X_1) ((times_times_int K_1) D)))))->(((ex int) (fun (Z_2:int)=> (forall (X_1:int), (((ord_less_int X_1) Z_2)->((iff (P X_1)) (P1 X_1))))))->((_TPTP_ex P1)->(_TPTP_ex P)))))). % Axiom fact_1094_plusinfinity:(forall (P:(int->Prop)) (P_1:(int->Prop)) (D:int), (((ord_less_int zero_zero_int) D)->((forall (X_1:int) (K_1:int), ((iff (P_1 X_1)) (P_1 ((minus_minus_int X_1) ((times_times_int K_1) D)))))->(((ex int) (fun (Z_2:int)=> (forall (X_1:int), (((ord_less_int Z_2) X_1)->((iff (P X_1)) (P_1 X_1))))))->((_TPTP_ex P_1)->(_TPTP_ex P)))))). % Axiom fact_1095_tsub__def:(forall (Y:int) (X:int), ((and (((ord_less_eq_int Y) X)->(((eq int) ((nat_tsub X) Y)) ((minus_minus_int X) Y)))) ((((ord_less_eq_int Y) X)->False)->(((eq int) ((nat_tsub X) Y)) zero_zero_int)))). % Axiom fact_1096_zero__zle__int:(forall (N:nat), ((ord_less_eq_int zero_zero_int) (semiri1621563631at_int N))). % Axiom fact_1097_int__less__0__conv:(forall (K:nat), (((ord_less_int (semiri1621563631at_int K)) zero_zero_int)->False)). % Axiom fact_1098_int__1:(((eq int) (semiri1621563631at_int one_one_nat)) one_one_int). % Axiom fact_1099_int__0:(((eq int) (semiri1621563631at_int zero_zero_nat)) zero_zero_int). % Axiom fact_1100_int__eq__0__conv:(forall (N:nat), ((iff (((eq int) (semiri1621563631at_int N)) zero_zero_int)) (((eq nat) N) zero_zero_nat))). % Axiom fact_1101_zless__int:(forall (M:nat) (N:nat), ((iff ((ord_less_int (semiri1621563631at_int M)) (semiri1621563631at_int N))) ((ord_less_nat M) N))). % Axiom fact_1102_zle__int:(forall (M:nat) (N:nat), ((iff ((ord_less_eq_int (semiri1621563631at_int M)) (semiri1621563631at_int N))) ((ord_less_eq_nat M) N))). % Axiom fact_1103_zadd__int:(forall (M:nat) (N:nat), (((eq int) ((plus_plus_int (semiri1621563631at_int M)) (semiri1621563631at_int N))) (semiri1621563631at_int ((plus_plus_nat M) N)))). % Axiom fact_1104_zadd__int__left:(forall (M:nat) (N:nat) (Z:int), (((eq int) ((plus_plus_int (semiri1621563631at_int M)) ((plus_plus_int (semiri1621563631at_int N)) Z))) ((plus_plus_int (semiri1621563631at_int ((plus_plus_nat M) N))) Z))). % Axiom fact_1105_zle__iff__zadd:(forall (W:int) (Z:int), ((iff ((ord_less_eq_int W) Z)) ((ex nat) (fun (N_1:nat)=> (((eq int) Z) ((plus_plus_int W) (semiri1621563631at_int N_1))))))). % Axiom fact_1106_zmult__int:(forall (M:nat) (N:nat), (((eq int) ((times_times_int (semiri1621563631at_int M)) (semiri1621563631at_int N))) (semiri1621563631at_int ((times_times_nat M) N)))). % Axiom fact_1107_int__mult:(forall (M:nat) (N:nat), (((eq int) (semiri1621563631at_int ((times_times_nat M) N))) ((times_times_int (semiri1621563631at_int M)) (semiri1621563631at_int N)))). % Axiom fact_1108_Nat__Transfer_Otransfer__int__nat__functions_I2_J:(forall (X:nat) (Y:nat), (((eq int) ((times_times_int (semiri1621563631at_int X)) (semiri1621563631at_int Y))) (semiri1621563631at_int ((times_times_nat X) Y)))). % Axiom fact_1109_transfer__int__nat__relations_I2_J:(forall (X:nat) (Y:nat), ((iff ((ord_less_int (semiri1621563631at_int X)) (semiri1621563631at_int Y))) ((ord_less_nat X) Y))). % Axiom fact_1110_transfer__int__nat__relations_I3_J:(forall (X:nat) (Y:nat), ((iff ((ord_less_eq_int (semiri1621563631at_int X)) (semiri1621563631at_int Y))) ((ord_less_eq_nat X) Y))). % Axiom fact_1111_Nat__Transfer_Otransfer__int__nat__functions_I3_J:(forall (X:nat) (Y:nat), (((eq int) ((nat_tsub (semiri1621563631at_int X)) (semiri1621563631at_int Y))) (semiri1621563631at_int ((minus_minus_nat X) Y)))). % Axiom fact_1112_Nat__Transfer_Otransfer__int__nat__functions_I1_J:(forall (X:nat) (Y:nat), (((eq int) ((plus_plus_int (semiri1621563631at_int X)) (semiri1621563631at_int Y))) (semiri1621563631at_int ((plus_plus_nat X) Y)))). % Axiom fact_1113_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J:(forall (A:(nat->Prop)), (((eq nat) (finite_card_nat A)) (finite_card_int ((image_nat_int semiri1621563631at_int) A)))). % Axiom fact_1114_transfer__nat__int__set__relations_I1_J:(forall (A:(nat->Prop)), ((iff (finite_finite_nat A)) (finite_finite_int ((image_nat_int semiri1621563631at_int) A)))). % Axiom fact_1115_transfer__int__nat__numerals_I2_J:(((eq int) one_one_int) (semiri1621563631at_int one_one_nat)). % Axiom fact_1116_transfer__int__nat__numerals_I1_J:(((eq int) zero_zero_int) (semiri1621563631at_int zero_zero_nat)). % Axiom fact_1117_Nat__Transfer_Otransfer__int__nat__set__functions_I5_J:(forall (P:(int->Prop)), (((eq (int->Prop)) (collect_int (fun (X_1:int)=> ((and ((ord_less_eq_int zero_zero_int) X_1)) (P X_1))))) ((image_nat_int semiri1621563631at_int) (collect_nat (fun (X_1:nat)=> (P (semiri1621563631at_int X_1))))))). % Axiom fact_1118_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J:(forall (Z:nat), ((ord_less_eq_int zero_zero_int) (semiri1621563631at_int Z))). % Axiom fact_1119_transfer__int__nat__quantifiers_I2_J:(forall (P:(int->Prop)), ((iff ((ex int) (fun (X_1:int)=> ((and ((ord_less_eq_int zero_zero_int) X_1)) (P X_1))))) ((ex nat) (fun (X_1:nat)=> (P (semiri1621563631at_int X_1)))))). % Axiom fact_1120_transfer__int__nat__quantifiers_I1_J:(forall (P:(int->Prop)), ((iff (forall (X_1:int), (((ord_less_eq_int zero_zero_int) X_1)->(P X_1)))) (forall (X_1:nat), (P (semiri1621563631at_int X_1))))). % Axiom fact_1121_int__le__0__conv:(forall (N:nat), ((iff ((ord_less_eq_int (semiri1621563631at_int N)) zero_zero_int)) (((eq nat) N) zero_zero_nat))). % Axiom fact_1122_int__Suc0__eq__1:(((eq int) (semiri1621563631at_int (suc zero_zero_nat))) one_one_int). % Axiom fact_1123_zless__iff__Suc__zadd:(forall (W:int) (Z:int), ((iff ((ord_less_int W) Z)) ((ex nat) (fun (N_1:nat)=> (((eq int) Z) ((plus_plus_int W) (semiri1621563631at_int (suc N_1)))))))). % Axiom fact_1124_int__Suc:(forall (M:nat), (((eq int) (semiri1621563631at_int (suc M))) ((plus_plus_int one_one_int) (semiri1621563631at_int M)))). % Axiom fact_1125_zdiff__int:(forall (N:nat) (M:nat), (((ord_less_eq_nat N) M)->(((eq int) ((minus_minus_int (semiri1621563631at_int M)) (semiri1621563631at_int N))) (semiri1621563631at_int ((minus_minus_nat M) N))))). % Axiom fact_1126_zero__less__int__conv:(forall (N:nat), ((iff ((ord_less_int zero_zero_int) (semiri1621563631at_int N))) ((ord_less_nat zero_zero_nat) N))). % Axiom fact_1127_zmult__zless__mono2__lemma:(forall (K:nat) (I_1:int) (J:int), (((ord_less_int I_1) J)->(((ord_less_nat zero_zero_nat) K)->((ord_less_int ((times_times_int (semiri1621563631at_int K)) I_1)) ((times_times_int (semiri1621563631at_int K)) J))))). % Axiom fact_1128_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J:(forall (Y:int) (X:int), (((ord_less_eq_int zero_zero_int) X)->(((ord_less_eq_int zero_zero_int) Y)->((ord_less_eq_int zero_zero_int) ((nat_tsub X) Y))))). % Axiom fact_1129_zdiff__int__split:(forall (P:(int->Prop)) (X:nat) (Y:nat), ((iff (P (semiri1621563631at_int ((minus_minus_nat X) Y)))) ((and (((ord_less_eq_nat Y) X)->(P ((minus_minus_int (semiri1621563631at_int X)) (semiri1621563631at_int Y))))) (((ord_less_nat X) Y)->(P zero_zero_int))))). % Axiom fact_1130_tsub__eq:(forall (Y:int) (X:int), (((ord_less_eq_int Y) X)->(((eq int) ((nat_tsub X) Y)) ((minus_minus_int X) Y)))). % Axiom fact_1131_zero__less__imp__eq__int:(forall (K:int), (((ord_less_int zero_zero_int) K)->((ex nat) (fun (N_1:nat)=> ((and ((ord_less_nat zero_zero_nat) N_1)) (((eq int) K) (semiri1621563631at_int N_1))))))). % Axiom fact_1132_int__int__eq:(forall (M:nat) (N:nat), ((iff (((eq int) (semiri1621563631at_int M)) (semiri1621563631at_int N))) (((eq nat) M) N))). % Axiom fact_1133_transfer__nat__int__set__relations_I4_J:(forall (A:(nat->Prop)) (B:(nat->Prop)), ((iff ((ord_less_nat_o A) B)) ((ord_less_int_o ((image_nat_int semiri1621563631at_int) A)) ((image_nat_int semiri1621563631at_int) B)))). % Axiom fact_1134_transfer__nat__int__set__relations_I5_J:(forall (A:(nat->Prop)) (B:(nat->Prop)), ((iff ((ord_less_eq_nat_o A) B)) ((ord_less_eq_int_o ((image_nat_int semiri1621563631at_int) A)) ((image_nat_int semiri1621563631at_int) B)))). % Axiom fact_1135_Nat__Transfer_Otransfer__int__nat__set__functions_I2_J:(((eq (int->Prop)) bot_bot_int_o) ((image_nat_int semiri1621563631at_int) bot_bot_nat_o)). % Axiom fact_1136_transfer__nat__int__set__relations_I3_J:(forall (A:(nat->Prop)) (B:(nat->Prop)), ((iff (((eq (nat->Prop)) A) B)) (((eq (int->Prop)) ((image_nat_int semiri1621563631at_int) A)) ((image_nat_int semiri1621563631at_int) B)))). % Axiom fact_1137_transfer__nat__int__set__relations_I2_J:(forall (X:nat) (A:(nat->Prop)), ((iff ((member_nat X) A)) ((member_int (semiri1621563631at_int X)) ((image_nat_int semiri1621563631at_int) A)))). % Axiom fact_1138_int__if__cong:(forall (X:nat) (Y:nat) (P:Prop), ((and (P->(((eq int) (semiri1621563631at_int X)) (semiri1621563631at_int (((if_nat P) X) Y))))) ((P->False)->(((eq int) (semiri1621563631at_int Y)) (semiri1621563631at_int (((if_nat P) X) Y)))))). % Axiom fact_1139_transfer__int__nat__relations_I1_J:(forall (X:nat) (Y:nat), ((iff (((eq int) (semiri1621563631at_int X)) (semiri1621563631at_int Y))) (((eq nat) X) Y))). % Axiom fact_1140_nonneg__int__cases:(forall (K:int), (((ord_less_eq_int zero_zero_int) K)->((forall (N_1:nat), (not (((eq int) K) (semiri1621563631at_int N_1))))->False))). % Axiom fact_1141_nonneg__eq__int:(forall (Z:int), (((ord_less_eq_int zero_zero_int) Z)->((forall (M_1:nat), (not (((eq int) Z) (semiri1621563631at_int M_1))))->False))). % Axiom fact_1142_zero__le__imp__eq__int:(forall (K:int), (((ord_less_eq_int zero_zero_int) K)->((ex nat) (fun (N_1:nat)=> (((eq int) K) (semiri1621563631at_int N_1)))))). % Axiom fact_1143_int__diff__cases:(forall (Z:int), ((forall (M_1:nat) (N_1:nat), (not (((eq int) Z) ((minus_minus_int (semiri1621563631at_int M_1)) (semiri1621563631at_int N_1)))))->False)). % Axiom fact_1144_decr__lemma:(forall (X:int) (Z:int) (D:int), (((ord_less_int zero_zero_int) D)->((ord_less_int ((minus_minus_int X) ((times_times_int ((plus_plus_int (abs_abs_int ((minus_minus_int X) Z))) one_one_int)) D))) Z))). % Axiom fact_1145_zabs__less__one__iff:(forall (Z:int), ((iff ((ord_less_int (abs_abs_int Z)) one_one_int)) (((eq int) Z) zero_zero_int))). % Axiom fact_1146_neg__def:(forall (Z_1:int), ((iff (nat_neg Z_1)) ((ord_less_int Z_1) zero_zero_int))). % Axiom fact_1147_not__neg__eq__ge__0:(forall (X:int), ((iff ((nat_neg X)->False)) ((ord_less_eq_int zero_zero_int) X))). % Axiom fact_1148_not__neg__1:((nat_neg one_one_int)->False). % Axiom fact_1149_not__neg__0:((nat_neg zero_zero_int)->False). % Axiom fact_1150_abs__zmult__eq__1:(forall (M:int) (N:int), ((((eq int) (abs_abs_int ((times_times_int M) N))) one_one_int)->(((eq int) (abs_abs_int M)) one_one_int))). % Axiom fact_1151_not__neg__int:(forall (N:nat), ((nat_neg (semiri1621563631at_int N))->False)). % Axiom fact_1152_abs__int__eq:(forall (M:nat), (((eq int) (abs_abs_int (semiri1621563631at_int M))) (semiri1621563631at_int M))). % Axiom fact_1153_neg__imp__number__of__eq__0:(forall (V:int), ((nat_neg (number_number_of_int V))->(((eq nat) (number_number_of_nat V)) zero_zero_nat))). % Axiom fact_1154_eq__nat__number__of:(forall (V:int) (V_1:int), ((iff (((eq nat) (number_number_of_nat V)) (number_number_of_nat V_1))) ((and ((nat_neg (number_number_of_int V))->((ord_less_eq_int (number_number_of_int V_1)) zero_zero_int))) (((nat_neg (number_number_of_int V))->False)->((and ((nat_neg (number_number_of_int V_1))->(((eq int) (number_number_of_int V)) zero_zero_int))) (((nat_neg (number_number_of_int V_1))->False)->(((eq int) V) V_1))))))). % Axiom fact_1155_nat__number__of__add__left:(forall (V_1:int) (K:nat) (V:int), ((and ((nat_neg (number_number_of_int V))->(((eq nat) ((plus_plus_nat (number_number_of_nat V)) ((plus_plus_nat (number_number_of_nat V_1)) K))) ((plus_plus_nat (number_number_of_nat V_1)) K)))) (((nat_neg (number_number_of_int V))->False)->((and ((nat_neg (number_number_of_int V_1))->(((eq nat) ((plus_plus_nat (number_number_of_nat V)) ((plus_plus_nat (number_number_of_nat V_1)) K))) ((plus_plus_nat (number_number_of_nat V)) K)))) (((nat_neg (number_number_of_int V_1))->False)->(((eq nat) ((plus_plus_nat (number_number_of_nat V)) ((plus_plus_nat (number_number_of_nat V_1)) K))) ((plus_plus_nat (number_number_of_nat ((plus_plus_int V) V_1))) K))))))). % Axiom fact_1156_int__nat__number__of:(forall (V:int), ((and ((nat_neg (number_number_of_int V))->(((eq int) (semiri1621563631at_int (number_number_of_nat V))) zero_zero_int))) (((nat_neg (number_number_of_int V))->False)->(((eq int) (semiri1621563631at_int (number_number_of_nat V))) (number_number_of_int V))))). % Axiom fact_1157_incr__lemma:(forall (Z:int) (X:int) (D:int), (((ord_less_int zero_zero_int) D)->((ord_less_int Z) ((plus_plus_int X) ((times_times_int ((plus_plus_int (abs_abs_int ((minus_minus_int X) Z))) one_one_int)) D))))). % Axiom fact_1158_int__val__lemma:(forall (K:int) (F:(nat->int)) (N:nat), ((forall (_TPTP_I:nat), (((ord_less_nat _TPTP_I) N)->((ord_less_eq_int (abs_abs_int ((minus_minus_int (F ((plus_plus_nat _TPTP_I) one_one_nat))) (F _TPTP_I)))) one_one_int)))->(((ord_less_eq_int (F zero_zero_nat)) K)->(((ord_less_eq_int K) (F N))->((ex nat) (fun (_TPTP_I:nat)=> ((and ((ord_less_eq_nat _TPTP_I) N)) (((eq int) (F _TPTP_I)) K)))))))). % Axiom fact_1159_nat0__intermed__int__val:(forall (K:int) (F:(nat->int)) (N:nat), ((forall (_TPTP_I:nat), (((ord_less_nat _TPTP_I) N)->((ord_less_eq_int (abs_abs_int ((minus_minus_int (F ((plus_plus_nat _TPTP_I) one_one_nat))) (F _TPTP_I)))) one_one_int)))->(((ord_less_eq_int (F zero_zero_nat)) K)->(((ord_less_eq_int K) (F N))->((ex nat) (fun (_TPTP_I:nat)=> ((and ((ord_less_eq_nat _TPTP_I) N)) (((eq int) (F _TPTP_I)) K)))))))). % Axiom fact_1160_nat__intermed__int__val:(forall (K:int) (F:(nat->int)) (N:nat) (M:nat), ((forall (_TPTP_I:nat), (((and ((ord_less_eq_nat M) _TPTP_I)) ((ord_less_nat _TPTP_I) N))->((ord_less_eq_int (abs_abs_int ((minus_minus_int (F ((plus_plus_nat _TPTP_I) one_one_nat))) (F _TPTP_I)))) one_one_int)))->(((ord_less_nat M) N)->(((ord_less_eq_int (F M)) K)->(((ord_less_eq_int K) (F N))->((ex nat) (fun (_TPTP_I:nat)=> ((and ((and ((ord_less_eq_nat M) _TPTP_I)) ((ord_less_eq_nat _TPTP_I) N))) (((eq int) (F _TPTP_I)) K))))))))). % Axiom fact_1161_Suc__nat__number__of__add:(forall (N:nat) (V:int), ((and ((nat_neg (number_number_of_int V))->(((eq nat) (suc ((plus_plus_nat (number_number_of_nat V)) N))) ((plus_plus_nat one_one_nat) N)))) (((nat_neg (number_number_of_int V))->False)->(((eq nat) (suc ((plus_plus_nat (number_number_of_nat V)) N))) ((plus_plus_nat (number_number_of_nat (succ V))) N))))). % Axiom fact_1162_succ__def:(forall (K:int), (((eq int) (succ K)) ((plus_plus_int K) one_one_int))). % Axiom fact_1163_Suc__nat__number__of:(forall (V:int), ((and ((nat_neg (number_number_of_int V))->(((eq nat) (suc (number_number_of_nat V))) one_one_nat))) (((nat_neg (number_number_of_int V))->False)->(((eq nat) (suc (number_number_of_nat V))) (number_number_of_nat (succ V)))))). % Axiom fact_1164_nat__number__of__Bit1:(forall (W:int), ((and ((nat_neg (number_number_of_int W))->(((eq nat) (number_number_of_nat (bit1 W))) zero_zero_nat))) (((nat_neg (number_number_of_int W))->False)->(((eq nat) (number_number_of_nat (bit1 W))) (suc ((plus_plus_nat (number_number_of_nat W)) (number_number_of_nat W))))))). % Axiom fact_1165_nat__1__add__number__of:(forall (V:int), ((and (((ord_less_int V) pls)->(((eq nat) ((plus_plus_nat one_one_nat) (number_number_of_nat V))) one_one_nat))) ((((ord_less_int V) pls)->False)->(((eq nat) ((plus_plus_nat one_one_nat) (number_number_of_nat V))) (number_number_of_nat (succ V)))))). % Axiom fact_1166_succ__Pls:(((eq int) (succ pls)) (bit1 pls)). % Axiom fact_1167_neg__number__of__Bit1:(forall (W:int), ((iff (nat_neg (number_number_of_int (bit1 W)))) (nat_neg (number_number_of_int W)))). % Axiom fact_1168_not__neg__number__of__Pls:((nat_neg (number_number_of_int pls))->False). % Axiom fact_1169_transfer__int__nat__numerals_I4_J:(((eq int) (number_number_of_int (bit1 (bit1 pls)))) (semiri1621563631at_int (number_number_of_nat (bit1 (bit1 pls))))). % Axiom fact_1170_numeral__1__eq__Suc__0:(((eq nat) (number_number_of_nat (bit1 pls))) (suc zero_zero_nat)). % Axiom fact_1171_numeral__3__eq__3:(((eq nat) (number_number_of_nat (bit1 (bit1 pls)))) (suc (suc (suc zero_zero_nat)))). % Axiom fact_1172_Suc3__eq__add__3:(forall (N:nat), (((eq nat) (suc (suc (suc N)))) ((plus_plus_nat (number_number_of_nat (bit1 (bit1 pls)))) N))). % Axiom fact_1173_Numeral1__eq1__nat:(((eq nat) one_one_nat) (number_number_of_nat (bit1 pls))). % Axiom fact_1174_nat__numeral__1__eq__1:(((eq nat) (number_number_of_nat (bit1 pls))) one_one_nat). % Axiom fact_1175_one__is__num__one:(((eq int) one_one_int) (number_number_of_int (bit1 pls))). % Axiom fact_1176_zero__is__num__zero:(((eq int) zero_zero_int) (number_number_of_int pls)). % Axiom fact_1177_Bit1__def:(forall (K:int), (((eq int) (bit1 K)) ((plus_plus_int ((plus_plus_int one_one_int) K)) K))). % Axiom fact_1178_nat__number__of__Pls:(((eq nat) (number_number_of_nat pls)) zero_zero_nat). % Axiom fact_1179_semiring__norm_I113_J:(((eq nat) zero_zero_nat) (number_number_of_nat pls)). % Axiom fact_1180_Pls__def:(((eq int) pls) zero_zero_int). % Axiom fact_1181_rel__simps_I51_J:(forall (K:int) (L:int), ((iff (((eq int) (bit1 K)) (bit1 L))) (((eq int) K) L))). % Axiom fact_1182_rel__simps_I46_J:(forall (K:int), (not (((eq int) (bit1 K)) pls))). % Axiom fact_1183_rel__simps_I39_J:(forall (L:int), (not (((eq int) pls) (bit1 L)))). % Axiom fact_1184_diff__bin__simps_I1_J:(forall (K:int), (((eq int) ((minus_minus_int K) pls)) K)). % Axiom fact_1185_add__Pls:(forall (K:int), (((eq int) ((plus_plus_int pls) K)) K)). % Axiom fact_1186_add__Pls__right:(forall (K:int), (((eq int) ((plus_plus_int K) pls)) K)). % Axiom fact_1187_mult__Pls:(forall (W:int), (((eq int) ((times_times_int pls) W)) pls)). % Axiom fact_1188_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J:((ord_less_eq_int zero_zero_int) (number_number_of_int (bit1 (bit1 pls)))). % Axiom fact_1189_rel__simps_I19_J:((ord_less_eq_int pls) pls). % Axiom fact_1190_rel__simps_I22_J:(forall (K:int), ((iff ((ord_less_eq_int pls) (bit1 K))) ((ord_less_eq_int pls) K))). % Axiom fact_1191_rel__simps_I34_J:(forall (K:int) (L:int), ((iff ((ord_less_eq_int (bit1 K)) (bit1 L))) ((ord_less_eq_int K) L))). % Axiom fact_1192_less__eq__int__code_I16_J:(forall (K1:int) (K2:int), ((iff ((ord_less_eq_int (bit1 K1)) (bit1 K2))) ((ord_less_eq_int K1) K2))). % Axiom fact_1193_rel__simps_I2_J:(((ord_less_int pls) pls)->False). % Axiom fact_1194_rel__simps_I12_J:(forall (K:int), ((iff ((ord_less_int (bit1 K)) pls)) ((ord_less_int K) pls))). % Axiom fact_1195_rel__simps_I17_J:(forall (K:int) (L:int), ((iff ((ord_less_int (bit1 K)) (bit1 L))) ((ord_less_int K) L))). % Axiom fact_1196_less__int__code_I16_J:(forall (K1:int) (K2:int), ((iff ((ord_less_int (bit1 K1)) (bit1 K2))) ((ord_less_int K1) K2))). % Axiom fact_1197_rel__simps_I29_J:(forall (K:int), ((iff ((ord_less_eq_int (bit1 K)) pls)) ((ord_less_int K) pls))). % Axiom fact_1198_rel__simps_I5_J:(forall (K:int), ((iff ((ord_less_int pls) (bit1 K))) ((ord_less_eq_int pls) K))). % Axiom help_fequal_1_1_fequal_000t__a_T:(forall (X:x_a) (Y:x_a), ((or (((fequal_a X) Y)->False)) (((eq x_a) X) Y))). % Axiom help_fequal_2_1_fequal_000t__a_T:(forall (X:x_a) (Y:x_a), ((or (not (((eq x_a) X) Y))) ((fequal_a X) Y))). % Axiom help_If_1_1_If_000tc__Nat__Onat_T:(forall (X:nat) (Y:nat), (((eq nat) (((if_nat True) X) Y)) X)). % Axiom help_If_2_1_If_000tc__Nat__Onat_T:(forall (X:nat) (Y:nat), (((eq nat) (((if_nat False) X) Y)) Y)). % Axiom help_If_3_1_If_000tc__Nat__Onat_T:(forall (P:Prop), ((or (((eq Prop) P) True)) (((eq Prop) P) False))). % Axiom help_fequal_1_1_fequal_000tc__Int__Oint_T:(forall (X:int) (Y:int), ((or (((fequal_int X) Y)->False)) (((eq int) X) Y))). % Axiom help_fequal_2_1_fequal_000tc__Int__Oint_T:(forall (X:int) (Y:int), ((or (not (((eq int) X) Y))) ((fequal_int X) Y))). % Axiom help_fequal_1_1_fequal_000tc__Nat__Onat_T:(forall (X:nat) (Y:nat), ((or (((fequal_nat X) Y)->False)) (((eq nat) X) Y))). % Axiom help_fequal_2_1_fequal_000tc__Nat__Onat_T:(forall (X:nat) (Y:nat), ((or (not (((eq nat) X) Y))) ((fequal_nat X) Y))). % Axiom conj_0:(finite_finite_pname u). % Axiom conj_1:((ord_less_eq_a_o g) ((image_pname_a mgt_call) u)). % Axiom conj_2:((ord_less_eq_nat (suc na)) (finite_card_a ((image_pname_a mgt_call) u))). % Axiom conj_3:(((eq nat) (finite_card_a g)) ((minus_minus_nat (finite_card_a ((image_pname_a mgt_call) u))) (suc na))). % Axiom conj_4:((member_pname pn) u). % Axiom conj_5:(((member_a (mgt_call pn)) g)->False). % Trying to prove ((ord_less_eq_a_o ((insert_a (mgt_call pn)) g)) ((image_pname_a mgt_call) u)) % Found conj_1:((ord_less_eq_a_o g) ((image_pname_a mgt_call) u)) % Instantiate: Y_5:=g:(x_a->Prop) % Found conj_1 as proof of ((ord_less_eq_a_o Y_5) ((image_pname_a mgt_call) u)) % Found fact_403_subset__refl0:=(fact_403_subset__refl ((insert_a (mgt_call pn)) g)):((ord_less_eq_a_o ((insert_a (mgt_call pn)) g)) ((insert_a (mgt_call pn)) g)) % Found (fact_403_subset__refl ((insert_a (mgt_call pn)) g)) as proof of ((ord_less_eq_a_o ((insert_a (mgt_call pn)) g)) Y_5) % Found (fact_403_subset__refl ((insert_a (mgt_call pn)) g)) as proof of ((ord_less_eq_a_o ((insert_a (mgt_call pn)) g)) Y_5) % Found (fact_403_subset__refl ((insert_a (mgt_call pn)) g)) as proof of ((ord_less_eq_a_o ((insert_a (mgt_call pn)) g)) Y_5) % Found conj_1:((ord_less_eq_a_o g) ((image_pname_a mgt_call) u)) % Found conj_1 as proof of ((ord_less_eq_a_o g) ((image_pname_a mgt_call) u)) % Found conj_1:((ord_less_eq_a_o g) ((image_pname_a mgt_call) u)) % Found conj_1 as proof of ((ord_less_eq_a_o g) ((image_pname_a mgt_call) u)) % Found conj_1:((ord_less_eq_a_o g) ((image_pname_a mgt_call) u)) % Instantiate: B_74:=g:(x_a->Prop) % Found conj_1 as proof of ((ord_less_eq_a_o B_74) ((image_pname_a mgt_call) u)) % Found fact_403_subset__refl0:=(fact_403_subset__refl ((insert_a (mgt_call pn)) g)):((ord_less_eq_a_o ((insert_a (mgt_call pn)) g)) ((insert_a (mgt_call pn)) g)) % Found (fact_403_subset__refl ((insert_a (mgt_call pn)) g)) as proof of ((ord_less_eq_a_o ((insert_a (mgt_call pn)) g)) B_76) % Found (fact_403_subset__refl ((insert_a (mgt_call pn)) g)) as proof of ((ord_less_eq_a_o ((insert_a (mgt_call pn)) g)) B_76) % Found (fact_403_subset__refl ((insert_a (mgt_call pn)) g)) as proof of ((ord_less_eq_a_o ((insert_a (mgt_call pn)) g)) B_76) % Found fact_403_subset__refl0:=(fact_403_subset__refl ((insert_a (mgt_call pn)) g)):((ord_less_eq_a_o ((insert_a (mgt_call pn)) g)) ((insert_a (mgt_call pn)) g)) % Found (fact_403_subset__refl ((insert_a (mgt_call pn)) g)) as proof of ((ord_less_eq_a_o ((insert_a (mgt_call pn)) g)) B_75) % Found (fact_403_subset__refl ((insert_a (mgt_call pn)) g)) as proof of ((ord_less_eq_a_o ((insert_a (mgt_call pn)) g)) B_75) % Found (fact_403_subset__refl ((insert_a (mgt_call pn)) g)) as proof of ((ord_less_eq_a_o ((insert_a (mgt_call pn)) g)) B_75) % Found conj_1:((ord_less_eq_a_o g) ((image_pname_a mgt_call) u)) % Found conj_1 as proof of ((ord_less_eq_a_o g) ((image_pname_a mgt_call) u)) % Found eq_ref00:=(eq_ref0 B_74):(((eq (x_a->Prop)) B_74) B_74) % Found (eq_ref0 B_74) as proof of (((eq (x_a->Prop)) B_74) ((insert_a (mgt_call pn)) g)) % Found ((eq_ref (x_a->Prop)) B_74) as proof of (((eq (x_a->Prop)) B_74) ((insert_a (mgt_call pn)) g)) % Found ((eq_ref (x_a->Prop)) B_74) as proof of (((eq (x_a->Prop)) B_74) ((insert_a (mgt_call pn)) g)) % Found ((eq_ref (x_a->Prop)) B_74) as proof of (((eq (x_a->Prop)) B_74) ((insert_a (mgt_call pn)) g)) % Found eq_ref00:=(eq_ref0 B_75):(((eq (x_a->Prop)) B_75) B_75) % Found (eq_ref0 B_75) as proof of (((eq (x_a->Prop)) B_75) ((image_pname_a mgt_call) u)) % Found ((eq_ref (x_a->Prop)) B_75) as proof of (((eq (x_a->Prop)) B_75) ((image_pname_a mgt_call) u)) % Found ((eq_ref (x_a->Prop)) B_75) as proof of (((eq (x_a->Prop)) B_75) ((image_pname_a mgt_call) u)) % Found ((eq_ref (x_a->Prop)) B_75) as proof of (((eq (x_a->Prop)) B_75) ((image_pname_a mgt_call) u)) % Found eta_expansion_dep000:=(eta_expansion_dep00 ((image_pname_a mgt_call) u)):(((eq (x_a->Prop)) ((image_pname_a mgt_call) u)) (fun (x:x_a)=> (((image_pname_a mgt_call) u) x))) % Found (eta_expansion_dep00 ((image_pname_a mgt_call) u)) as proof of (((eq (x_a->Prop)) ((image_pname_a mgt_call) u)) B_76) % Found ((eta_expansion_dep0 (fun (x1:x_a)=> Prop)) ((image_pname_a mgt_call) u)) as proof of (((eq (x_a->Prop)) ((image_pname_a mgt_call) u)) B_76) % Found (((eta_expansion_dep x_a) (fun (x1:x_a)=> Prop)) ((image_pname_a mgt_call) u)) as proof of (((eq (x_a->Prop)) ((image_pname_a mgt_call) u)) B_76) % Found (((eta_expansion_dep x_a) (fun (x1:x_a)=> Prop)) ((image_pname_a mgt_call) u)) as proof of (((eq (x_a->Prop)) ((image_pname_a mgt_call) u)) B_76) % Found (((eta_expansion_dep x_a) (fun (x1:x_a)=> Prop)) ((image_pname_a mgt_call) u)) as proof of (((eq (x_a->Prop)) ((image_pname_a mgt_call) u)) B_76) % Found fact_403_subset__refl0:=(fact_403_subset__refl B_61):((ord_less_eq_a_o B_61) B_61) % Found (fact_403_subset__refl B_61) as proof of ((ord_less_eq_a_o B_61) g) % Found (fact_403_subset__refl B_61) as proof of ((ord_less_eq_a_o B_61) g) % Found (fact_403_subset__refl B_61) as proof of ((ord_less_eq_a_o B_61) g) % Found fact_403_subset__refl0:=(fact_403_subset__refl ((insert_a (mgt_call pn)) g)):((ord_less_eq_a_o ((insert_a (mgt_call pn)) g)) ((insert_a (mgt_call pn)) g)) % Found (fact_403_subset__refl ((insert_a (mgt_call pn)) g)) as proof of ((ord_less_eq_a_o ((insert_a (mgt_call pn)) g)) B_61) % Found (fact_403_subset__refl ((insert_a (mgt_call pn)) g)) as proof of ((ord_less_eq_a_o ((insert_a (mgt_call pn)) g)) B_61) % Found (fact_403_subset__refl ((insert_a (mgt_call pn)) g)) as proof of ((ord_less_eq_a_o ((insert_a (mgt_call pn)) g)) B_61) % Found fact_629_bot__least0:=(fact_629_bot__least g):((ord_less_eq_a_o bot_bot_a_o) g) % Found (fact_629_bot__least g) as proof of ((ord_less_eq_a_o B_61) g) % Found (fact_629_bot__least g) as proof of ((ord_less_eq_a_o B_61) g) % Found (fact_629_bot__least g) as proof of ((ord_less_eq_a_o B_61) g) % Found fact_403_subset__refl0:=(fact_403_subset__refl ((insert_a (mgt_call pn)) g)):((ord_less_eq_a_o ((insert_a (mgt_call pn)) g)) ((insert_a (mgt_call pn)) g)) % Found (fact_403_subset__refl ((insert_a (mgt_call pn)) g)) as proof of ((ord_less_eq_a_o ((insert_a (mgt_call pn)) g)) B_61) % Found (fact_403_subset__refl ((insert_a (mgt_call pn)) g)) as proof of ((ord_less_eq_a_o ((insert_a (mgt_call pn)) g)) B_61) % Found (fact_403_subset__refl ((insert_a (mgt_call pn)) g)) as proof of ((ord_less_eq_a_o ((insert_a (mgt_call pn)) g)) B_61) % Found fact_305_order__refl0:=(fact_305_order__refl Y_7):((ord_less_eq_a_o Y_7) Y_7) % Found (fact_305_order__refl Y_7) as proof of ((ord_less_eq_a_o Y_7) g) % Found (fact_305_order__refl Y_7) as proof of ((ord_less_eq_a_o Y_7) g) % Found (fact_305_order__refl Y_7) as proof of ((ord_less_eq_a_o Y_7) g) % Found fact_403_subset__refl0:=(fact_403_subset__refl ((insert_a (mgt_call pn)) g)):((ord_less_eq_a_o ((insert_a (mgt_call pn)) g)) ((insert_a (mgt_call pn)) g)) % Found (fact_403_subset__refl ((insert_a (mgt_call pn)) g)) as proof of ((ord_less_eq_a_o ((insert_a (mgt_call pn)) g)) Y_7) % Found (fact_403_subset__refl ((insert_a (mgt_call pn)) g)) as proof of ((ord_less_eq_a_o ((insert_a (mgt_call pn)) g)) Y_7) % Found (fact_403_subset__refl ((insert_a (mgt_call pn)) g)) as proof of ((ord_less_eq_a_o ((insert_a (mgt_call pn)) g)) Y_7) % Found fact_503_empty__subsetI0:=(fact_503_empty__subsetI g):((ord_less_eq_a_o bot_bot_a_o) g) % Found (fact_503_empty__subsetI g) as proof of ((ord_less_eq_a_o Y_7) g) % Found (fact_503_empty__subsetI g) as proof of ((ord_less_eq_a_o Y_7) g) % Found (fact_503_empty__subsetI g) as proof of ((ord_less_eq_a_o Y_7) g) % Found fact_403_subset__refl0:=(fact_403_subset__refl ((insert_a (mgt_call pn)) g)):((ord_less_eq_a_o ((insert_a (mgt_call pn)) g)) ((insert_a (mgt_call pn)) g)) % Found (fact_403_subset__refl ((insert_a (mgt_call pn)) g)) as proof of ((ord_less_eq_a_o ((insert_a (mgt_call pn)) g)) Y_7) % Found (fact_403_subset__refl ((insert_a (mgt_call pn)) g)) as proof of ((ord_less_eq_a_o ((insert_a (mgt_call pn)) g)) Y_7) % Found (fact_403_subset__refl ((insert_a (mgt_call pn)) g)) as proof of ((ord_less_eq_a_o ((insert_a (mgt_call pn)) g)) Y_7) % Found fact_503_empty__subsetI0:=(fact_503_empty__subsetI g):((ord_less_eq_a_o bot_bot_a_o) g) % Found (fact_503_empty__subsetI g) as proof of ((ord_less_eq_a_o Y_5) g) % Found (fact_503_empty__subsetI g) as proof of ((ord_less_eq_a_o Y_5) g) % Found (fact_503_empty__subsetI g) as proof of ((ord_less_eq_a_o Y_5) g) % Found fact_403_subset__refl0:=(fact_403_subset__refl ((insert_a (mgt_call pn)) g)):((ord_less_eq_a_o ((insert_a (mgt_call pn)) g)) ((insert_a (mgt_call pn)) g)) % Found (fact_403_subset__refl ((insert_a (mgt_call pn)) g)) as proof of ((ord_less_eq_a_o ((insert_a (mgt_call pn)) g)) Y_5) % Found (fact_403_subset__refl ((insert_a (mgt_call pn)) g)) as proof of ((ord_less_eq_a_o ((insert_a (mgt_call pn)) g)) Y_5) % Found (fact_403_subset__refl ((insert_a (mgt_call pn)) g)) as proof of ((ord_less_eq_a_o ((insert_a (mgt_call pn)) g)) Y_5) % Found fact_503_empty__subsetI0:=(fact_503_empty__subsetI g):((ord_less_eq_a_o bot_bot_a_o) g) % Found (fact_503_empty__subsetI g) as proof of ((ord_less_eq_a_o Y_5) g) % Found (fact_503_empty__subsetI g) as proof of ((ord_less_eq_a_o Y_5) g) % Found (fact_503_empty__subsetI g) as proof of ((ord_less_eq_a_o Y_5) g) % Found fact_403_subset__refl0:=(fact_403_subset__refl ((insert_a (mgt_call pn)) g)):((ord_less_eq_a_o ((insert_a (mgt_call pn)) g)) ((insert_a (mgt_call pn)) g)) % Found (fact_403_subset__refl ((insert_a (mgt_call pn)) g)) as proof of ((ord_less_eq_a_o ((insert_a (mgt_call pn)) g)) Y_5) % Found (fact_403_subset__refl ((insert_a (mgt_call pn)) g)) as proof of ((ord_less_eq_a_o ((insert_a (mgt_call pn)) g)) Y_5) % Found (fact_403_subset__refl ((insert_a (mgt_call pn)) g)) as proof of ((ord_less_eq_a_o ((insert_a (mgt_call pn)) g)) Y_5) % Found conj_1:((ord_less_eq_a_o g) ((image_pname_a mgt_call) u)) % Instantiate: A_143:=g:(x_a->Prop) % Found conj_1 as proof of ((ord_less_eq_a_o A_143) ((image_pname_a mgt_call) u)) % Found x:((member_a X_1) ((insert_a (mgt_call pn)) g)) % Instantiate: A_143:=((insert_a (mgt_call pn)) g):(x_a->Prop) % Found x as proof of ((member_a X_1) A_143) % Found conj_1:((ord_less_eq_a_o g) ((image_pname_a mgt_call) u)) % Instantiate: A_118:=g:(x_a->Prop) % Found conj_1 as proof of ((ord_less_eq_a_o A_118) ((image_pname_a mgt_call) u)) % Found x:((member_a X_1) ((insert_a (mgt_call pn)) g)) % Instantiate: A_118:=((insert_a (mgt_call pn)) g):(x_a->Prop) % Found x as proof of ((member_a X_1) A_118) % Found x:((member_a X_1) ((insert_a (mgt_call pn)) g)) % Instantiate: A_116:=((insert_a (mgt_call pn)) g):(x_a->Prop) % Found x as proof of ((member_a X_1) A_116) % Found conj_1:((ord_less_eq_a_o g) ((image_pname_a mgt_call) u)) % Instantiate: A_116:=g:(x_a->Prop) % Found conj_1 as proof of ((ord_less_eq_a_o A_116) ((image_pname_a mgt_call) u)) % Found fact_503_empty__subsetI0:=(fact_503_empty__subsetI g):((ord_less_eq_a_o bot_bot_a_o) g) % Found (fact_503_empty__subsetI g) as proof of ((ord_less_eq_a_o B_61) g) % Found (fact_503_empty__subsetI g) as proof of ((ord_less_eq_a_o B_61) g) % Found (fact_503_empty__subsetI g) as proof of ((ord_less_eq_a_o B_61) g) % Found fact_403_subset__refl0:=(fact_403_subset__refl ((insert_a (mgt_call pn)) g)):((ord_less_eq_a_o ((insert_a (mgt_call pn)) g)) ((insert_a (mgt_call pn)) g)) % Found (fact_403_subset__refl ((insert_a (mgt_call pn)) g)) as proof of ((ord_less_eq_a_o ((insert_a (mgt_call pn)) g)) B_61) % Found (fact_403_subset__refl ((insert_a (mgt_call pn)) g)) as proof of ((ord_less_eq_a_o ((insert_a (mgt_call pn)) g)) B_61) % Found (fact_403_subset__refl ((insert_a (mgt_call pn)) g)) as proof of ((ord_less_eq_a_o ((insert_a (mgt_call pn)) g)) B_61) % Found fact_403_subset__refl0:=(fact_403_subset__refl B_61):((ord_less_eq_a_o B_61) B_61) % Found (fact_403_subset__refl B_61) as proof of ((ord_less_eq_a_o B_61) g) % Found (fact_403_subset__refl B_61) as proof of ((ord_less_eq_a_o B_61) g) % Found (fact_403_subset__refl B_61) as proof of ((ord_less_eq_a_o B_61) g) % Found fact_403_subset__refl0:=(fact_403_subset__refl ((insert_a (mgt_call pn)) g)):((ord_less_eq_a_o ((insert_a (mgt_call pn)) g)) ((insert_a (mgt_call pn)) g)) % Found (fact_403_subset__refl ((insert_a (mgt_call pn)) g)) as proof of ((ord_less_eq_a_o ((insert_a (mgt_call pn)) g)) B_61) % Found (fact_403_subset__refl ((insert_a (mgt_call pn)) g)) as proof of ((ord_less_eq_a_o ((insert_a (mgt_call pn)) g)) B_61) % Found (fact_403_subset__refl ((insert_a (mgt_call pn)) g)) as proof of ((ord_less_eq_a_o ((insert_a (mgt_call pn)) g)) B_61) % Found fact_503_empty__subsetI0:=(fact_503_empty__subsetI g):((ord_less_eq_a_o bot_bot_a_o) g) % Found (fact_503_empty__subsetI g) as proof of ((ord_less_eq_a_o Y_7) g) % Found (fact_503_empty__subsetI g) as proof of ((ord_less_eq_a_o Y_7) g) % Found (fact_503_empty__subsetI g) as proof of ((ord_less_eq_a_o Y_7) g) % Found fact_403_subset__refl0:=(fact_403_subset__refl ((insert_a (mgt_call pn)) g)):((ord_less_eq_a_o ((insert_a (mgt_call pn)) g)) ((insert_a (mgt_call pn)) g)) % Found (fact_403_subset__refl ((insert_a (mgt_call pn)) g)) as proof of ((ord_less_eq_a_o ((insert_a (mgt_call pn)) g)) Y_7) % Found (fact_403_subset__refl ((insert_a (mgt_call pn)) g)) as proof of ((ord_less_eq_a_o ((insert_a (mgt_call pn)) g)) Y_7) % Found (fact_403_subset__refl ((insert_a (mgt_call pn)) g)) as proof of ((ord_less_eq_a_o ((insert_a (mgt_call pn)) g)) Y_7) % Found fact_503_empty__subsetI0:=(fact_503_empty__subsetI g):((ord_less_eq_a_o bot_bot_a_o) g) % Found (fact_503_empty__subsetI g) as proof of ((ord_less_eq_a_o Y_7) g) % Found (fact_5 % EOF %------------------------------------------------------------------------------