TSTP Solution File: ITP129^1 by cocATP---0.2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : ITP129^1 : TPTP v7.5.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n021.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% DateTime : Sun Mar 21 13:24:16 EDT 2021
% Result : Unknown 0.58s
% Output : None
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : ITP129^1 : TPTP v7.5.0. Released v7.5.0.
% 0.04/0.12 % Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.34 % Computer : n021.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % DateTime : Fri Mar 19 06:30:13 EDT 2021
% 0.12/0.34 % CPUTime :
% 0.12/0.34 ModuleCmd_Load.c(213):ERROR:105: Unable to locate a modulefile for 'python/python27'
% 0.12/0.35 Python 2.7.5
% 0.41/0.62 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox2/benchmark/', '/export/starexec/sandbox2/benchmark/']
% 0.41/0.62 FOF formula (<kernel.Constant object at 0x227b7a0>, <kernel.Type object at 0x227b998>) of role type named ty_n_t__Nat__Onat
% 0.41/0.62 Using role type
% 0.41/0.62 Declaring nat:Type
% 0.41/0.62 FOF formula (<kernel.Constant object at 0x1fd1ea8>, <kernel.Type object at 0x227b830>) of role type named ty_n_t__Int__Oint
% 0.41/0.62 Using role type
% 0.41/0.62 Declaring int:Type
% 0.41/0.62 FOF formula (<kernel.Constant object at 0x227bbd8>, <kernel.DependentProduct object at 0x227b908>) of role type named sy_c_Binomial_Ogbinomial_001t__Int__Oint
% 0.41/0.62 Using role type
% 0.41/0.62 Declaring gbinomial_int:(int->(nat->int))
% 0.41/0.62 FOF formula (<kernel.Constant object at 0x227b758>, <kernel.DependentProduct object at 0x227b7a0>) of role type named sy_c_Binomial_Ogbinomial_001t__Nat__Onat
% 0.41/0.62 Using role type
% 0.41/0.62 Declaring gbinomial_nat:(nat->(nat->nat))
% 0.41/0.62 FOF formula (<kernel.Constant object at 0x227bb90>, <kernel.Constant object at 0x227b7a0>) of role type named sy_c_Groups_Oone__class_Oone_001t__Int__Oint
% 0.41/0.62 Using role type
% 0.41/0.62 Declaring one_one_int:int
% 0.41/0.62 FOF formula (<kernel.Constant object at 0x227bbd8>, <kernel.Constant object at 0x227b7a0>) of role type named sy_c_Groups_Oone__class_Oone_001t__Nat__Onat
% 0.41/0.62 Using role type
% 0.41/0.62 Declaring one_one_nat:nat
% 0.41/0.62 FOF formula (<kernel.Constant object at 0x227b758>, <kernel.DependentProduct object at 0x1fb4dd0>) of role type named sy_c_Groups_Oplus__class_Oplus_001t__Int__Oint
% 0.41/0.62 Using role type
% 0.41/0.62 Declaring plus_plus_int:(int->(int->int))
% 0.41/0.62 FOF formula (<kernel.Constant object at 0x227bb90>, <kernel.DependentProduct object at 0x1fb4a70>) of role type named sy_c_Groups_Oplus__class_Oplus_001t__Nat__Onat
% 0.41/0.62 Using role type
% 0.41/0.62 Declaring plus_plus_nat:(nat->(nat->nat))
% 0.41/0.62 FOF formula (<kernel.Constant object at 0x227b758>, <kernel.DependentProduct object at 0x1fb45a8>) of role type named sy_c_Groups_Otimes__class_Otimes_001t__Int__Oint
% 0.41/0.62 Using role type
% 0.41/0.62 Declaring times_times_int:(int->(int->int))
% 0.41/0.62 FOF formula (<kernel.Constant object at 0x227bb90>, <kernel.DependentProduct object at 0x1fb4d40>) of role type named sy_c_Groups_Otimes__class_Otimes_001t__Nat__Onat
% 0.41/0.62 Using role type
% 0.41/0.62 Declaring times_times_nat:(nat->(nat->nat))
% 0.41/0.62 FOF formula (<kernel.Constant object at 0x227b7a0>, <kernel.Constant object at 0x1fb4d40>) of role type named sy_c_Groups_Ozero__class_Ozero_001t__Int__Oint
% 0.41/0.62 Using role type
% 0.41/0.62 Declaring zero_zero_int:int
% 0.41/0.62 FOF formula (<kernel.Constant object at 0x227b7a0>, <kernel.Constant object at 0x1fb4d40>) of role type named sy_c_Groups_Ozero__class_Ozero_001t__Nat__Onat
% 0.41/0.62 Using role type
% 0.41/0.62 Declaring zero_zero_nat:nat
% 0.41/0.62 FOF formula (<kernel.Constant object at 0x1fb4dd0>, <kernel.DependentProduct object at 0x1fb4cb0>) of role type named sy_c_HOL_ONO__MATCH_001t__Int__Oint_001t__Int__Oint
% 0.41/0.62 Using role type
% 0.41/0.62 Declaring nO_MATCH_int_int:(int->(int->Prop))
% 0.41/0.62 FOF formula (<kernel.Constant object at 0x1fb4950>, <kernel.DependentProduct object at 0x1fb4a70>) of role type named sy_c_HOL_ONO__MATCH_001t__Int__Oint_001t__Nat__Onat
% 0.41/0.62 Using role type
% 0.41/0.62 Declaring nO_MATCH_int_nat:(int->(nat->Prop))
% 0.41/0.62 FOF formula (<kernel.Constant object at 0x1fb4d40>, <kernel.DependentProduct object at 0x2afdf2b65d88>) of role type named sy_c_HOL_ONO__MATCH_001t__Nat__Onat_001t__Int__Oint
% 0.41/0.62 Using role type
% 0.41/0.62 Declaring nO_MATCH_nat_int:(nat->(int->Prop))
% 0.41/0.62 FOF formula (<kernel.Constant object at 0x1fb4cb0>, <kernel.DependentProduct object at 0x2afdf2b65368>) of role type named sy_c_HOL_ONO__MATCH_001t__Nat__Onat_001t__Nat__Onat
% 0.41/0.62 Using role type
% 0.41/0.62 Declaring nO_MATCH_nat_nat:(nat->(nat->Prop))
% 0.41/0.62 FOF formula (<kernel.Constant object at 0x1fb4dd0>, <kernel.DependentProduct object at 0x2afdf2b65d88>) of role type named sy_c_If_001t__Nat__Onat
% 0.41/0.62 Using role type
% 0.41/0.62 Declaring if_nat:(Prop->(nat->(nat->nat)))
% 0.41/0.62 FOF formula (<kernel.Constant object at 0x1fb4a70>, <kernel.DependentProduct object at 0x1fd6e60>) of role type named sy_c_Nat_OSuc
% 0.41/0.62 Using role type
% 0.41/0.62 Declaring suc:(nat->nat)
% 0.41/0.62 FOF formula (<kernel.Constant object at 0x2afdf2b65518>, <kernel.DependentProduct object at 0x1fd6ea8>) of role type named sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Int__Oint
% 0.41/0.62 Using role type
% 0.41/0.62 Declaring semiri2019852685at_int:(nat->int)
% 0.41/0.63 FOF formula (<kernel.Constant object at 0x2afdf2b65320>, <kernel.DependentProduct object at 0x1fd6d40>) of role type named sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Nat__Onat
% 0.41/0.63 Using role type
% 0.41/0.63 Declaring semiri1382578993at_nat:(nat->nat)
% 0.41/0.63 FOF formula (<kernel.Constant object at 0x2afdf2b65320>, <kernel.DependentProduct object at 0x1fd6e60>) of role type named sy_c_NthRoot__Impl__Mirabelle__bcfbdygymo_Ofixed__root
% 0.41/0.63 Using role type
% 0.41/0.63 Declaring nthRoo1352626670d_root:(nat->(nat->Prop))
% 0.41/0.63 FOF formula (<kernel.Constant object at 0x1fb4dd0>, <kernel.DependentProduct object at 0x1fd6d88>) of role type named sy_c_Power_Opower__class_Opower_001t__Int__Oint
% 0.41/0.63 Using role type
% 0.41/0.63 Declaring power_power_int:(int->(nat->int))
% 0.41/0.63 FOF formula (<kernel.Constant object at 0x1fb4a70>, <kernel.DependentProduct object at 0x1fd6c68>) of role type named sy_c_Power_Opower__class_Opower_001t__Nat__Onat
% 0.41/0.63 Using role type
% 0.41/0.63 Declaring power_power_nat:(nat->(nat->nat))
% 0.41/0.63 FOF formula (<kernel.Constant object at 0x1fb4dd0>, <kernel.DependentProduct object at 0x1fd6b00>) of role type named sy_c_Rings_Odivide__class_Odivide_001t__Int__Oint
% 0.41/0.63 Using role type
% 0.41/0.63 Declaring divide_divide_int:(int->(int->int))
% 0.41/0.63 FOF formula (<kernel.Constant object at 0x1fb4a70>, <kernel.DependentProduct object at 0x1fd6ea8>) of role type named sy_c_Rings_Odivide__class_Odivide_001t__Nat__Onat
% 0.41/0.63 Using role type
% 0.41/0.63 Declaring divide_divide_nat:(nat->(nat->nat))
% 0.41/0.63 FOF formula (<kernel.Constant object at 0x1fb4cb0>, <kernel.Constant object at 0x1fd6ea8>) of role type named sy_v_n
% 0.41/0.63 Using role type
% 0.41/0.63 Declaring n:int
% 0.41/0.63 FOF formula (<kernel.Constant object at 0x1fb4cb0>, <kernel.Constant object at 0x1fd6ea8>) of role type named sy_v_p
% 0.41/0.63 Using role type
% 0.41/0.63 Declaring p:nat
% 0.41/0.63 FOF formula (<kernel.Constant object at 0x1fd6d88>, <kernel.Constant object at 0x1fd6ea8>) of role type named sy_v_pm
% 0.41/0.63 Using role type
% 0.41/0.63 Declaring pm:nat
% 0.41/0.63 FOF formula (<kernel.Constant object at 0x1fd6e60>, <kernel.Constant object at 0x1fd6ea8>) of role type named sy_v_x
% 0.41/0.63 Using role type
% 0.41/0.63 Declaring x:int
% 0.41/0.63 FOF formula (((eq int) ((power_power_int x) p)) n) of role axiom named fact_0_xn
% 0.41/0.63 A new axiom: (((eq int) ((power_power_int x) p)) n)
% 0.41/0.63 FOF formula (forall (M:nat) (N:nat), (((eq nat) (semiri1382578993at_nat ((power_power_nat M) N))) ((power_power_nat (semiri1382578993at_nat M)) N))) of role axiom named fact_1_of__nat__power
% 0.41/0.63 A new axiom: (forall (M:nat) (N:nat), (((eq nat) (semiri1382578993at_nat ((power_power_nat M) N))) ((power_power_nat (semiri1382578993at_nat M)) N)))
% 0.41/0.63 FOF formula (forall (M:nat) (N:nat), (((eq int) (semiri2019852685at_int ((power_power_nat M) N))) ((power_power_int (semiri2019852685at_int M)) N))) of role axiom named fact_2_of__nat__power
% 0.41/0.63 A new axiom: (forall (M:nat) (N:nat), (((eq int) (semiri2019852685at_int ((power_power_nat M) N))) ((power_power_int (semiri2019852685at_int M)) N)))
% 0.41/0.63 FOF formula (forall (B:nat) (W:nat) (X:nat), (((eq Prop) (((eq nat) ((power_power_nat (semiri1382578993at_nat B)) W)) (semiri1382578993at_nat X))) (((eq nat) ((power_power_nat B) W)) X))) of role axiom named fact_3_of__nat__eq__of__nat__power__cancel__iff
% 0.41/0.63 A new axiom: (forall (B:nat) (W:nat) (X:nat), (((eq Prop) (((eq nat) ((power_power_nat (semiri1382578993at_nat B)) W)) (semiri1382578993at_nat X))) (((eq nat) ((power_power_nat B) W)) X)))
% 0.41/0.63 FOF formula (forall (B:nat) (W:nat) (X:nat), (((eq Prop) (((eq int) ((power_power_int (semiri2019852685at_int B)) W)) (semiri2019852685at_int X))) (((eq nat) ((power_power_nat B) W)) X))) of role axiom named fact_4_of__nat__eq__of__nat__power__cancel__iff
% 0.41/0.63 A new axiom: (forall (B:nat) (W:nat) (X:nat), (((eq Prop) (((eq int) ((power_power_int (semiri2019852685at_int B)) W)) (semiri2019852685at_int X))) (((eq nat) ((power_power_nat B) W)) X)))
% 0.41/0.63 FOF formula (forall (X:nat) (B:nat) (W:nat), (((eq Prop) (((eq nat) (semiri1382578993at_nat X)) ((power_power_nat (semiri1382578993at_nat B)) W))) (((eq nat) X) ((power_power_nat B) W)))) of role axiom named fact_5_of__nat__power__eq__of__nat__cancel__iff
% 0.41/0.63 A new axiom: (forall (X:nat) (B:nat) (W:nat), (((eq Prop) (((eq nat) (semiri1382578993at_nat X)) ((power_power_nat (semiri1382578993at_nat B)) W))) (((eq nat) X) ((power_power_nat B) W))))
% 0.48/0.64 FOF formula (forall (X:nat) (B:nat) (W:nat), (((eq Prop) (((eq int) (semiri2019852685at_int X)) ((power_power_int (semiri2019852685at_int B)) W))) (((eq nat) X) ((power_power_nat B) W)))) of role axiom named fact_6_of__nat__power__eq__of__nat__cancel__iff
% 0.48/0.64 A new axiom: (forall (X:nat) (B:nat) (W:nat), (((eq Prop) (((eq int) (semiri2019852685at_int X)) ((power_power_int (semiri2019852685at_int B)) W))) (((eq nat) X) ((power_power_nat B) W))))
% 0.48/0.64 FOF formula (forall (M:nat) (N:nat), (((eq nat) (semiri1382578993at_nat ((plus_plus_nat M) N))) ((plus_plus_nat (semiri1382578993at_nat M)) (semiri1382578993at_nat N)))) of role axiom named fact_7_of__nat__add
% 0.48/0.64 A new axiom: (forall (M:nat) (N:nat), (((eq nat) (semiri1382578993at_nat ((plus_plus_nat M) N))) ((plus_plus_nat (semiri1382578993at_nat M)) (semiri1382578993at_nat N))))
% 0.48/0.64 FOF formula (forall (M:nat) (N:nat), (((eq int) (semiri2019852685at_int ((plus_plus_nat M) N))) ((plus_plus_int (semiri2019852685at_int M)) (semiri2019852685at_int N)))) of role axiom named fact_8_of__nat__add
% 0.48/0.64 A new axiom: (forall (M:nat) (N:nat), (((eq int) (semiri2019852685at_int ((plus_plus_nat M) N))) ((plus_plus_int (semiri2019852685at_int M)) (semiri2019852685at_int N))))
% 0.48/0.64 FOF formula (forall (M:nat) (N:nat), (((eq nat) (semiri1382578993at_nat ((times_times_nat M) N))) ((times_times_nat (semiri1382578993at_nat M)) (semiri1382578993at_nat N)))) of role axiom named fact_9_of__nat__mult
% 0.48/0.64 A new axiom: (forall (M:nat) (N:nat), (((eq nat) (semiri1382578993at_nat ((times_times_nat M) N))) ((times_times_nat (semiri1382578993at_nat M)) (semiri1382578993at_nat N))))
% 0.48/0.64 FOF formula (forall (M:nat) (N:nat), (((eq int) (semiri2019852685at_int ((times_times_nat M) N))) ((times_times_int (semiri2019852685at_int M)) (semiri2019852685at_int N)))) of role axiom named fact_10_of__nat__mult
% 0.48/0.64 A new axiom: (forall (M:nat) (N:nat), (((eq int) (semiri2019852685at_int ((times_times_nat M) N))) ((times_times_int (semiri2019852685at_int M)) (semiri2019852685at_int N))))
% 0.48/0.64 FOF formula (forall (A:int) (M:nat) (N:nat), (((eq int) ((divide_divide_int A) ((times_times_int (semiri2019852685at_int M)) (semiri2019852685at_int N)))) ((divide_divide_int ((divide_divide_int A) (semiri2019852685at_int M))) (semiri2019852685at_int N)))) of role axiom named fact_11_div__mult2__eq_H
% 0.48/0.64 A new axiom: (forall (A:int) (M:nat) (N:nat), (((eq int) ((divide_divide_int A) ((times_times_int (semiri2019852685at_int M)) (semiri2019852685at_int N)))) ((divide_divide_int ((divide_divide_int A) (semiri2019852685at_int M))) (semiri2019852685at_int N))))
% 0.48/0.64 FOF formula (forall (A:nat) (M:nat) (N:nat), (((eq nat) ((divide_divide_nat A) ((times_times_nat (semiri1382578993at_nat M)) (semiri1382578993at_nat N)))) ((divide_divide_nat ((divide_divide_nat A) (semiri1382578993at_nat M))) (semiri1382578993at_nat N)))) of role axiom named fact_12_div__mult2__eq_H
% 0.48/0.64 A new axiom: (forall (A:nat) (M:nat) (N:nat), (((eq nat) ((divide_divide_nat A) ((times_times_nat (semiri1382578993at_nat M)) (semiri1382578993at_nat N)))) ((divide_divide_nat ((divide_divide_nat A) (semiri1382578993at_nat M))) (semiri1382578993at_nat N))))
% 0.48/0.64 FOF formula (forall (A:int) (N:nat), (((eq int) ((power_power_int A) (suc N))) ((times_times_int A) ((power_power_int A) N)))) of role axiom named fact_13_power__Suc
% 0.48/0.64 A new axiom: (forall (A:int) (N:nat), (((eq int) ((power_power_int A) (suc N))) ((times_times_int A) ((power_power_int A) N))))
% 0.48/0.64 FOF formula (forall (A:nat) (N:nat), (((eq nat) ((power_power_nat A) (suc N))) ((times_times_nat A) ((power_power_nat A) N)))) of role axiom named fact_14_power__Suc
% 0.48/0.64 A new axiom: (forall (A:nat) (N:nat), (((eq nat) ((power_power_nat A) (suc N))) ((times_times_nat A) ((power_power_nat A) N))))
% 0.48/0.64 FOF formula ((nthRoo1352626670d_root p) pm) of role axiom named fact_15_fixed__root__axioms
% 0.48/0.64 A new axiom: ((nthRoo1352626670d_root p) pm)
% 0.48/0.64 FOF formula (forall (Nat:nat) (Nat2:nat), (((eq Prop) (((eq nat) (suc Nat)) (suc Nat2))) (((eq nat) Nat) Nat2))) of role axiom named fact_16_old_Onat_Oinject
% 0.48/0.64 A new axiom: (forall (Nat:nat) (Nat2:nat), (((eq Prop) (((eq nat) (suc Nat)) (suc Nat2))) (((eq nat) Nat) Nat2)))
% 0.48/0.65 FOF formula (forall (X2:nat) (Y2:nat), (((eq Prop) (((eq nat) (suc X2)) (suc Y2))) (((eq nat) X2) Y2))) of role axiom named fact_17_nat_Oinject
% 0.48/0.65 A new axiom: (forall (X2:nat) (Y2:nat), (((eq Prop) (((eq nat) (suc X2)) (suc Y2))) (((eq nat) X2) Y2)))
% 0.48/0.65 FOF formula (forall (M:nat) (N:nat), (((eq Prop) (((eq int) (semiri2019852685at_int M)) (semiri2019852685at_int N))) (((eq nat) M) N))) of role axiom named fact_18_of__nat__eq__iff
% 0.48/0.65 A new axiom: (forall (M:nat) (N:nat), (((eq Prop) (((eq int) (semiri2019852685at_int M)) (semiri2019852685at_int N))) (((eq nat) M) N)))
% 0.48/0.65 FOF formula (forall (M:nat) (N:nat), (((eq Prop) (((eq nat) (semiri1382578993at_nat M)) (semiri1382578993at_nat N))) (((eq nat) M) N))) of role axiom named fact_19_of__nat__eq__iff
% 0.48/0.65 A new axiom: (forall (M:nat) (N:nat), (((eq Prop) (((eq nat) (semiri1382578993at_nat M)) (semiri1382578993at_nat N))) (((eq nat) M) N)))
% 0.48/0.65 FOF formula (((eq nat) p) (suc pm)) of role axiom named fact_20_p
% 0.48/0.65 A new axiom: (((eq nat) p) (suc pm))
% 0.48/0.65 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_21_add__Suc__right
% 0.48/0.65 A new axiom: (forall (M:nat) (N:nat), (((eq nat) ((plus_plus_nat M) (suc N))) (suc ((plus_plus_nat M) N))))
% 0.48/0.65 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_22_mult__Suc__right
% 0.48/0.65 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))))
% 0.48/0.65 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_23_add__mult__distrib
% 0.48/0.65 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))))
% 0.48/0.65 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_24_add__mult__distrib2
% 0.48/0.65 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))))
% 0.48/0.65 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_25_mult__Suc
% 0.48/0.65 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))))
% 0.48/0.65 FOF formula (forall (M:nat) (N:nat) (Q:nat), (((eq nat) ((divide_divide_nat M) ((times_times_nat N) Q))) ((divide_divide_nat ((divide_divide_nat M) N)) Q))) of role axiom named fact_26_div__mult2__eq
% 0.48/0.65 A new axiom: (forall (M:nat) (N:nat) (Q:nat), (((eq nat) ((divide_divide_nat M) ((times_times_nat N) Q))) ((divide_divide_nat ((divide_divide_nat M) N)) Q)))
% 0.48/0.65 FOF formula (forall (A:int) (M:nat) (N:nat), (((eq int) ((power_power_int A) ((times_times_nat M) N))) ((power_power_int ((power_power_int A) M)) N))) of role axiom named fact_27_power__mult
% 0.48/0.65 A new axiom: (forall (A:int) (M:nat) (N:nat), (((eq int) ((power_power_int A) ((times_times_nat M) N))) ((power_power_int ((power_power_int A) M)) N)))
% 0.48/0.65 FOF formula (forall (A:nat) (M:nat) (N:nat), (((eq nat) ((power_power_nat A) ((times_times_nat M) N))) ((power_power_nat ((power_power_nat A) M)) N))) of role axiom named fact_28_power__mult
% 0.48/0.65 A new axiom: (forall (A:nat) (M:nat) (N:nat), (((eq nat) ((power_power_nat A) ((times_times_nat M) N))) ((power_power_nat ((power_power_nat A) M)) N)))
% 0.48/0.65 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_29_add__Suc
% 0.48/0.65 A new axiom: (forall (M:nat) (N:nat), (((eq nat) ((plus_plus_nat (suc M)) N)) (suc ((plus_plus_nat M) N))))
% 0.48/0.65 FOF formula (forall (A2:nat) (K:nat) (A:nat), ((((eq nat) A2) ((plus_plus_nat K) A))->(((eq nat) (suc A2)) ((plus_plus_nat K) (suc A))))) of role axiom named fact_30_nat__arith_Osuc1
% 0.51/0.67 A new axiom: (forall (A2:nat) (K:nat) (A:nat), ((((eq nat) A2) ((plus_plus_nat K) A))->(((eq nat) (suc A2)) ((plus_plus_nat K) (suc A)))))
% 0.51/0.67 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_31_add__Suc__shift
% 0.51/0.67 A new axiom: (forall (M:nat) (N:nat), (((eq nat) ((plus_plus_nat (suc M)) N)) ((plus_plus_nat M) (suc N))))
% 0.51/0.67 FOF formula (forall (K:nat) (M:nat) (N:nat), (((eq Prop) (((eq nat) ((times_times_nat (suc K)) M)) ((times_times_nat (suc K)) N))) (((eq nat) M) N))) of role axiom named fact_32_Suc__mult__cancel1
% 0.51/0.67 A new axiom: (forall (K:nat) (M:nat) (N:nat), (((eq Prop) (((eq nat) ((times_times_nat (suc K)) M)) ((times_times_nat (suc K)) N))) (((eq nat) M) N)))
% 0.51/0.67 FOF formula (forall (A:int) (M:nat) (N:nat), (((eq int) ((power_power_int A) ((plus_plus_nat M) N))) ((times_times_int ((power_power_int A) M)) ((power_power_int A) N)))) of role axiom named fact_33_power__add
% 0.51/0.67 A new axiom: (forall (A:int) (M:nat) (N:nat), (((eq int) ((power_power_int A) ((plus_plus_nat M) N))) ((times_times_int ((power_power_int A) M)) ((power_power_int A) N))))
% 0.51/0.67 FOF formula (forall (A:nat) (M:nat) (N:nat), (((eq nat) ((power_power_nat A) ((plus_plus_nat M) N))) ((times_times_nat ((power_power_nat A) M)) ((power_power_nat A) N)))) of role axiom named fact_34_power__add
% 0.51/0.67 A new axiom: (forall (A:nat) (M:nat) (N:nat), (((eq nat) ((power_power_nat A) ((plus_plus_nat M) N))) ((times_times_nat ((power_power_nat A) M)) ((power_power_nat A) N))))
% 0.51/0.67 FOF formula (forall (N:nat), (not (((eq nat) N) (suc N)))) of role axiom named fact_35_n__not__Suc__n
% 0.51/0.67 A new axiom: (forall (N:nat), (not (((eq nat) N) (suc N))))
% 0.51/0.67 FOF formula (forall (X:nat) (Y:nat), ((((eq nat) (suc X)) (suc Y))->(((eq nat) X) Y))) of role axiom named fact_36_Suc__inject
% 0.51/0.67 A new axiom: (forall (X:nat) (Y:nat), ((((eq nat) (suc X)) (suc Y))->(((eq nat) X) Y)))
% 0.51/0.67 FOF formula (forall (X:int) (Y:int) (N:nat), ((((eq int) ((times_times_int X) Y)) ((times_times_int Y) X))->(((eq int) ((times_times_int ((power_power_int X) N)) Y)) ((times_times_int Y) ((power_power_int X) N))))) of role axiom named fact_37_power__commuting__commutes
% 0.51/0.67 A new axiom: (forall (X:int) (Y:int) (N:nat), ((((eq int) ((times_times_int X) Y)) ((times_times_int Y) X))->(((eq int) ((times_times_int ((power_power_int X) N)) Y)) ((times_times_int Y) ((power_power_int X) N)))))
% 0.51/0.67 FOF formula (forall (X:nat) (Y:nat) (N:nat), ((((eq nat) ((times_times_nat X) Y)) ((times_times_nat Y) X))->(((eq nat) ((times_times_nat ((power_power_nat X) N)) Y)) ((times_times_nat Y) ((power_power_nat X) N))))) of role axiom named fact_38_power__commuting__commutes
% 0.51/0.67 A new axiom: (forall (X:nat) (Y:nat) (N:nat), ((((eq nat) ((times_times_nat X) Y)) ((times_times_nat Y) X))->(((eq nat) ((times_times_nat ((power_power_nat X) N)) Y)) ((times_times_nat Y) ((power_power_nat X) N)))))
% 0.51/0.67 FOF formula (forall (A:int) (B:int) (N:nat), (((eq int) ((power_power_int ((times_times_int A) B)) N)) ((times_times_int ((power_power_int A) N)) ((power_power_int B) N)))) of role axiom named fact_39_power__mult__distrib
% 0.51/0.67 A new axiom: (forall (A:int) (B:int) (N:nat), (((eq int) ((power_power_int ((times_times_int A) B)) N)) ((times_times_int ((power_power_int A) N)) ((power_power_int B) N))))
% 0.51/0.67 FOF formula (forall (A:nat) (B:nat) (N:nat), (((eq nat) ((power_power_nat ((times_times_nat A) B)) N)) ((times_times_nat ((power_power_nat A) N)) ((power_power_nat B) N)))) of role axiom named fact_40_power__mult__distrib
% 0.51/0.67 A new axiom: (forall (A:nat) (B:nat) (N:nat), (((eq nat) ((power_power_nat ((times_times_nat A) B)) N)) ((times_times_nat ((power_power_nat A) N)) ((power_power_nat B) N))))
% 0.51/0.67 FOF formula (forall (A:int) (N:nat), (((eq int) ((times_times_int ((power_power_int A) N)) A)) ((times_times_int A) ((power_power_int A) N)))) of role axiom named fact_41_power__commutes
% 0.51/0.67 A new axiom: (forall (A:int) (N:nat), (((eq int) ((times_times_int ((power_power_int A) N)) A)) ((times_times_int A) ((power_power_int A) N))))
% 0.51/0.67 FOF formula (forall (A:nat) (N:nat), (((eq nat) ((times_times_nat ((power_power_nat A) N)) A)) ((times_times_nat A) ((power_power_nat A) N)))) of role axiom named fact_42_power__commutes
% 0.51/0.68 A new axiom: (forall (A:nat) (N:nat), (((eq nat) ((times_times_nat ((power_power_nat A) N)) A)) ((times_times_nat A) ((power_power_nat A) N))))
% 0.51/0.68 FOF formula (forall (X:nat) (Y:int), (((eq int) ((times_times_int (semiri2019852685at_int X)) Y)) ((times_times_int Y) (semiri2019852685at_int X)))) of role axiom named fact_43_mult__of__nat__commute
% 0.51/0.68 A new axiom: (forall (X:nat) (Y:int), (((eq int) ((times_times_int (semiri2019852685at_int X)) Y)) ((times_times_int Y) (semiri2019852685at_int X))))
% 0.51/0.68 FOF formula (forall (X:nat) (Y:nat), (((eq nat) ((times_times_nat (semiri1382578993at_nat X)) Y)) ((times_times_nat Y) (semiri1382578993at_nat X)))) of role axiom named fact_44_mult__of__nat__commute
% 0.51/0.68 A new axiom: (forall (X:nat) (Y:nat), (((eq nat) ((times_times_nat (semiri1382578993at_nat X)) Y)) ((times_times_nat Y) (semiri1382578993at_nat X))))
% 0.51/0.68 FOF formula (forall (M:nat) (N:nat), (((eq int) (semiri2019852685at_int ((divide_divide_nat M) N))) ((divide_divide_int (semiri2019852685at_int M)) (semiri2019852685at_int N)))) of role axiom named fact_45_unique__euclidean__semiring__with__nat__class_Oof__nat__div
% 0.51/0.68 A new axiom: (forall (M:nat) (N:nat), (((eq int) (semiri2019852685at_int ((divide_divide_nat M) N))) ((divide_divide_int (semiri2019852685at_int M)) (semiri2019852685at_int N))))
% 0.51/0.68 FOF formula (forall (M:nat) (N:nat), (((eq nat) (semiri1382578993at_nat ((divide_divide_nat M) N))) ((divide_divide_nat (semiri1382578993at_nat M)) (semiri1382578993at_nat N)))) of role axiom named fact_46_unique__euclidean__semiring__with__nat__class_Oof__nat__div
% 0.51/0.68 A new axiom: (forall (M:nat) (N:nat), (((eq nat) (semiri1382578993at_nat ((divide_divide_nat M) N))) ((divide_divide_nat (semiri1382578993at_nat M)) (semiri1382578993at_nat N))))
% 0.51/0.68 FOF formula (forall (A:int) (N:nat), (((eq int) ((power_power_int A) (suc N))) ((times_times_int ((power_power_int A) N)) A))) of role axiom named fact_47_power__Suc2
% 0.51/0.68 A new axiom: (forall (A:int) (N:nat), (((eq int) ((power_power_int A) (suc N))) ((times_times_int ((power_power_int A) N)) A)))
% 0.51/0.68 FOF formula (forall (A:nat) (N:nat), (((eq nat) ((power_power_nat A) (suc N))) ((times_times_nat ((power_power_nat A) N)) A))) of role axiom named fact_48_power__Suc2
% 0.51/0.68 A new axiom: (forall (A:nat) (N:nat), (((eq nat) ((power_power_nat A) (suc N))) ((times_times_nat ((power_power_nat A) N)) A)))
% 0.51/0.68 FOF formula (forall (A:nat) (B:nat), (((eq int) (semiri2019852685at_int ((times_times_nat A) B))) ((times_times_int (semiri2019852685at_int A)) (semiri2019852685at_int B)))) of role axiom named fact_49_int__ops_I7_J
% 0.51/0.68 A new axiom: (forall (A:nat) (B:nat), (((eq int) (semiri2019852685at_int ((times_times_nat A) B))) ((times_times_int (semiri2019852685at_int A)) (semiri2019852685at_int B))))
% 0.51/0.68 FOF formula (forall (M:nat) (N:nat) (Z:int), (((eq int) ((plus_plus_int (semiri2019852685at_int M)) ((plus_plus_int (semiri2019852685at_int N)) Z))) ((plus_plus_int (semiri2019852685at_int ((plus_plus_nat M) N))) Z))) of role axiom named fact_50_zadd__int__left
% 0.51/0.68 A new axiom: (forall (M:nat) (N:nat) (Z:int), (((eq int) ((plus_plus_int (semiri2019852685at_int M)) ((plus_plus_int (semiri2019852685at_int N)) Z))) ((plus_plus_int (semiri2019852685at_int ((plus_plus_nat M) N))) Z)))
% 0.51/0.68 FOF formula (forall (N:nat) (M:nat), (((eq int) (semiri2019852685at_int ((plus_plus_nat N) M))) ((plus_plus_int (semiri2019852685at_int N)) (semiri2019852685at_int M)))) of role axiom named fact_51_int__plus
% 0.51/0.68 A new axiom: (forall (N:nat) (M:nat), (((eq int) (semiri2019852685at_int ((plus_plus_nat N) M))) ((plus_plus_int (semiri2019852685at_int N)) (semiri2019852685at_int M))))
% 0.51/0.68 FOF formula (forall (A:nat) (B:nat), (((eq int) (semiri2019852685at_int ((plus_plus_nat A) B))) ((plus_plus_int (semiri2019852685at_int A)) (semiri2019852685at_int B)))) of role axiom named fact_52_int__ops_I5_J
% 0.51/0.68 A new axiom: (forall (A:nat) (B:nat), (((eq int) (semiri2019852685at_int ((plus_plus_nat A) B))) ((plus_plus_int (semiri2019852685at_int A)) (semiri2019852685at_int B))))
% 0.51/0.69 FOF formula (forall (B:int) (A:int) (C:int), (((eq Prop) (((eq int) ((plus_plus_int B) A)) ((plus_plus_int C) A))) (((eq int) B) C))) of role axiom named fact_53_add__right__cancel
% 0.51/0.69 A new axiom: (forall (B:int) (A:int) (C:int), (((eq Prop) (((eq int) ((plus_plus_int B) A)) ((plus_plus_int C) A))) (((eq int) B) C)))
% 0.51/0.69 FOF formula (forall (B:nat) (A:nat) (C:nat), (((eq Prop) (((eq nat) ((plus_plus_nat B) A)) ((plus_plus_nat C) A))) (((eq nat) B) C))) of role axiom named fact_54_add__right__cancel
% 0.51/0.69 A new axiom: (forall (B:nat) (A:nat) (C:nat), (((eq Prop) (((eq nat) ((plus_plus_nat B) A)) ((plus_plus_nat C) A))) (((eq nat) B) C)))
% 0.51/0.69 FOF formula (forall (A:int) (B:int) (C:int), (((eq Prop) (((eq int) ((plus_plus_int A) B)) ((plus_plus_int A) C))) (((eq int) B) C))) of role axiom named fact_55_add__left__cancel
% 0.51/0.69 A new axiom: (forall (A:int) (B:int) (C:int), (((eq Prop) (((eq int) ((plus_plus_int A) B)) ((plus_plus_int A) C))) (((eq int) B) C)))
% 0.51/0.69 FOF formula (forall (A:nat) (B:nat) (C:nat), (((eq Prop) (((eq nat) ((plus_plus_nat A) B)) ((plus_plus_nat A) C))) (((eq nat) B) C))) of role axiom named fact_56_add__left__cancel
% 0.51/0.69 A new axiom: (forall (A:nat) (B:nat) (C:nat), (((eq Prop) (((eq nat) ((plus_plus_nat A) B)) ((plus_plus_nat A) C))) (((eq nat) B) C)))
% 0.51/0.69 FOF formula (forall (A:nat) (B:nat), (((eq int) (semiri2019852685at_int ((divide_divide_nat A) B))) ((divide_divide_int (semiri2019852685at_int A)) (semiri2019852685at_int B)))) of role axiom named fact_57_zdiv__int
% 0.51/0.69 A new axiom: (forall (A:nat) (B:nat), (((eq int) (semiri2019852685at_int ((divide_divide_nat A) B))) ((divide_divide_int (semiri2019852685at_int A)) (semiri2019852685at_int B))))
% 0.51/0.69 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_58_int__distrib_I1_J
% 0.51/0.69 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))))
% 0.51/0.69 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_59_int__distrib_I2_J
% 0.51/0.69 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))))
% 0.51/0.69 FOF formula (forall (_TPTP_I:nat) (U:nat) (J:nat) (K:nat), (((eq nat) ((plus_plus_nat ((times_times_nat _TPTP_I) U)) ((plus_plus_nat ((times_times_nat J) U)) K))) ((plus_plus_nat ((times_times_nat ((plus_plus_nat _TPTP_I) J)) U)) K))) of role axiom named fact_60_left__add__mult__distrib
% 0.51/0.69 A new axiom: (forall (_TPTP_I:nat) (U:nat) (J:nat) (K:nat), (((eq nat) ((plus_plus_nat ((times_times_nat _TPTP_I) U)) ((plus_plus_nat ((times_times_nat J) U)) K))) ((plus_plus_nat ((times_times_nat ((plus_plus_nat _TPTP_I) J)) U)) K)))
% 0.51/0.69 FOF formula (forall (A:int) (B:int) (C:int) (D:int), (((eq Prop) ((and (not (((eq int) A) B))) (not (((eq int) C) D)))) (not (((eq int) ((plus_plus_int ((times_times_int A) C)) ((times_times_int B) D))) ((plus_plus_int ((times_times_int A) D)) ((times_times_int B) C)))))) of role axiom named fact_61_crossproduct__noteq
% 0.51/0.69 A new axiom: (forall (A:int) (B:int) (C:int) (D:int), (((eq Prop) ((and (not (((eq int) A) B))) (not (((eq int) C) D)))) (not (((eq int) ((plus_plus_int ((times_times_int A) C)) ((times_times_int B) D))) ((plus_plus_int ((times_times_int A) D)) ((times_times_int B) C))))))
% 0.51/0.69 FOF formula (forall (A:nat) (B:nat) (C:nat) (D:nat), (((eq Prop) ((and (not (((eq nat) A) B))) (not (((eq nat) C) D)))) (not (((eq nat) ((plus_plus_nat ((times_times_nat A) C)) ((times_times_nat B) D))) ((plus_plus_nat ((times_times_nat A) D)) ((times_times_nat B) C)))))) of role axiom named fact_62_crossproduct__noteq
% 0.51/0.69 A new axiom: (forall (A:nat) (B:nat) (C:nat) (D:nat), (((eq Prop) ((and (not (((eq nat) A) B))) (not (((eq nat) C) D)))) (not (((eq nat) ((plus_plus_nat ((times_times_nat A) C)) ((times_times_nat B) D))) ((plus_plus_nat ((times_times_nat A) D)) ((times_times_nat B) C))))))
% 0.51/0.71 FOF formula (forall (P:nat) (Pm:nat), (((nthRoo1352626670d_root P) Pm)->(((eq nat) P) (suc Pm)))) of role axiom named fact_63_fixed__root_Op
% 0.51/0.71 A new axiom: (forall (P:nat) (Pm:nat), (((nthRoo1352626670d_root P) Pm)->(((eq nat) P) (suc Pm))))
% 0.51/0.71 FOF formula (((eq (nat->(nat->Prop))) nthRoo1352626670d_root) (fun (P2:nat) (Pm2:nat)=> (((eq nat) P2) (suc Pm2)))) of role axiom named fact_64_fixed__root__def
% 0.51/0.71 A new axiom: (((eq (nat->(nat->Prop))) nthRoo1352626670d_root) (fun (P2:nat) (Pm2:nat)=> (((eq nat) P2) (suc Pm2))))
% 0.51/0.71 FOF formula (forall (P:nat) (Pm:nat), ((((eq nat) P) (suc Pm))->((nthRoo1352626670d_root P) Pm))) of role axiom named fact_65_fixed__root_Ointro
% 0.51/0.71 A new axiom: (forall (P:nat) (Pm:nat), ((((eq nat) P) (suc Pm))->((nthRoo1352626670d_root P) Pm)))
% 0.51/0.71 FOF formula (forall (A:int) (B:int) (C:int), (((eq int) ((times_times_int ((times_times_int A) B)) C)) ((times_times_int A) ((times_times_int B) C)))) of role axiom named fact_66_ab__semigroup__mult__class_Omult__ac_I1_J
% 0.51/0.71 A new axiom: (forall (A:int) (B:int) (C:int), (((eq int) ((times_times_int ((times_times_int A) B)) C)) ((times_times_int A) ((times_times_int B) C))))
% 0.51/0.71 FOF formula (forall (A:nat) (B:nat) (C:nat), (((eq nat) ((times_times_nat ((times_times_nat A) B)) C)) ((times_times_nat A) ((times_times_nat B) C)))) of role axiom named fact_67_ab__semigroup__mult__class_Omult__ac_I1_J
% 0.51/0.71 A new axiom: (forall (A:nat) (B:nat) (C:nat), (((eq nat) ((times_times_nat ((times_times_nat A) B)) C)) ((times_times_nat A) ((times_times_nat B) C))))
% 0.51/0.71 FOF formula (forall (A:int) (B:int) (C:int), (((eq int) ((times_times_int ((times_times_int A) B)) C)) ((times_times_int A) ((times_times_int B) C)))) of role axiom named fact_68_mult_Oassoc
% 0.51/0.71 A new axiom: (forall (A:int) (B:int) (C:int), (((eq int) ((times_times_int ((times_times_int A) B)) C)) ((times_times_int A) ((times_times_int B) C))))
% 0.51/0.71 FOF formula (forall (A:nat) (B:nat) (C:nat), (((eq nat) ((times_times_nat ((times_times_nat A) B)) C)) ((times_times_nat A) ((times_times_nat B) C)))) of role axiom named fact_69_mult_Oassoc
% 0.51/0.71 A new axiom: (forall (A:nat) (B:nat) (C:nat), (((eq nat) ((times_times_nat ((times_times_nat A) B)) C)) ((times_times_nat A) ((times_times_nat B) C))))
% 0.51/0.71 FOF formula (((eq (int->(int->int))) times_times_int) (fun (A3:int) (B2:int)=> ((times_times_int B2) A3))) of role axiom named fact_70_mult_Ocommute
% 0.51/0.71 A new axiom: (((eq (int->(int->int))) times_times_int) (fun (A3:int) (B2:int)=> ((times_times_int B2) A3)))
% 0.51/0.71 FOF formula (((eq (nat->(nat->nat))) times_times_nat) (fun (A3:nat) (B2:nat)=> ((times_times_nat B2) A3))) of role axiom named fact_71_mult_Ocommute
% 0.51/0.71 A new axiom: (((eq (nat->(nat->nat))) times_times_nat) (fun (A3:nat) (B2:nat)=> ((times_times_nat B2) A3)))
% 0.51/0.71 FOF formula (forall (B:int) (A:int) (C:int), (((eq int) ((times_times_int B) ((times_times_int A) C))) ((times_times_int A) ((times_times_int B) C)))) of role axiom named fact_72_mult_Oleft__commute
% 0.51/0.71 A new axiom: (forall (B:int) (A:int) (C:int), (((eq int) ((times_times_int B) ((times_times_int A) C))) ((times_times_int A) ((times_times_int B) C))))
% 0.51/0.71 FOF formula (forall (B:nat) (A:nat) (C:nat), (((eq nat) ((times_times_nat B) ((times_times_nat A) C))) ((times_times_nat A) ((times_times_nat B) C)))) of role axiom named fact_73_mult_Oleft__commute
% 0.51/0.71 A new axiom: (forall (B:nat) (A:nat) (C:nat), (((eq nat) ((times_times_nat B) ((times_times_nat A) C))) ((times_times_nat A) ((times_times_nat B) C))))
% 0.51/0.71 FOF formula (forall (A:int) (B:int) (C:int), (((eq int) ((plus_plus_int ((plus_plus_int A) B)) C)) ((plus_plus_int A) ((plus_plus_int B) C)))) of role axiom named fact_74_ab__semigroup__add__class_Oadd__ac_I1_J
% 0.51/0.71 A new axiom: (forall (A:int) (B:int) (C:int), (((eq int) ((plus_plus_int ((plus_plus_int A) B)) C)) ((plus_plus_int A) ((plus_plus_int B) C))))
% 0.51/0.71 FOF formula (forall (A:nat) (B:nat) (C:nat), (((eq nat) ((plus_plus_nat ((plus_plus_nat A) B)) C)) ((plus_plus_nat A) ((plus_plus_nat B) C)))) of role axiom named fact_75_ab__semigroup__add__class_Oadd__ac_I1_J
% 0.51/0.71 A new axiom: (forall (A:nat) (B:nat) (C:nat), (((eq nat) ((plus_plus_nat ((plus_plus_nat A) B)) C)) ((plus_plus_nat A) ((plus_plus_nat B) C))))
% 0.51/0.72 FOF formula (forall (_TPTP_I:int) (J:int) (K:int) (L:int), (((and (((eq int) _TPTP_I) J)) (((eq int) K) L))->(((eq int) ((plus_plus_int _TPTP_I) K)) ((plus_plus_int J) L)))) of role axiom named fact_76_add__mono__thms__linordered__semiring_I4_J
% 0.51/0.72 A new axiom: (forall (_TPTP_I:int) (J:int) (K:int) (L:int), (((and (((eq int) _TPTP_I) J)) (((eq int) K) L))->(((eq int) ((plus_plus_int _TPTP_I) K)) ((plus_plus_int J) L))))
% 0.51/0.72 FOF formula (forall (_TPTP_I:nat) (J:nat) (K:nat) (L:nat), (((and (((eq nat) _TPTP_I) J)) (((eq nat) K) L))->(((eq nat) ((plus_plus_nat _TPTP_I) K)) ((plus_plus_nat J) L)))) of role axiom named fact_77_add__mono__thms__linordered__semiring_I4_J
% 0.51/0.72 A new axiom: (forall (_TPTP_I:nat) (J:nat) (K:nat) (L:nat), (((and (((eq nat) _TPTP_I) J)) (((eq nat) K) L))->(((eq nat) ((plus_plus_nat _TPTP_I) K)) ((plus_plus_nat J) L))))
% 0.51/0.72 FOF formula (forall (A2:int) (K:int) (A:int) (B:int), ((((eq int) A2) ((plus_plus_int K) A))->(((eq int) ((plus_plus_int A2) B)) ((plus_plus_int K) ((plus_plus_int A) B))))) of role axiom named fact_78_group__cancel_Oadd1
% 0.51/0.72 A new axiom: (forall (A2:int) (K:int) (A:int) (B:int), ((((eq int) A2) ((plus_plus_int K) A))->(((eq int) ((plus_plus_int A2) B)) ((plus_plus_int K) ((plus_plus_int A) B)))))
% 0.51/0.72 FOF formula (forall (A2:nat) (K:nat) (A:nat) (B:nat), ((((eq nat) A2) ((plus_plus_nat K) A))->(((eq nat) ((plus_plus_nat A2) B)) ((plus_plus_nat K) ((plus_plus_nat A) B))))) of role axiom named fact_79_group__cancel_Oadd1
% 0.51/0.72 A new axiom: (forall (A2:nat) (K:nat) (A:nat) (B:nat), ((((eq nat) A2) ((plus_plus_nat K) A))->(((eq nat) ((plus_plus_nat A2) B)) ((plus_plus_nat K) ((plus_plus_nat A) B)))))
% 0.51/0.72 FOF formula (forall (B3:int) (K:int) (B:int) (A:int), ((((eq int) B3) ((plus_plus_int K) B))->(((eq int) ((plus_plus_int A) B3)) ((plus_plus_int K) ((plus_plus_int A) B))))) of role axiom named fact_80_group__cancel_Oadd2
% 0.51/0.72 A new axiom: (forall (B3:int) (K:int) (B:int) (A:int), ((((eq int) B3) ((plus_plus_int K) B))->(((eq int) ((plus_plus_int A) B3)) ((plus_plus_int K) ((plus_plus_int A) B)))))
% 0.51/0.72 FOF formula (forall (B3:nat) (K:nat) (B:nat) (A:nat), ((((eq nat) B3) ((plus_plus_nat K) B))->(((eq nat) ((plus_plus_nat A) B3)) ((plus_plus_nat K) ((plus_plus_nat A) B))))) of role axiom named fact_81_group__cancel_Oadd2
% 0.51/0.72 A new axiom: (forall (B3:nat) (K:nat) (B:nat) (A:nat), ((((eq nat) B3) ((plus_plus_nat K) B))->(((eq nat) ((plus_plus_nat A) B3)) ((plus_plus_nat K) ((plus_plus_nat A) B)))))
% 0.51/0.72 FOF formula (forall (A:int) (B:int) (C:int), (((eq int) ((plus_plus_int ((plus_plus_int A) B)) C)) ((plus_plus_int A) ((plus_plus_int B) C)))) of role axiom named fact_82_add_Oassoc
% 0.51/0.72 A new axiom: (forall (A:int) (B:int) (C:int), (((eq int) ((plus_plus_int ((plus_plus_int A) B)) C)) ((plus_plus_int A) ((plus_plus_int B) C))))
% 0.51/0.72 FOF formula (forall (A:nat) (B:nat) (C:nat), (((eq nat) ((plus_plus_nat ((plus_plus_nat A) B)) C)) ((plus_plus_nat A) ((plus_plus_nat B) C)))) of role axiom named fact_83_add_Oassoc
% 0.51/0.72 A new axiom: (forall (A:nat) (B:nat) (C:nat), (((eq nat) ((plus_plus_nat ((plus_plus_nat A) B)) C)) ((plus_plus_nat A) ((plus_plus_nat B) C))))
% 0.51/0.72 FOF formula (forall (A:int) (B:int) (C:int), (((eq Prop) (((eq int) ((plus_plus_int A) B)) ((plus_plus_int A) C))) (((eq int) B) C))) of role axiom named fact_84_add_Oleft__cancel
% 0.51/0.72 A new axiom: (forall (A:int) (B:int) (C:int), (((eq Prop) (((eq int) ((plus_plus_int A) B)) ((plus_plus_int A) C))) (((eq int) B) C)))
% 0.51/0.72 FOF formula (forall (B:int) (A:int) (C:int), (((eq Prop) (((eq int) ((plus_plus_int B) A)) ((plus_plus_int C) A))) (((eq int) B) C))) of role axiom named fact_85_add_Oright__cancel
% 0.51/0.72 A new axiom: (forall (B:int) (A:int) (C:int), (((eq Prop) (((eq int) ((plus_plus_int B) A)) ((plus_plus_int C) A))) (((eq int) B) C)))
% 0.51/0.72 FOF formula (((eq (int->(int->int))) plus_plus_int) (fun (A3:int) (B2:int)=> ((plus_plus_int B2) A3))) of role axiom named fact_86_add_Ocommute
% 0.51/0.72 A new axiom: (((eq (int->(int->int))) plus_plus_int) (fun (A3:int) (B2:int)=> ((plus_plus_int B2) A3)))
% 0.51/0.72 FOF formula (((eq (nat->(nat->nat))) plus_plus_nat) (fun (A3:nat) (B2:nat)=> ((plus_plus_nat B2) A3))) of role axiom named fact_87_add_Ocommute
% 0.58/0.73 A new axiom: (((eq (nat->(nat->nat))) plus_plus_nat) (fun (A3:nat) (B2:nat)=> ((plus_plus_nat B2) A3)))
% 0.58/0.73 FOF formula (forall (B:int) (A:int) (C:int), (((eq int) ((plus_plus_int B) ((plus_plus_int A) C))) ((plus_plus_int A) ((plus_plus_int B) C)))) of role axiom named fact_88_add_Oleft__commute
% 0.58/0.73 A new axiom: (forall (B:int) (A:int) (C:int), (((eq int) ((plus_plus_int B) ((plus_plus_int A) C))) ((plus_plus_int A) ((plus_plus_int B) C))))
% 0.58/0.73 FOF formula (forall (B:nat) (A:nat) (C:nat), (((eq nat) ((plus_plus_nat B) ((plus_plus_nat A) C))) ((plus_plus_nat A) ((plus_plus_nat B) C)))) of role axiom named fact_89_add_Oleft__commute
% 0.58/0.73 A new axiom: (forall (B:nat) (A:nat) (C:nat), (((eq nat) ((plus_plus_nat B) ((plus_plus_nat A) C))) ((plus_plus_nat A) ((plus_plus_nat B) C))))
% 0.58/0.73 FOF formula (forall (A:int) (B:int) (C:int), ((((eq int) ((plus_plus_int A) B)) ((plus_plus_int A) C))->(((eq int) B) C))) of role axiom named fact_90_add__left__imp__eq
% 0.58/0.73 A new axiom: (forall (A:int) (B:int) (C:int), ((((eq int) ((plus_plus_int A) B)) ((plus_plus_int A) C))->(((eq int) B) C)))
% 0.58/0.73 FOF formula (forall (A:nat) (B:nat) (C:nat), ((((eq nat) ((plus_plus_nat A) B)) ((plus_plus_nat A) C))->(((eq nat) B) C))) of role axiom named fact_91_add__left__imp__eq
% 0.58/0.73 A new axiom: (forall (A:nat) (B:nat) (C:nat), ((((eq nat) ((plus_plus_nat A) B)) ((plus_plus_nat A) C))->(((eq nat) B) C)))
% 0.58/0.73 FOF formula (forall (B:int) (A:int) (C:int), ((((eq int) ((plus_plus_int B) A)) ((plus_plus_int C) A))->(((eq int) B) C))) of role axiom named fact_92_add__right__imp__eq
% 0.58/0.73 A new axiom: (forall (B:int) (A:int) (C:int), ((((eq int) ((plus_plus_int B) A)) ((plus_plus_int C) A))->(((eq int) B) C)))
% 0.58/0.73 FOF formula (forall (B:nat) (A:nat) (C:nat), ((((eq nat) ((plus_plus_nat B) A)) ((plus_plus_nat C) A))->(((eq nat) B) C))) of role axiom named fact_93_add__right__imp__eq
% 0.58/0.73 A new axiom: (forall (B:nat) (A:nat) (C:nat), ((((eq nat) ((plus_plus_nat B) A)) ((plus_plus_nat C) A))->(((eq nat) B) C)))
% 0.58/0.73 FOF formula (((eq (nat->(nat->Prop))) (fun (Y3:nat) (Z3:nat)=> (((eq nat) Y3) Z3))) (fun (A3:nat) (B2:nat)=> (((eq int) (semiri2019852685at_int A3)) (semiri2019852685at_int B2)))) of role axiom named fact_94_nat__int__comparison_I1_J
% 0.58/0.73 A new axiom: (((eq (nat->(nat->Prop))) (fun (Y3:nat) (Z3:nat)=> (((eq nat) Y3) Z3))) (fun (A3:nat) (B2:nat)=> (((eq int) (semiri2019852685at_int A3)) (semiri2019852685at_int B2))))
% 0.58/0.73 <<< @ ( if_nat @ P3 @ A @ B ) )
% 0.58/0.73 = ( semiri2019852685at_int @ A ) ) )
% 0.58/0.73 & ( ~ P3>>>!!!<<<
% 0.58/0.73 => ( ( semiri2019852685at_int @ ( if_nat @ P3 @ A @ B ) )
% 0.58/0.73 = ( semiri2019>>>
% 0.58/0.73 statestack=[0, 1, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 11, 22, 30, 36, 43, 50, 99, 113, 185, 229, 265, 285, 300, 221, 120, 189, 221, 124]
% 0.58/0.73 symstack=[$end, TPTP_file_pre, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, LexToken(THF,'thf',1,24778), LexToken(LPAR,'(',1,24781), name, LexToken(COMMA,',',1,24797), formula_role, LexToken(COMMA,',',1,24803), LexToken(LPAR,'(',1,24804), thf_quantified_formula_PRE, thf_quantifier, LexToken(LBRACKET,'[',1,24812), thf_variable_list, LexToken(RBRACKET,']',1,24833), LexToken(COLON,':',1,24835), LexToken(LPAR,'(',1,24843), thf_unitary_formula, LexToken(AMP,'&',1,24968), LexToken(LPAR,'(',1,24970), unary_connective]
% 0.58/0.73 Unexpected exception Syntax error at 'P3':UPPERWORD
% 0.58/0.73 Traceback (most recent call last):
% 0.58/0.73 File "CASC.py", line 79, in <module>
% 0.58/0.73 problem=TPTP.TPTPproblem(env=environment,debug=1,file=file)
% 0.58/0.73 File "/export/starexec/sandbox2/solver/bin/TPTP.py", line 38, in __init__
% 0.58/0.73 parser.parse(file.read(),debug=0,lexer=lexer)
% 0.58/0.73 File "/export/starexec/sandbox2/solver/bin/ply/yacc.py", line 265, in parse
% 0.58/0.73 return self.parseopt_notrack(input,lexer,debug,tracking,tokenfunc)
% 0.58/0.73 File "/export/starexec/sandbox2/solver/bin/ply/yacc.py", line 1047, in parseopt_notrack
% 0.58/0.73 tok = self.errorfunc(errtoken)
% 0.58/0.73 File "/export/starexec/sandbox2/solver/bin/TPTPparser.py", line 2099, in p_error
% 0.58/0.73 raise TPTPParsingError("Syntax error at '%s':%s" % (t.value,t.type))
% 0.58/0.73 TPTPparser.TPTPParsingError: Syntax error at 'P3':UPPERWORD
%------------------------------------------------------------------------------