TSTP Solution File: ITP102^1 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : ITP102^1 : TPTP v7.5.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n006.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 13:24:11 EDT 2021
% Result : Unknown 0.69s
% 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 : ITP102^1 : TPTP v7.5.0. Released v7.5.0.
% 0.04/0.12 % Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.33 % Computer : n006.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % DateTime : Fri Mar 19 05:47:36 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
% 0.39/0.62 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox2/benchmark/', '/export/starexec/sandbox2/benchmark/']
% 0.39/0.62 FOF formula (<kernel.Constant object at 0xbd4cf8>, <kernel.Type object at 0xbcfa70>) of role type named ty_n_t__List__Olist_It__Nat__Onat_J
% 0.39/0.62 Using role type
% 0.39/0.62 Declaring list_nat:Type
% 0.39/0.62 FOF formula (<kernel.Constant object at 0xbd4440>, <kernel.Type object at 0xbcfd88>) of role type named ty_n_t__List__Olist_Itf__a_J
% 0.39/0.62 Using role type
% 0.39/0.62 Declaring list_a:Type
% 0.39/0.62 FOF formula (<kernel.Constant object at 0xbd4cf8>, <kernel.Type object at 0xbcf6c8>) of role type named ty_n_t__Nat__Onat
% 0.39/0.62 Using role type
% 0.39/0.62 Declaring nat:Type
% 0.39/0.62 FOF formula (<kernel.Constant object at 0xbd4440>, <kernel.Type object at 0xbcf7e8>) of role type named ty_n_tf__a
% 0.39/0.62 Using role type
% 0.39/0.62 Declaring a:Type
% 0.39/0.62 FOF formula (<kernel.Constant object at 0xbd4440>, <kernel.DependentProduct object at 0xbcfd88>) of role type named sy_c_Groups_Ominus__class_Ominus_001t__Nat__Onat
% 0.39/0.62 Using role type
% 0.39/0.62 Declaring minus_minus_nat:(nat->(nat->nat))
% 0.39/0.62 FOF formula (<kernel.Constant object at 0xbd4440>, <kernel.DependentProduct object at 0xbcfcb0>) of role type named sy_c_List2_Olist__asc_001t__Nat__Onat
% 0.39/0.62 Using role type
% 0.39/0.62 Declaring list_asc_nat:(list_nat->Prop)
% 0.39/0.62 FOF formula (<kernel.Constant object at 0xbcfa70>, <kernel.DependentProduct object at 0xbcfcf8>) of role type named sy_c_List2_Olist__desc_001t__Nat__Onat
% 0.39/0.62 Using role type
% 0.39/0.62 Declaring list_desc_nat:(list_nat->Prop)
% 0.39/0.62 FOF formula (<kernel.Constant object at 0xbcfd88>, <kernel.DependentProduct object at 0xbcf6c8>) of role type named sy_c_List2_Olist__strict__asc_001t__Nat__Onat
% 0.39/0.62 Using role type
% 0.39/0.62 Declaring list_strict_asc_nat:(list_nat->Prop)
% 0.39/0.62 FOF formula (<kernel.Constant object at 0xbcfcb0>, <kernel.DependentProduct object at 0xbcf128>) of role type named sy_c_List2_Olist__strict__desc_001t__Nat__Onat
% 0.39/0.62 Using role type
% 0.39/0.62 Declaring list_strict_desc_nat:(list_nat->Prop)
% 0.39/0.62 FOF formula (<kernel.Constant object at 0xbcfcf8>, <kernel.DependentProduct object at 0xbcf638>) of role type named sy_c_ListInf__Mirabelle__akbajwqfbr_Oi__append_001t__Nat__Onat
% 0.39/0.62 Using role type
% 0.39/0.62 Declaring listIn923761578nd_nat:(list_nat->((nat->nat)->(nat->nat)))
% 0.39/0.62 FOF formula (<kernel.Constant object at 0xbcf6c8>, <kernel.DependentProduct object at 0xbcf5f0>) of role type named sy_c_ListInf__Mirabelle__akbajwqfbr_Oi__append_001tf__a
% 0.39/0.62 Using role type
% 0.39/0.62 Declaring listIn1312259492pend_a:(list_a->((nat->a)->(nat->a)))
% 0.39/0.62 FOF formula (<kernel.Constant object at 0xbcf128>, <kernel.DependentProduct object at 0xbcfd88>) of role type named sy_c_List_Olinorder__class_Osorted_001t__Nat__Onat
% 0.39/0.62 Using role type
% 0.39/0.62 Declaring linorder_sorted_nat:(list_nat->Prop)
% 0.39/0.62 FOF formula (<kernel.Constant object at 0xbcfab8>, <kernel.DependentProduct object at 0xbcf128>) of role type named sy_c_List_Olist__ex_001t__Nat__Onat
% 0.39/0.62 Using role type
% 0.39/0.62 Declaring list_ex_nat:((nat->Prop)->(list_nat->Prop))
% 0.39/0.62 FOF formula (<kernel.Constant object at 0xbcf638>, <kernel.DependentProduct object at 0xbcf6c8>) of role type named sy_c_List_Olist__ex_001tf__a
% 0.39/0.62 Using role type
% 0.39/0.62 Declaring list_ex_a:((a->Prop)->(list_a->Prop))
% 0.39/0.62 FOF formula (<kernel.Constant object at 0xbcfcb0>, <kernel.DependentProduct object at 0xbcf128>) of role type named sy_c_List_Onth_001t__Nat__Onat
% 0.39/0.62 Using role type
% 0.39/0.62 Declaring nth_nat:(list_nat->(nat->nat))
% 0.39/0.62 FOF formula (<kernel.Constant object at 0xbcfd40>, <kernel.DependentProduct object at 0xbcff38>) of role type named sy_c_List_Onth_001tf__a
% 0.39/0.62 Using role type
% 0.39/0.62 Declaring nth_a:(list_a->(nat->a))
% 0.39/0.62 FOF formula (<kernel.Constant object at 0xbcfef0>, <kernel.DependentProduct object at 0xbcf128>) of role type named sy_c_List_Orev_001t__Nat__Onat
% 0.39/0.62 Using role type
% 0.39/0.62 Declaring rev_nat:(list_nat->list_nat)
% 0.39/0.62 FOF formula (<kernel.Constant object at 0xbcf6c8>, <kernel.DependentProduct object at 0xbcfd40>) of role type named sy_c_List_Orev_001tf__a
% 0.39/0.62 Using role type
% 0.39/0.62 Declaring rev_a:(list_a->list_a)
% 0.39/0.62 FOF formula (<kernel.Constant object at 0xbcff38>, <kernel.DependentProduct object at 0xbcf440>) of role type named sy_c_Nat_OSuc
% 0.39/0.62 Using role type
% 0.39/0.62 Declaring suc:(nat->nat)
% 0.39/0.62 FOF formula (<kernel.Constant object at 0xbcfef0>, <kernel.DependentProduct object at 0xbcf098>) of role type named sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Nat__Onat_J
% 0.45/0.64 Using role type
% 0.45/0.64 Declaring size_size_list_nat:(list_nat->nat)
% 0.45/0.64 FOF formula (<kernel.Constant object at 0xbcfd40>, <kernel.DependentProduct object at 0xbcf050>) of role type named sy_c_Nat_Osize__class_Osize_001t__List__Olist_Itf__a_J
% 0.45/0.64 Using role type
% 0.45/0.64 Declaring size_size_list_a:(list_a->nat)
% 0.45/0.64 FOF formula (<kernel.Constant object at 0xbcf440>, <kernel.DependentProduct object at 0xbcff38>) of role type named sy_c_Orderings_Oord__class_Oless_001t__Nat__Onat
% 0.45/0.64 Using role type
% 0.45/0.64 Declaring ord_less_nat:(nat->(nat->Prop))
% 0.45/0.64 FOF formula (<kernel.Constant object at 0xbcf098>, <kernel.DependentProduct object at 0xbcfcb0>) of role type named sy_c_Orderings_Oord__class_Oless__eq_001t__Nat__Onat
% 0.45/0.64 Using role type
% 0.45/0.64 Declaring ord_less_eq_nat:(nat->(nat->Prop))
% 0.45/0.64 FOF formula (<kernel.Constant object at 0xbcf050>, <kernel.DependentProduct object at 0xbcfc68>) of role type named sy_v_f
% 0.45/0.64 Using role type
% 0.45/0.64 Declaring f:(nat->a)
% 0.45/0.64 FOF formula (<kernel.Constant object at 0xbcff38>, <kernel.DependentProduct object at 0xbcf320>) of role type named sy_v_g
% 0.45/0.64 Using role type
% 0.45/0.64 Declaring g:(nat->a)
% 0.45/0.64 FOF formula (<kernel.Constant object at 0xbcfcb0>, <kernel.Constant object at 0xbcf320>) of role type named sy_v_xs
% 0.45/0.64 Using role type
% 0.45/0.64 Declaring xs:list_a
% 0.45/0.64 FOF formula (<kernel.Constant object at 0xbcf050>, <kernel.Constant object at 0xbcf320>) of role type named sy_v_ys
% 0.45/0.64 Using role type
% 0.45/0.64 Declaring ys:list_a
% 0.45/0.64 FOF formula (forall (Xs:list_nat) (Ys:list_nat) (F:(nat->nat)) (G:(nat->nat)), ((((eq nat) (size_size_list_nat Xs)) (size_size_list_nat Ys))->(((eq Prop) (((eq (nat->nat)) ((listIn923761578nd_nat Xs) F)) ((listIn923761578nd_nat Ys) G))) ((and (((eq list_nat) Xs) Ys)) (((eq (nat->nat)) F) G))))) of role axiom named fact_0_i__append__eq__i__append__conv
% 0.45/0.64 A new axiom: (forall (Xs:list_nat) (Ys:list_nat) (F:(nat->nat)) (G:(nat->nat)), ((((eq nat) (size_size_list_nat Xs)) (size_size_list_nat Ys))->(((eq Prop) (((eq (nat->nat)) ((listIn923761578nd_nat Xs) F)) ((listIn923761578nd_nat Ys) G))) ((and (((eq list_nat) Xs) Ys)) (((eq (nat->nat)) F) G)))))
% 0.45/0.64 FOF formula (forall (Xs:list_a) (Ys:list_a) (F:(nat->a)) (G:(nat->a)), ((((eq nat) (size_size_list_a Xs)) (size_size_list_a Ys))->(((eq Prop) (((eq (nat->a)) ((listIn1312259492pend_a Xs) F)) ((listIn1312259492pend_a Ys) G))) ((and (((eq list_a) Xs) Ys)) (((eq (nat->a)) F) G))))) of role axiom named fact_1_i__append__eq__i__append__conv
% 0.45/0.64 A new axiom: (forall (Xs:list_a) (Ys:list_a) (F:(nat->a)) (G:(nat->a)), ((((eq nat) (size_size_list_a Xs)) (size_size_list_a Ys))->(((eq Prop) (((eq (nat->a)) ((listIn1312259492pend_a Xs) F)) ((listIn1312259492pend_a Ys) G))) ((and (((eq list_a) Xs) Ys)) (((eq (nat->a)) F) G)))))
% 0.45/0.64 FOF formula (forall (N:nat) (Xs:list_nat) (F:(nat->nat)), (((ord_less_nat N) (size_size_list_nat Xs))->(((eq nat) (((listIn923761578nd_nat Xs) F) N)) ((nth_nat Xs) N)))) of role axiom named fact_2_i__append__nth1
% 0.45/0.64 A new axiom: (forall (N:nat) (Xs:list_nat) (F:(nat->nat)), (((ord_less_nat N) (size_size_list_nat Xs))->(((eq nat) (((listIn923761578nd_nat Xs) F) N)) ((nth_nat Xs) N))))
% 0.45/0.64 FOF formula (forall (N:nat) (Xs:list_a) (F:(nat->a)), (((ord_less_nat N) (size_size_list_a Xs))->(((eq a) (((listIn1312259492pend_a Xs) F) N)) ((nth_a Xs) N)))) of role axiom named fact_3_i__append__nth1
% 0.45/0.64 A new axiom: (forall (N:nat) (Xs:list_a) (F:(nat->a)), (((ord_less_nat N) (size_size_list_a Xs))->(((eq a) (((listIn1312259492pend_a Xs) F) N)) ((nth_a Xs) N))))
% 0.45/0.64 FOF formula (forall (Xs:list_nat) (Ys:list_nat), ((((eq nat) (size_size_list_nat Xs)) (size_size_list_nat Ys))->((forall (_TPTP_I:nat), (((ord_less_nat _TPTP_I) (size_size_list_nat Xs))->(((eq nat) ((nth_nat Xs) _TPTP_I)) ((nth_nat Ys) _TPTP_I))))->(((eq list_nat) Xs) Ys)))) of role axiom named fact_4_nth__equalityI
% 0.45/0.64 A new axiom: (forall (Xs:list_nat) (Ys:list_nat), ((((eq nat) (size_size_list_nat Xs)) (size_size_list_nat Ys))->((forall (_TPTP_I:nat), (((ord_less_nat _TPTP_I) (size_size_list_nat Xs))->(((eq nat) ((nth_nat Xs) _TPTP_I)) ((nth_nat Ys) _TPTP_I))))->(((eq list_nat) Xs) Ys))))
% 0.45/0.64 FOF formula (forall (Xs:list_a) (Ys:list_a), ((((eq nat) (size_size_list_a Xs)) (size_size_list_a Ys))->((forall (_TPTP_I:nat), (((ord_less_nat _TPTP_I) (size_size_list_a Xs))->(((eq a) ((nth_a Xs) _TPTP_I)) ((nth_a Ys) _TPTP_I))))->(((eq list_a) Xs) Ys)))) of role axiom named fact_5_nth__equalityI
% 0.45/0.65 A new axiom: (forall (Xs:list_a) (Ys:list_a), ((((eq nat) (size_size_list_a Xs)) (size_size_list_a Ys))->((forall (_TPTP_I:nat), (((ord_less_nat _TPTP_I) (size_size_list_a Xs))->(((eq a) ((nth_a Xs) _TPTP_I)) ((nth_a Ys) _TPTP_I))))->(((eq list_a) Xs) Ys))))
% 0.45/0.65 FOF formula (forall (K:nat) (P:(nat->(nat->Prop))), (((eq Prop) (forall (I2:nat), (((ord_less_nat I2) K)->((ex nat) (fun (X:nat)=> ((P I2) X)))))) ((ex list_nat) (fun (Xs2:list_nat)=> ((and (((eq nat) (size_size_list_nat Xs2)) K)) (forall (I2:nat), (((ord_less_nat I2) K)->((P I2) ((nth_nat Xs2) I2))))))))) of role axiom named fact_6_Skolem__list__nth
% 0.45/0.65 A new axiom: (forall (K:nat) (P:(nat->(nat->Prop))), (((eq Prop) (forall (I2:nat), (((ord_less_nat I2) K)->((ex nat) (fun (X:nat)=> ((P I2) X)))))) ((ex list_nat) (fun (Xs2:list_nat)=> ((and (((eq nat) (size_size_list_nat Xs2)) K)) (forall (I2:nat), (((ord_less_nat I2) K)->((P I2) ((nth_nat Xs2) I2)))))))))
% 0.45/0.65 FOF formula (forall (K:nat) (P:(nat->(a->Prop))), (((eq Prop) (forall (I2:nat), (((ord_less_nat I2) K)->((ex a) (fun (X:a)=> ((P I2) X)))))) ((ex list_a) (fun (Xs2:list_a)=> ((and (((eq nat) (size_size_list_a Xs2)) K)) (forall (I2:nat), (((ord_less_nat I2) K)->((P I2) ((nth_a Xs2) I2))))))))) of role axiom named fact_7_Skolem__list__nth
% 0.45/0.65 A new axiom: (forall (K:nat) (P:(nat->(a->Prop))), (((eq Prop) (forall (I2:nat), (((ord_less_nat I2) K)->((ex a) (fun (X:a)=> ((P I2) X)))))) ((ex list_a) (fun (Xs2:list_a)=> ((and (((eq nat) (size_size_list_a Xs2)) K)) (forall (I2:nat), (((ord_less_nat I2) K)->((P I2) ((nth_a Xs2) I2)))))))))
% 0.45/0.65 FOF formula (((eq (list_nat->(list_nat->Prop))) (fun (Y:list_nat) (Z:list_nat)=> (((eq list_nat) Y) Z))) (fun (Xs2:list_nat) (Ys2:list_nat)=> ((and (((eq nat) (size_size_list_nat Xs2)) (size_size_list_nat Ys2))) (forall (I2:nat), (((ord_less_nat I2) (size_size_list_nat Xs2))->(((eq nat) ((nth_nat Xs2) I2)) ((nth_nat Ys2) I2))))))) of role axiom named fact_8_list__eq__iff__nth__eq
% 0.45/0.65 A new axiom: (((eq (list_nat->(list_nat->Prop))) (fun (Y:list_nat) (Z:list_nat)=> (((eq list_nat) Y) Z))) (fun (Xs2:list_nat) (Ys2:list_nat)=> ((and (((eq nat) (size_size_list_nat Xs2)) (size_size_list_nat Ys2))) (forall (I2:nat), (((ord_less_nat I2) (size_size_list_nat Xs2))->(((eq nat) ((nth_nat Xs2) I2)) ((nth_nat Ys2) I2)))))))
% 0.45/0.65 FOF formula (((eq (list_a->(list_a->Prop))) (fun (Y:list_a) (Z:list_a)=> (((eq list_a) Y) Z))) (fun (Xs2:list_a) (Ys2:list_a)=> ((and (((eq nat) (size_size_list_a Xs2)) (size_size_list_a Ys2))) (forall (I2:nat), (((ord_less_nat I2) (size_size_list_a Xs2))->(((eq a) ((nth_a Xs2) I2)) ((nth_a Ys2) I2))))))) of role axiom named fact_9_list__eq__iff__nth__eq
% 0.45/0.65 A new axiom: (((eq (list_a->(list_a->Prop))) (fun (Y:list_a) (Z:list_a)=> (((eq list_a) Y) Z))) (fun (Xs2:list_a) (Ys2:list_a)=> ((and (((eq nat) (size_size_list_a Xs2)) (size_size_list_a Ys2))) (forall (I2:nat), (((ord_less_nat I2) (size_size_list_a Xs2))->(((eq a) ((nth_a Xs2) I2)) ((nth_a Ys2) I2)))))))
% 0.45/0.65 FOF formula (forall (X2:nat), ((ord_less_eq_nat X2) X2)) of role axiom named fact_10_order__refl
% 0.45/0.65 A new axiom: (forall (X2:nat), ((ord_less_eq_nat X2) X2))
% 0.45/0.65 FOF formula (((eq (list_nat->Prop)) list_desc_nat) (fun (Xs2:list_nat)=> (forall (J:nat), (((ord_less_nat J) (size_size_list_nat Xs2))->(forall (I2:nat), (((ord_less_eq_nat I2) J)->((ord_less_eq_nat ((nth_nat Xs2) J)) ((nth_nat Xs2) I2)))))))) of role axiom named fact_11_list__desc__trans__le
% 0.45/0.65 A new axiom: (((eq (list_nat->Prop)) list_desc_nat) (fun (Xs2:list_nat)=> (forall (J:nat), (((ord_less_nat J) (size_size_list_nat Xs2))->(forall (I2:nat), (((ord_less_eq_nat I2) J)->((ord_less_eq_nat ((nth_nat Xs2) J)) ((nth_nat Xs2) I2))))))))
% 0.45/0.65 FOF formula (forall (P:(list_nat->Prop)) (Xs:list_nat), ((forall (Xs3:list_nat), ((forall (Ys3:list_nat), (((ord_less_nat (size_size_list_nat Ys3)) (size_size_list_nat Xs3))->(P Ys3)))->(P Xs3)))->(P Xs))) of role axiom named fact_12_length__induct
% 0.49/0.66 A new axiom: (forall (P:(list_nat->Prop)) (Xs:list_nat), ((forall (Xs3:list_nat), ((forall (Ys3:list_nat), (((ord_less_nat (size_size_list_nat Ys3)) (size_size_list_nat Xs3))->(P Ys3)))->(P Xs3)))->(P Xs)))
% 0.49/0.66 FOF formula (forall (P:(list_a->Prop)) (Xs:list_a), ((forall (Xs3:list_a), ((forall (Ys3:list_a), (((ord_less_nat (size_size_list_a Ys3)) (size_size_list_a Xs3))->(P Ys3)))->(P Xs3)))->(P Xs))) of role axiom named fact_13_length__induct
% 0.49/0.66 A new axiom: (forall (P:(list_a->Prop)) (Xs:list_a), ((forall (Xs3:list_a), ((forall (Ys3:list_a), (((ord_less_nat (size_size_list_a Ys3)) (size_size_list_a Xs3))->(P Ys3)))->(P Xs3)))->(P Xs)))
% 0.49/0.66 FOF formula (((eq (nat->(nat->Prop))) ord_less_nat) (fun (M:nat) (N2:nat)=> ((and ((ord_less_eq_nat M) N2)) (not (((eq nat) M) N2))))) of role axiom named fact_14_nat__less__le
% 0.49/0.66 A new axiom: (((eq (nat->(nat->Prop))) ord_less_nat) (fun (M:nat) (N2:nat)=> ((and ((ord_less_eq_nat M) N2)) (not (((eq nat) M) N2)))))
% 0.49/0.66 FOF formula (forall (M2:nat) (N:nat), (((ord_less_nat M2) N)->((ord_less_eq_nat M2) N))) of role axiom named fact_15_less__imp__le__nat
% 0.49/0.66 A new axiom: (forall (M2:nat) (N:nat), (((ord_less_nat M2) N)->((ord_less_eq_nat M2) N)))
% 0.49/0.66 FOF formula (((eq (nat->(nat->Prop))) ord_less_eq_nat) (fun (M:nat) (N2:nat)=> ((or ((ord_less_nat M) N2)) (((eq nat) M) N2)))) of role axiom named fact_16_le__eq__less__or__eq
% 0.49/0.66 A new axiom: (((eq (nat->(nat->Prop))) ord_less_eq_nat) (fun (M:nat) (N2:nat)=> ((or ((ord_less_nat M) N2)) (((eq nat) M) N2))))
% 0.49/0.66 FOF formula (forall (M2:nat) (N:nat), (((or ((ord_less_nat M2) N)) (((eq nat) M2) N))->((ord_less_eq_nat M2) N))) of role axiom named fact_17_less__or__eq__imp__le
% 0.49/0.66 A new axiom: (forall (M2:nat) (N:nat), (((or ((ord_less_nat M2) N)) (((eq nat) M2) N))->((ord_less_eq_nat M2) N)))
% 0.49/0.66 FOF formula (forall (M2:nat) (N:nat), (((ord_less_eq_nat M2) N)->((not (((eq nat) M2) N))->((ord_less_nat M2) N)))) of role axiom named fact_18_le__neq__implies__less
% 0.49/0.66 A new axiom: (forall (M2:nat) (N:nat), (((ord_less_eq_nat M2) N)->((not (((eq nat) M2) N))->((ord_less_nat M2) N))))
% 0.49/0.66 FOF formula (forall (F:(nat->nat)) (I3:nat) (J2:nat), ((forall (_TPTP_I:nat) (J3:nat), (((ord_less_nat _TPTP_I) J3)->((ord_less_nat (F _TPTP_I)) (F J3))))->(((ord_less_eq_nat I3) J2)->((ord_less_eq_nat (F I3)) (F J2))))) of role axiom named fact_19_less__mono__imp__le__mono
% 0.49/0.66 A new axiom: (forall (F:(nat->nat)) (I3:nat) (J2:nat), ((forall (_TPTP_I:nat) (J3:nat), (((ord_less_nat _TPTP_I) J3)->((ord_less_nat (F _TPTP_I)) (F J3))))->(((ord_less_eq_nat I3) J2)->((ord_less_eq_nat (F I3)) (F J2)))))
% 0.49/0.66 FOF formula (forall (B:nat) (A:nat), (((ord_less_eq_nat B) A)->(((ord_less_eq_nat A) B)->(((eq nat) A) B)))) of role axiom named fact_20_dual__order_Oantisym
% 0.49/0.66 A new axiom: (forall (B:nat) (A:nat), (((ord_less_eq_nat B) A)->(((ord_less_eq_nat A) B)->(((eq nat) A) B))))
% 0.49/0.66 FOF formula (((eq (nat->(nat->Prop))) (fun (Y:nat) (Z:nat)=> (((eq nat) Y) Z))) (fun (A2:nat) (B2:nat)=> ((and ((ord_less_eq_nat B2) A2)) ((ord_less_eq_nat A2) B2)))) of role axiom named fact_21_dual__order_Oeq__iff
% 0.49/0.66 A new axiom: (((eq (nat->(nat->Prop))) (fun (Y:nat) (Z:nat)=> (((eq nat) Y) Z))) (fun (A2:nat) (B2:nat)=> ((and ((ord_less_eq_nat B2) A2)) ((ord_less_eq_nat A2) B2))))
% 0.49/0.66 FOF formula (forall (B:nat) (A:nat) (C:nat), (((ord_less_eq_nat B) A)->(((ord_less_eq_nat C) B)->((ord_less_eq_nat C) A)))) of role axiom named fact_22_dual__order_Otrans
% 0.49/0.66 A new axiom: (forall (B:nat) (A:nat) (C:nat), (((ord_less_eq_nat B) A)->(((ord_less_eq_nat C) B)->((ord_less_eq_nat C) A))))
% 0.49/0.66 FOF formula (forall (P:(nat->(nat->Prop))) (A:nat) (B:nat), ((forall (A3:nat) (B3:nat), (((ord_less_eq_nat A3) B3)->((P A3) B3)))->((forall (A3:nat) (B3:nat), (((P B3) A3)->((P A3) B3)))->((P A) B)))) of role axiom named fact_23_linorder__wlog
% 0.49/0.66 A new axiom: (forall (P:(nat->(nat->Prop))) (A:nat) (B:nat), ((forall (A3:nat) (B3:nat), (((ord_less_eq_nat A3) B3)->((P A3) B3)))->((forall (A3:nat) (B3:nat), (((P B3) A3)->((P A3) B3)))->((P A) B))))
% 0.49/0.66 FOF formula (forall (A:nat), ((ord_less_eq_nat A) A)) of role axiom named fact_24_dual__order_Orefl
% 0.49/0.68 A new axiom: (forall (A:nat), ((ord_less_eq_nat A) A))
% 0.49/0.68 FOF formula (forall (X2:nat) (Y2:nat) (Z2:nat), (((ord_less_eq_nat X2) Y2)->(((ord_less_eq_nat Y2) Z2)->((ord_less_eq_nat X2) Z2)))) of role axiom named fact_25_order__trans
% 0.49/0.68 A new axiom: (forall (X2:nat) (Y2:nat) (Z2:nat), (((ord_less_eq_nat X2) Y2)->(((ord_less_eq_nat Y2) Z2)->((ord_less_eq_nat X2) Z2))))
% 0.49/0.68 FOF formula (forall (A:nat) (B:nat), (((ord_less_eq_nat A) B)->(((ord_less_eq_nat B) A)->(((eq nat) A) B)))) of role axiom named fact_26_order__class_Oorder_Oantisym
% 0.49/0.68 A new axiom: (forall (A:nat) (B:nat), (((ord_less_eq_nat A) B)->(((ord_less_eq_nat B) A)->(((eq nat) A) B))))
% 0.49/0.68 FOF formula (forall (A:nat) (B:nat) (C:nat), (((ord_less_eq_nat A) B)->((((eq nat) B) C)->((ord_less_eq_nat A) C)))) of role axiom named fact_27_ord__le__eq__trans
% 0.49/0.68 A new axiom: (forall (A:nat) (B:nat) (C:nat), (((ord_less_eq_nat A) B)->((((eq nat) B) C)->((ord_less_eq_nat A) C))))
% 0.49/0.68 FOF formula (forall (A:nat) (B:nat) (C:nat), ((((eq nat) A) B)->(((ord_less_eq_nat B) C)->((ord_less_eq_nat A) C)))) of role axiom named fact_28_ord__eq__le__trans
% 0.49/0.68 A new axiom: (forall (A:nat) (B:nat) (C:nat), ((((eq nat) A) B)->(((ord_less_eq_nat B) C)->((ord_less_eq_nat A) C))))
% 0.49/0.68 FOF formula (((eq (nat->(nat->Prop))) (fun (Y:nat) (Z:nat)=> (((eq nat) Y) Z))) (fun (A2:nat) (B2:nat)=> ((and ((ord_less_eq_nat A2) B2)) ((ord_less_eq_nat B2) A2)))) of role axiom named fact_29_order__class_Oorder_Oeq__iff
% 0.49/0.68 A new axiom: (((eq (nat->(nat->Prop))) (fun (Y:nat) (Z:nat)=> (((eq nat) Y) Z))) (fun (A2:nat) (B2:nat)=> ((and ((ord_less_eq_nat A2) B2)) ((ord_less_eq_nat B2) A2))))
% 0.49/0.68 FOF formula (forall (Y2:nat) (X2:nat), (((ord_less_eq_nat Y2) X2)->(((eq Prop) ((ord_less_eq_nat X2) Y2)) (((eq nat) X2) Y2)))) of role axiom named fact_30_antisym__conv
% 0.49/0.68 A new axiom: (forall (Y2:nat) (X2:nat), (((ord_less_eq_nat Y2) X2)->(((eq Prop) ((ord_less_eq_nat X2) Y2)) (((eq nat) X2) Y2))))
% 0.49/0.68 FOF formula (forall (X2:nat) (Y2:nat) (Z2:nat), ((((ord_less_eq_nat X2) Y2)->(((ord_less_eq_nat Y2) Z2)->False))->((((ord_less_eq_nat Y2) X2)->(((ord_less_eq_nat X2) Z2)->False))->((((ord_less_eq_nat X2) Z2)->(((ord_less_eq_nat Z2) Y2)->False))->((((ord_less_eq_nat Z2) Y2)->(((ord_less_eq_nat Y2) X2)->False))->((((ord_less_eq_nat Y2) Z2)->(((ord_less_eq_nat Z2) X2)->False))->((((ord_less_eq_nat Z2) X2)->(((ord_less_eq_nat X2) Y2)->False))->False))))))) of role axiom named fact_31_le__cases3
% 0.49/0.68 A new axiom: (forall (X2:nat) (Y2:nat) (Z2:nat), ((((ord_less_eq_nat X2) Y2)->(((ord_less_eq_nat Y2) Z2)->False))->((((ord_less_eq_nat Y2) X2)->(((ord_less_eq_nat X2) Z2)->False))->((((ord_less_eq_nat X2) Z2)->(((ord_less_eq_nat Z2) Y2)->False))->((((ord_less_eq_nat Z2) Y2)->(((ord_less_eq_nat Y2) X2)->False))->((((ord_less_eq_nat Y2) Z2)->(((ord_less_eq_nat Z2) X2)->False))->((((ord_less_eq_nat Z2) X2)->(((ord_less_eq_nat X2) Y2)->False))->False)))))))
% 0.49/0.68 FOF formula (forall (A:nat) (B:nat) (C:nat), (((ord_less_eq_nat A) B)->(((ord_less_eq_nat B) C)->((ord_less_eq_nat A) C)))) of role axiom named fact_32_order_Otrans
% 0.49/0.68 A new axiom: (forall (A:nat) (B:nat) (C:nat), (((ord_less_eq_nat A) B)->(((ord_less_eq_nat B) C)->((ord_less_eq_nat A) C))))
% 0.49/0.68 FOF formula (forall (X2:nat) (Y2:nat), ((((ord_less_eq_nat X2) Y2)->False)->((ord_less_eq_nat Y2) X2))) of role axiom named fact_33_le__cases
% 0.49/0.68 A new axiom: (forall (X2:nat) (Y2:nat), ((((ord_less_eq_nat X2) Y2)->False)->((ord_less_eq_nat Y2) X2)))
% 0.49/0.68 FOF formula (forall (X2:nat) (Y2:nat), ((((eq nat) X2) Y2)->((ord_less_eq_nat X2) Y2))) of role axiom named fact_34_eq__refl
% 0.49/0.68 A new axiom: (forall (X2:nat) (Y2:nat), ((((eq nat) X2) Y2)->((ord_less_eq_nat X2) Y2)))
% 0.49/0.68 FOF formula (forall (X2:nat) (Y2:nat), ((or ((ord_less_eq_nat X2) Y2)) ((ord_less_eq_nat Y2) X2))) of role axiom named fact_35_linear
% 0.49/0.68 A new axiom: (forall (X2:nat) (Y2:nat), ((or ((ord_less_eq_nat X2) Y2)) ((ord_less_eq_nat Y2) X2)))
% 0.49/0.68 FOF formula (forall (X2:nat) (Y2:nat), (((ord_less_eq_nat X2) Y2)->(((ord_less_eq_nat Y2) X2)->(((eq nat) X2) Y2)))) of role axiom named fact_36_antisym
% 0.49/0.68 A new axiom: (forall (X2:nat) (Y2:nat), (((ord_less_eq_nat X2) Y2)->(((ord_less_eq_nat Y2) X2)->(((eq nat) X2) Y2))))
% 0.49/0.70 FOF formula (((eq (nat->(nat->Prop))) (fun (Y:nat) (Z:nat)=> (((eq nat) Y) Z))) (fun (X3:nat) (Y3:nat)=> ((and ((ord_less_eq_nat X3) Y3)) ((ord_less_eq_nat Y3) X3)))) of role axiom named fact_37_eq__iff
% 0.49/0.70 A new axiom: (((eq (nat->(nat->Prop))) (fun (Y:nat) (Z:nat)=> (((eq nat) Y) Z))) (fun (X3:nat) (Y3:nat)=> ((and ((ord_less_eq_nat X3) Y3)) ((ord_less_eq_nat Y3) X3))))
% 0.49/0.70 FOF formula (forall (A:nat) (B:nat) (F:(nat->nat)) (C:nat), (((ord_less_eq_nat A) B)->((((eq nat) (F B)) C)->((forall (X4:nat) (Y4:nat), (((ord_less_eq_nat X4) Y4)->((ord_less_eq_nat (F X4)) (F Y4))))->((ord_less_eq_nat (F A)) C))))) of role axiom named fact_38_ord__le__eq__subst
% 0.49/0.70 A new axiom: (forall (A:nat) (B:nat) (F:(nat->nat)) (C:nat), (((ord_less_eq_nat A) B)->((((eq nat) (F B)) C)->((forall (X4:nat) (Y4:nat), (((ord_less_eq_nat X4) Y4)->((ord_less_eq_nat (F X4)) (F Y4))))->((ord_less_eq_nat (F A)) C)))))
% 0.49/0.70 FOF formula (forall (A:nat) (F:(nat->nat)) (B:nat) (C:nat), ((((eq nat) A) (F B))->(((ord_less_eq_nat B) C)->((forall (X4:nat) (Y4:nat), (((ord_less_eq_nat X4) Y4)->((ord_less_eq_nat (F X4)) (F Y4))))->((ord_less_eq_nat A) (F C)))))) of role axiom named fact_39_ord__eq__le__subst
% 0.49/0.70 A new axiom: (forall (A:nat) (F:(nat->nat)) (B:nat) (C:nat), ((((eq nat) A) (F B))->(((ord_less_eq_nat B) C)->((forall (X4:nat) (Y4:nat), (((ord_less_eq_nat X4) Y4)->((ord_less_eq_nat (F X4)) (F Y4))))->((ord_less_eq_nat A) (F C))))))
% 0.49/0.70 FOF formula (forall (A:nat) (B:nat) (F:(nat->nat)) (C:nat), (((ord_less_eq_nat A) B)->(((ord_less_eq_nat (F B)) C)->((forall (X4:nat) (Y4:nat), (((ord_less_eq_nat X4) Y4)->((ord_less_eq_nat (F X4)) (F Y4))))->((ord_less_eq_nat (F A)) C))))) of role axiom named fact_40_order__subst2
% 0.49/0.70 A new axiom: (forall (A:nat) (B:nat) (F:(nat->nat)) (C:nat), (((ord_less_eq_nat A) B)->(((ord_less_eq_nat (F B)) C)->((forall (X4:nat) (Y4:nat), (((ord_less_eq_nat X4) Y4)->((ord_less_eq_nat (F X4)) (F Y4))))->((ord_less_eq_nat (F A)) C)))))
% 0.49/0.70 FOF formula (forall (A:nat) (F:(nat->nat)) (B:nat) (C:nat), (((ord_less_eq_nat A) (F B))->(((ord_less_eq_nat B) C)->((forall (X4:nat) (Y4:nat), (((ord_less_eq_nat X4) Y4)->((ord_less_eq_nat (F X4)) (F Y4))))->((ord_less_eq_nat A) (F C)))))) of role axiom named fact_41_order__subst1
% 0.49/0.70 A new axiom: (forall (A:nat) (F:(nat->nat)) (B:nat) (C:nat), (((ord_less_eq_nat A) (F B))->(((ord_less_eq_nat B) C)->((forall (X4:nat) (Y4:nat), (((ord_less_eq_nat X4) Y4)->((ord_less_eq_nat (F X4)) (F Y4))))->((ord_less_eq_nat A) (F C))))))
% 0.49/0.70 FOF formula (forall (B:nat) (A:nat), (((ord_less_nat B) A)->(not (((eq nat) A) B)))) of role axiom named fact_42_dual__order_Ostrict__implies__not__eq
% 0.49/0.70 A new axiom: (forall (B:nat) (A:nat), (((ord_less_nat B) A)->(not (((eq nat) A) B))))
% 0.49/0.70 FOF formula (forall (A:nat) (B:nat), (((ord_less_nat A) B)->(not (((eq nat) A) B)))) of role axiom named fact_43_order_Ostrict__implies__not__eq
% 0.49/0.70 A new axiom: (forall (A:nat) (B:nat), (((ord_less_nat A) B)->(not (((eq nat) A) B))))
% 0.49/0.70 FOF formula (forall (X2:nat) (Y2:nat), (((eq Prop) (((ord_less_nat X2) Y2)->False)) ((or ((ord_less_nat Y2) X2)) (((eq nat) X2) Y2)))) of role axiom named fact_44_not__less__iff__gr__or__eq
% 0.49/0.70 A new axiom: (forall (X2:nat) (Y2:nat), (((eq Prop) (((ord_less_nat X2) Y2)->False)) ((or ((ord_less_nat Y2) X2)) (((eq nat) X2) Y2))))
% 0.49/0.70 FOF formula (forall (B:nat) (A:nat) (C:nat), (((ord_less_nat B) A)->(((ord_less_nat C) B)->((ord_less_nat C) A)))) of role axiom named fact_45_dual__order_Ostrict__trans
% 0.49/0.70 A new axiom: (forall (B:nat) (A:nat) (C:nat), (((ord_less_nat B) A)->(((ord_less_nat C) B)->((ord_less_nat C) A))))
% 0.49/0.70 FOF formula (forall (P:(nat->(nat->Prop))) (A:nat) (B:nat), ((forall (A3:nat) (B3:nat), (((ord_less_nat A3) B3)->((P A3) B3)))->((forall (A3:nat), ((P A3) A3))->((forall (A3:nat) (B3:nat), (((P B3) A3)->((P A3) B3)))->((P A) B))))) of role axiom named fact_46_linorder__less__wlog
% 0.49/0.70 A new axiom: (forall (P:(nat->(nat->Prop))) (A:nat) (B:nat), ((forall (A3:nat) (B3:nat), (((ord_less_nat A3) B3)->((P A3) B3)))->((forall (A3:nat), ((P A3) A3))->((forall (A3:nat) (B3:nat), (((P B3) A3)->((P A3) B3)))->((P A) B)))))
% 0.49/0.70 FOF formula (((eq ((nat->Prop)->Prop)) (fun (P2:(nat->Prop))=> ((ex nat) (fun (X:nat)=> (P2 X))))) (fun (P3:(nat->Prop))=> ((ex nat) (fun (N2:nat)=> ((and (P3 N2)) (forall (M:nat), (((ord_less_nat M) N2)->((P3 M)->False)))))))) of role axiom named fact_47_exists__least__iff
% 0.49/0.71 A new axiom: (((eq ((nat->Prop)->Prop)) (fun (P2:(nat->Prop))=> ((ex nat) (fun (X:nat)=> (P2 X))))) (fun (P3:(nat->Prop))=> ((ex nat) (fun (N2:nat)=> ((and (P3 N2)) (forall (M:nat), (((ord_less_nat M) N2)->((P3 M)->False))))))))
% 0.49/0.71 FOF formula (forall (X2:nat) (Y2:nat), (((ord_less_nat X2) Y2)->(((ord_less_nat Y2) X2)->False))) of role axiom named fact_48_less__imp__not__less
% 0.49/0.71 A new axiom: (forall (X2:nat) (Y2:nat), (((ord_less_nat X2) Y2)->(((ord_less_nat Y2) X2)->False)))
% 0.49/0.71 FOF formula (forall (A:nat) (B:nat) (C:nat), (((ord_less_nat A) B)->(((ord_less_nat B) C)->((ord_less_nat A) C)))) of role axiom named fact_49_order_Ostrict__trans
% 0.49/0.71 A new axiom: (forall (A:nat) (B:nat) (C:nat), (((ord_less_nat A) B)->(((ord_less_nat B) C)->((ord_less_nat A) C))))
% 0.49/0.71 FOF formula (forall (A:nat), (((ord_less_nat A) A)->False)) of role axiom named fact_50_dual__order_Oirrefl
% 0.49/0.71 A new axiom: (forall (A:nat), (((ord_less_nat A) A)->False))
% 0.49/0.71 FOF formula (forall (X2:nat) (Y2:nat), ((((ord_less_nat X2) Y2)->False)->((not (((eq nat) X2) Y2))->((ord_less_nat Y2) X2)))) of role axiom named fact_51_linorder__cases
% 0.49/0.71 A new axiom: (forall (X2:nat) (Y2:nat), ((((ord_less_nat X2) Y2)->False)->((not (((eq nat) X2) Y2))->((ord_less_nat Y2) X2))))
% 0.49/0.71 FOF formula (forall (X2:nat) (Y2:nat) (P:Prop), (((ord_less_nat X2) Y2)->(((ord_less_nat Y2) X2)->P))) of role axiom named fact_52_less__imp__triv
% 0.49/0.71 A new axiom: (forall (X2:nat) (Y2:nat) (P:Prop), (((ord_less_nat X2) Y2)->(((ord_less_nat Y2) X2)->P)))
% 0.49/0.71 FOF formula (forall (X2:nat) (Y2:nat), (((ord_less_nat X2) Y2)->(not (((eq nat) Y2) X2)))) of role axiom named fact_53_less__imp__not__eq2
% 0.49/0.71 A new axiom: (forall (X2:nat) (Y2:nat), (((ord_less_nat X2) Y2)->(not (((eq nat) Y2) X2))))
% 0.49/0.71 FOF formula (forall (Y2:nat) (X2:nat), ((((ord_less_nat Y2) X2)->False)->(((eq Prop) (((ord_less_nat X2) Y2)->False)) (((eq nat) X2) Y2)))) of role axiom named fact_54_antisym__conv3
% 0.49/0.71 A new axiom: (forall (Y2:nat) (X2:nat), ((((ord_less_nat Y2) X2)->False)->(((eq Prop) (((ord_less_nat X2) Y2)->False)) (((eq nat) X2) Y2))))
% 0.49/0.71 FOF formula (forall (P:(nat->Prop)) (A:nat), ((forall (X4:nat), ((forall (Y5:nat), (((ord_less_nat Y5) X4)->(P Y5)))->(P X4)))->(P A))) of role axiom named fact_55_less__induct
% 0.49/0.71 A new axiom: (forall (P:(nat->Prop)) (A:nat), ((forall (X4:nat), ((forall (Y5:nat), (((ord_less_nat Y5) X4)->(P Y5)))->(P X4)))->(P A)))
% 0.49/0.71 FOF formula (forall (X2:nat) (Y2:nat), (((ord_less_nat X2) Y2)->(((ord_less_nat Y2) X2)->False))) of role axiom named fact_56_less__not__sym
% 0.49/0.71 A new axiom: (forall (X2:nat) (Y2:nat), (((ord_less_nat X2) Y2)->(((ord_less_nat Y2) X2)->False)))
% 0.49/0.71 FOF formula (forall (X2:nat) (Y2:nat), (((ord_less_nat X2) Y2)->(not (((eq nat) X2) Y2)))) of role axiom named fact_57_less__imp__not__eq
% 0.49/0.71 A new axiom: (forall (X2:nat) (Y2:nat), (((ord_less_nat X2) Y2)->(not (((eq nat) X2) Y2))))
% 0.49/0.71 FOF formula (forall (B:nat) (A:nat), (((ord_less_nat B) A)->(((ord_less_nat A) B)->False))) of role axiom named fact_58_dual__order_Oasym
% 0.49/0.71 A new axiom: (forall (B:nat) (A:nat), (((ord_less_nat B) A)->(((ord_less_nat A) B)->False)))
% 0.49/0.71 FOF formula (forall (A:nat) (B:nat) (C:nat), (((ord_less_nat A) B)->((((eq nat) B) C)->((ord_less_nat A) C)))) of role axiom named fact_59_ord__less__eq__trans
% 0.49/0.71 A new axiom: (forall (A:nat) (B:nat) (C:nat), (((ord_less_nat A) B)->((((eq nat) B) C)->((ord_less_nat A) C))))
% 0.49/0.71 FOF formula (forall (A:nat) (B:nat) (C:nat), ((((eq nat) A) B)->(((ord_less_nat B) C)->((ord_less_nat A) C)))) of role axiom named fact_60_ord__eq__less__trans
% 0.49/0.71 A new axiom: (forall (A:nat) (B:nat) (C:nat), ((((eq nat) A) B)->(((ord_less_nat B) C)->((ord_less_nat A) C))))
% 0.49/0.71 FOF formula (forall (X2:nat), (((ord_less_nat X2) X2)->False)) of role axiom named fact_61_less__irrefl
% 0.49/0.71 A new axiom: (forall (X2:nat), (((ord_less_nat X2) X2)->False))
% 0.49/0.71 FOF formula (forall (X2:nat) (Y2:nat), ((or ((or ((ord_less_nat X2) Y2)) (((eq nat) X2) Y2))) ((ord_less_nat Y2) X2))) of role axiom named fact_62_less__linear
% 0.56/0.73 A new axiom: (forall (X2:nat) (Y2:nat), ((or ((or ((ord_less_nat X2) Y2)) (((eq nat) X2) Y2))) ((ord_less_nat Y2) X2)))
% 0.56/0.73 FOF formula (forall (X2:nat) (Y2:nat) (Z2:nat), (((ord_less_nat X2) Y2)->(((ord_less_nat Y2) Z2)->((ord_less_nat X2) Z2)))) of role axiom named fact_63_less__trans
% 0.56/0.73 A new axiom: (forall (X2:nat) (Y2:nat) (Z2:nat), (((ord_less_nat X2) Y2)->(((ord_less_nat Y2) Z2)->((ord_less_nat X2) Z2))))
% 0.56/0.73 FOF formula (forall (A:nat) (B:nat), (((ord_less_nat A) B)->(((ord_less_nat B) A)->False))) of role axiom named fact_64_less__asym_H
% 0.56/0.73 A new axiom: (forall (A:nat) (B:nat), (((ord_less_nat A) B)->(((ord_less_nat B) A)->False)))
% 0.56/0.73 FOF formula (forall (X2:nat) (Y2:nat), (((ord_less_nat X2) Y2)->(((ord_less_nat Y2) X2)->False))) of role axiom named fact_65_less__asym
% 0.56/0.73 A new axiom: (forall (X2:nat) (Y2:nat), (((ord_less_nat X2) Y2)->(((ord_less_nat Y2) X2)->False)))
% 0.56/0.73 FOF formula (forall (X2:nat) (Y2:nat), (((ord_less_nat X2) Y2)->(not (((eq nat) X2) Y2)))) of role axiom named fact_66_less__imp__neq
% 0.56/0.73 A new axiom: (forall (X2:nat) (Y2:nat), (((ord_less_nat X2) Y2)->(not (((eq nat) X2) Y2))))
% 0.56/0.73 FOF formula (forall (A:nat) (B:nat), (((ord_less_nat A) B)->(((ord_less_nat B) A)->False))) of role axiom named fact_67_order_Oasym
% 0.56/0.73 A new axiom: (forall (A:nat) (B:nat), (((ord_less_nat A) B)->(((ord_less_nat B) A)->False)))
% 0.56/0.73 FOF formula (forall (X2:nat) (Y2:nat), (((eq Prop) (not (((eq nat) X2) Y2))) ((or ((ord_less_nat X2) Y2)) ((ord_less_nat Y2) X2)))) of role axiom named fact_68_neq__iff
% 0.56/0.73 A new axiom: (forall (X2:nat) (Y2:nat), (((eq Prop) (not (((eq nat) X2) Y2))) ((or ((ord_less_nat X2) Y2)) ((ord_less_nat Y2) X2))))
% 0.56/0.73 FOF formula (forall (X2:nat) (Y2:nat), ((not (((eq nat) X2) Y2))->((((ord_less_nat X2) Y2)->False)->((ord_less_nat Y2) X2)))) of role axiom named fact_69_neqE
% 0.56/0.73 A new axiom: (forall (X2:nat) (Y2:nat), ((not (((eq nat) X2) Y2))->((((ord_less_nat X2) Y2)->False)->((ord_less_nat Y2) X2))))
% 0.56/0.73 FOF formula (forall (X2:nat), ((ex nat) (fun (X_1:nat)=> ((ord_less_nat X2) X_1)))) of role axiom named fact_70_gt__ex
% 0.56/0.73 A new axiom: (forall (X2:nat), ((ex nat) (fun (X_1:nat)=> ((ord_less_nat X2) X_1))))
% 0.56/0.73 FOF formula (forall (A:nat) (B:nat) (F:(nat->nat)) (C:nat), (((ord_less_nat A) B)->(((ord_less_nat (F B)) C)->((forall (X4:nat) (Y4:nat), (((ord_less_nat X4) Y4)->((ord_less_nat (F X4)) (F Y4))))->((ord_less_nat (F A)) C))))) of role axiom named fact_71_order__less__subst2
% 0.56/0.73 A new axiom: (forall (A:nat) (B:nat) (F:(nat->nat)) (C:nat), (((ord_less_nat A) B)->(((ord_less_nat (F B)) C)->((forall (X4:nat) (Y4:nat), (((ord_less_nat X4) Y4)->((ord_less_nat (F X4)) (F Y4))))->((ord_less_nat (F A)) C)))))
% 0.56/0.73 FOF formula (forall (A:nat) (F:(nat->nat)) (B:nat) (C:nat), (((ord_less_nat A) (F B))->(((ord_less_nat B) C)->((forall (X4:nat) (Y4:nat), (((ord_less_nat X4) Y4)->((ord_less_nat (F X4)) (F Y4))))->((ord_less_nat A) (F C)))))) of role axiom named fact_72_order__less__subst1
% 0.56/0.73 A new axiom: (forall (A:nat) (F:(nat->nat)) (B:nat) (C:nat), (((ord_less_nat A) (F B))->(((ord_less_nat B) C)->((forall (X4:nat) (Y4:nat), (((ord_less_nat X4) Y4)->((ord_less_nat (F X4)) (F Y4))))->((ord_less_nat A) (F C))))))
% 0.56/0.73 FOF formula (forall (A:nat) (B:nat) (F:(nat->nat)) (C:nat), (((ord_less_nat A) B)->((((eq nat) (F B)) C)->((forall (X4:nat) (Y4:nat), (((ord_less_nat X4) Y4)->((ord_less_nat (F X4)) (F Y4))))->((ord_less_nat (F A)) C))))) of role axiom named fact_73_ord__less__eq__subst
% 0.56/0.73 A new axiom: (forall (A:nat) (B:nat) (F:(nat->nat)) (C:nat), (((ord_less_nat A) B)->((((eq nat) (F B)) C)->((forall (X4:nat) (Y4:nat), (((ord_less_nat X4) Y4)->((ord_less_nat (F X4)) (F Y4))))->((ord_less_nat (F A)) C)))))
% 0.56/0.73 FOF formula (forall (A:nat) (F:(nat->nat)) (B:nat) (C:nat), ((((eq nat) A) (F B))->(((ord_less_nat B) C)->((forall (X4:nat) (Y4:nat), (((ord_less_nat X4) Y4)->((ord_less_nat (F X4)) (F Y4))))->((ord_less_nat A) (F C)))))) of role axiom named fact_74_ord__eq__less__subst
% 0.56/0.73 A new axiom: (forall (A:nat) (F:(nat->nat)) (B:nat) (C:nat), ((((eq nat) A) (F B))->(((ord_less_nat B) C)->((forall (X4:nat) (Y4:nat), (((ord_less_nat X4) Y4)->((ord_less_nat (F X4)) (F Y4))))->((ord_less_nat A) (F C))))))
% 0.56/0.75 FOF formula (forall (X2:nat) (Y2:nat), ((not (((eq nat) X2) Y2))->((((ord_less_nat X2) Y2)->False)->((ord_less_nat Y2) X2)))) of role axiom named fact_75_linorder__neqE__nat
% 0.56/0.75 A new axiom: (forall (X2:nat) (Y2:nat), ((not (((eq nat) X2) Y2))->((((ord_less_nat X2) Y2)->False)->((ord_less_nat Y2) X2))))
% 0.56/0.75 FOF formula (forall (P:(nat->Prop)) (N:nat), ((forall (N3:nat), (((P N3)->False)->((ex nat) (fun (M3:nat)=> ((and ((ord_less_nat M3) N3)) ((P M3)->False))))))->(P N))) of role axiom named fact_76_infinite__descent
% 0.56/0.75 A new axiom: (forall (P:(nat->Prop)) (N:nat), ((forall (N3:nat), (((P N3)->False)->((ex nat) (fun (M3:nat)=> ((and ((ord_less_nat M3) N3)) ((P M3)->False))))))->(P N)))
% 0.56/0.75 FOF formula (forall (P:(nat->Prop)) (N:nat), ((forall (N3:nat), ((forall (M3:nat), (((ord_less_nat M3) N3)->(P M3)))->(P N3)))->(P N))) of role axiom named fact_77_nat__less__induct
% 0.56/0.75 A new axiom: (forall (P:(nat->Prop)) (N:nat), ((forall (N3:nat), ((forall (M3:nat), (((ord_less_nat M3) N3)->(P M3)))->(P N3)))->(P N)))
% 0.56/0.75 FOF formula (forall (N:nat), (((ord_less_nat N) N)->False)) of role axiom named fact_78_less__irrefl__nat
% 0.56/0.75 A new axiom: (forall (N:nat), (((ord_less_nat N) N)->False))
% 0.56/0.75 FOF formula (forall (S:nat) (T:nat), (((ord_less_nat S) T)->(not (((eq nat) S) T)))) of role axiom named fact_79_less__not__refl3
% 0.56/0.75 A new axiom: (forall (S:nat) (T:nat), (((ord_less_nat S) T)->(not (((eq nat) S) T))))
% 0.56/0.75 FOF formula (forall (N:nat) (M2:nat), (((ord_less_nat N) M2)->(not (((eq nat) M2) N)))) of role axiom named fact_80_less__not__refl2
% 0.56/0.75 A new axiom: (forall (N:nat) (M2:nat), (((ord_less_nat N) M2)->(not (((eq nat) M2) N))))
% 0.56/0.75 FOF formula (forall (N:nat), (((ord_less_nat N) N)->False)) of role axiom named fact_81_less__not__refl
% 0.56/0.75 A new axiom: (forall (N:nat), (((ord_less_nat N) N)->False))
% 0.56/0.75 FOF formula (forall (M2:nat) (N:nat), (((eq Prop) (not (((eq nat) M2) N))) ((or ((ord_less_nat M2) N)) ((ord_less_nat N) M2)))) of role axiom named fact_82_nat__neq__iff
% 0.56/0.75 A new axiom: (forall (M2:nat) (N:nat), (((eq Prop) (not (((eq nat) M2) N))) ((or ((ord_less_nat M2) N)) ((ord_less_nat N) M2))))
% 0.56/0.75 FOF formula (forall (P:(nat->Prop)) (K:nat) (B:nat), ((P K)->((forall (Y4:nat), ((P Y4)->((ord_less_eq_nat Y4) B)))->((ex nat) (fun (X4:nat)=> ((and (P X4)) (forall (Y5:nat), ((P Y5)->((ord_less_eq_nat Y5) X4))))))))) of role axiom named fact_83_Nat_Oex__has__greatest__nat
% 0.56/0.75 A new axiom: (forall (P:(nat->Prop)) (K:nat) (B:nat), ((P K)->((forall (Y4:nat), ((P Y4)->((ord_less_eq_nat Y4) B)))->((ex nat) (fun (X4:nat)=> ((and (P X4)) (forall (Y5:nat), ((P Y5)->((ord_less_eq_nat Y5) X4)))))))))
% 0.56/0.75 FOF formula (forall (M2:nat) (N:nat), ((or ((ord_less_eq_nat M2) N)) ((ord_less_eq_nat N) M2))) of role axiom named fact_84_nat__le__linear
% 0.56/0.75 A new axiom: (forall (M2:nat) (N:nat), ((or ((ord_less_eq_nat M2) N)) ((ord_less_eq_nat N) M2)))
% 0.56/0.75 FOF formula (forall (M2:nat) (N:nat), (((ord_less_eq_nat M2) N)->(((ord_less_eq_nat N) M2)->(((eq nat) M2) N)))) of role axiom named fact_85_le__antisym
% 0.56/0.75 A new axiom: (forall (M2:nat) (N:nat), (((ord_less_eq_nat M2) N)->(((ord_less_eq_nat N) M2)->(((eq nat) M2) N))))
% 0.56/0.75 FOF formula (forall (M2:nat) (N:nat), ((((eq nat) M2) N)->((ord_less_eq_nat M2) N))) of role axiom named fact_86_eq__imp__le
% 0.56/0.75 A new axiom: (forall (M2:nat) (N:nat), ((((eq nat) M2) N)->((ord_less_eq_nat M2) N)))
% 0.56/0.75 FOF formula (forall (I3:nat) (J2:nat) (K:nat), (((ord_less_eq_nat I3) J2)->(((ord_less_eq_nat J2) K)->((ord_less_eq_nat I3) K)))) of role axiom named fact_87_le__trans
% 0.56/0.75 A new axiom: (forall (I3:nat) (J2:nat) (K:nat), (((ord_less_eq_nat I3) J2)->(((ord_less_eq_nat J2) K)->((ord_less_eq_nat I3) K))))
% 0.56/0.75 FOF formula (forall (N:nat), ((ord_less_eq_nat N) N)) of role axiom named fact_88_le__refl
% 0.56/0.75 A new axiom: (forall (N:nat), ((ord_less_eq_nat N) N))
% 0.56/0.75 FOF formula (forall (X2:list_a) (Y2:list_a), ((not (((eq nat) (size_size_list_a X2)) (size_size_list_a Y2)))->(not (((eq list_a) X2) Y2)))) of role axiom named fact_89_size__neq__size__imp__neq
% 0.56/0.75 A new axiom: (forall (X2:list_a) (Y2:list_a), ((not (((eq nat) (size_size_list_a X2)) (size_size_list_a Y2)))->(not (((eq list_a) X2) Y2))))
% 0.56/0.76 FOF formula (forall (X2:list_nat) (Y2:list_nat), ((not (((eq nat) (size_size_list_nat X2)) (size_size_list_nat Y2)))->(not (((eq list_nat) X2) Y2)))) of role axiom named fact_90_size__neq__size__imp__neq
% 0.56/0.76 A new axiom: (forall (X2:list_nat) (Y2:list_nat), ((not (((eq nat) (size_size_list_nat X2)) (size_size_list_nat Y2)))->(not (((eq list_nat) X2) Y2))))
% 0.56/0.76 FOF formula (forall (Xs:list_a) (Ys:list_a), ((not (((eq nat) (size_size_list_a Xs)) (size_size_list_a Ys)))->(not (((eq list_a) Xs) Ys)))) of role axiom named fact_91_neq__if__length__neq
% 0.56/0.76 A new axiom: (forall (Xs:list_a) (Ys:list_a), ((not (((eq nat) (size_size_list_a Xs)) (size_size_list_a Ys)))->(not (((eq list_a) Xs) Ys))))
% 0.56/0.76 FOF formula (forall (Xs:list_nat) (Ys:list_nat), ((not (((eq nat) (size_size_list_nat Xs)) (size_size_list_nat Ys)))->(not (((eq list_nat) Xs) Ys)))) of role axiom named fact_92_neq__if__length__neq
% 0.56/0.76 A new axiom: (forall (Xs:list_nat) (Ys:list_nat), ((not (((eq nat) (size_size_list_nat Xs)) (size_size_list_nat Ys)))->(not (((eq list_nat) Xs) Ys))))
% 0.56/0.76 FOF formula (forall (N:nat), ((ex list_a) (fun (Xs3:list_a)=> (((eq nat) (size_size_list_a Xs3)) N)))) of role axiom named fact_93_Ex__list__of__length
% 0.56/0.76 A new axiom: (forall (N:nat), ((ex list_a) (fun (Xs3:list_a)=> (((eq nat) (size_size_list_a Xs3)) N))))
% 0.56/0.76 FOF formula (forall (N:nat), ((ex list_nat) (fun (Xs3:list_nat)=> (((eq nat) (size_size_list_nat Xs3)) N)))) of role axiom named fact_94_Ex__list__of__length
% 0.56/0.76 A new axiom: (forall (N:nat), ((ex list_nat) (fun (Xs3:list_nat)=> (((eq nat) (size_size_list_nat Xs3)) N))))
% 0.56/0.76 FOF formula (((eq (list_nat->Prop)) list_desc_nat) (fun (Xs2:list_nat)=> (forall (J:nat), (((ord_less_nat J) (size_size_list_nat Xs2))->(forall (I2:nat), (((ord_less_nat I2) J)->((ord_less_eq_nat ((nth_nat Xs2) J)) ((nth_nat Xs2) I2)))))))) of role axiom named fact_95_list__desc__trans
% 0.56/0.76 A new axiom: (((eq (list_nat->Prop)) list_desc_nat) (fun (Xs2:list_nat)=> (forall (J:nat), (((ord_less_nat J) (size_size_list_nat Xs2))->(forall (I2:nat), (((ord_less_nat I2) J)->((ord_less_eq_nat ((nth_nat Xs2) J)) ((nth_nat Xs2) I2))))))))
% 0.56/0.76 FOF formula (forall (A:nat) (B:nat), ((not (((eq nat) A) B))->(((ord_less_eq_nat A) B)->((ord_less_nat A) B)))) of role axiom named fact_96_order_Onot__eq__order__implies__strict
% 0.56/0.76 A new axiom: (forall (A:nat) (B:nat), ((not (((eq nat) A) B))->(((ord_less_eq_nat A) B)->((ord_less_nat A) B))))
% 0.56/0.76 FOF formula (forall (B:nat) (A:nat), (((ord_less_nat B) A)->((ord_less_eq_nat B) A))) of role axiom named fact_97_dual__order_Ostrict__implies__order
% 0.56/0.76 A new axiom: (forall (B:nat) (A:nat), (((ord_less_nat B) A)->((ord_less_eq_nat B) A)))
% 0.56/0.76 FOF formula (((eq (nat->(nat->Prop))) ord_less_nat) (fun (B2:nat) (A2:nat)=> ((and ((ord_less_eq_nat B2) A2)) (not (((eq nat) A2) B2))))) of role axiom named fact_98_dual__order_Ostrict__iff__order
% 0.56/0.76 A new axiom: (((eq (nat->(nat->Prop))) ord_less_nat) (fun (B2:nat) (A2:nat)=> ((and ((ord_less_eq_nat B2) A2)) (not (((eq nat) A2) B2)))))
% 0.56/0.76 FOF formula (((eq (nat->(nat->Prop))) ord_less_eq_nat) (fun (B2:nat) (A2:nat)=> ((or ((ord_less_nat B2) A2)) (((eq nat) A2) B2)))) of role axiom named fact_99_dual__order_Oorder__iff__strict
% 0.56/0.76 A new axiom: (((eq (nat->(nat->Prop))) ord_less_eq_nat) (fun (B2:nat) (A2:nat)=> ((or ((ord_less_nat B2) A2)) (((eq nat) A2) B2))))
% 0.56/0.76 FOF formula (forall (A:nat) (B:nat), (((ord_less_nat A) B)->((ord_less_eq_nat A) B))) of role axiom named fact_100_order_Ostrict__implies__order
% 0.56/0.76 A new axiom: (forall (A:nat) (B:nat), (((ord_less_nat A) B)->((ord_less_eq_nat A) B)))
% 0.56/0.76 FOF formula (forall (B:nat) (A:nat) (C:nat), (((ord_less_nat B) A)->(((ord_less_eq_nat C) B)->((ord_less_nat C) A)))) of role axiom named fact_101_dual__order_Ostrict__trans2
% 0.56/0.76 A new axiom: (forall (B:nat) (A:nat) (C:nat), (((ord_less_nat B) A)->(((ord_less_eq_nat C) B)->((ord_less_nat C) A))))
% 0.56/0.76 FOF formula (forall (B:nat) (A:nat) (C:nat), (((ord_less_eq_nat B) A)->(((ord_less_nat C) B)->((ord_less_nat C) A)))) of role axiom named fact_102_dual__order_Ostrict__trans1
% 0.56/0.76 A new axiom: (forall (B:nat) (A:nat) (C:nat), (((ord_less_eq_nat B) A)->(((ord_less_nat C) B)->((ord_less_nat C) A))))
% 0.60/0.78 FOF formula (((eq (nat->(nat->Prop))) ord_less_nat) (fun (A2:nat) (B2:nat)=> ((and ((ord_less_eq_nat A2) B2)) (not (((eq nat) A2) B2))))) of role axiom named fact_103_order_Ostrict__iff__order
% 0.60/0.78 A new axiom: (((eq (nat->(nat->Prop))) ord_less_nat) (fun (A2:nat) (B2:nat)=> ((and ((ord_less_eq_nat A2) B2)) (not (((eq nat) A2) B2)))))
% 0.60/0.78 FOF formula (((eq (nat->(nat->Prop))) ord_less_eq_nat) (fun (A2:nat) (B2:nat)=> ((or ((ord_less_nat A2) B2)) (((eq nat) A2) B2)))) of role axiom named fact_104_order_Oorder__iff__strict
% 0.60/0.78 A new axiom: (((eq (nat->(nat->Prop))) ord_less_eq_nat) (fun (A2:nat) (B2:nat)=> ((or ((ord_less_nat A2) B2)) (((eq nat) A2) B2))))
% 0.60/0.78 FOF formula (forall (A:nat) (B:nat) (C:nat), (((ord_less_nat A) B)->(((ord_less_eq_nat B) C)->((ord_less_nat A) C)))) of role axiom named fact_105_order_Ostrict__trans2
% 0.60/0.78 A new axiom: (forall (A:nat) (B:nat) (C:nat), (((ord_less_nat A) B)->(((ord_less_eq_nat B) C)->((ord_less_nat A) C))))
% 0.60/0.78 FOF formula (forall (A:nat) (B:nat) (C:nat), (((ord_less_eq_nat A) B)->(((ord_less_nat B) C)->((ord_less_nat A) C)))) of role axiom named fact_106_order_Ostrict__trans1
% 0.60/0.78 A new axiom: (forall (A:nat) (B:nat) (C:nat), (((ord_less_eq_nat A) B)->(((ord_less_nat B) C)->((ord_less_nat A) C))))
% 0.60/0.78 FOF formula (forall (Y2:nat) (X2:nat), ((((ord_less_eq_nat Y2) X2)->False)->((ord_less_nat X2) Y2))) of role axiom named fact_107_not__le__imp__less
% 0.60/0.78 A new axiom: (forall (Y2:nat) (X2:nat), ((((ord_less_eq_nat Y2) X2)->False)->((ord_less_nat X2) Y2)))
% 0.60/0.78 FOF formula (((eq (nat->(nat->Prop))) ord_less_nat) (fun (X3:nat) (Y3:nat)=> ((and ((ord_less_eq_nat X3) Y3)) (((ord_less_eq_nat Y3) X3)->False)))) of role axiom named fact_108_less__le__not__le
% 0.60/0.78 A new axiom: (((eq (nat->(nat->Prop))) ord_less_nat) (fun (X3:nat) (Y3:nat)=> ((and ((ord_less_eq_nat X3) Y3)) (((ord_less_eq_nat Y3) X3)->False))))
% 0.60/0.78 FOF formula (forall (X2:nat) (Y2:nat), (((ord_less_eq_nat X2) Y2)->((or ((ord_less_nat X2) Y2)) (((eq nat) X2) Y2)))) of role axiom named fact_109_le__imp__less__or__eq
% 0.60/0.78 A new axiom: (forall (X2:nat) (Y2:nat), (((ord_less_eq_nat X2) Y2)->((or ((ord_less_nat X2) Y2)) (((eq nat) X2) Y2))))
% 0.60/0.78 FOF formula (forall (X2:nat) (Y2:nat), ((or ((ord_less_eq_nat X2) Y2)) ((ord_less_nat Y2) X2))) of role axiom named fact_110_le__less__linear
% 0.60/0.78 A new axiom: (forall (X2:nat) (Y2:nat), ((or ((ord_less_eq_nat X2) Y2)) ((ord_less_nat Y2) X2)))
% 0.60/0.78 FOF formula (forall (X2:nat) (Y2:nat) (Z2:nat), (((ord_less_nat X2) Y2)->(((ord_less_eq_nat Y2) Z2)->((ord_less_nat X2) Z2)))) of role axiom named fact_111_less__le__trans
% 0.60/0.78 A new axiom: (forall (X2:nat) (Y2:nat) (Z2:nat), (((ord_less_nat X2) Y2)->(((ord_less_eq_nat Y2) Z2)->((ord_less_nat X2) Z2))))
% 0.60/0.78 FOF formula (forall (X2:nat) (Y2:nat) (Z2:nat), (((ord_less_eq_nat X2) Y2)->(((ord_less_nat Y2) Z2)->((ord_less_nat X2) Z2)))) of role axiom named fact_112_le__less__trans
% 0.60/0.78 A new axiom: (forall (X2:nat) (Y2:nat) (Z2:nat), (((ord_less_eq_nat X2) Y2)->(((ord_less_nat Y2) Z2)->((ord_less_nat X2) Z2))))
% 0.60/0.78 FOF formula (forall (X2:nat) (Y2:nat), (((ord_less_nat X2) Y2)->((ord_less_eq_nat X2) Y2))) of role axiom named fact_113_less__imp__le
% 0.60/0.78 A new axiom: (forall (X2:nat) (Y2:nat), (((ord_less_nat X2) Y2)->((ord_less_eq_nat X2) Y2)))
% 0.60/0.78 FOF formula (forall (X2:nat) (Y2:nat), (((ord_less_eq_nat X2) Y2)->(((eq Prop) (((ord_less_nat X2) Y2)->False)) (((eq nat) X2) Y2)))) of role axiom named fact_114_antisym__conv2
% 0.60/0.78 A new axiom: (forall (X2:nat) (Y2:nat), (((ord_less_eq_nat X2) Y2)->(((eq Prop) (((ord_less_nat X2) Y2)->False)) (((eq nat) X2) Y2))))
% 0.60/0.78 FOF formula (forall (X2:nat) (Y2:nat), ((((ord_less_nat X2) Y2)->False)->(((eq Prop) ((ord_less_eq_nat X2) Y2)) (((eq nat) X2) Y2)))) of role axiom named fact_115_antisym__conv1
% 0.60/0.78 A new axiom: (forall (X2:nat) (Y2:nat), ((((ord_less_nat X2) Y2)->False)->(((eq Prop) ((ord_less_eq_nat X2) Y2)) (((eq nat) X2) Y2))))
% 0.60/0.78 FOF formula (forall (A:nat) (B:nat), (((ord_less_eq_nat A) B)->((not (((eq nat) A) B))->((ord_less_nat A) B)))) of role axiom named fact_116_le__neq__trans
% 0.60/0.78 A new axiom: (forall (A:nat) (B:nat), (((ord_less_eq_nat A) B)->((not (((eq nat) A) B))->((ord_less_nat A) B))))
% 0.60/0.79 FOF formula (forall (X2:nat) (Y2:nat), (((eq Prop) (((ord_less_nat X2) Y2)->False)) ((ord_less_eq_nat Y2) X2))) of role axiom named fact_117_not__less
% 0.60/0.79 A new axiom: (forall (X2:nat) (Y2:nat), (((eq Prop) (((ord_less_nat X2) Y2)->False)) ((ord_less_eq_nat Y2) X2)))
% 0.60/0.79 FOF formula (forall (X2:nat) (Y2:nat), (((eq Prop) (((ord_less_eq_nat X2) Y2)->False)) ((ord_less_nat Y2) X2))) of role axiom named fact_118_not__le
% 0.60/0.79 A new axiom: (forall (X2:nat) (Y2:nat), (((eq Prop) (((ord_less_eq_nat X2) Y2)->False)) ((ord_less_nat Y2) X2)))
% 0.60/0.79 FOF formula (forall (A:nat) (B:nat) (F:(nat->nat)) (C:nat), (((ord_less_nat A) B)->(((ord_less_eq_nat (F B)) C)->((forall (X4:nat) (Y4:nat), (((ord_less_nat X4) Y4)->((ord_less_nat (F X4)) (F Y4))))->((ord_less_nat (F A)) C))))) of role axiom named fact_119_order__less__le__subst2
% 0.60/0.79 A new axiom: (forall (A:nat) (B:nat) (F:(nat->nat)) (C:nat), (((ord_less_nat A) B)->(((ord_less_eq_nat (F B)) C)->((forall (X4:nat) (Y4:nat), (((ord_less_nat X4) Y4)->((ord_less_nat (F X4)) (F Y4))))->((ord_less_nat (F A)) C)))))
% 0.60/0.79 FOF formula (forall (A:nat) (F:(nat->nat)) (B:nat) (C:nat), (((ord_less_nat A) (F B))->(((ord_less_eq_nat B) C)->((forall (X4:nat) (Y4:nat), (((ord_less_eq_nat X4) Y4)->((ord_less_eq_nat (F X4)) (F Y4))))->((ord_less_nat A) (F C)))))) of role axiom named fact_120_order__less__le__subst1
% 0.60/0.79 A new axiom: (forall (A:nat) (F:(nat->nat)) (B:nat) (C:nat), (((ord_less_nat A) (F B))->(((ord_less_eq_nat B) C)->((forall (X4:nat) (Y4:nat), (((ord_less_eq_nat X4) Y4)->((ord_less_eq_nat (F X4)) (F Y4))))->((ord_less_nat A) (F C))))))
% 0.60/0.79 FOF formula (forall (A:nat) (B:nat) (F:(nat->nat)) (C:nat), (((ord_less_eq_nat A) B)->(((ord_less_nat (F B)) C)->((forall (X4:nat) (Y4:nat), (((ord_less_eq_nat X4) Y4)->((ord_less_eq_nat (F X4)) (F Y4))))->((ord_less_nat (F A)) C))))) of role axiom named fact_121_order__le__less__subst2
% 0.60/0.79 A new axiom: (forall (A:nat) (B:nat) (F:(nat->nat)) (C:nat), (((ord_less_eq_nat A) B)->(((ord_less_nat (F B)) C)->((forall (X4:nat) (Y4:nat), (((ord_less_eq_nat X4) Y4)->((ord_less_eq_nat (F X4)) (F Y4))))->((ord_less_nat (F A)) C)))))
% 0.60/0.79 FOF formula (forall (A:nat) (F:(nat->nat)) (B:nat) (C:nat), (((ord_less_eq_nat A) (F B))->(((ord_less_nat B) C)->((forall (X4:nat) (Y4:nat), (((ord_less_nat X4) Y4)->((ord_less_nat (F X4)) (F Y4))))->((ord_less_nat A) (F C)))))) of role axiom named fact_122_order__le__less__subst1
% 0.60/0.79 A new axiom: (forall (A:nat) (F:(nat->nat)) (B:nat) (C:nat), (((ord_less_eq_nat A) (F B))->(((ord_less_nat B) C)->((forall (X4:nat) (Y4:nat), (((ord_less_nat X4) Y4)->((ord_less_nat (F X4)) (F Y4))))->((ord_less_nat A) (F C))))))
% 0.60/0.79 FOF formula (((eq (nat->(nat->Prop))) ord_less_nat) (fun (X3:nat) (Y3:nat)=> ((and ((ord_less_eq_nat X3) Y3)) (not (((eq nat) X3) Y3))))) of role axiom named fact_123_less__le
% 0.60/0.79 A new axiom: (((eq (nat->(nat->Prop))) ord_less_nat) (fun (X3:nat) (Y3:nat)=> ((and ((ord_less_eq_nat X3) Y3)) (not (((eq nat) X3) Y3)))))
% 0.60/0.79 FOF formula (((eq (nat->(nat->Prop))) ord_less_eq_nat) (fun (X3:nat) (Y3:nat)=> ((or ((ord_less_nat X3) Y3)) (((eq nat) X3) Y3)))) of role axiom named fact_124_le__less
% 0.60/0.79 A new axiom: (((eq (nat->(nat->Prop))) ord_less_eq_nat) (fun (X3:nat) (Y3:nat)=> ((or ((ord_less_nat X3) Y3)) (((eq nat) X3) Y3))))
% 0.60/0.79 FOF formula (forall (X2:nat) (Y2:nat), ((((ord_less_nat X2) Y2)->False)->((ord_less_eq_nat Y2) X2))) of role axiom named fact_125_leI
% 0.60/0.79 A new axiom: (forall (X2:nat) (Y2:nat), ((((ord_less_nat X2) Y2)->False)->((ord_less_eq_nat Y2) X2)))
% 0.60/0.79 FOF formula (forall (Y2:nat) (X2:nat), (((ord_less_eq_nat Y2) X2)->(((ord_less_nat X2) Y2)->False))) of role axiom named fact_126_leD
% 0.60/0.79 A new axiom: (forall (Y2:nat) (X2:nat), (((ord_less_eq_nat Y2) X2)->(((ord_less_nat X2) Y2)->False)))
% 0.60/0.79 FOF formula (forall (Xs:list_nat), ((list_strict_asc_nat Xs)->(forall (J4:nat), (((ord_less_nat J4) (size_size_list_nat Xs))->(forall (I4:nat), (((ord_less_eq_nat I4) J4)->((ord_less_eq_nat ((nth_nat Xs) I4)) ((nth_nat Xs) J4)))))))) of role axiom named fact_127_list__strict__asc__trans__le
% 0.60/0.79 A new axiom: (forall (Xs:list_nat), ((list_strict_asc_nat Xs)->(forall (J4:nat), (((ord_less_nat J4) (size_size_list_nat Xs))->(forall (I4:nat), (((ord_less_eq_nat I4) J4)->((ord_less_eq_nat ((nth_nat Xs) I4)) ((nth_nat Xs) J4))))))))
% 0.60/0.81 FOF formula (((eq (list_nat->Prop)) list_asc_nat) (fun (Xs2:list_nat)=> (forall (J:nat), (((ord_less_nat J) (size_size_list_nat Xs2))->(forall (I2:nat), (((ord_less_eq_nat I2) J)->((ord_less_eq_nat ((nth_nat Xs2) I2)) ((nth_nat Xs2) J)))))))) of role axiom named fact_128_list__asc__trans__le
% 0.60/0.81 A new axiom: (((eq (list_nat->Prop)) list_asc_nat) (fun (Xs2:list_nat)=> (forall (J:nat), (((ord_less_nat J) (size_size_list_nat Xs2))->(forall (I2:nat), (((ord_less_eq_nat I2) J)->((ord_less_eq_nat ((nth_nat Xs2) I2)) ((nth_nat Xs2) J))))))))
% 0.60/0.81 FOF formula (((eq (list_nat->Prop)) list_strict_desc_nat) (fun (Xs2:list_nat)=> (forall (J:nat), (((ord_less_nat J) (size_size_list_nat Xs2))->(forall (I2:nat), (((ord_less_nat I2) J)->((ord_less_nat ((nth_nat Xs2) J)) ((nth_nat Xs2) I2)))))))) of role axiom named fact_129_list__strict__desc__trans
% 0.60/0.81 A new axiom: (((eq (list_nat->Prop)) list_strict_desc_nat) (fun (Xs2:list_nat)=> (forall (J:nat), (((ord_less_nat J) (size_size_list_nat Xs2))->(forall (I2:nat), (((ord_less_nat I2) J)->((ord_less_nat ((nth_nat Xs2) J)) ((nth_nat Xs2) I2))))))))
% 0.60/0.81 FOF formula (((eq (list_nat->Prop)) list_strict_asc_nat) (fun (Xs2:list_nat)=> (forall (J:nat), (((ord_less_nat J) (size_size_list_nat Xs2))->(forall (I2:nat), (((ord_less_nat I2) J)->((ord_less_nat ((nth_nat Xs2) I2)) ((nth_nat Xs2) J)))))))) of role axiom named fact_130_list__strict__asc__trans
% 0.60/0.81 A new axiom: (((eq (list_nat->Prop)) list_strict_asc_nat) (fun (Xs2:list_nat)=> (forall (J:nat), (((ord_less_nat J) (size_size_list_nat Xs2))->(forall (I2:nat), (((ord_less_nat I2) J)->((ord_less_nat ((nth_nat Xs2) I2)) ((nth_nat Xs2) J))))))))
% 0.60/0.81 FOF formula (((eq (list_nat->Prop)) list_asc_nat) (fun (Xs2:list_nat)=> (forall (J:nat), (((ord_less_nat J) (size_size_list_nat Xs2))->(forall (I2:nat), (((ord_less_nat I2) J)->((ord_less_eq_nat ((nth_nat Xs2) I2)) ((nth_nat Xs2) J)))))))) of role axiom named fact_131_list__asc__trans
% 0.60/0.81 A new axiom: (((eq (list_nat->Prop)) list_asc_nat) (fun (Xs2:list_nat)=> (forall (J:nat), (((ord_less_nat J) (size_size_list_nat Xs2))->(forall (I2:nat), (((ord_less_nat I2) J)->((ord_less_eq_nat ((nth_nat Xs2) I2)) ((nth_nat Xs2) J))))))))
% 0.60/0.81 FOF formula (forall (N:nat) (P:(nat->Prop)) (M2:nat), ((forall (K2:nat), (((ord_less_nat N) K2)->(P K2)))->((forall (K2:nat), (((ord_less_eq_nat K2) N)->((forall (I4:nat), (((ord_less_nat K2) I4)->(P I4)))->(P K2))))->(P M2)))) of role axiom named fact_132_nat__descend__induct
% 0.60/0.81 A new axiom: (forall (N:nat) (P:(nat->Prop)) (M2:nat), ((forall (K2:nat), (((ord_less_nat N) K2)->(P K2)))->((forall (K2:nat), (((ord_less_eq_nat K2) N)->((forall (I4:nat), (((ord_less_nat K2) I4)->(P I4)))->(P K2))))->(P M2))))
% 0.60/0.81 FOF formula (forall (A:nat) (B:nat) (P:(nat->Prop)), (((ord_less_nat A) B)->((P A)->(((P B)->False)->((ex nat) (fun (C2:nat)=> ((and ((and ((and ((ord_less_eq_nat A) C2)) ((ord_less_eq_nat C2) B))) (forall (X5:nat), (((and ((ord_less_eq_nat A) X5)) ((ord_less_nat X5) C2))->(P X5))))) (forall (D:nat), ((forall (X4:nat), (((and ((ord_less_eq_nat A) X4)) ((ord_less_nat X4) D))->(P X4)))->((ord_less_eq_nat D) C2)))))))))) of role axiom named fact_133_complete__interval
% 0.60/0.81 A new axiom: (forall (A:nat) (B:nat) (P:(nat->Prop)), (((ord_less_nat A) B)->((P A)->(((P B)->False)->((ex nat) (fun (C2:nat)=> ((and ((and ((and ((ord_less_eq_nat A) C2)) ((ord_less_eq_nat C2) B))) (forall (X5:nat), (((and ((ord_less_eq_nat A) X5)) ((ord_less_nat X5) C2))->(P X5))))) (forall (D:nat), ((forall (X4:nat), (((and ((ord_less_eq_nat A) X4)) ((ord_less_nat X4) D))->(P X4)))->((ord_less_eq_nat D) C2))))))))))
% 0.60/0.81 FOF formula (((eq (nat->(nat->Prop))) ord_less_eq_nat) (fun (N2:nat) (A2:nat)=> (forall (X3:nat), (((ord_less_nat A2) X3)->(not (((eq nat) N2) X3)))))) of role axiom named fact_134_le__greater__neq__conv
% 0.60/0.81 A new axiom: (((eq (nat->(nat->Prop))) ord_less_eq_nat) (fun (N2:nat) (A2:nat)=> (forall (X3:nat), (((ord_less_nat A2) X3)->(not (((eq nat) N2) X3))))))
% 0.60/0.81 FOF formula (((eq (nat->(nat->Prop))) ord_less_nat) (fun (A2:nat) (N2:nat)=> (forall (X3:nat), (((ord_less_eq_nat X3) A2)->(not (((eq nat) N2) X3)))))) of role axiom named fact_135_greater__le__neq__conv
% 0.60/0.82 A new axiom: (((eq (nat->(nat->Prop))) ord_less_nat) (fun (A2:nat) (N2:nat)=> (forall (X3:nat), (((ord_less_eq_nat X3) A2)->(not (((eq nat) N2) X3))))))
% 0.60/0.82 FOF formula (((eq (nat->(nat->Prop))) ord_less_nat) (fun (N2:nat) (A2:nat)=> (forall (X3:nat), (((ord_less_eq_nat A2) X3)->(not (((eq nat) N2) X3)))))) of role axiom named fact_136_less__ge__neq__conv
% 0.60/0.82 A new axiom: (((eq (nat->(nat->Prop))) ord_less_nat) (fun (N2:nat) (A2:nat)=> (forall (X3:nat), (((ord_less_eq_nat A2) X3)->(not (((eq nat) N2) X3))))))
% 0.60/0.82 FOF formula (forall (Xs:list_nat), ((list_strict_asc_nat Xs)->(list_asc_nat Xs))) of role axiom named fact_137_list__strict__asc__imp__list__asc
% 0.60/0.82 A new axiom: (forall (Xs:list_nat), ((list_strict_asc_nat Xs)->(list_asc_nat Xs)))
% 0.60/0.82 FOF formula (forall (Xs:list_nat), ((list_strict_desc_nat Xs)->(list_desc_nat Xs))) of role axiom named fact_138_list__strict__desc__imp__list__desc
% 0.60/0.82 A new axiom: (forall (Xs:list_nat), ((list_strict_desc_nat Xs)->(list_desc_nat Xs)))
% 0.60/0.82 FOF formula (((eq (nat->(nat->Prop))) ord_less_eq_nat) (fun (A2:nat) (N2:nat)=> (forall (X3:nat), (((ord_less_nat X3) A2)->(not (((eq nat) N2) X3)))))) of role axiom named fact_139_ge__less__neq__conv
% 0.60/0.82 A new axiom: (((eq (nat->(nat->Prop))) ord_less_eq_nat) (fun (A2:nat) (N2:nat)=> (forall (X3:nat), (((ord_less_nat X3) A2)->(not (((eq nat) N2) X3))))))
% 0.60/0.82 FOF formula (forall (T:nat), ((ex nat) (fun (Z3:nat)=> (forall (X5:nat), (((ord_less_nat X5) Z3)->(((ord_less_eq_nat T) X5)->False)))))) of role axiom named fact_140_minf_I8_J
% 0.60/0.82 A new axiom: (forall (T:nat), ((ex nat) (fun (Z3:nat)=> (forall (X5:nat), (((ord_less_nat X5) Z3)->(((ord_less_eq_nat T) X5)->False))))))
% 0.60/0.82 FOF formula (forall (T:nat), ((ex nat) (fun (Z3:nat)=> (forall (X5:nat), (((ord_less_nat X5) Z3)->((ord_less_eq_nat X5) T)))))) of role axiom named fact_141_minf_I6_J
% 0.60/0.82 A new axiom: (forall (T:nat), ((ex nat) (fun (Z3:nat)=> (forall (X5:nat), (((ord_less_nat X5) Z3)->((ord_less_eq_nat X5) T))))))
% 0.60/0.82 FOF formula (forall (T:nat), ((ex nat) (fun (Z3:nat)=> (forall (X5:nat), (((ord_less_nat Z3) X5)->((ord_less_eq_nat T) X5)))))) of role axiom named fact_142_pinf_I8_J
% 0.60/0.82 A new axiom: (forall (T:nat), ((ex nat) (fun (Z3:nat)=> (forall (X5:nat), (((ord_less_nat Z3) X5)->((ord_less_eq_nat T) X5))))))
% 0.60/0.82 FOF formula (forall (P:(nat->Prop)) (P4:(nat->Prop)) (Q:(nat->Prop)) (Q2:(nat->Prop)), (((ex nat) (fun (Z4:nat)=> (forall (X4:nat), (((ord_less_nat Z4) X4)->(((eq Prop) (P X4)) (P4 X4))))))->(((ex nat) (fun (Z4:nat)=> (forall (X4:nat), (((ord_less_nat Z4) X4)->(((eq Prop) (Q X4)) (Q2 X4))))))->((ex nat) (fun (Z3:nat)=> (forall (X5:nat), (((ord_less_nat Z3) X5)->(((eq Prop) ((and (P X5)) (Q X5))) ((and (P4 X5)) (Q2 X5)))))))))) of role axiom named fact_143_pinf_I1_J
% 0.60/0.82 A new axiom: (forall (P:(nat->Prop)) (P4:(nat->Prop)) (Q:(nat->Prop)) (Q2:(nat->Prop)), (((ex nat) (fun (Z4:nat)=> (forall (X4:nat), (((ord_less_nat Z4) X4)->(((eq Prop) (P X4)) (P4 X4))))))->(((ex nat) (fun (Z4:nat)=> (forall (X4:nat), (((ord_less_nat Z4) X4)->(((eq Prop) (Q X4)) (Q2 X4))))))->((ex nat) (fun (Z3:nat)=> (forall (X5:nat), (((ord_less_nat Z3) X5)->(((eq Prop) ((and (P X5)) (Q X5))) ((and (P4 X5)) (Q2 X5))))))))))
% 0.60/0.82 FOF formula (forall (P:(nat->Prop)) (P4:(nat->Prop)) (Q:(nat->Prop)) (Q2:(nat->Prop)), (((ex nat) (fun (Z4:nat)=> (forall (X4:nat), (((ord_less_nat Z4) X4)->(((eq Prop) (P X4)) (P4 X4))))))->(((ex nat) (fun (Z4:nat)=> (forall (X4:nat), (((ord_less_nat Z4) X4)->(((eq Prop) (Q X4)) (Q2 X4))))))->((ex nat) (fun (Z3:nat)=> (forall (X5:nat), (((ord_less_nat Z3) X5)->(((eq Prop) ((or (P X5)) (Q X5))) ((or (P4 X5)) (Q2 X5)))))))))) of role axiom named fact_144_pinf_I2_J
% 0.60/0.82 A new axiom: (forall (P:(nat->Prop)) (P4:(nat->Prop)) (Q:(nat->Prop)) (Q2:(nat->Prop)), (((ex nat) (fun (Z4:nat)=> (forall (X4:nat), (((ord_less_nat Z4) X4)->(((eq Prop) (P X4)) (P4 X4))))))->(((ex nat) (fun (Z4:nat)=> (forall (X4:nat), (((ord_less_nat Z4) X4)->(((eq Prop) (Q X4)) (Q2 X4))))))->((ex nat) (fun (Z3:nat)=> (forall (X5:nat), (((ord_less_nat Z3) X5)->(((eq Prop) ((or (P X5)) (Q X5))) ((or (P4 X5)) (Q2 X5))))))))))
% 0.60/0.83 FOF formula (forall (T:nat), ((ex nat) (fun (Z3:nat)=> (forall (X5:nat), (((ord_less_nat Z3) X5)->(not (((eq nat) X5) T))))))) of role axiom named fact_145_pinf_I3_J
% 0.60/0.83 A new axiom: (forall (T:nat), ((ex nat) (fun (Z3:nat)=> (forall (X5:nat), (((ord_less_nat Z3) X5)->(not (((eq nat) X5) T)))))))
% 0.60/0.83 FOF formula (forall (T:nat), ((ex nat) (fun (Z3:nat)=> (forall (X5:nat), (((ord_less_nat Z3) X5)->(not (((eq nat) X5) T))))))) of role axiom named fact_146_pinf_I4_J
% 0.60/0.83 A new axiom: (forall (T:nat), ((ex nat) (fun (Z3:nat)=> (forall (X5:nat), (((ord_less_nat Z3) X5)->(not (((eq nat) X5) T)))))))
% 0.60/0.83 FOF formula (forall (T:nat), ((ex nat) (fun (Z3:nat)=> (forall (X5:nat), (((ord_less_nat Z3) X5)->(((ord_less_nat X5) T)->False)))))) of role axiom named fact_147_pinf_I5_J
% 0.60/0.83 A new axiom: (forall (T:nat), ((ex nat) (fun (Z3:nat)=> (forall (X5:nat), (((ord_less_nat Z3) X5)->(((ord_less_nat X5) T)->False))))))
% 0.60/0.83 FOF formula (forall (T:nat), ((ex nat) (fun (Z3:nat)=> (forall (X5:nat), (((ord_less_nat Z3) X5)->((ord_less_nat T) X5)))))) of role axiom named fact_148_pinf_I7_J
% 0.60/0.83 A new axiom: (forall (T:nat), ((ex nat) (fun (Z3:nat)=> (forall (X5:nat), (((ord_less_nat Z3) X5)->((ord_less_nat T) X5))))))
% 0.60/0.83 FOF formula (forall (P:(nat->Prop)) (P4:(nat->Prop)) (Q:(nat->Prop)) (Q2:(nat->Prop)), (((ex nat) (fun (Z4:nat)=> (forall (X4:nat), (((ord_less_nat X4) Z4)->(((eq Prop) (P X4)) (P4 X4))))))->(((ex nat) (fun (Z4:nat)=> (forall (X4:nat), (((ord_less_nat X4) Z4)->(((eq Prop) (Q X4)) (Q2 X4))))))->((ex nat) (fun (Z3:nat)=> (forall (X5:nat), (((ord_less_nat X5) Z3)->(((eq Prop) ((and (P X5)) (Q X5))) ((and (P4 X5)) (Q2 X5)))))))))) of role axiom named fact_149_minf_I1_J
% 0.60/0.83 A new axiom: (forall (P:(nat->Prop)) (P4:(nat->Prop)) (Q:(nat->Prop)) (Q2:(nat->Prop)), (((ex nat) (fun (Z4:nat)=> (forall (X4:nat), (((ord_less_nat X4) Z4)->(((eq Prop) (P X4)) (P4 X4))))))->(((ex nat) (fun (Z4:nat)=> (forall (X4:nat), (((ord_less_nat X4) Z4)->(((eq Prop) (Q X4)) (Q2 X4))))))->((ex nat) (fun (Z3:nat)=> (forall (X5:nat), (((ord_less_nat X5) Z3)->(((eq Prop) ((and (P X5)) (Q X5))) ((and (P4 X5)) (Q2 X5))))))))))
% 0.60/0.83 FOF formula (forall (P:(nat->Prop)) (P4:(nat->Prop)) (Q:(nat->Prop)) (Q2:(nat->Prop)), (((ex nat) (fun (Z4:nat)=> (forall (X4:nat), (((ord_less_nat X4) Z4)->(((eq Prop) (P X4)) (P4 X4))))))->(((ex nat) (fun (Z4:nat)=> (forall (X4:nat), (((ord_less_nat X4) Z4)->(((eq Prop) (Q X4)) (Q2 X4))))))->((ex nat) (fun (Z3:nat)=> (forall (X5:nat), (((ord_less_nat X5) Z3)->(((eq Prop) ((or (P X5)) (Q X5))) ((or (P4 X5)) (Q2 X5)))))))))) of role axiom named fact_150_minf_I2_J
% 0.60/0.83 A new axiom: (forall (P:(nat->Prop)) (P4:(nat->Prop)) (Q:(nat->Prop)) (Q2:(nat->Prop)), (((ex nat) (fun (Z4:nat)=> (forall (X4:nat), (((ord_less_nat X4) Z4)->(((eq Prop) (P X4)) (P4 X4))))))->(((ex nat) (fun (Z4:nat)=> (forall (X4:nat), (((ord_less_nat X4) Z4)->(((eq Prop) (Q X4)) (Q2 X4))))))->((ex nat) (fun (Z3:nat)=> (forall (X5:nat), (((ord_less_nat X5) Z3)->(((eq Prop) ((or (P X5)) (Q X5))) ((or (P4 X5)) (Q2 X5))))))))))
% 0.60/0.83 FOF formula (forall (T:nat), ((ex nat) (fun (Z3:nat)=> (forall (X5:nat), (((ord_less_nat X5) Z3)->(not (((eq nat) X5) T))))))) of role axiom named fact_151_minf_I3_J
% 0.60/0.83 A new axiom: (forall (T:nat), ((ex nat) (fun (Z3:nat)=> (forall (X5:nat), (((ord_less_nat X5) Z3)->(not (((eq nat) X5) T)))))))
% 0.60/0.83 FOF formula (forall (T:nat), ((ex nat) (fun (Z3:nat)=> (forall (X5:nat), (((ord_less_nat X5) Z3)->(not (((eq nat) X5) T))))))) of role axiom named fact_152_minf_I4_J
% 0.60/0.83 A new axiom: (forall (T:nat), ((ex nat) (fun (Z3:nat)=> (forall (X5:nat), (((ord_less_nat X5) Z3)->(not (((eq nat) X5) T)))))))
% 0.60/0.83 FOF formula (forall (T:nat), ((ex nat) (fun (Z3:nat)=> (forall (X5:nat), (((ord_less_nat X5) Z3)->((ord_less_nat X5) T)))))) of role axiom named fact_153_minf_I5_J
% 0.60/0.83 A new axiom: (forall (T:nat), ((ex nat) (fun (Z3:nat)=> (forall (X5:nat), (((ord_less_nat X5) Z3)->((ord_less_nat X5) T))))))
% 0.60/0.83 FOF formula (forall (T:nat), ((ex nat) (fun (Z3:nat)=> (forall (X5:nat), (((ord_less_nat X5) Z3)->(((ord_less_nat T) X5)->False)))))) of role axiom named fact_154_minf_I7_J
% 0.66/0.84 A new axiom: (forall (T:nat), ((ex nat) (fun (Z3:nat)=> (forall (X5:nat), (((ord_less_nat X5) Z3)->(((ord_less_nat T) X5)->False))))))
% 0.66/0.84 FOF formula (forall (T:nat), ((ex nat) (fun (Z3:nat)=> (forall (X5:nat), (((ord_less_nat Z3) X5)->(((ord_less_eq_nat X5) T)->False)))))) of role axiom named fact_155_pinf_I6_J
% 0.66/0.84 A new axiom: (forall (T:nat), ((ex nat) (fun (Z3:nat)=> (forall (X5:nat), (((ord_less_nat Z3) X5)->(((ord_less_eq_nat X5) T)->False))))))
% 0.66/0.84 FOF formula (forall (B4:nat) (A4:nat), (((eq Prop) (((ord_less_eq_nat B4) A4)->False)) ((ord_less_nat A4) B4))) of role axiom named fact_156_verit__comp__simplify1_I3_J
% 0.66/0.84 A new axiom: (forall (B4:nat) (A4:nat), (((eq Prop) (((ord_less_eq_nat B4) A4)->False)) ((ord_less_nat A4) B4)))
% 0.66/0.84 FOF formula (((eq (list_nat->Prop)) linorder_sorted_nat) (fun (Xs2:list_nat)=> (forall (I2:nat) (J:nat), (((ord_less_eq_nat I2) J)->(((ord_less_nat J) (size_size_list_nat Xs2))->((ord_less_eq_nat ((nth_nat Xs2) I2)) ((nth_nat Xs2) J))))))) of role axiom named fact_157_sorted__iff__nth__mono
% 0.66/0.84 A new axiom: (((eq (list_nat->Prop)) linorder_sorted_nat) (fun (Xs2:list_nat)=> (forall (I2:nat) (J:nat), (((ord_less_eq_nat I2) J)->(((ord_less_nat J) (size_size_list_nat Xs2))->((ord_less_eq_nat ((nth_nat Xs2) I2)) ((nth_nat Xs2) J)))))))
% 0.66/0.84 FOF formula (forall (Xs:list_nat) (I3:nat) (J2:nat), ((linorder_sorted_nat Xs)->(((ord_less_eq_nat I3) J2)->(((ord_less_nat J2) (size_size_list_nat Xs))->((ord_less_eq_nat ((nth_nat Xs) I3)) ((nth_nat Xs) J2)))))) of role axiom named fact_158_sorted__nth__mono
% 0.66/0.84 A new axiom: (forall (Xs:list_nat) (I3:nat) (J2:nat), ((linorder_sorted_nat Xs)->(((ord_less_eq_nat I3) J2)->(((ord_less_nat J2) (size_size_list_nat Xs))->((ord_less_eq_nat ((nth_nat Xs) I3)) ((nth_nat Xs) J2))))))
% 0.66/0.84 FOF formula (((eq (list_nat->Prop)) list_asc_nat) linorder_sorted_nat) of role axiom named fact_159_list__ord__le__sorted__eq
% 0.66/0.84 A new axiom: (((eq (list_nat->Prop)) list_asc_nat) linorder_sorted_nat)
% 0.66/0.84 FOF formula (forall (A:nat) (B:nat), ((or ((or (((eq nat) A) B)) (((ord_less_eq_nat A) B)->False))) (((ord_less_eq_nat B) A)->False))) of role axiom named fact_160_verit__la__disequality
% 0.66/0.84 A new axiom: (forall (A:nat) (B:nat), ((or ((or (((eq nat) A) B)) (((ord_less_eq_nat A) B)->False))) (((ord_less_eq_nat B) A)->False)))
% 0.66/0.84 FOF formula (forall (A:nat), (((ord_less_nat A) A)->False)) of role axiom named fact_161_verit__comp__simplify1_I1_J
% 0.66/0.84 A new axiom: (forall (A:nat), (((ord_less_nat A) A)->False))
% 0.66/0.84 FOF formula (((eq (list_nat->Prop)) linorder_sorted_nat) (fun (Xs2:list_nat)=> (forall (I2:nat) (J:nat), (((ord_less_nat I2) J)->(((ord_less_nat J) (size_size_list_nat Xs2))->((ord_less_eq_nat ((nth_nat Xs2) I2)) ((nth_nat Xs2) J))))))) of role axiom named fact_162_sorted__iff__nth__mono__less
% 0.66/0.84 A new axiom: (((eq (list_nat->Prop)) linorder_sorted_nat) (fun (Xs2:list_nat)=> (forall (I2:nat) (J:nat), (((ord_less_nat I2) J)->(((ord_less_nat J) (size_size_list_nat Xs2))->((ord_less_eq_nat ((nth_nat Xs2) I2)) ((nth_nat Xs2) J)))))))
% 0.66/0.84 FOF formula (forall (Xs:list_nat) (I3:nat) (J2:nat), ((linorder_sorted_nat (rev_nat Xs))->(((ord_less_eq_nat I3) J2)->(((ord_less_nat J2) (size_size_list_nat Xs))->((ord_less_eq_nat ((nth_nat Xs) J2)) ((nth_nat Xs) I3)))))) of role axiom named fact_163_sorted__rev__nth__mono
% 0.66/0.84 A new axiom: (forall (Xs:list_nat) (I3:nat) (J2:nat), ((linorder_sorted_nat (rev_nat Xs))->(((ord_less_eq_nat I3) J2)->(((ord_less_nat J2) (size_size_list_nat Xs))->((ord_less_eq_nat ((nth_nat Xs) J2)) ((nth_nat Xs) I3))))))
% 0.66/0.84 FOF formula (forall (Xs:list_nat), (((eq Prop) (linorder_sorted_nat (rev_nat Xs))) (forall (I2:nat) (J:nat), (((ord_less_eq_nat I2) J)->(((ord_less_nat J) (size_size_list_nat Xs))->((ord_less_eq_nat ((nth_nat Xs) J)) ((nth_nat Xs) I2))))))) of role axiom named fact_164_sorted__rev__iff__nth__mono
% 0.66/0.84 A new axiom: (forall (Xs:list_nat), (((eq Prop) (linorder_sorted_nat (rev_nat Xs))) (forall (I2:nat) (J:nat), (((ord_less_eq_nat I2) J)->(((ord_less_nat J) (size_size_list_nat Xs))->((ord_less_eq_nat ((nth_nat Xs) J)) ((nth_nat Xs) I2)))))))
% 0.66/0.84 FOF formula (((eq (list_nat->Prop)) linorder_sorted_nat) (fun (Xs2:list_nat)=> (forall (I2:nat), (((ord_less_nat (suc I2)) (size_size_list_nat Xs2))->((ord_less_eq_nat ((nth_nat Xs2) I2)) ((nth_nat Xs2) (suc I2))))))) of role axiom named fact_165_sorted__iff__nth__Suc
% 0.66/0.85 A new axiom: (((eq (list_nat->Prop)) linorder_sorted_nat) (fun (Xs2:list_nat)=> (forall (I2:nat), (((ord_less_nat (suc I2)) (size_size_list_nat Xs2))->((ord_less_eq_nat ((nth_nat Xs2) I2)) ((nth_nat Xs2) (suc I2)))))))
% 0.66/0.85 FOF formula (forall (Nat:nat) (Nat2:nat), (((eq Prop) (((eq nat) (suc Nat)) (suc Nat2))) (((eq nat) Nat) Nat2))) of role axiom named fact_166_old_Onat_Oinject
% 0.66/0.85 A new axiom: (forall (Nat:nat) (Nat2:nat), (((eq Prop) (((eq nat) (suc Nat)) (suc Nat2))) (((eq nat) Nat) Nat2)))
% 0.66/0.85 FOF formula (forall (X22:nat) (Y22:nat), (((eq Prop) (((eq nat) (suc X22)) (suc Y22))) (((eq nat) X22) Y22))) of role axiom named fact_167_nat_Oinject
% 0.66/0.85 A new axiom: (forall (X22:nat) (Y22:nat), (((eq Prop) (((eq nat) (suc X22)) (suc Y22))) (((eq nat) X22) Y22)))
% 0.66/0.85 FOF formula (forall (Xs:list_nat) (Ys:list_nat), (((eq Prop) (((eq list_nat) (rev_nat Xs)) (rev_nat Ys))) (((eq list_nat) Xs) Ys))) of role axiom named fact_168_rev__is__rev__conv
% 0.66/0.85 A new axiom: (forall (Xs:list_nat) (Ys:list_nat), (((eq Prop) (((eq list_nat) (rev_nat Xs)) (rev_nat Ys))) (((eq list_nat) Xs) Ys)))
% 0.66/0.85 FOF formula (forall (Xs:list_a) (Ys:list_a), (((eq Prop) (((eq list_a) (rev_a Xs)) (rev_a Ys))) (((eq list_a) Xs) Ys))) of role axiom named fact_169_rev__is__rev__conv
% 0.66/0.85 A new axiom: (forall (Xs:list_a) (Ys:list_a), (((eq Prop) (((eq list_a) (rev_a Xs)) (rev_a Ys))) (((eq list_a) Xs) Ys)))
% 0.66/0.85 FOF formula (forall (Xs:list_nat), (((eq list_nat) (rev_nat (rev_nat Xs))) Xs)) of role axiom named fact_170_rev__rev__ident
% 0.66/0.85 A new axiom: (forall (Xs:list_nat), (((eq list_nat) (rev_nat (rev_nat Xs))) Xs))
% 0.66/0.85 FOF formula (forall (Xs:list_a), (((eq list_a) (rev_a (rev_a Xs))) Xs)) of role axiom named fact_171_rev__rev__ident
% 0.66/0.85 A new axiom: (forall (Xs:list_a), (((eq list_a) (rev_a (rev_a Xs))) Xs))
% 0.66/0.85 FOF formula (forall (M2:nat) (N:nat), (((eq Prop) ((ord_less_nat (suc M2)) (suc N))) ((ord_less_nat M2) N))) of role axiom named fact_172_Suc__less__eq
% 0.66/0.85 A new axiom: (forall (M2:nat) (N:nat), (((eq Prop) ((ord_less_nat (suc M2)) (suc N))) ((ord_less_nat M2) N)))
% 0.66/0.85 FOF formula (forall (M2:nat) (N:nat), (((ord_less_nat M2) N)->((ord_less_nat (suc M2)) (suc N)))) of role axiom named fact_173_Suc__mono
% 0.66/0.85 A new axiom: (forall (M2:nat) (N:nat), (((ord_less_nat M2) N)->((ord_less_nat (suc M2)) (suc N))))
% 0.66/0.85 FOF formula (forall (N:nat), ((ord_less_nat N) (suc N))) of role axiom named fact_174_lessI
% 0.66/0.85 A new axiom: (forall (N:nat), ((ord_less_nat N) (suc N)))
% 0.66/0.85 FOF formula (forall (N:nat) (M2:nat), (((eq Prop) ((ord_less_eq_nat (suc N)) (suc M2))) ((ord_less_eq_nat N) M2))) of role axiom named fact_175_Suc__le__mono
% 0.66/0.85 A new axiom: (forall (N:nat) (M2:nat), (((eq Prop) ((ord_less_eq_nat (suc N)) (suc M2))) ((ord_less_eq_nat N) M2)))
% 0.66/0.85 FOF formula (forall (Xs:list_a), (((eq nat) (size_size_list_a (rev_a Xs))) (size_size_list_a Xs))) of role axiom named fact_176_length__rev
% 0.66/0.85 A new axiom: (forall (Xs:list_a), (((eq nat) (size_size_list_a (rev_a Xs))) (size_size_list_a Xs)))
% 0.66/0.85 FOF formula (forall (Xs:list_nat), (((eq nat) (size_size_list_nat (rev_nat Xs))) (size_size_list_nat Xs))) of role axiom named fact_177_length__rev
% 0.66/0.85 A new axiom: (forall (Xs:list_nat), (((eq nat) (size_size_list_nat (rev_nat Xs))) (size_size_list_nat Xs)))
% 0.66/0.85 FOF formula (forall (M2:nat) (N:nat), (((ord_less_eq_nat (suc M2)) N)->((ord_less_eq_nat M2) N))) of role axiom named fact_178_Suc__leD
% 0.66/0.85 A new axiom: (forall (M2:nat) (N:nat), (((ord_less_eq_nat (suc M2)) N)->((ord_less_eq_nat M2) N)))
% 0.66/0.85 FOF formula (forall (M2:nat) (N:nat), (((ord_less_eq_nat M2) (suc N))->((((ord_less_eq_nat M2) N)->False)->(((eq nat) M2) (suc N))))) of role axiom named fact_179_le__SucE
% 0.66/0.85 A new axiom: (forall (M2:nat) (N:nat), (((ord_less_eq_nat M2) (suc N))->((((ord_less_eq_nat M2) N)->False)->(((eq nat) M2) (suc N)))))
% 0.66/0.85 FOF formula (forall (M2:nat) (N:nat), (((ord_less_eq_nat M2) N)->((ord_less_eq_nat M2) (suc N)))) of role axiom named fact_180_le__SucI
% 0.66/0.85 A new axiom: (forall (M2:nat) (N:nat), (((ord_less_eq_nat M2) N)->((ord_less_eq_nat M2) (suc N))))
% 0.69/0.86 FOF formula (forall (N:nat) (M4:nat), (((ord_less_eq_nat (suc N)) M4)->((ex nat) (fun (M5:nat)=> (((eq nat) M4) (suc M5)))))) of role axiom named fact_181_Suc__le__D
% 0.69/0.86 A new axiom: (forall (N:nat) (M4:nat), (((ord_less_eq_nat (suc N)) M4)->((ex nat) (fun (M5:nat)=> (((eq nat) M4) (suc M5))))))
% 0.69/0.86 FOF formula (forall (M2:nat) (N:nat), (((eq Prop) ((ord_less_eq_nat M2) (suc N))) ((or ((ord_less_eq_nat M2) N)) (((eq nat) M2) (suc N))))) of role axiom named fact_182_le__Suc__eq
% 0.69/0.86 A new axiom: (forall (M2:nat) (N:nat), (((eq Prop) ((ord_less_eq_nat M2) (suc N))) ((or ((ord_less_eq_nat M2) N)) (((eq nat) M2) (suc N)))))
% 0.69/0.86 FOF formula (forall (N:nat), (((ord_less_eq_nat (suc N)) N)->False)) of role axiom named fact_183_Suc__n__not__le__n
% 0.69/0.86 A new axiom: (forall (N:nat), (((ord_less_eq_nat (suc N)) N)->False))
% 0.69/0.86 FOF formula (forall (M2:nat) (N:nat), (((eq Prop) (((ord_less_eq_nat M2) N)->False)) ((ord_less_eq_nat (suc N)) M2))) of role axiom named fact_184_not__less__eq__eq
% 0.69/0.86 A new axiom: (forall (M2:nat) (N:nat), (((eq Prop) (((ord_less_eq_nat M2) N)->False)) ((ord_less_eq_nat (suc N)) M2)))
% 0.69/0.86 FOF formula (forall (P:(nat->Prop)) (N:nat), ((forall (N3:nat), ((forall (M3:nat), (((ord_less_eq_nat (suc M3)) N3)->(P M3)))->(P N3)))->(P N))) of role axiom named fact_185_full__nat__induct
% 0.69/0.86 A new axiom: (forall (P:(nat->Prop)) (N:nat), ((forall (N3:nat), ((forall (M3:nat), (((ord_less_eq_nat (suc M3)) N3)->(P M3)))->(P N3)))->(P N)))
% 0.69/0.86 FOF formula (forall (M2:nat) (N:nat) (P:(nat->Prop)), (((ord_less_eq_nat M2) N)->((P M2)->((forall (N3:nat), (((ord_less_eq_nat M2) N3)->((P N3)->(P (suc N3)))))->(P N))))) of role axiom named fact_186_nat__induct__at__least
% 0.69/0.86 A new axiom: (forall (M2:nat) (N:nat) (P:(nat->Prop)), (((ord_less_eq_nat M2) N)->((P M2)->((forall (N3:nat), (((ord_less_eq_nat M2) N3)->((P N3)->(P (suc N3)))))->(P N)))))
% 0.69/0.86 FOF formula (forall (M2:nat) (N:nat) (R:(nat->(nat->Prop))), (((ord_less_eq_nat M2) N)->((forall (X4:nat), ((R X4) X4))->((forall (X4:nat) (Y4:nat) (Z3:nat), (((R X4) Y4)->(((R Y4) Z3)->((R X4) Z3))))->((forall (N3:nat), ((R N3) (suc N3)))->((R M2) N)))))) of role axiom named fact_187_transitive__stepwise__le
% 0.69/0.86 A new axiom: (forall (M2:nat) (N:nat) (R:(nat->(nat->Prop))), (((ord_less_eq_nat M2) N)->((forall (X4:nat), ((R X4) X4))->((forall (X4:nat) (Y4:nat) (Z3:nat), (((R X4) Y4)->(((R Y4) Z3)->((R X4) Z3))))->((forall (N3:nat), ((R N3) (suc N3)))->((R M2) N))))))
% 0.69/0.86 FOF formula (forall (N:nat), (not (((eq nat) N) (suc N)))) of role axiom named fact_188_n__not__Suc__n
% 0.69/0.86 A new axiom: (forall (N:nat), (not (((eq nat) N) (suc N))))
% 0.69/0.86 FOF formula (forall (X2:nat) (Y2:nat), ((((eq nat) (suc X2)) (suc Y2))->(((eq nat) X2) Y2))) of role axiom named fact_189_Suc__inject
% 0.69/0.86 A new axiom: (forall (X2:nat) (Y2:nat), ((((eq nat) (suc X2)) (suc Y2))->(((eq nat) X2) Y2)))
% 0.69/0.86 FOF formula (forall (Xs:list_nat) (Ys:list_nat), (((eq Prop) (((eq list_nat) (rev_nat Xs)) Ys)) (((eq list_nat) Xs) (rev_nat Ys)))) of role axiom named fact_190_rev__swap
% 0.69/0.86 A new axiom: (forall (Xs:list_nat) (Ys:list_nat), (((eq Prop) (((eq list_nat) (rev_nat Xs)) Ys)) (((eq list_nat) Xs) (rev_nat Ys))))
% 0.69/0.86 FOF formula (forall (Xs:list_a) (Ys:list_a), (((eq Prop) (((eq list_a) (rev_a Xs)) Ys)) (((eq list_a) Xs) (rev_a Ys)))) of role axiom named fact_191_rev__swap
% 0.69/0.86 A new axiom: (forall (Xs:list_a) (Ys:list_a), (((eq Prop) (((eq list_a) (rev_a Xs)) Ys)) (((eq list_a) Xs) (rev_a Ys))))
% 0.69/0.86 FOF formula (forall (N:nat) (M2:nat), ((((ord_less_nat N) M2)->False)->(((eq Prop) ((ord_less_nat N) (suc M2))) (((eq nat) N) M2)))) of role axiom named fact_192_not__less__less__Suc__eq
% 0.69/0.86 A new axiom: (forall (N:nat) (M2:nat), ((((ord_less_nat N) M2)->False)->(((eq Prop) ((ord_less_nat N) (suc M2))) (((eq nat) N) M2))))
% 0.69/0.86 FOF formula (forall (I3:nat) (J2:nat) (P:(nat->Prop)), (((ord_less_nat I3) J2)->((forall (_TPTP_I:nat), ((((eq nat) J2) (suc _TPTP_I))->(P _TPTP_I)))->((forall (_TPTP_I:nat), (((ord_less_nat _TPTP_I) J2)->((P (suc _TPTP_I))->(P _TPTP_I))))->(P I3))))) of role axiom named fact_193_strict__inc__induct
% 0.69/0.86 A new axiom: (forall (I3:nat) (J2:nat) (P:(nat->Prop)), (((ord_less_nat I3) J2)->((forall (_TPTP_I:nat), ((((eq nat) J2) (suc _TPTP_I))->(P _TPTP_I)))->((forall (_TPTP_I:nat), (((ord_less_nat _TPTP_I) J2)->((P (suc _TPTP_I))->(P _TPTP_I))))->(P I3)))))
% 0.69/0.87 FOF formula (forall (I3:nat) (J2:nat) (P:(nat->(nat->Prop))), (((ord_less_nat I3) J2)->((forall (_TPTP_I:nat), ((P _TPTP_I) (suc _TPTP_I)))->((forall (_TPTP_I:nat) (J3:nat) (K2:nat), (((ord_less_nat _TPTP_I) J3)->(((ord_less_nat J3) K2)->(((P _TPTP_I) J3)->(((P J3) K2)->((P _TPTP_I) K2))))))->((P I3) J2))))) of role axiom named fact_194_less__Suc__induct
% 0.69/0.87 A new axiom: (forall (I3:nat) (J2:nat) (P:(nat->(nat->Prop))), (((ord_less_nat I3) J2)->((forall (_TPTP_I:nat), ((P _TPTP_I) (suc _TPTP_I)))->((forall (_TPTP_I:nat) (J3:nat) (K2:nat), (((ord_less_nat _TPTP_I) J3)->(((ord_less_nat J3) K2)->(((P _TPTP_I) J3)->(((P J3) K2)->((P _TPTP_I) K2))))))->((P I3) J2)))))
% 0.69/0.87 FOF formula (forall (I3:nat) (J2:nat) (K:nat), (((ord_less_nat I3) J2)->(((ord_less_nat J2) K)->((ord_less_nat (suc I3)) K)))) of role axiom named fact_195_less__trans__Suc
% 0.69/0.87 A new axiom: (forall (I3:nat) (J2:nat) (K:nat), (((ord_less_nat I3) J2)->(((ord_less_nat J2) K)->((ord_less_nat (suc I3)) K))))
% 0.69/0.87 FOF formula (forall (M2:nat) (N:nat), (((ord_less_nat (suc M2)) (suc N))->((ord_less_nat M2) N))) of role axiom named fact_196_Suc__less__SucD
% 0.69/0.87 A new axiom: (forall (M2:nat) (N:nat), (((ord_less_nat (suc M2)) (suc N))->((ord_less_nat M2) N)))
% 0.69/0.87 FOF formula (forall (N:nat) (M2:nat), ((((ord_less_nat N) M2)->False)->(((ord_less_nat N) (suc M2))->(((eq nat) M2) N)))) of role axiom named fact_197_less__antisym
% 0.69/0.87 A new axiom: (forall (N:nat) (M2:nat), ((((ord_less_nat N) M2)->False)->(((ord_less_nat N) (suc M2))->(((eq nat) M2) N))))
% 0.69/0.87 FOF formula (forall (N:nat) (M2:nat), (((eq Prop) ((ord_less_nat (suc N)) M2)) ((ex nat) (fun (M6:nat)=> ((and (((eq nat) M2) (suc M6))) ((ord_less_nat N) M6)))))) of role axiom named fact_198_Suc__less__eq2
% 0.69/0.87 A new axiom: (forall (N:nat) (M2:nat), (((eq Prop) ((ord_less_nat (suc N)) M2)) ((ex nat) (fun (M6:nat)=> ((and (((eq nat) M2) (suc M6))) ((ord_less_nat N) M6))))))
% 0.69/0.87 FOF formula (forall (N:nat) (P:(nat->Prop)), (((eq Prop) (forall (I2:nat), (((ord_less_nat I2) (suc N))->(P I2)))) ((and (P N)) (forall (I2:nat), (((ord_less_nat I2) N)->(P I2)))))) of role axiom named fact_199_All__less__Suc
% 0.69/0.87 A new axiom: (forall (N:nat) (P:(nat->Prop)), (((eq Prop) (forall (I2:nat), (((ord_less_nat I2) (suc N))->(P I2)))) ((and (P N)) (forall (I2:nat), (((ord_less_nat I2) N)->(P I2))))))
% 0.69/0.87 FOF formula (forall (M2:nat) (N:nat), (((eq Prop) (((ord_less_nat M2) N)->False)) ((ord_less_nat N) (suc M2)))) of role axiom named fact_200_not__less__eq
% 0.69/0.87 A new axiom: (forall (M2:nat) (N:nat), (((eq Prop) (((ord_less_nat M2) N)->False)) ((ord_less_nat N) (suc M2))))
% 0.69/0.87 FOF formula (forall (M2:nat) (N:nat), (((eq Prop) ((ord_less_nat M2) (suc N))) ((or ((ord_less_nat M2) N)) (((eq nat) M2) N)))) of role axiom named fact_201_less__Suc__eq
% 0.69/0.87 A new axiom: (forall (M2:nat) (N:nat), (((eq Prop) ((ord_less_nat M2) (suc N))) ((or ((ord_less_nat M2) N)) (((eq nat) M2) N))))
% 0.69/0.87 FOF formula (forall (N:nat) (P:(nat->Prop)), (((eq Prop) ((ex nat) (fun (I2:nat)=> ((and ((ord_less_nat I2) (suc N))) (P I2))))) ((or (P N)) ((ex nat) (fun (I2:nat)=> ((and ((ord_less_nat I2) N)) (P I2))))))) of role axiom named fact_202_Ex__less__Suc
% 0.69/0.87 A new axiom: (forall (N:nat) (P:(nat->Prop)), (((eq Prop) ((ex nat) (fun (I2:nat)=> ((and ((ord_less_nat I2) (suc N))) (P I2))))) ((or (P N)) ((ex nat) (fun (I2:nat)=> ((and ((ord_less_nat I2) N)) (P I2)))))))
% 0.69/0.87 FOF formula (forall (M2:nat) (N:nat), (((ord_less_nat M2) N)->((ord_less_nat M2) (suc N)))) of role axiom named fact_203_less__SucI
% 0.69/0.87 A new axiom: (forall (M2:nat) (N:nat), (((ord_less_nat M2) N)->((ord_less_nat M2) (suc N))))
% 0.69/0.87 FOF formula (forall (M2:nat) (N:nat), (((ord_less_nat M2) (suc N))->((((ord_less_nat M2) N)->False)->(((eq nat) M2) N)))) of role axiom named fact_204_less__SucE
% 0.69/0.87 A new axiom: (forall (M2:nat) (N:nat), (((ord_less_nat M2) (suc N))->((((ord_less_nat M2) N)->False)->(((eq nat) M2) N))))
% 0.69/0.87 FOF formula (forall (M2:nat) (N:nat), (((ord_less_nat M2) N)->((not (((eq nat) (suc M2)) N))->((ord_less_nat (suc M2)) N)))) of role axiom named fact_205_Suc__lessI
% 0.69/0.87 A new axiom: (forall (M2:nat) (N:nat), (((ord_less_nat M2) N)->((not (((eq nat) (suc M2)) N))->((ord_less_nat (suc M2)) N))))
% 0.69/0.87 <<<E,axiom,(
% 0.69/0.87 ! [I3: nat,K: nat] :
% 0.69/0.87 ( ( ord_less_nat @ ( suc @ I3 ) @ K )
% 0.69/0.87 => ~ !>>>!!!<<< [J3: nat] :
% 0.69/0.87 ( ( ord_less_nat @ I3 @ J3 )
% 0.69/0.87 => ( K
% 0.69/0.87 != ( >>>
% 0.69/0.87 statestack=[0, 1, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 11, 22, 30, 36, 43, 50, 99, 113, 185, 229, 265, 285, 300, 221, 120, 187, 124]
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LexToken(COLON,':',1,51975), LexToken(LPAR,'(',1,51983), thf_unitary_formula, thf_pair_connective, unary_connective]
% 0.69/0.87 Unexpected exception Syntax error at '!':BANG
% 0.69/0.87 Traceback (most recent call last):
% 0.69/0.87 File "CASC.py", line 79, in <module>
% 0.69/0.87 problem=TPTP.TPTPproblem(env=environment,debug=1,file=file)
% 0.69/0.87 File "/export/starexec/sandbox2/solver/bin/TPTP.py", line 38, in __init__
% 0.69/0.87 parser.parse(file.read(),debug=0,lexer=lexer)
% 0.69/0.87 File "/export/starexec/sandbox2/solver/bin/ply/yacc.py", line 265, in parse
% 0.69/0.87 return self.parseopt_notrack(input,lexer,debug,tracking,tokenfunc)
% 0.69/0.87 File "/export/starexec/sandbox2/solver/bin/ply/yacc.py", line 1047, in parseopt_notrack
% 0.69/0.88 tok = self.errorfunc(errtoken)
% 0.69/0.88 File "/export/starexec/sandbox2/solver/bin/TPTPparser.py", line 2099, in p_error
% 0.69/0.88 raise TPTPParsingError("Syntax error at '%s':%s" % (t.value,t.type))
% 0.69/0.88 TPTPparser.TPTPParsingError: Syntax error at '!':BANG
%------------------------------------------------------------------------------