TSTP Solution File: ITP125^1 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : ITP125^1 : TPTP v7.5.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n004.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 13:24:15 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
% 0.07/0.12 % Problem : ITP125^1 : TPTP v7.5.0. Released v7.5.0.
% 0.07/0.12 % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.34 % Computer : n004.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % DateTime : Fri Mar 19 06:14:43 EDT 2021
% 0.13/0.34 % CPUTime :
% 0.13/0.35 ModuleCmd_Load.c(213):ERROR:105: Unable to locate a modulefile for 'python/python27'
% 0.13/0.35 Python 2.7.5
% 0.40/0.62 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% 0.40/0.62 FOF formula (<kernel.Constant object at 0xc40518>, <kernel.Type object at 0xc40488>) of role type named ty_n_t__Trace__Oprefix_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_Itf__a_J_J_J
% 0.40/0.62 Using role type
% 0.40/0.62 Declaring prefix1027212443list_a:Type
% 0.40/0.62 FOF formula (<kernel.Constant object at 0xc3bc68>, <kernel.Type object at 0xc40758>) of role type named ty_n_t__Trace__Otrace_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_Itf__a_J_J_J
% 0.40/0.62 Using role type
% 0.40/0.62 Declaring trace_1367752404list_a:Type
% 0.40/0.62 FOF formula (<kernel.Constant object at 0xc401b8>, <kernel.Type object at 0xc40488>) of role type named ty_n_t__Interval__O__092__060I__062
% 0.40/0.62 Using role type
% 0.40/0.62 Declaring i:Type
% 0.40/0.62 FOF formula (<kernel.Constant object at 0xc402d8>, <kernel.Type object at 0xc40d88>) of role type named ty_n_t__MFOTL__Oformula_Itf__a_J
% 0.40/0.62 Using role type
% 0.40/0.62 Declaring formula_a:Type
% 0.40/0.62 FOF formula (<kernel.Constant object at 0xc407e8>, <kernel.Type object at 0xc40488>) of role type named ty_n_t__List__Olist_Itf__a_J
% 0.40/0.62 Using role type
% 0.40/0.62 Declaring list_a:Type
% 0.40/0.62 FOF formula (<kernel.Constant object at 0xc40f38>, <kernel.Type object at 0xc40878>) of role type named ty_n_t__Nat__Onat
% 0.40/0.62 Using role type
% 0.40/0.62 Declaring nat:Type
% 0.40/0.62 FOF formula (<kernel.Constant object at 0xc40758>, <kernel.Constant object at 0xc402d8>) of role type named sy_c_Groups_Oone__class_Oone_001t__Nat__Onat
% 0.40/0.62 Using role type
% 0.40/0.62 Declaring one_one_nat:nat
% 0.40/0.62 FOF formula (<kernel.Constant object at 0x2abce95c5dd0>, <kernel.DependentProduct object at 0xc40488>) of role type named sy_c_Groups_Oplus__class_Oplus_001t__Nat__Onat
% 0.40/0.62 Using role type
% 0.40/0.62 Declaring plus_plus_nat:(nat->(nat->nat))
% 0.40/0.62 FOF formula (<kernel.Constant object at 0x2abce95a7710>, <kernel.DependentProduct object at 0xc1ef38>) of role type named sy_c_MFOTL_Oformula_OUntil_001tf__a
% 0.40/0.62 Using role type
% 0.40/0.62 Declaring until_a:(formula_a->(i->(formula_a->formula_a)))
% 0.40/0.62 FOF formula (<kernel.Constant object at 0x2abce95a70e0>, <kernel.DependentProduct object at 0xc40758>) of role type named sy_c_MFOTL_Osat_001tf__a
% 0.40/0.62 Using role type
% 0.40/0.62 Declaring sat_a:(trace_1367752404list_a->(list_a->(nat->(formula_a->Prop))))
% 0.40/0.62 FOF formula (<kernel.Constant object at 0x2abce95a7710>, <kernel.DependentProduct object at 0xc40dd0>) of role type named sy_c_Monitor__Mirabelle__prbptmgypa_Oprogress_001tf__a
% 0.40/0.62 Using role type
% 0.40/0.62 Declaring monito1457594016ress_a:(trace_1367752404list_a->(formula_a->(nat->nat)))
% 0.40/0.62 FOF formula (<kernel.Constant object at 0x2abce95a7710>, <kernel.DependentProduct object at 0xc1ef38>) of role type named sy_c_Orderings_Oord__class_Oless_001t__Nat__Onat
% 0.40/0.62 Using role type
% 0.40/0.62 Declaring ord_less_nat:(nat->(nat->Prop))
% 0.40/0.62 FOF formula (<kernel.Constant object at 0xc1eb48>, <kernel.DependentProduct object at 0xda6fc8>) of role type named sy_c_Orderings_Oord__class_Oless_001t__Trace__Oprefix_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_Itf__a_J_J_J
% 0.40/0.62 Using role type
% 0.40/0.62 Declaring ord_le887097159list_a:(prefix1027212443list_a->(prefix1027212443list_a->Prop))
% 0.40/0.62 FOF formula (<kernel.Constant object at 0xc1ef38>, <kernel.DependentProduct object at 0xda6f80>) of role type named sy_c_Orderings_Oord__class_Oless__eq_001t__Nat__Onat
% 0.40/0.62 Using role type
% 0.40/0.62 Declaring ord_less_eq_nat:(nat->(nat->Prop))
% 0.40/0.62 FOF formula (<kernel.Constant object at 0xc1ef38>, <kernel.DependentProduct object at 0xda6f38>) of role type named sy_c_Orderings_Oord__class_Oless__eq_001t__Trace__Oprefix_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_Itf__a_J_J_J
% 0.40/0.62 Using role type
% 0.40/0.62 Declaring ord_le699472955list_a:(prefix1027212443list_a->(prefix1027212443list_a->Prop))
% 0.40/0.62 FOF formula (<kernel.Constant object at 0xc40dd0>, <kernel.DependentProduct object at 0xda6e60>) of role type named sy_c_Trace_O_092_060tau_062_001t__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_Itf__a_J_J
% 0.40/0.62 Using role type
% 0.40/0.62 Declaring tau_Pr257024512list_a:(trace_1367752404list_a->(nat->nat))
% 0.40/0.62 FOF formula (<kernel.Constant object at 0xc402d8>, <kernel.DependentProduct object at 0xda6ea8>) of role type named sy_c_Trace_Oplen_001t__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_Itf__a_J_J
% 0.40/0.63 Using role type
% 0.40/0.63 Declaring plen_P694648887list_a:(prefix1027212443list_a->nat)
% 0.40/0.63 FOF formula (<kernel.Constant object at 0xc40dd0>, <kernel.DependentProduct object at 0xda6dd0>) of role type named sy_c_Trace_Oprefix__of_001t__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_Itf__a_J_J
% 0.40/0.63 Using role type
% 0.40/0.63 Declaring prefix1041802747list_a:(prefix1027212443list_a->(trace_1367752404list_a->Prop))
% 0.40/0.63 FOF formula (<kernel.Constant object at 0xc402d8>, <kernel.Constant object at 0xda6ef0>) of role type named sy_v_I____
% 0.40/0.63 Using role type
% 0.40/0.63 Declaring i2:i
% 0.40/0.63 FOF formula (<kernel.Constant object at 0xc40f38>, <kernel.Constant object at 0xda6ef0>) of role type named sy_v__092_060phi_062
% 0.40/0.63 Using role type
% 0.40/0.63 Declaring phi:formula_a
% 0.40/0.63 FOF formula (<kernel.Constant object at 0xc40f38>, <kernel.Constant object at 0xda6ef0>) of role type named sy_v__092_060phi_0621____
% 0.40/0.63 Using role type
% 0.40/0.63 Declaring phi_1:formula_a
% 0.40/0.63 FOF formula (<kernel.Constant object at 0xda6f80>, <kernel.Constant object at 0xda6ef0>) of role type named sy_v__092_060phi_0622____
% 0.40/0.63 Using role type
% 0.40/0.63 Declaring phi_2:formula_a
% 0.40/0.63 FOF formula (<kernel.Constant object at 0xda6ea8>, <kernel.Constant object at 0xda6ef0>) of role type named sy_v__092_060pi_062
% 0.40/0.63 Using role type
% 0.40/0.63 Declaring pi:prefix1027212443list_a
% 0.40/0.63 FOF formula (<kernel.Constant object at 0xda6e18>, <kernel.Constant object at 0xda6ef0>) of role type named sy_v__092_060sigma_062
% 0.40/0.63 Using role type
% 0.40/0.63 Declaring sigma:trace_1367752404list_a
% 0.40/0.63 FOF formula (<kernel.Constant object at 0xda6f80>, <kernel.Constant object at 0xda6ef0>) of role type named sy_v__092_060sigma_062_H
% 0.40/0.63 Using role type
% 0.40/0.63 Declaring sigma2:trace_1367752404list_a
% 0.40/0.63 FOF formula (<kernel.Constant object at 0xda6ea8>, <kernel.Constant object at 0xda6ef0>) of role type named sy_v_b____
% 0.40/0.63 Using role type
% 0.40/0.63 Declaring b:nat
% 0.40/0.63 FOF formula (<kernel.Constant object at 0xda6e18>, <kernel.Constant object at 0xda6ef0>) of role type named sy_v_i
% 0.40/0.63 Using role type
% 0.40/0.63 Declaring i3:nat
% 0.40/0.63 FOF formula (<kernel.Constant object at 0xda6f80>, <kernel.Constant object at 0xda6ef0>) of role type named sy_v_ia____
% 0.40/0.63 Using role type
% 0.40/0.63 Declaring ia:nat
% 0.40/0.63 FOF formula (<kernel.Constant object at 0xda6ea8>, <kernel.Constant object at 0xda6ef0>) of role type named sy_v_j____
% 0.40/0.63 Using role type
% 0.40/0.63 Declaring j:nat
% 0.40/0.63 FOF formula (<kernel.Constant object at 0xda6e18>, <kernel.Constant object at 0xda6ef0>) of role type named sy_v_ja____
% 0.40/0.63 Using role type
% 0.40/0.63 Declaring ja:nat
% 0.40/0.63 FOF formula (<kernel.Constant object at 0xda6f80>, <kernel.Constant object at 0xda6ef0>) of role type named sy_v_k____
% 0.40/0.63 Using role type
% 0.40/0.63 Declaring k:nat
% 0.40/0.63 FOF formula ((ord_less_nat k) (((monito1457594016ress_a sigma) phi_1) (plen_P694648887list_a pi))) of role axiom named fact_0__092_060open_062k_A_060_AMonitor__Mirabelle__prbptmgypa_Oprogress_A_092_060sigma_062_A_092_060phi_0621_A_Iplen_A_092_060pi_062_J_092_060close_062
% 0.40/0.63 A new axiom: ((ord_less_nat k) (((monito1457594016ress_a sigma) phi_1) (plen_P694648887list_a pi)))
% 0.40/0.63 FOF formula ((ord_less_nat i3) (((monito1457594016ress_a sigma) phi) (plen_P694648887list_a pi))) of role axiom named fact_1_assms_I3_J
% 0.40/0.63 A new axiom: ((ord_less_nat i3) (((monito1457594016ress_a sigma) phi) (plen_P694648887list_a pi)))
% 0.40/0.63 FOF formula ((prefix1041802747list_a pi) sigma) of role axiom named fact_2_assms_I1_J
% 0.40/0.63 A new axiom: ((prefix1041802747list_a pi) sigma)
% 0.40/0.63 FOF formula (forall (M:nat) (N:nat), (((eq Prop) (not (((eq nat) M) N))) ((or ((ord_less_nat M) N)) ((ord_less_nat N) M)))) of role axiom named fact_3_nat__neq__iff
% 0.40/0.63 A new axiom: (forall (M:nat) (N:nat), (((eq Prop) (not (((eq nat) M) N))) ((or ((ord_less_nat M) N)) ((ord_less_nat N) M))))
% 0.40/0.63 FOF formula (forall (N:nat), (((ord_less_nat N) N)->False)) of role axiom named fact_4_less__not__refl
% 0.40/0.63 A new axiom: (forall (N:nat), (((ord_less_nat N) N)->False))
% 0.40/0.63 FOF formula (forall (N:nat) (M:nat), (((ord_less_nat N) M)->(not (((eq nat) M) N)))) of role axiom named fact_5_less__not__refl2
% 0.40/0.63 A new axiom: (forall (N:nat) (M:nat), (((ord_less_nat N) M)->(not (((eq nat) M) N))))
% 0.48/0.64 FOF formula (forall (S:nat) (T:nat), (((ord_less_nat S) T)->(not (((eq nat) S) T)))) of role axiom named fact_6_less__not__refl3
% 0.48/0.64 A new axiom: (forall (S:nat) (T:nat), (((ord_less_nat S) T)->(not (((eq nat) S) T))))
% 0.48/0.64 FOF formula (forall (N:nat), (((ord_less_nat N) N)->False)) of role axiom named fact_7_less__irrefl__nat
% 0.48/0.64 A new axiom: (forall (N:nat), (((ord_less_nat N) N)->False))
% 0.48/0.64 FOF formula (forall (P:(nat->Prop)) (N:nat), ((forall (N2:nat), ((forall (M2:nat), (((ord_less_nat M2) N2)->(P M2)))->(P N2)))->(P N))) of role axiom named fact_8_nat__less__induct
% 0.48/0.64 A new axiom: (forall (P:(nat->Prop)) (N:nat), ((forall (N2:nat), ((forall (M2:nat), (((ord_less_nat M2) N2)->(P M2)))->(P N2)))->(P N)))
% 0.48/0.64 FOF formula (forall (P:(nat->Prop)) (N:nat), ((forall (N2:nat), (((P N2)->False)->((ex nat) (fun (M2:nat)=> ((and ((ord_less_nat M2) N2)) ((P M2)->False))))))->(P N))) of role axiom named fact_9_infinite__descent
% 0.48/0.64 A new axiom: (forall (P:(nat->Prop)) (N:nat), ((forall (N2:nat), (((P N2)->False)->((ex nat) (fun (M2:nat)=> ((and ((ord_less_nat M2) N2)) ((P M2)->False))))))->(P N)))
% 0.48/0.64 FOF formula (forall (X:nat) (Y:nat), ((not (((eq nat) X) Y))->((((ord_less_nat X) Y)->False)->((ord_less_nat Y) X)))) of role axiom named fact_10_linorder__neqE__nat
% 0.48/0.64 A new axiom: (forall (X:nat) (Y:nat), ((not (((eq nat) X) Y))->((((ord_less_nat X) Y)->False)->((ord_less_nat Y) X))))
% 0.48/0.64 FOF formula ((ord_less_eq_nat j) (((monito1457594016ress_a sigma) phi_1) (plen_P694648887list_a pi))) of role axiom named fact_11__092_060open_062j_____A_092_060le_062_AMonitor__Mirabelle__prbptmgypa_Oprogress_A_092_060sigma_062_A_092_060phi_0621_A_Iplen_A_092_060pi_062_J_092_060close_062
% 0.48/0.64 A new axiom: ((ord_less_eq_nat j) (((monito1457594016ress_a sigma) phi_1) (plen_P694648887list_a pi)))
% 0.48/0.64 FOF formula ((prefix1041802747list_a pi) sigma2) of role axiom named fact_12_assms_I2_J
% 0.48/0.64 A new axiom: ((prefix1041802747list_a pi) sigma2)
% 0.48/0.64 FOF formula ((ord_less_eq_nat j) (((monito1457594016ress_a sigma) phi_2) (plen_P694648887list_a pi))) of role axiom named fact_13__092_060open_062j_____A_092_060le_062_AMonitor__Mirabelle__prbptmgypa_Oprogress_A_092_060sigma_062_A_092_060phi_0622_A_Iplen_A_092_060pi_062_J_092_060close_062
% 0.48/0.64 A new axiom: ((ord_less_eq_nat j) (((monito1457594016ress_a sigma) phi_2) (plen_P694648887list_a pi)))
% 0.48/0.64 FOF formula (forall (N:nat), ((ord_less_eq_nat N) N)) of role axiom named fact_14_le__refl
% 0.48/0.64 A new axiom: (forall (N:nat), ((ord_less_eq_nat N) N))
% 0.48/0.64 FOF formula (forall (_TPTP_I:nat) (J:nat) (K:nat), (((ord_less_eq_nat _TPTP_I) J)->(((ord_less_eq_nat J) K)->((ord_less_eq_nat _TPTP_I) K)))) of role axiom named fact_15_le__trans
% 0.48/0.64 A new axiom: (forall (_TPTP_I:nat) (J:nat) (K:nat), (((ord_less_eq_nat _TPTP_I) J)->(((ord_less_eq_nat J) K)->((ord_less_eq_nat _TPTP_I) K))))
% 0.48/0.64 FOF formula (forall (M:nat) (N:nat), ((((eq nat) M) N)->((ord_less_eq_nat M) N))) of role axiom named fact_16_eq__imp__le
% 0.48/0.64 A new axiom: (forall (M:nat) (N:nat), ((((eq nat) M) N)->((ord_less_eq_nat M) N)))
% 0.48/0.64 FOF formula (forall (M:nat) (N:nat), (((ord_less_eq_nat M) N)->(((ord_less_eq_nat N) M)->(((eq nat) M) N)))) of role axiom named fact_17_le__antisym
% 0.48/0.64 A new axiom: (forall (M:nat) (N:nat), (((ord_less_eq_nat M) N)->(((ord_less_eq_nat N) M)->(((eq nat) M) N))))
% 0.48/0.64 FOF formula (forall (M:nat) (N:nat), ((or ((ord_less_eq_nat M) N)) ((ord_less_eq_nat N) M))) of role axiom named fact_18_nat__le__linear
% 0.48/0.64 A new axiom: (forall (M:nat) (N:nat), ((or ((ord_less_eq_nat M) N)) ((ord_less_eq_nat N) M)))
% 0.48/0.64 FOF formula (forall (P:(nat->Prop)) (K:nat) (B:nat), ((P K)->((forall (Y2:nat), ((P Y2)->((ord_less_eq_nat Y2) B)))->((ex nat) (fun (X2:nat)=> ((and (P X2)) (forall (Y3:nat), ((P Y3)->((ord_less_eq_nat Y3) X2))))))))) of role axiom named fact_19_Nat_Oex__has__greatest__nat
% 0.48/0.64 A new axiom: (forall (P:(nat->Prop)) (K:nat) (B:nat), ((P K)->((forall (Y2:nat), ((P Y2)->((ord_less_eq_nat Y2) B)))->((ex nat) (fun (X2:nat)=> ((and (P X2)) (forall (Y3:nat), ((P Y3)->((ord_less_eq_nat Y3) X2)))))))))
% 0.48/0.64 FOF formula (forall (Sigma:trace_1367752404list_a) (Phi:formula_a) (J:nat), ((ord_less_eq_nat (((monito1457594016ress_a Sigma) Phi) J)) J)) of role axiom named fact_20_progress__le
% 0.48/0.66 A new axiom: (forall (Sigma:trace_1367752404list_a) (Phi:formula_a) (J:nat), ((ord_less_eq_nat (((monito1457594016ress_a Sigma) Phi) J)) J))
% 0.48/0.66 FOF formula (forall (J:nat) (J2:nat) (Sigma:trace_1367752404list_a) (Phi:formula_a), (((ord_less_eq_nat J) J2)->((ord_less_eq_nat (((monito1457594016ress_a Sigma) Phi) J)) (((monito1457594016ress_a Sigma) Phi) J2)))) of role axiom named fact_21_progress__mono
% 0.48/0.66 A new axiom: (forall (J:nat) (J2:nat) (Sigma:trace_1367752404list_a) (Phi:formula_a), (((ord_less_eq_nat J) J2)->((ord_less_eq_nat (((monito1457594016ress_a Sigma) Phi) J)) (((monito1457594016ress_a Sigma) Phi) J2))))
% 0.48/0.66 FOF formula (forall (T:nat), ((ex nat) (fun (Z:nat)=> (forall (X3:nat), (((ord_less_nat Z) X3)->(((ord_less_eq_nat X3) T)->False)))))) of role axiom named fact_22_pinf_I6_J
% 0.48/0.66 A new axiom: (forall (T:nat), ((ex nat) (fun (Z:nat)=> (forall (X3:nat), (((ord_less_nat Z) X3)->(((ord_less_eq_nat X3) T)->False))))))
% 0.48/0.66 FOF formula (forall (T:nat), ((ex nat) (fun (Z:nat)=> (forall (X3:nat), (((ord_less_nat Z) X3)->((ord_less_eq_nat T) X3)))))) of role axiom named fact_23_pinf_I8_J
% 0.48/0.66 A new axiom: (forall (T:nat), ((ex nat) (fun (Z:nat)=> (forall (X3:nat), (((ord_less_nat Z) X3)->((ord_less_eq_nat T) X3))))))
% 0.48/0.66 FOF formula (forall (T:nat), ((ex nat) (fun (Z:nat)=> (forall (X3:nat), (((ord_less_nat X3) Z)->((ord_less_eq_nat X3) T)))))) of role axiom named fact_24_minf_I6_J
% 0.48/0.66 A new axiom: (forall (T:nat), ((ex nat) (fun (Z:nat)=> (forall (X3:nat), (((ord_less_nat X3) Z)->((ord_less_eq_nat X3) T))))))
% 0.48/0.66 FOF formula (forall (T:nat), ((ex nat) (fun (Z:nat)=> (forall (X3:nat), (((ord_less_nat X3) Z)->(((ord_less_eq_nat T) X3)->False)))))) of role axiom named fact_25_minf_I8_J
% 0.48/0.66 A new axiom: (forall (T:nat), ((ex nat) (fun (Z:nat)=> (forall (X3:nat), (((ord_less_nat X3) Z)->(((ord_less_eq_nat T) X3)->False))))))
% 0.48/0.66 FOF formula (forall (F:(nat->nat)) (_TPTP_I:nat) (J:nat), ((forall (I2:nat) (J3:nat), (((ord_less_nat I2) J3)->((ord_less_nat (F I2)) (F J3))))->(((ord_less_eq_nat _TPTP_I) J)->((ord_less_eq_nat (F _TPTP_I)) (F J))))) of role axiom named fact_26_less__mono__imp__le__mono
% 0.48/0.66 A new axiom: (forall (F:(nat->nat)) (_TPTP_I:nat) (J:nat), ((forall (I2:nat) (J3:nat), (((ord_less_nat I2) J3)->((ord_less_nat (F I2)) (F J3))))->(((ord_less_eq_nat _TPTP_I) J)->((ord_less_eq_nat (F _TPTP_I)) (F J)))))
% 0.48/0.66 FOF formula (forall (M:nat) (N:nat), (((ord_less_eq_nat M) N)->((not (((eq nat) M) N))->((ord_less_nat M) N)))) of role axiom named fact_27_le__neq__implies__less
% 0.48/0.66 A new axiom: (forall (M:nat) (N:nat), (((ord_less_eq_nat M) N)->((not (((eq nat) M) N))->((ord_less_nat M) N))))
% 0.48/0.66 FOF formula (forall (M:nat) (N:nat), (((or ((ord_less_nat M) N)) (((eq nat) M) N))->((ord_less_eq_nat M) N))) of role axiom named fact_28_less__or__eq__imp__le
% 0.48/0.66 A new axiom: (forall (M:nat) (N:nat), (((or ((ord_less_nat M) N)) (((eq nat) M) N))->((ord_less_eq_nat M) N)))
% 0.48/0.66 FOF formula (((eq (nat->(nat->Prop))) ord_less_eq_nat) (fun (M3:nat) (N3:nat)=> ((or ((ord_less_nat M3) N3)) (((eq nat) M3) N3)))) of role axiom named fact_29_le__eq__less__or__eq
% 0.48/0.66 A new axiom: (((eq (nat->(nat->Prop))) ord_less_eq_nat) (fun (M3:nat) (N3:nat)=> ((or ((ord_less_nat M3) N3)) (((eq nat) M3) N3))))
% 0.48/0.66 FOF formula (forall (M:nat) (N:nat), (((ord_less_nat M) N)->((ord_less_eq_nat M) N))) of role axiom named fact_30_less__imp__le__nat
% 0.48/0.66 A new axiom: (forall (M:nat) (N:nat), (((ord_less_nat M) N)->((ord_less_eq_nat M) N)))
% 0.48/0.66 FOF formula (((eq (nat->(nat->Prop))) ord_less_nat) (fun (M3:nat) (N3:nat)=> ((and ((ord_less_eq_nat M3) N3)) (not (((eq nat) M3) N3))))) of role axiom named fact_31_nat__less__le
% 0.48/0.66 A new axiom: (((eq (nat->(nat->Prop))) ord_less_nat) (fun (M3:nat) (N3:nat)=> ((and ((ord_less_eq_nat M3) N3)) (not (((eq nat) M3) N3)))))
% 0.48/0.66 FOF formula (forall (Pi:prefix1027212443list_a) (Sigma:trace_1367752404list_a) (Sigma2:trace_1367752404list_a) (Phi:formula_a), (((prefix1041802747list_a Pi) Sigma)->(((prefix1041802747list_a Pi) Sigma2)->(((eq nat) (((monito1457594016ress_a Sigma) Phi) (plen_P694648887list_a Pi))) (((monito1457594016ress_a Sigma2) Phi) (plen_P694648887list_a Pi)))))) of role axiom named fact_32_progress__prefix__conv
% 0.48/0.67 A new axiom: (forall (Pi:prefix1027212443list_a) (Sigma:trace_1367752404list_a) (Sigma2:trace_1367752404list_a) (Phi:formula_a), (((prefix1041802747list_a Pi) Sigma)->(((prefix1041802747list_a Pi) Sigma2)->(((eq nat) (((monito1457594016ress_a Sigma) Phi) (plen_P694648887list_a Pi))) (((monito1457594016ress_a Sigma2) Phi) (plen_P694648887list_a Pi))))))
% 0.48/0.67 FOF formula (forall (P:(nat->Prop)) (P2:(nat->Prop)) (Q:(nat->Prop)) (Q2:(nat->Prop)), (((ex nat) (fun (Z2:nat)=> (forall (X2:nat), (((ord_less_nat Z2) X2)->(((eq Prop) (P X2)) (P2 X2))))))->(((ex nat) (fun (Z2:nat)=> (forall (X2:nat), (((ord_less_nat Z2) X2)->(((eq Prop) (Q X2)) (Q2 X2))))))->((ex nat) (fun (Z:nat)=> (forall (X3:nat), (((ord_less_nat Z) X3)->(((eq Prop) ((and (P X3)) (Q X3))) ((and (P2 X3)) (Q2 X3)))))))))) of role axiom named fact_33_pinf_I1_J
% 0.48/0.67 A new axiom: (forall (P:(nat->Prop)) (P2:(nat->Prop)) (Q:(nat->Prop)) (Q2:(nat->Prop)), (((ex nat) (fun (Z2:nat)=> (forall (X2:nat), (((ord_less_nat Z2) X2)->(((eq Prop) (P X2)) (P2 X2))))))->(((ex nat) (fun (Z2:nat)=> (forall (X2:nat), (((ord_less_nat Z2) X2)->(((eq Prop) (Q X2)) (Q2 X2))))))->((ex nat) (fun (Z:nat)=> (forall (X3:nat), (((ord_less_nat Z) X3)->(((eq Prop) ((and (P X3)) (Q X3))) ((and (P2 X3)) (Q2 X3))))))))))
% 0.48/0.67 FOF formula (forall (P:(nat->Prop)) (P2:(nat->Prop)) (Q:(nat->Prop)) (Q2:(nat->Prop)), (((ex nat) (fun (Z2:nat)=> (forall (X2:nat), (((ord_less_nat Z2) X2)->(((eq Prop) (P X2)) (P2 X2))))))->(((ex nat) (fun (Z2:nat)=> (forall (X2:nat), (((ord_less_nat Z2) X2)->(((eq Prop) (Q X2)) (Q2 X2))))))->((ex nat) (fun (Z:nat)=> (forall (X3:nat), (((ord_less_nat Z) X3)->(((eq Prop) ((or (P X3)) (Q X3))) ((or (P2 X3)) (Q2 X3)))))))))) of role axiom named fact_34_pinf_I2_J
% 0.48/0.67 A new axiom: (forall (P:(nat->Prop)) (P2:(nat->Prop)) (Q:(nat->Prop)) (Q2:(nat->Prop)), (((ex nat) (fun (Z2:nat)=> (forall (X2:nat), (((ord_less_nat Z2) X2)->(((eq Prop) (P X2)) (P2 X2))))))->(((ex nat) (fun (Z2:nat)=> (forall (X2:nat), (((ord_less_nat Z2) X2)->(((eq Prop) (Q X2)) (Q2 X2))))))->((ex nat) (fun (Z:nat)=> (forall (X3:nat), (((ord_less_nat Z) X3)->(((eq Prop) ((or (P X3)) (Q X3))) ((or (P2 X3)) (Q2 X3))))))))))
% 0.48/0.67 FOF formula (forall (T:nat), ((ex nat) (fun (Z:nat)=> (forall (X3:nat), (((ord_less_nat Z) X3)->(not (((eq nat) X3) T))))))) of role axiom named fact_35_pinf_I3_J
% 0.48/0.67 A new axiom: (forall (T:nat), ((ex nat) (fun (Z:nat)=> (forall (X3:nat), (((ord_less_nat Z) X3)->(not (((eq nat) X3) T)))))))
% 0.48/0.67 FOF formula (forall (T:nat), ((ex nat) (fun (Z:nat)=> (forall (X3:nat), (((ord_less_nat Z) X3)->(not (((eq nat) X3) T))))))) of role axiom named fact_36_pinf_I4_J
% 0.48/0.67 A new axiom: (forall (T:nat), ((ex nat) (fun (Z:nat)=> (forall (X3:nat), (((ord_less_nat Z) X3)->(not (((eq nat) X3) T)))))))
% 0.48/0.67 FOF formula (forall (T:nat), ((ex nat) (fun (Z:nat)=> (forall (X3:nat), (((ord_less_nat Z) X3)->(((ord_less_nat X3) T)->False)))))) of role axiom named fact_37_pinf_I5_J
% 0.48/0.67 A new axiom: (forall (T:nat), ((ex nat) (fun (Z:nat)=> (forall (X3:nat), (((ord_less_nat Z) X3)->(((ord_less_nat X3) T)->False))))))
% 0.48/0.67 FOF formula (forall (T:nat), ((ex nat) (fun (Z:nat)=> (forall (X3:nat), (((ord_less_nat Z) X3)->((ord_less_nat T) X3)))))) of role axiom named fact_38_pinf_I7_J
% 0.48/0.67 A new axiom: (forall (T:nat), ((ex nat) (fun (Z:nat)=> (forall (X3:nat), (((ord_less_nat Z) X3)->((ord_less_nat T) X3))))))
% 0.48/0.67 FOF formula (forall (P:(nat->Prop)) (P2:(nat->Prop)) (Q:(nat->Prop)) (Q2:(nat->Prop)), (((ex nat) (fun (Z2:nat)=> (forall (X2:nat), (((ord_less_nat X2) Z2)->(((eq Prop) (P X2)) (P2 X2))))))->(((ex nat) (fun (Z2:nat)=> (forall (X2:nat), (((ord_less_nat X2) Z2)->(((eq Prop) (Q X2)) (Q2 X2))))))->((ex nat) (fun (Z:nat)=> (forall (X3:nat), (((ord_less_nat X3) Z)->(((eq Prop) ((and (P X3)) (Q X3))) ((and (P2 X3)) (Q2 X3)))))))))) of role axiom named fact_39_minf_I1_J
% 0.48/0.67 A new axiom: (forall (P:(nat->Prop)) (P2:(nat->Prop)) (Q:(nat->Prop)) (Q2:(nat->Prop)), (((ex nat) (fun (Z2:nat)=> (forall (X2:nat), (((ord_less_nat X2) Z2)->(((eq Prop) (P X2)) (P2 X2))))))->(((ex nat) (fun (Z2:nat)=> (forall (X2:nat), (((ord_less_nat X2) Z2)->(((eq Prop) (Q X2)) (Q2 X2))))))->((ex nat) (fun (Z:nat)=> (forall (X3:nat), (((ord_less_nat X3) Z)->(((eq Prop) ((and (P X3)) (Q X3))) ((and (P2 X3)) (Q2 X3))))))))))
% 0.52/0.69 FOF formula (forall (P:(nat->Prop)) (P2:(nat->Prop)) (Q:(nat->Prop)) (Q2:(nat->Prop)), (((ex nat) (fun (Z2:nat)=> (forall (X2:nat), (((ord_less_nat X2) Z2)->(((eq Prop) (P X2)) (P2 X2))))))->(((ex nat) (fun (Z2:nat)=> (forall (X2:nat), (((ord_less_nat X2) Z2)->(((eq Prop) (Q X2)) (Q2 X2))))))->((ex nat) (fun (Z:nat)=> (forall (X3:nat), (((ord_less_nat X3) Z)->(((eq Prop) ((or (P X3)) (Q X3))) ((or (P2 X3)) (Q2 X3)))))))))) of role axiom named fact_40_minf_I2_J
% 0.52/0.69 A new axiom: (forall (P:(nat->Prop)) (P2:(nat->Prop)) (Q:(nat->Prop)) (Q2:(nat->Prop)), (((ex nat) (fun (Z2:nat)=> (forall (X2:nat), (((ord_less_nat X2) Z2)->(((eq Prop) (P X2)) (P2 X2))))))->(((ex nat) (fun (Z2:nat)=> (forall (X2:nat), (((ord_less_nat X2) Z2)->(((eq Prop) (Q X2)) (Q2 X2))))))->((ex nat) (fun (Z:nat)=> (forall (X3:nat), (((ord_less_nat X3) Z)->(((eq Prop) ((or (P X3)) (Q X3))) ((or (P2 X3)) (Q2 X3))))))))))
% 0.52/0.69 FOF formula (forall (T:nat), ((ex nat) (fun (Z:nat)=> (forall (X3:nat), (((ord_less_nat X3) Z)->(not (((eq nat) X3) T))))))) of role axiom named fact_41_minf_I3_J
% 0.52/0.69 A new axiom: (forall (T:nat), ((ex nat) (fun (Z:nat)=> (forall (X3:nat), (((ord_less_nat X3) Z)->(not (((eq nat) X3) T)))))))
% 0.52/0.69 FOF formula (forall (T:nat), ((ex nat) (fun (Z:nat)=> (forall (X3:nat), (((ord_less_nat X3) Z)->(not (((eq nat) X3) T))))))) of role axiom named fact_42_minf_I4_J
% 0.52/0.69 A new axiom: (forall (T:nat), ((ex nat) (fun (Z:nat)=> (forall (X3:nat), (((ord_less_nat X3) Z)->(not (((eq nat) X3) T)))))))
% 0.52/0.69 FOF formula (forall (T:nat), ((ex nat) (fun (Z:nat)=> (forall (X3:nat), (((ord_less_nat X3) Z)->((ord_less_nat X3) T)))))) of role axiom named fact_43_minf_I5_J
% 0.52/0.69 A new axiom: (forall (T:nat), ((ex nat) (fun (Z:nat)=> (forall (X3:nat), (((ord_less_nat X3) Z)->((ord_less_nat X3) T))))))
% 0.52/0.69 FOF formula (forall (T:nat), ((ex nat) (fun (Z:nat)=> (forall (X3:nat), (((ord_less_nat X3) Z)->(((ord_less_nat T) X3)->False)))))) of role axiom named fact_44_minf_I7_J
% 0.52/0.69 A new axiom: (forall (T:nat), ((ex nat) (fun (Z:nat)=> (forall (X3:nat), (((ord_less_nat X3) Z)->(((ord_less_nat T) X3)->False))))))
% 0.52/0.69 FOF formula ((ord_less_eq_nat ja) (((monito1457594016ress_a sigma2) phi_1) (plen_P694648887list_a pi))) of role axiom named fact_45__092_060open_062j_A_092_060le_062_AMonitor__Mirabelle__prbptmgypa_Oprogress_A_092_060sigma_062_H_A_092_060phi_0621_A_Iplen_A_092_060pi_062_J_092_060close_062
% 0.52/0.69 A new axiom: ((ord_less_eq_nat ja) (((monito1457594016ress_a sigma2) phi_1) (plen_P694648887list_a pi)))
% 0.52/0.69 FOF formula (forall (X:prefix1027212443list_a), ((ord_le699472955list_a X) X)) of role axiom named fact_46_order__refl
% 0.52/0.69 A new axiom: (forall (X:prefix1027212443list_a), ((ord_le699472955list_a X) X))
% 0.52/0.69 FOF formula (forall (X:nat), ((ord_less_eq_nat X) X)) of role axiom named fact_47_order__refl
% 0.52/0.69 A new axiom: (forall (X:nat), ((ord_less_eq_nat X) X))
% 0.52/0.69 FOF formula (forall (_TPTP_I:nat) (V:list_a), (((ord_less_nat _TPTP_I) (((monito1457594016ress_a sigma) phi_1) (plen_P694648887list_a pi)))->(((eq Prop) ((((sat_a sigma) V) _TPTP_I) phi_1)) ((((sat_a sigma2) V) _TPTP_I) phi_1)))) of role axiom named fact_48_Until_OIH_I1_J
% 0.52/0.69 A new axiom: (forall (_TPTP_I:nat) (V:list_a), (((ord_less_nat _TPTP_I) (((monito1457594016ress_a sigma) phi_1) (plen_P694648887list_a pi)))->(((eq Prop) ((((sat_a sigma) V) _TPTP_I) phi_1)) ((((sat_a sigma2) V) _TPTP_I) phi_1))))
% 0.52/0.69 FOF formula (forall (N:nat) (P:(nat->Prop)) (M:nat), ((forall (K2:nat), (((ord_less_nat N) K2)->(P K2)))->((forall (K2:nat), (((ord_less_eq_nat K2) N)->((forall (I3:nat), (((ord_less_nat K2) I3)->(P I3)))->(P K2))))->(P M)))) of role axiom named fact_49_nat__descend__induct
% 0.52/0.69 A new axiom: (forall (N:nat) (P:(nat->Prop)) (M:nat), ((forall (K2:nat), (((ord_less_nat N) K2)->(P K2)))->((forall (K2:nat), (((ord_less_eq_nat K2) N)->((forall (I3:nat), (((ord_less_nat K2) I3)->(P I3)))->(P K2))))->(P M))))
% 0.52/0.69 FOF formula (forall (A:nat) (B:nat) (P:(nat->Prop)), (((ord_less_nat A) B)->((P A)->(((P B)->False)->((ex nat) (fun (C:nat)=> ((and ((and ((and ((ord_less_eq_nat A) C)) ((ord_less_eq_nat C) B))) (forall (X3:nat), (((and ((ord_less_eq_nat A) X3)) ((ord_less_nat X3) C))->(P X3))))) (forall (D:nat), ((forall (X2:nat), (((and ((ord_less_eq_nat A) X2)) ((ord_less_nat X2) D))->(P X2)))->((ord_less_eq_nat D) C)))))))))) of role axiom named fact_50_complete__interval
% 0.52/0.70 A new axiom: (forall (A:nat) (B:nat) (P:(nat->Prop)), (((ord_less_nat A) B)->((P A)->(((P B)->False)->((ex nat) (fun (C:nat)=> ((and ((and ((and ((ord_less_eq_nat A) C)) ((ord_less_eq_nat C) B))) (forall (X3:nat), (((and ((ord_less_eq_nat A) X3)) ((ord_less_nat X3) C))->(P X3))))) (forall (D:nat), ((forall (X2:nat), (((and ((ord_less_eq_nat A) X2)) ((ord_less_nat X2) D))->(P X2)))->((ord_less_eq_nat D) C))))))))))
% 0.52/0.70 FOF formula (forall (A:prefix1027212443list_a) (B:prefix1027212443list_a), ((not (((eq prefix1027212443list_a) A) B))->(((ord_le699472955list_a A) B)->((ord_le887097159list_a A) B)))) of role axiom named fact_51_order_Onot__eq__order__implies__strict
% 0.52/0.70 A new axiom: (forall (A:prefix1027212443list_a) (B:prefix1027212443list_a), ((not (((eq prefix1027212443list_a) A) B))->(((ord_le699472955list_a A) B)->((ord_le887097159list_a A) B))))
% 0.52/0.70 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_52_order_Onot__eq__order__implies__strict
% 0.52/0.70 A new axiom: (forall (A:nat) (B:nat), ((not (((eq nat) A) B))->(((ord_less_eq_nat A) B)->((ord_less_nat A) B))))
% 0.52/0.70 FOF formula (forall (B:prefix1027212443list_a) (A:prefix1027212443list_a), (((ord_le887097159list_a B) A)->((ord_le699472955list_a B) A))) of role axiom named fact_53_dual__order_Ostrict__implies__order
% 0.52/0.70 A new axiom: (forall (B:prefix1027212443list_a) (A:prefix1027212443list_a), (((ord_le887097159list_a B) A)->((ord_le699472955list_a B) A)))
% 0.52/0.70 FOF formula (forall (B:nat) (A:nat), (((ord_less_nat B) A)->((ord_less_eq_nat B) A))) of role axiom named fact_54_dual__order_Ostrict__implies__order
% 0.52/0.70 A new axiom: (forall (B:nat) (A:nat), (((ord_less_nat B) A)->((ord_less_eq_nat B) A)))
% 0.52/0.70 FOF formula (((eq (prefix1027212443list_a->(prefix1027212443list_a->Prop))) ord_le887097159list_a) (fun (B2:prefix1027212443list_a) (A2:prefix1027212443list_a)=> ((and ((ord_le699472955list_a B2) A2)) (not (((eq prefix1027212443list_a) A2) B2))))) of role axiom named fact_55_dual__order_Ostrict__iff__order
% 0.52/0.70 A new axiom: (((eq (prefix1027212443list_a->(prefix1027212443list_a->Prop))) ord_le887097159list_a) (fun (B2:prefix1027212443list_a) (A2:prefix1027212443list_a)=> ((and ((ord_le699472955list_a B2) A2)) (not (((eq prefix1027212443list_a) A2) B2)))))
% 0.52/0.70 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_56_dual__order_Ostrict__iff__order
% 0.52/0.70 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)))))
% 0.52/0.70 FOF formula (((eq (prefix1027212443list_a->(prefix1027212443list_a->Prop))) ord_le699472955list_a) (fun (B2:prefix1027212443list_a) (A2:prefix1027212443list_a)=> ((or ((ord_le887097159list_a B2) A2)) (((eq prefix1027212443list_a) A2) B2)))) of role axiom named fact_57_dual__order_Oorder__iff__strict
% 0.52/0.70 A new axiom: (((eq (prefix1027212443list_a->(prefix1027212443list_a->Prop))) ord_le699472955list_a) (fun (B2:prefix1027212443list_a) (A2:prefix1027212443list_a)=> ((or ((ord_le887097159list_a B2) A2)) (((eq prefix1027212443list_a) A2) B2))))
% 0.52/0.70 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_58_dual__order_Oorder__iff__strict
% 0.52/0.70 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))))
% 0.52/0.70 FOF formula (forall (A:prefix1027212443list_a) (B:prefix1027212443list_a), (((ord_le887097159list_a A) B)->((ord_le699472955list_a A) B))) of role axiom named fact_59_order_Ostrict__implies__order
% 0.52/0.70 A new axiom: (forall (A:prefix1027212443list_a) (B:prefix1027212443list_a), (((ord_le887097159list_a A) B)->((ord_le699472955list_a A) B)))
% 0.52/0.71 FOF formula (forall (A:nat) (B:nat), (((ord_less_nat A) B)->((ord_less_eq_nat A) B))) of role axiom named fact_60_order_Ostrict__implies__order
% 0.52/0.71 A new axiom: (forall (A:nat) (B:nat), (((ord_less_nat A) B)->((ord_less_eq_nat A) B)))
% 0.52/0.71 FOF formula ((ord_less_eq_nat ja) (((monito1457594016ress_a sigma2) phi_2) (plen_P694648887list_a pi))) of role axiom named fact_61__092_060open_062j_A_092_060le_062_AMonitor__Mirabelle__prbptmgypa_Oprogress_A_092_060sigma_062_H_A_092_060phi_0622_A_Iplen_A_092_060pi_062_J_092_060close_062
% 0.52/0.71 A new axiom: ((ord_less_eq_nat ja) (((monito1457594016ress_a sigma2) phi_2) (plen_P694648887list_a pi)))
% 0.52/0.71 FOF formula (forall (_TPTP_I:nat) (V:list_a), (((ord_less_nat _TPTP_I) (((monito1457594016ress_a sigma) phi_2) (plen_P694648887list_a pi)))->(((eq Prop) ((((sat_a sigma) V) _TPTP_I) phi_2)) ((((sat_a sigma2) V) _TPTP_I) phi_2)))) of role axiom named fact_62_Until_OIH_I2_J
% 0.52/0.71 A new axiom: (forall (_TPTP_I:nat) (V:list_a), (((ord_less_nat _TPTP_I) (((monito1457594016ress_a sigma) phi_2) (plen_P694648887list_a pi)))->(((eq Prop) ((((sat_a sigma) V) _TPTP_I) phi_2)) ((((sat_a sigma2) V) _TPTP_I) phi_2))))
% 0.52/0.71 FOF formula (forall (B:prefix1027212443list_a) (A:prefix1027212443list_a), (((ord_le699472955list_a B) A)->(((ord_le699472955list_a A) B)->(((eq prefix1027212443list_a) A) B)))) of role axiom named fact_63_dual__order_Oantisym
% 0.52/0.71 A new axiom: (forall (B:prefix1027212443list_a) (A:prefix1027212443list_a), (((ord_le699472955list_a B) A)->(((ord_le699472955list_a A) B)->(((eq prefix1027212443list_a) A) B))))
% 0.52/0.71 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_64_dual__order_Oantisym
% 0.52/0.71 A new axiom: (forall (B:nat) (A:nat), (((ord_less_eq_nat B) A)->(((ord_less_eq_nat A) B)->(((eq nat) A) B))))
% 0.52/0.71 FOF formula (((eq (prefix1027212443list_a->(prefix1027212443list_a->Prop))) (fun (Y4:prefix1027212443list_a) (Z3:prefix1027212443list_a)=> (((eq prefix1027212443list_a) Y4) Z3))) (fun (A2:prefix1027212443list_a) (B2:prefix1027212443list_a)=> ((and ((ord_le699472955list_a B2) A2)) ((ord_le699472955list_a A2) B2)))) of role axiom named fact_65_dual__order_Oeq__iff
% 0.52/0.71 A new axiom: (((eq (prefix1027212443list_a->(prefix1027212443list_a->Prop))) (fun (Y4:prefix1027212443list_a) (Z3:prefix1027212443list_a)=> (((eq prefix1027212443list_a) Y4) Z3))) (fun (A2:prefix1027212443list_a) (B2:prefix1027212443list_a)=> ((and ((ord_le699472955list_a B2) A2)) ((ord_le699472955list_a A2) B2))))
% 0.52/0.71 FOF formula (((eq (nat->(nat->Prop))) (fun (Y4:nat) (Z3:nat)=> (((eq nat) Y4) Z3))) (fun (A2:nat) (B2:nat)=> ((and ((ord_less_eq_nat B2) A2)) ((ord_less_eq_nat A2) B2)))) of role axiom named fact_66_dual__order_Oeq__iff
% 0.52/0.71 A new axiom: (((eq (nat->(nat->Prop))) (fun (Y4:nat) (Z3:nat)=> (((eq nat) Y4) Z3))) (fun (A2:nat) (B2:nat)=> ((and ((ord_less_eq_nat B2) A2)) ((ord_less_eq_nat A2) B2))))
% 0.52/0.71 FOF formula (forall (B:prefix1027212443list_a) (A:prefix1027212443list_a) (C2:prefix1027212443list_a), (((ord_le699472955list_a B) A)->(((ord_le699472955list_a C2) B)->((ord_le699472955list_a C2) A)))) of role axiom named fact_67_dual__order_Otrans
% 0.52/0.71 A new axiom: (forall (B:prefix1027212443list_a) (A:prefix1027212443list_a) (C2:prefix1027212443list_a), (((ord_le699472955list_a B) A)->(((ord_le699472955list_a C2) B)->((ord_le699472955list_a C2) A))))
% 0.52/0.71 FOF formula (forall (B:nat) (A:nat) (C2:nat), (((ord_less_eq_nat B) A)->(((ord_less_eq_nat C2) B)->((ord_less_eq_nat C2) A)))) of role axiom named fact_68_dual__order_Otrans
% 0.52/0.71 A new axiom: (forall (B:nat) (A:nat) (C2:nat), (((ord_less_eq_nat B) A)->(((ord_less_eq_nat C2) B)->((ord_less_eq_nat C2) A))))
% 0.52/0.71 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_69_linorder__wlog
% 0.52/0.71 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))))
% 0.52/0.73 FOF formula (forall (A:prefix1027212443list_a), ((ord_le699472955list_a A) A)) of role axiom named fact_70_dual__order_Orefl
% 0.52/0.73 A new axiom: (forall (A:prefix1027212443list_a), ((ord_le699472955list_a A) A))
% 0.52/0.73 FOF formula (forall (A:nat), ((ord_less_eq_nat A) A)) of role axiom named fact_71_dual__order_Orefl
% 0.52/0.73 A new axiom: (forall (A:nat), ((ord_less_eq_nat A) A))
% 0.52/0.73 FOF formula (forall (X:prefix1027212443list_a) (Y:prefix1027212443list_a) (Z4:prefix1027212443list_a), (((ord_le699472955list_a X) Y)->(((ord_le699472955list_a Y) Z4)->((ord_le699472955list_a X) Z4)))) of role axiom named fact_72_order__trans
% 0.52/0.73 A new axiom: (forall (X:prefix1027212443list_a) (Y:prefix1027212443list_a) (Z4:prefix1027212443list_a), (((ord_le699472955list_a X) Y)->(((ord_le699472955list_a Y) Z4)->((ord_le699472955list_a X) Z4))))
% 0.52/0.73 FOF formula (forall (X:nat) (Y:nat) (Z4:nat), (((ord_less_eq_nat X) Y)->(((ord_less_eq_nat Y) Z4)->((ord_less_eq_nat X) Z4)))) of role axiom named fact_73_order__trans
% 0.52/0.73 A new axiom: (forall (X:nat) (Y:nat) (Z4:nat), (((ord_less_eq_nat X) Y)->(((ord_less_eq_nat Y) Z4)->((ord_less_eq_nat X) Z4))))
% 0.52/0.73 FOF formula (forall (A:prefix1027212443list_a) (B:prefix1027212443list_a), (((ord_le699472955list_a A) B)->(((ord_le699472955list_a B) A)->(((eq prefix1027212443list_a) A) B)))) of role axiom named fact_74_order__class_Oorder_Oantisym
% 0.52/0.73 A new axiom: (forall (A:prefix1027212443list_a) (B:prefix1027212443list_a), (((ord_le699472955list_a A) B)->(((ord_le699472955list_a B) A)->(((eq prefix1027212443list_a) A) B))))
% 0.52/0.73 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_75_order__class_Oorder_Oantisym
% 0.52/0.73 A new axiom: (forall (A:nat) (B:nat), (((ord_less_eq_nat A) B)->(((ord_less_eq_nat B) A)->(((eq nat) A) B))))
% 0.52/0.73 FOF formula (forall (A:prefix1027212443list_a) (B:prefix1027212443list_a) (C2:prefix1027212443list_a), (((ord_le699472955list_a A) B)->((((eq prefix1027212443list_a) B) C2)->((ord_le699472955list_a A) C2)))) of role axiom named fact_76_ord__le__eq__trans
% 0.52/0.73 A new axiom: (forall (A:prefix1027212443list_a) (B:prefix1027212443list_a) (C2:prefix1027212443list_a), (((ord_le699472955list_a A) B)->((((eq prefix1027212443list_a) B) C2)->((ord_le699472955list_a A) C2))))
% 0.52/0.73 FOF formula (forall (A:nat) (B:nat) (C2:nat), (((ord_less_eq_nat A) B)->((((eq nat) B) C2)->((ord_less_eq_nat A) C2)))) of role axiom named fact_77_ord__le__eq__trans
% 0.52/0.73 A new axiom: (forall (A:nat) (B:nat) (C2:nat), (((ord_less_eq_nat A) B)->((((eq nat) B) C2)->((ord_less_eq_nat A) C2))))
% 0.52/0.73 FOF formula (forall (A:prefix1027212443list_a) (B:prefix1027212443list_a) (C2:prefix1027212443list_a), ((((eq prefix1027212443list_a) A) B)->(((ord_le699472955list_a B) C2)->((ord_le699472955list_a A) C2)))) of role axiom named fact_78_ord__eq__le__trans
% 0.52/0.73 A new axiom: (forall (A:prefix1027212443list_a) (B:prefix1027212443list_a) (C2:prefix1027212443list_a), ((((eq prefix1027212443list_a) A) B)->(((ord_le699472955list_a B) C2)->((ord_le699472955list_a A) C2))))
% 0.52/0.73 FOF formula (forall (A:nat) (B:nat) (C2:nat), ((((eq nat) A) B)->(((ord_less_eq_nat B) C2)->((ord_less_eq_nat A) C2)))) of role axiom named fact_79_ord__eq__le__trans
% 0.52/0.73 A new axiom: (forall (A:nat) (B:nat) (C2:nat), ((((eq nat) A) B)->(((ord_less_eq_nat B) C2)->((ord_less_eq_nat A) C2))))
% 0.52/0.73 FOF formula (((eq (prefix1027212443list_a->(prefix1027212443list_a->Prop))) (fun (Y4:prefix1027212443list_a) (Z3:prefix1027212443list_a)=> (((eq prefix1027212443list_a) Y4) Z3))) (fun (A2:prefix1027212443list_a) (B2:prefix1027212443list_a)=> ((and ((ord_le699472955list_a A2) B2)) ((ord_le699472955list_a B2) A2)))) of role axiom named fact_80_order__class_Oorder_Oeq__iff
% 0.52/0.73 A new axiom: (((eq (prefix1027212443list_a->(prefix1027212443list_a->Prop))) (fun (Y4:prefix1027212443list_a) (Z3:prefix1027212443list_a)=> (((eq prefix1027212443list_a) Y4) Z3))) (fun (A2:prefix1027212443list_a) (B2:prefix1027212443list_a)=> ((and ((ord_le699472955list_a A2) B2)) ((ord_le699472955list_a B2) A2))))
% 0.52/0.73 FOF formula (((eq (nat->(nat->Prop))) (fun (Y4:nat) (Z3:nat)=> (((eq nat) Y4) Z3))) (fun (A2:nat) (B2:nat)=> ((and ((ord_less_eq_nat A2) B2)) ((ord_less_eq_nat B2) A2)))) of role axiom named fact_81_order__class_Oorder_Oeq__iff
% 0.52/0.74 A new axiom: (((eq (nat->(nat->Prop))) (fun (Y4:nat) (Z3:nat)=> (((eq nat) Y4) Z3))) (fun (A2:nat) (B2:nat)=> ((and ((ord_less_eq_nat A2) B2)) ((ord_less_eq_nat B2) A2))))
% 0.52/0.74 FOF formula (forall (Y:prefix1027212443list_a) (X:prefix1027212443list_a), (((ord_le699472955list_a Y) X)->(((eq Prop) ((ord_le699472955list_a X) Y)) (((eq prefix1027212443list_a) X) Y)))) of role axiom named fact_82_antisym__conv
% 0.52/0.74 A new axiom: (forall (Y:prefix1027212443list_a) (X:prefix1027212443list_a), (((ord_le699472955list_a Y) X)->(((eq Prop) ((ord_le699472955list_a X) Y)) (((eq prefix1027212443list_a) X) Y))))
% 0.52/0.74 FOF formula (forall (Y:nat) (X:nat), (((ord_less_eq_nat Y) X)->(((eq Prop) ((ord_less_eq_nat X) Y)) (((eq nat) X) Y)))) of role axiom named fact_83_antisym__conv
% 0.52/0.74 A new axiom: (forall (Y:nat) (X:nat), (((ord_less_eq_nat Y) X)->(((eq Prop) ((ord_less_eq_nat X) Y)) (((eq nat) X) Y))))
% 0.52/0.74 FOF formula (forall (X:nat) (Y:nat) (Z4:nat), ((((ord_less_eq_nat X) Y)->(((ord_less_eq_nat Y) Z4)->False))->((((ord_less_eq_nat Y) X)->(((ord_less_eq_nat X) Z4)->False))->((((ord_less_eq_nat X) Z4)->(((ord_less_eq_nat Z4) Y)->False))->((((ord_less_eq_nat Z4) Y)->(((ord_less_eq_nat Y) X)->False))->((((ord_less_eq_nat Y) Z4)->(((ord_less_eq_nat Z4) X)->False))->((((ord_less_eq_nat Z4) X)->(((ord_less_eq_nat X) Y)->False))->False))))))) of role axiom named fact_84_le__cases3
% 0.52/0.74 A new axiom: (forall (X:nat) (Y:nat) (Z4:nat), ((((ord_less_eq_nat X) Y)->(((ord_less_eq_nat Y) Z4)->False))->((((ord_less_eq_nat Y) X)->(((ord_less_eq_nat X) Z4)->False))->((((ord_less_eq_nat X) Z4)->(((ord_less_eq_nat Z4) Y)->False))->((((ord_less_eq_nat Z4) Y)->(((ord_less_eq_nat Y) X)->False))->((((ord_less_eq_nat Y) Z4)->(((ord_less_eq_nat Z4) X)->False))->((((ord_less_eq_nat Z4) X)->(((ord_less_eq_nat X) Y)->False))->False)))))))
% 0.52/0.74 FOF formula (forall (A:prefix1027212443list_a) (B:prefix1027212443list_a) (C2:prefix1027212443list_a), (((ord_le699472955list_a A) B)->(((ord_le699472955list_a B) C2)->((ord_le699472955list_a A) C2)))) of role axiom named fact_85_order_Otrans
% 0.52/0.74 A new axiom: (forall (A:prefix1027212443list_a) (B:prefix1027212443list_a) (C2:prefix1027212443list_a), (((ord_le699472955list_a A) B)->(((ord_le699472955list_a B) C2)->((ord_le699472955list_a A) C2))))
% 0.52/0.74 FOF formula (forall (A:nat) (B:nat) (C2:nat), (((ord_less_eq_nat A) B)->(((ord_less_eq_nat B) C2)->((ord_less_eq_nat A) C2)))) of role axiom named fact_86_order_Otrans
% 0.52/0.74 A new axiom: (forall (A:nat) (B:nat) (C2:nat), (((ord_less_eq_nat A) B)->(((ord_less_eq_nat B) C2)->((ord_less_eq_nat A) C2))))
% 0.52/0.74 FOF formula (forall (X:nat) (Y:nat), ((((ord_less_eq_nat X) Y)->False)->((ord_less_eq_nat Y) X))) of role axiom named fact_87_le__cases
% 0.52/0.74 A new axiom: (forall (X:nat) (Y:nat), ((((ord_less_eq_nat X) Y)->False)->((ord_less_eq_nat Y) X)))
% 0.52/0.74 FOF formula (forall (X:prefix1027212443list_a) (Y:prefix1027212443list_a), ((((eq prefix1027212443list_a) X) Y)->((ord_le699472955list_a X) Y))) of role axiom named fact_88_eq__refl
% 0.52/0.74 A new axiom: (forall (X:prefix1027212443list_a) (Y:prefix1027212443list_a), ((((eq prefix1027212443list_a) X) Y)->((ord_le699472955list_a X) Y)))
% 0.52/0.74 FOF formula (forall (X:nat) (Y:nat), ((((eq nat) X) Y)->((ord_less_eq_nat X) Y))) of role axiom named fact_89_eq__refl
% 0.52/0.74 A new axiom: (forall (X:nat) (Y:nat), ((((eq nat) X) Y)->((ord_less_eq_nat X) Y)))
% 0.52/0.74 FOF formula (forall (X:nat) (Y:nat), ((or ((ord_less_eq_nat X) Y)) ((ord_less_eq_nat Y) X))) of role axiom named fact_90_linear
% 0.52/0.74 A new axiom: (forall (X:nat) (Y:nat), ((or ((ord_less_eq_nat X) Y)) ((ord_less_eq_nat Y) X)))
% 0.52/0.74 FOF formula (forall (X:prefix1027212443list_a) (Y:prefix1027212443list_a), (((ord_le699472955list_a X) Y)->(((ord_le699472955list_a Y) X)->(((eq prefix1027212443list_a) X) Y)))) of role axiom named fact_91_antisym
% 0.52/0.74 A new axiom: (forall (X:prefix1027212443list_a) (Y:prefix1027212443list_a), (((ord_le699472955list_a X) Y)->(((ord_le699472955list_a Y) X)->(((eq prefix1027212443list_a) X) Y))))
% 0.59/0.75 FOF formula (forall (X:nat) (Y:nat), (((ord_less_eq_nat X) Y)->(((ord_less_eq_nat Y) X)->(((eq nat) X) Y)))) of role axiom named fact_92_antisym
% 0.59/0.75 A new axiom: (forall (X:nat) (Y:nat), (((ord_less_eq_nat X) Y)->(((ord_less_eq_nat Y) X)->(((eq nat) X) Y))))
% 0.59/0.75 FOF formula (((eq (prefix1027212443list_a->(prefix1027212443list_a->Prop))) (fun (Y4:prefix1027212443list_a) (Z3:prefix1027212443list_a)=> (((eq prefix1027212443list_a) Y4) Z3))) (fun (X4:prefix1027212443list_a) (Y5:prefix1027212443list_a)=> ((and ((ord_le699472955list_a X4) Y5)) ((ord_le699472955list_a Y5) X4)))) of role axiom named fact_93_eq__iff
% 0.59/0.75 A new axiom: (((eq (prefix1027212443list_a->(prefix1027212443list_a->Prop))) (fun (Y4:prefix1027212443list_a) (Z3:prefix1027212443list_a)=> (((eq prefix1027212443list_a) Y4) Z3))) (fun (X4:prefix1027212443list_a) (Y5:prefix1027212443list_a)=> ((and ((ord_le699472955list_a X4) Y5)) ((ord_le699472955list_a Y5) X4))))
% 0.59/0.75 FOF formula (((eq (nat->(nat->Prop))) (fun (Y4:nat) (Z3:nat)=> (((eq nat) Y4) Z3))) (fun (X4:nat) (Y5:nat)=> ((and ((ord_less_eq_nat X4) Y5)) ((ord_less_eq_nat Y5) X4)))) of role axiom named fact_94_eq__iff
% 0.59/0.75 A new axiom: (((eq (nat->(nat->Prop))) (fun (Y4:nat) (Z3:nat)=> (((eq nat) Y4) Z3))) (fun (X4:nat) (Y5:nat)=> ((and ((ord_less_eq_nat X4) Y5)) ((ord_less_eq_nat Y5) X4))))
% 0.59/0.75 FOF formula (forall (A:nat) (B:nat) (F:(nat->prefix1027212443list_a)) (C2:prefix1027212443list_a), (((ord_less_eq_nat A) B)->((((eq prefix1027212443list_a) (F B)) C2)->((forall (X2:nat) (Y2:nat), (((ord_less_eq_nat X2) Y2)->((ord_le699472955list_a (F X2)) (F Y2))))->((ord_le699472955list_a (F A)) C2))))) of role axiom named fact_95_ord__le__eq__subst
% 0.59/0.75 A new axiom: (forall (A:nat) (B:nat) (F:(nat->prefix1027212443list_a)) (C2:prefix1027212443list_a), (((ord_less_eq_nat A) B)->((((eq prefix1027212443list_a) (F B)) C2)->((forall (X2:nat) (Y2:nat), (((ord_less_eq_nat X2) Y2)->((ord_le699472955list_a (F X2)) (F Y2))))->((ord_le699472955list_a (F A)) C2)))))
% 0.59/0.75 FOF formula (forall (A:prefix1027212443list_a) (B:prefix1027212443list_a) (F:(prefix1027212443list_a->nat)) (C2:nat), (((ord_le699472955list_a A) B)->((((eq nat) (F B)) C2)->((forall (X2:prefix1027212443list_a) (Y2:prefix1027212443list_a), (((ord_le699472955list_a X2) Y2)->((ord_less_eq_nat (F X2)) (F Y2))))->((ord_less_eq_nat (F A)) C2))))) of role axiom named fact_96_ord__le__eq__subst
% 0.59/0.75 A new axiom: (forall (A:prefix1027212443list_a) (B:prefix1027212443list_a) (F:(prefix1027212443list_a->nat)) (C2:nat), (((ord_le699472955list_a A) B)->((((eq nat) (F B)) C2)->((forall (X2:prefix1027212443list_a) (Y2:prefix1027212443list_a), (((ord_le699472955list_a X2) Y2)->((ord_less_eq_nat (F X2)) (F Y2))))->((ord_less_eq_nat (F A)) C2)))))
% 0.59/0.75 FOF formula (forall (A:prefix1027212443list_a) (B:prefix1027212443list_a) (F:(prefix1027212443list_a->prefix1027212443list_a)) (C2:prefix1027212443list_a), (((ord_le699472955list_a A) B)->((((eq prefix1027212443list_a) (F B)) C2)->((forall (X2:prefix1027212443list_a) (Y2:prefix1027212443list_a), (((ord_le699472955list_a X2) Y2)->((ord_le699472955list_a (F X2)) (F Y2))))->((ord_le699472955list_a (F A)) C2))))) of role axiom named fact_97_ord__le__eq__subst
% 0.59/0.75 A new axiom: (forall (A:prefix1027212443list_a) (B:prefix1027212443list_a) (F:(prefix1027212443list_a->prefix1027212443list_a)) (C2:prefix1027212443list_a), (((ord_le699472955list_a A) B)->((((eq prefix1027212443list_a) (F B)) C2)->((forall (X2:prefix1027212443list_a) (Y2:prefix1027212443list_a), (((ord_le699472955list_a X2) Y2)->((ord_le699472955list_a (F X2)) (F Y2))))->((ord_le699472955list_a (F A)) C2)))))
% 0.59/0.75 FOF formula (forall (A:nat) (B:nat) (F:(nat->nat)) (C2:nat), (((ord_less_eq_nat A) B)->((((eq nat) (F B)) C2)->((forall (X2:nat) (Y2:nat), (((ord_less_eq_nat X2) Y2)->((ord_less_eq_nat (F X2)) (F Y2))))->((ord_less_eq_nat (F A)) C2))))) of role axiom named fact_98_ord__le__eq__subst
% 0.59/0.75 A new axiom: (forall (A:nat) (B:nat) (F:(nat->nat)) (C2:nat), (((ord_less_eq_nat A) B)->((((eq nat) (F B)) C2)->((forall (X2:nat) (Y2:nat), (((ord_less_eq_nat X2) Y2)->((ord_less_eq_nat (F X2)) (F Y2))))->((ord_less_eq_nat (F A)) C2)))))
% 0.61/0.77 FOF formula (forall (A:prefix1027212443list_a) (F:(nat->prefix1027212443list_a)) (B:nat) (C2:nat), ((((eq prefix1027212443list_a) A) (F B))->(((ord_less_eq_nat B) C2)->((forall (X2:nat) (Y2:nat), (((ord_less_eq_nat X2) Y2)->((ord_le699472955list_a (F X2)) (F Y2))))->((ord_le699472955list_a A) (F C2)))))) of role axiom named fact_99_ord__eq__le__subst
% 0.61/0.77 A new axiom: (forall (A:prefix1027212443list_a) (F:(nat->prefix1027212443list_a)) (B:nat) (C2:nat), ((((eq prefix1027212443list_a) A) (F B))->(((ord_less_eq_nat B) C2)->((forall (X2:nat) (Y2:nat), (((ord_less_eq_nat X2) Y2)->((ord_le699472955list_a (F X2)) (F Y2))))->((ord_le699472955list_a A) (F C2))))))
% 0.61/0.77 FOF formula (forall (A:nat) (F:(prefix1027212443list_a->nat)) (B:prefix1027212443list_a) (C2:prefix1027212443list_a), ((((eq nat) A) (F B))->(((ord_le699472955list_a B) C2)->((forall (X2:prefix1027212443list_a) (Y2:prefix1027212443list_a), (((ord_le699472955list_a X2) Y2)->((ord_less_eq_nat (F X2)) (F Y2))))->((ord_less_eq_nat A) (F C2)))))) of role axiom named fact_100_ord__eq__le__subst
% 0.61/0.77 A new axiom: (forall (A:nat) (F:(prefix1027212443list_a->nat)) (B:prefix1027212443list_a) (C2:prefix1027212443list_a), ((((eq nat) A) (F B))->(((ord_le699472955list_a B) C2)->((forall (X2:prefix1027212443list_a) (Y2:prefix1027212443list_a), (((ord_le699472955list_a X2) Y2)->((ord_less_eq_nat (F X2)) (F Y2))))->((ord_less_eq_nat A) (F C2))))))
% 0.61/0.77 FOF formula (forall (A:prefix1027212443list_a) (F:(prefix1027212443list_a->prefix1027212443list_a)) (B:prefix1027212443list_a) (C2:prefix1027212443list_a), ((((eq prefix1027212443list_a) A) (F B))->(((ord_le699472955list_a B) C2)->((forall (X2:prefix1027212443list_a) (Y2:prefix1027212443list_a), (((ord_le699472955list_a X2) Y2)->((ord_le699472955list_a (F X2)) (F Y2))))->((ord_le699472955list_a A) (F C2)))))) of role axiom named fact_101_ord__eq__le__subst
% 0.61/0.77 A new axiom: (forall (A:prefix1027212443list_a) (F:(prefix1027212443list_a->prefix1027212443list_a)) (B:prefix1027212443list_a) (C2:prefix1027212443list_a), ((((eq prefix1027212443list_a) A) (F B))->(((ord_le699472955list_a B) C2)->((forall (X2:prefix1027212443list_a) (Y2:prefix1027212443list_a), (((ord_le699472955list_a X2) Y2)->((ord_le699472955list_a (F X2)) (F Y2))))->((ord_le699472955list_a A) (F C2))))))
% 0.61/0.77 FOF formula (forall (A:nat) (F:(nat->nat)) (B:nat) (C2:nat), ((((eq nat) A) (F B))->(((ord_less_eq_nat B) C2)->((forall (X2:nat) (Y2:nat), (((ord_less_eq_nat X2) Y2)->((ord_less_eq_nat (F X2)) (F Y2))))->((ord_less_eq_nat A) (F C2)))))) of role axiom named fact_102_ord__eq__le__subst
% 0.61/0.77 A new axiom: (forall (A:nat) (F:(nat->nat)) (B:nat) (C2:nat), ((((eq nat) A) (F B))->(((ord_less_eq_nat B) C2)->((forall (X2:nat) (Y2:nat), (((ord_less_eq_nat X2) Y2)->((ord_less_eq_nat (F X2)) (F Y2))))->((ord_less_eq_nat A) (F C2))))))
% 0.61/0.77 FOF formula (forall (A:nat) (B:nat) (F:(nat->prefix1027212443list_a)) (C2:prefix1027212443list_a), (((ord_less_eq_nat A) B)->(((ord_le699472955list_a (F B)) C2)->((forall (X2:nat) (Y2:nat), (((ord_less_eq_nat X2) Y2)->((ord_le699472955list_a (F X2)) (F Y2))))->((ord_le699472955list_a (F A)) C2))))) of role axiom named fact_103_order__subst2
% 0.61/0.77 A new axiom: (forall (A:nat) (B:nat) (F:(nat->prefix1027212443list_a)) (C2:prefix1027212443list_a), (((ord_less_eq_nat A) B)->(((ord_le699472955list_a (F B)) C2)->((forall (X2:nat) (Y2:nat), (((ord_less_eq_nat X2) Y2)->((ord_le699472955list_a (F X2)) (F Y2))))->((ord_le699472955list_a (F A)) C2)))))
% 0.61/0.77 FOF formula (forall (A:prefix1027212443list_a) (B:prefix1027212443list_a) (F:(prefix1027212443list_a->nat)) (C2:nat), (((ord_le699472955list_a A) B)->(((ord_less_eq_nat (F B)) C2)->((forall (X2:prefix1027212443list_a) (Y2:prefix1027212443list_a), (((ord_le699472955list_a X2) Y2)->((ord_less_eq_nat (F X2)) (F Y2))))->((ord_less_eq_nat (F A)) C2))))) of role axiom named fact_104_order__subst2
% 0.61/0.77 A new axiom: (forall (A:prefix1027212443list_a) (B:prefix1027212443list_a) (F:(prefix1027212443list_a->nat)) (C2:nat), (((ord_le699472955list_a A) B)->(((ord_less_eq_nat (F B)) C2)->((forall (X2:prefix1027212443list_a) (Y2:prefix1027212443list_a), (((ord_le699472955list_a X2) Y2)->((ord_less_eq_nat (F X2)) (F Y2))))->((ord_less_eq_nat (F A)) C2)))))
% 0.61/0.78 FOF formula (forall (A:prefix1027212443list_a) (B:prefix1027212443list_a) (F:(prefix1027212443list_a->prefix1027212443list_a)) (C2:prefix1027212443list_a), (((ord_le699472955list_a A) B)->(((ord_le699472955list_a (F B)) C2)->((forall (X2:prefix1027212443list_a) (Y2:prefix1027212443list_a), (((ord_le699472955list_a X2) Y2)->((ord_le699472955list_a (F X2)) (F Y2))))->((ord_le699472955list_a (F A)) C2))))) of role axiom named fact_105_order__subst2
% 0.61/0.78 A new axiom: (forall (A:prefix1027212443list_a) (B:prefix1027212443list_a) (F:(prefix1027212443list_a->prefix1027212443list_a)) (C2:prefix1027212443list_a), (((ord_le699472955list_a A) B)->(((ord_le699472955list_a (F B)) C2)->((forall (X2:prefix1027212443list_a) (Y2:prefix1027212443list_a), (((ord_le699472955list_a X2) Y2)->((ord_le699472955list_a (F X2)) (F Y2))))->((ord_le699472955list_a (F A)) C2)))))
% 0.61/0.78 FOF formula (forall (A:nat) (B:nat) (F:(nat->nat)) (C2:nat), (((ord_less_eq_nat A) B)->(((ord_less_eq_nat (F B)) C2)->((forall (X2:nat) (Y2:nat), (((ord_less_eq_nat X2) Y2)->((ord_less_eq_nat (F X2)) (F Y2))))->((ord_less_eq_nat (F A)) C2))))) of role axiom named fact_106_order__subst2
% 0.61/0.78 A new axiom: (forall (A:nat) (B:nat) (F:(nat->nat)) (C2:nat), (((ord_less_eq_nat A) B)->(((ord_less_eq_nat (F B)) C2)->((forall (X2:nat) (Y2:nat), (((ord_less_eq_nat X2) Y2)->((ord_less_eq_nat (F X2)) (F Y2))))->((ord_less_eq_nat (F A)) C2)))))
% 0.61/0.78 FOF formula (forall (A:nat) (F:(prefix1027212443list_a->nat)) (B:prefix1027212443list_a) (C2:prefix1027212443list_a), (((ord_less_eq_nat A) (F B))->(((ord_le699472955list_a B) C2)->((forall (X2:prefix1027212443list_a) (Y2:prefix1027212443list_a), (((ord_le699472955list_a X2) Y2)->((ord_less_eq_nat (F X2)) (F Y2))))->((ord_less_eq_nat A) (F C2)))))) of role axiom named fact_107_order__subst1
% 0.61/0.78 A new axiom: (forall (A:nat) (F:(prefix1027212443list_a->nat)) (B:prefix1027212443list_a) (C2:prefix1027212443list_a), (((ord_less_eq_nat A) (F B))->(((ord_le699472955list_a B) C2)->((forall (X2:prefix1027212443list_a) (Y2:prefix1027212443list_a), (((ord_le699472955list_a X2) Y2)->((ord_less_eq_nat (F X2)) (F Y2))))->((ord_less_eq_nat A) (F C2))))))
% 0.61/0.78 FOF formula (forall (A:prefix1027212443list_a) (F:(nat->prefix1027212443list_a)) (B:nat) (C2:nat), (((ord_le699472955list_a A) (F B))->(((ord_less_eq_nat B) C2)->((forall (X2:nat) (Y2:nat), (((ord_less_eq_nat X2) Y2)->((ord_le699472955list_a (F X2)) (F Y2))))->((ord_le699472955list_a A) (F C2)))))) of role axiom named fact_108_order__subst1
% 0.61/0.78 A new axiom: (forall (A:prefix1027212443list_a) (F:(nat->prefix1027212443list_a)) (B:nat) (C2:nat), (((ord_le699472955list_a A) (F B))->(((ord_less_eq_nat B) C2)->((forall (X2:nat) (Y2:nat), (((ord_less_eq_nat X2) Y2)->((ord_le699472955list_a (F X2)) (F Y2))))->((ord_le699472955list_a A) (F C2))))))
% 0.61/0.78 FOF formula (forall (A:prefix1027212443list_a) (F:(prefix1027212443list_a->prefix1027212443list_a)) (B:prefix1027212443list_a) (C2:prefix1027212443list_a), (((ord_le699472955list_a A) (F B))->(((ord_le699472955list_a B) C2)->((forall (X2:prefix1027212443list_a) (Y2:prefix1027212443list_a), (((ord_le699472955list_a X2) Y2)->((ord_le699472955list_a (F X2)) (F Y2))))->((ord_le699472955list_a A) (F C2)))))) of role axiom named fact_109_order__subst1
% 0.61/0.78 A new axiom: (forall (A:prefix1027212443list_a) (F:(prefix1027212443list_a->prefix1027212443list_a)) (B:prefix1027212443list_a) (C2:prefix1027212443list_a), (((ord_le699472955list_a A) (F B))->(((ord_le699472955list_a B) C2)->((forall (X2:prefix1027212443list_a) (Y2:prefix1027212443list_a), (((ord_le699472955list_a X2) Y2)->((ord_le699472955list_a (F X2)) (F Y2))))->((ord_le699472955list_a A) (F C2))))))
% 0.61/0.78 FOF formula (forall (A:nat) (F:(nat->nat)) (B:nat) (C2:nat), (((ord_less_eq_nat A) (F B))->(((ord_less_eq_nat B) C2)->((forall (X2:nat) (Y2:nat), (((ord_less_eq_nat X2) Y2)->((ord_less_eq_nat (F X2)) (F Y2))))->((ord_less_eq_nat A) (F C2)))))) of role axiom named fact_110_order__subst1
% 0.61/0.78 A new axiom: (forall (A:nat) (F:(nat->nat)) (B:nat) (C2:nat), (((ord_less_eq_nat A) (F B))->(((ord_less_eq_nat B) C2)->((forall (X2:nat) (Y2:nat), (((ord_less_eq_nat X2) Y2)->((ord_less_eq_nat (F X2)) (F Y2))))->((ord_less_eq_nat A) (F C2))))))
% 0.61/0.80 FOF formula (forall (A:nat) (F:(nat->nat)) (B:nat) (C2:nat), ((((eq nat) A) (F B))->(((ord_less_nat B) C2)->((forall (X2:nat) (Y2:nat), (((ord_less_nat X2) Y2)->((ord_less_nat (F X2)) (F Y2))))->((ord_less_nat A) (F C2)))))) of role axiom named fact_111_ord__eq__less__subst
% 0.61/0.80 A new axiom: (forall (A:nat) (F:(nat->nat)) (B:nat) (C2:nat), ((((eq nat) A) (F B))->(((ord_less_nat B) C2)->((forall (X2:nat) (Y2:nat), (((ord_less_nat X2) Y2)->((ord_less_nat (F X2)) (F Y2))))->((ord_less_nat A) (F C2))))))
% 0.61/0.80 FOF formula (forall (A:nat) (B:nat) (F:(nat->nat)) (C2:nat), (((ord_less_nat A) B)->((((eq nat) (F B)) C2)->((forall (X2:nat) (Y2:nat), (((ord_less_nat X2) Y2)->((ord_less_nat (F X2)) (F Y2))))->((ord_less_nat (F A)) C2))))) of role axiom named fact_112_ord__less__eq__subst
% 0.61/0.80 A new axiom: (forall (A:nat) (B:nat) (F:(nat->nat)) (C2:nat), (((ord_less_nat A) B)->((((eq nat) (F B)) C2)->((forall (X2:nat) (Y2:nat), (((ord_less_nat X2) Y2)->((ord_less_nat (F X2)) (F Y2))))->((ord_less_nat (F A)) C2)))))
% 0.61/0.80 FOF formula (forall (A:nat) (F:(nat->nat)) (B:nat) (C2:nat), (((ord_less_nat A) (F B))->(((ord_less_nat B) C2)->((forall (X2:nat) (Y2:nat), (((ord_less_nat X2) Y2)->((ord_less_nat (F X2)) (F Y2))))->((ord_less_nat A) (F C2)))))) of role axiom named fact_113_order__less__subst1
% 0.61/0.80 A new axiom: (forall (A:nat) (F:(nat->nat)) (B:nat) (C2:nat), (((ord_less_nat A) (F B))->(((ord_less_nat B) C2)->((forall (X2:nat) (Y2:nat), (((ord_less_nat X2) Y2)->((ord_less_nat (F X2)) (F Y2))))->((ord_less_nat A) (F C2))))))
% 0.61/0.80 FOF formula (forall (A:nat) (B:nat) (F:(nat->nat)) (C2:nat), (((ord_less_nat A) B)->(((ord_less_nat (F B)) C2)->((forall (X2:nat) (Y2:nat), (((ord_less_nat X2) Y2)->((ord_less_nat (F X2)) (F Y2))))->((ord_less_nat (F A)) C2))))) of role axiom named fact_114_order__less__subst2
% 0.61/0.80 A new axiom: (forall (A:nat) (B:nat) (F:(nat->nat)) (C2:nat), (((ord_less_nat A) B)->(((ord_less_nat (F B)) C2)->((forall (X2:nat) (Y2:nat), (((ord_less_nat X2) Y2)->((ord_less_nat (F X2)) (F Y2))))->((ord_less_nat (F A)) C2)))))
% 0.61/0.80 FOF formula (forall (X:nat), ((ex nat) (fun (X_1:nat)=> ((ord_less_nat X) X_1)))) of role axiom named fact_115_gt__ex
% 0.61/0.80 A new axiom: (forall (X:nat), ((ex nat) (fun (X_1:nat)=> ((ord_less_nat X) X_1))))
% 0.61/0.80 FOF formula (forall (X:nat) (Y:nat), ((not (((eq nat) X) Y))->((((ord_less_nat X) Y)->False)->((ord_less_nat Y) X)))) of role axiom named fact_116_neqE
% 0.61/0.80 A new axiom: (forall (X:nat) (Y:nat), ((not (((eq nat) X) Y))->((((ord_less_nat X) Y)->False)->((ord_less_nat Y) X))))
% 0.61/0.80 FOF formula (forall (X:nat) (Y:nat), (((eq Prop) (not (((eq nat) X) Y))) ((or ((ord_less_nat X) Y)) ((ord_less_nat Y) X)))) of role axiom named fact_117_neq__iff
% 0.61/0.80 A new axiom: (forall (X:nat) (Y:nat), (((eq Prop) (not (((eq nat) X) Y))) ((or ((ord_less_nat X) Y)) ((ord_less_nat Y) X))))
% 0.61/0.80 FOF formula (forall (A:nat) (B:nat), (((ord_less_nat A) B)->(((ord_less_nat B) A)->False))) of role axiom named fact_118_order_Oasym
% 0.61/0.80 A new axiom: (forall (A:nat) (B:nat), (((ord_less_nat A) B)->(((ord_less_nat B) A)->False)))
% 0.61/0.80 FOF formula (forall (X:nat) (Y:nat), (((ord_less_nat X) Y)->(not (((eq nat) X) Y)))) of role axiom named fact_119_less__imp__neq
% 0.61/0.80 A new axiom: (forall (X:nat) (Y:nat), (((ord_less_nat X) Y)->(not (((eq nat) X) Y))))
% 0.61/0.80 FOF formula (forall (X:nat) (Y:nat), (((ord_less_nat X) Y)->(((ord_less_nat Y) X)->False))) of role axiom named fact_120_less__asym
% 0.61/0.80 A new axiom: (forall (X:nat) (Y:nat), (((ord_less_nat X) Y)->(((ord_less_nat Y) X)->False)))
% 0.61/0.80 FOF formula (forall (A:nat) (B:nat), (((ord_less_nat A) B)->(((ord_less_nat B) A)->False))) of role axiom named fact_121_less__asym_H
% 0.61/0.80 A new axiom: (forall (A:nat) (B:nat), (((ord_less_nat A) B)->(((ord_less_nat B) A)->False)))
% 0.61/0.80 FOF formula (forall (X:nat) (Y:nat) (Z4:nat), (((ord_less_nat X) Y)->(((ord_less_nat Y) Z4)->((ord_less_nat X) Z4)))) of role axiom named fact_122_less__trans
% 0.61/0.80 A new axiom: (forall (X:nat) (Y:nat) (Z4:nat), (((ord_less_nat X) Y)->(((ord_less_nat Y) Z4)->((ord_less_nat X) Z4))))
% 0.66/0.82 FOF formula (forall (X:nat) (Y:nat), ((or ((or ((ord_less_nat X) Y)) (((eq nat) X) Y))) ((ord_less_nat Y) X))) of role axiom named fact_123_less__linear
% 0.66/0.82 A new axiom: (forall (X:nat) (Y:nat), ((or ((or ((ord_less_nat X) Y)) (((eq nat) X) Y))) ((ord_less_nat Y) X)))
% 0.66/0.82 FOF formula (forall (X:nat), (((ord_less_nat X) X)->False)) of role axiom named fact_124_less__irrefl
% 0.66/0.82 A new axiom: (forall (X:nat), (((ord_less_nat X) X)->False))
% 0.66/0.82 FOF formula (forall (A:nat) (B:nat) (C2:nat), ((((eq nat) A) B)->(((ord_less_nat B) C2)->((ord_less_nat A) C2)))) of role axiom named fact_125_ord__eq__less__trans
% 0.66/0.82 A new axiom: (forall (A:nat) (B:nat) (C2:nat), ((((eq nat) A) B)->(((ord_less_nat B) C2)->((ord_less_nat A) C2))))
% 0.66/0.82 FOF formula (forall (A:nat) (B:nat) (C2:nat), (((ord_less_nat A) B)->((((eq nat) B) C2)->((ord_less_nat A) C2)))) of role axiom named fact_126_ord__less__eq__trans
% 0.66/0.82 A new axiom: (forall (A:nat) (B:nat) (C2:nat), (((ord_less_nat A) B)->((((eq nat) B) C2)->((ord_less_nat A) C2))))
% 0.66/0.82 FOF formula (forall (B:nat) (A:nat), (((ord_less_nat B) A)->(((ord_less_nat A) B)->False))) of role axiom named fact_127_dual__order_Oasym
% 0.66/0.82 A new axiom: (forall (B:nat) (A:nat), (((ord_less_nat B) A)->(((ord_less_nat A) B)->False)))
% 0.66/0.82 FOF formula (forall (X:nat) (Y:nat), (((ord_less_nat X) Y)->(not (((eq nat) X) Y)))) of role axiom named fact_128_less__imp__not__eq
% 0.66/0.82 A new axiom: (forall (X:nat) (Y:nat), (((ord_less_nat X) Y)->(not (((eq nat) X) Y))))
% 0.66/0.82 FOF formula (forall (X:nat) (Y:nat), (((ord_less_nat X) Y)->(((ord_less_nat Y) X)->False))) of role axiom named fact_129_less__not__sym
% 0.66/0.82 A new axiom: (forall (X:nat) (Y:nat), (((ord_less_nat X) Y)->(((ord_less_nat Y) X)->False)))
% 0.66/0.82 FOF formula (forall (P:(nat->Prop)) (A:nat), ((forall (X2:nat), ((forall (Y3:nat), (((ord_less_nat Y3) X2)->(P Y3)))->(P X2)))->(P A))) of role axiom named fact_130_less__induct
% 0.66/0.82 A new axiom: (forall (P:(nat->Prop)) (A:nat), ((forall (X2:nat), ((forall (Y3:nat), (((ord_less_nat Y3) X2)->(P Y3)))->(P X2)))->(P A)))
% 0.66/0.82 FOF formula (forall (Y:nat) (X:nat), ((((ord_less_nat Y) X)->False)->(((eq Prop) (((ord_less_nat X) Y)->False)) (((eq nat) X) Y)))) of role axiom named fact_131_antisym__conv3
% 0.66/0.82 A new axiom: (forall (Y:nat) (X:nat), ((((ord_less_nat Y) X)->False)->(((eq Prop) (((ord_less_nat X) Y)->False)) (((eq nat) X) Y))))
% 0.66/0.82 FOF formula (forall (X:nat) (Y:nat), (((ord_less_nat X) Y)->(not (((eq nat) Y) X)))) of role axiom named fact_132_less__imp__not__eq2
% 0.66/0.82 A new axiom: (forall (X:nat) (Y:nat), (((ord_less_nat X) Y)->(not (((eq nat) Y) X))))
% 0.66/0.82 FOF formula (forall (X:nat) (Y:nat) (P:Prop), (((ord_less_nat X) Y)->(((ord_less_nat Y) X)->P))) of role axiom named fact_133_less__imp__triv
% 0.66/0.82 A new axiom: (forall (X:nat) (Y:nat) (P:Prop), (((ord_less_nat X) Y)->(((ord_less_nat Y) X)->P)))
% 0.66/0.82 FOF formula (forall (X:nat) (Y:nat), ((((ord_less_nat X) Y)->False)->((not (((eq nat) X) Y))->((ord_less_nat Y) X)))) of role axiom named fact_134_linorder__cases
% 0.66/0.82 A new axiom: (forall (X:nat) (Y:nat), ((((ord_less_nat X) Y)->False)->((not (((eq nat) X) Y))->((ord_less_nat Y) X))))
% 0.66/0.82 FOF formula (forall (A:nat), (((ord_less_nat A) A)->False)) of role axiom named fact_135_dual__order_Oirrefl
% 0.66/0.82 A new axiom: (forall (A:nat), (((ord_less_nat A) A)->False))
% 0.66/0.82 FOF formula (forall (A:nat) (B:nat) (C2:nat), (((ord_less_nat A) B)->(((ord_less_nat B) C2)->((ord_less_nat A) C2)))) of role axiom named fact_136_order_Ostrict__trans
% 0.66/0.82 A new axiom: (forall (A:nat) (B:nat) (C2:nat), (((ord_less_nat A) B)->(((ord_less_nat B) C2)->((ord_less_nat A) C2))))
% 0.66/0.82 FOF formula (forall (X:nat) (Y:nat), (((ord_less_nat X) Y)->(((ord_less_nat Y) X)->False))) of role axiom named fact_137_less__imp__not__less
% 0.66/0.82 A new axiom: (forall (X:nat) (Y:nat), (((ord_less_nat X) Y)->(((ord_less_nat Y) X)->False)))
% 0.66/0.82 FOF formula (((eq ((nat->Prop)->Prop)) (fun (P3:(nat->Prop))=> ((ex nat) (fun (X5:nat)=> (P3 X5))))) (fun (P4:(nat->Prop))=> ((ex nat) (fun (N3:nat)=> ((and (P4 N3)) (forall (M3:nat), (((ord_less_nat M3) N3)->((P4 M3)->False)))))))) of role axiom named fact_138_exists__least__iff
% 0.66/0.82 A new axiom: (((eq ((nat->Prop)->Prop)) (fun (P3:(nat->Prop))=> ((ex nat) (fun (X5:nat)=> (P3 X5))))) (fun (P4:(nat->Prop))=> ((ex nat) (fun (N3:nat)=> ((and (P4 N3)) (forall (M3:nat), (((ord_less_nat M3) N3)->((P4 M3)->False))))))))
% 0.66/0.83 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_139_linorder__less__wlog
% 0.66/0.83 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)))))
% 0.66/0.83 FOF formula (forall (B:nat) (A:nat) (C2:nat), (((ord_less_nat B) A)->(((ord_less_nat C2) B)->((ord_less_nat C2) A)))) of role axiom named fact_140_dual__order_Ostrict__trans
% 0.66/0.83 A new axiom: (forall (B:nat) (A:nat) (C2:nat), (((ord_less_nat B) A)->(((ord_less_nat C2) B)->((ord_less_nat C2) A))))
% 0.66/0.83 FOF formula (forall (X:nat) (Y:nat), (((eq Prop) (((ord_less_nat X) Y)->False)) ((or ((ord_less_nat Y) X)) (((eq nat) X) Y)))) of role axiom named fact_141_not__less__iff__gr__or__eq
% 0.66/0.83 A new axiom: (forall (X:nat) (Y:nat), (((eq Prop) (((ord_less_nat X) Y)->False)) ((or ((ord_less_nat Y) X)) (((eq nat) X) Y))))
% 0.66/0.83 FOF formula (forall (A:nat) (B:nat), (((ord_less_nat A) B)->(not (((eq nat) A) B)))) of role axiom named fact_142_order_Ostrict__implies__not__eq
% 0.66/0.83 A new axiom: (forall (A:nat) (B:nat), (((ord_less_nat A) B)->(not (((eq nat) A) B))))
% 0.66/0.83 FOF formula (forall (B:nat) (A:nat), (((ord_less_nat B) A)->(not (((eq nat) A) B)))) of role axiom named fact_143_dual__order_Ostrict__implies__not__eq
% 0.66/0.83 A new axiom: (forall (B:nat) (A:nat), (((ord_less_nat B) A)->(not (((eq nat) A) B))))
% 0.66/0.83 FOF formula (forall (Y:prefix1027212443list_a) (X:prefix1027212443list_a), (((ord_le699472955list_a Y) X)->(((ord_le887097159list_a X) Y)->False))) of role axiom named fact_144_leD
% 0.66/0.83 A new axiom: (forall (Y:prefix1027212443list_a) (X:prefix1027212443list_a), (((ord_le699472955list_a Y) X)->(((ord_le887097159list_a X) Y)->False)))
% 0.66/0.83 FOF formula (forall (Y:nat) (X:nat), (((ord_less_eq_nat Y) X)->(((ord_less_nat X) Y)->False))) of role axiom named fact_145_leD
% 0.66/0.83 A new axiom: (forall (Y:nat) (X:nat), (((ord_less_eq_nat Y) X)->(((ord_less_nat X) Y)->False)))
% 0.66/0.83 FOF formula (forall (X:nat) (Y:nat), ((((ord_less_nat X) Y)->False)->((ord_less_eq_nat Y) X))) of role axiom named fact_146_leI
% 0.66/0.83 A new axiom: (forall (X:nat) (Y:nat), ((((ord_less_nat X) Y)->False)->((ord_less_eq_nat Y) X)))
% 0.66/0.83 FOF formula (((eq (prefix1027212443list_a->(prefix1027212443list_a->Prop))) ord_le699472955list_a) (fun (X4:prefix1027212443list_a) (Y5:prefix1027212443list_a)=> ((or ((ord_le887097159list_a X4) Y5)) (((eq prefix1027212443list_a) X4) Y5)))) of role axiom named fact_147_le__less
% 0.66/0.83 A new axiom: (((eq (prefix1027212443list_a->(prefix1027212443list_a->Prop))) ord_le699472955list_a) (fun (X4:prefix1027212443list_a) (Y5:prefix1027212443list_a)=> ((or ((ord_le887097159list_a X4) Y5)) (((eq prefix1027212443list_a) X4) Y5))))
% 0.66/0.83 FOF formula (((eq (nat->(nat->Prop))) ord_less_eq_nat) (fun (X4:nat) (Y5:nat)=> ((or ((ord_less_nat X4) Y5)) (((eq nat) X4) Y5)))) of role axiom named fact_148_le__less
% 0.66/0.83 A new axiom: (((eq (nat->(nat->Prop))) ord_less_eq_nat) (fun (X4:nat) (Y5:nat)=> ((or ((ord_less_nat X4) Y5)) (((eq nat) X4) Y5))))
% 0.66/0.83 FOF formula (((eq (prefix1027212443list_a->(prefix1027212443list_a->Prop))) ord_le887097159list_a) (fun (X4:prefix1027212443list_a) (Y5:prefix1027212443list_a)=> ((and ((ord_le699472955list_a X4) Y5)) (not (((eq prefix1027212443list_a) X4) Y5))))) of role axiom named fact_149_less__le
% 0.66/0.83 A new axiom: (((eq (prefix1027212443list_a->(prefix1027212443list_a->Prop))) ord_le887097159list_a) (fun (X4:prefix1027212443list_a) (Y5:prefix1027212443list_a)=> ((and ((ord_le699472955list_a X4) Y5)) (not (((eq prefix1027212443list_a) X4) Y5)))))
% 0.66/0.83 FOF formula (((eq (nat->(nat->Prop))) ord_less_nat) (fun (X4:nat) (Y5:nat)=> ((and ((ord_less_eq_nat X4) Y5)) (not (((eq nat) X4) Y5))))) of role axiom named fact_150_less__le
% 0.66/0.83 A new axiom: (((eq (nat->(nat->Prop))) ord_less_nat) (fun (X4:nat) (Y5:nat)=> ((and ((ord_less_eq_nat X4) Y5)) (not (((eq nat) X4) Y5)))))
% 0.66/0.85 FOF formula (forall (A:prefix1027212443list_a) (F:(nat->prefix1027212443list_a)) (B:nat) (C2:nat), (((ord_le699472955list_a A) (F B))->(((ord_less_nat B) C2)->((forall (X2:nat) (Y2:nat), (((ord_less_nat X2) Y2)->((ord_le887097159list_a (F X2)) (F Y2))))->((ord_le887097159list_a A) (F C2)))))) of role axiom named fact_151_order__le__less__subst1
% 0.66/0.85 A new axiom: (forall (A:prefix1027212443list_a) (F:(nat->prefix1027212443list_a)) (B:nat) (C2:nat), (((ord_le699472955list_a A) (F B))->(((ord_less_nat B) C2)->((forall (X2:nat) (Y2:nat), (((ord_less_nat X2) Y2)->((ord_le887097159list_a (F X2)) (F Y2))))->((ord_le887097159list_a A) (F C2))))))
% 0.66/0.85 FOF formula (forall (A:nat) (F:(nat->nat)) (B:nat) (C2:nat), (((ord_less_eq_nat A) (F B))->(((ord_less_nat B) C2)->((forall (X2:nat) (Y2:nat), (((ord_less_nat X2) Y2)->((ord_less_nat (F X2)) (F Y2))))->((ord_less_nat A) (F C2)))))) of role axiom named fact_152_order__le__less__subst1
% 0.66/0.85 A new axiom: (forall (A:nat) (F:(nat->nat)) (B:nat) (C2:nat), (((ord_less_eq_nat A) (F B))->(((ord_less_nat B) C2)->((forall (X2:nat) (Y2:nat), (((ord_less_nat X2) Y2)->((ord_less_nat (F X2)) (F Y2))))->((ord_less_nat A) (F C2))))))
% 0.66/0.85 FOF formula (forall (A:nat) (B:nat) (F:(nat->prefix1027212443list_a)) (C2:prefix1027212443list_a), (((ord_less_eq_nat A) B)->(((ord_le887097159list_a (F B)) C2)->((forall (X2:nat) (Y2:nat), (((ord_less_eq_nat X2) Y2)->((ord_le699472955list_a (F X2)) (F Y2))))->((ord_le887097159list_a (F A)) C2))))) of role axiom named fact_153_order__le__less__subst2
% 0.66/0.85 A new axiom: (forall (A:nat) (B:nat) (F:(nat->prefix1027212443list_a)) (C2:prefix1027212443list_a), (((ord_less_eq_nat A) B)->(((ord_le887097159list_a (F B)) C2)->((forall (X2:nat) (Y2:nat), (((ord_less_eq_nat X2) Y2)->((ord_le699472955list_a (F X2)) (F Y2))))->((ord_le887097159list_a (F A)) C2)))))
% 0.66/0.85 FOF formula (forall (A:prefix1027212443list_a) (B:prefix1027212443list_a) (F:(prefix1027212443list_a->nat)) (C2:nat), (((ord_le699472955list_a A) B)->(((ord_less_nat (F B)) C2)->((forall (X2:prefix1027212443list_a) (Y2:prefix1027212443list_a), (((ord_le699472955list_a X2) Y2)->((ord_less_eq_nat (F X2)) (F Y2))))->((ord_less_nat (F A)) C2))))) of role axiom named fact_154_order__le__less__subst2
% 0.66/0.85 A new axiom: (forall (A:prefix1027212443list_a) (B:prefix1027212443list_a) (F:(prefix1027212443list_a->nat)) (C2:nat), (((ord_le699472955list_a A) B)->(((ord_less_nat (F B)) C2)->((forall (X2:prefix1027212443list_a) (Y2:prefix1027212443list_a), (((ord_le699472955list_a X2) Y2)->((ord_less_eq_nat (F X2)) (F Y2))))->((ord_less_nat (F A)) C2)))))
% 0.66/0.85 FOF formula (forall (A:prefix1027212443list_a) (B:prefix1027212443list_a) (F:(prefix1027212443list_a->prefix1027212443list_a)) (C2:prefix1027212443list_a), (((ord_le699472955list_a A) B)->(((ord_le887097159list_a (F B)) C2)->((forall (X2:prefix1027212443list_a) (Y2:prefix1027212443list_a), (((ord_le699472955list_a X2) Y2)->((ord_le699472955list_a (F X2)) (F Y2))))->((ord_le887097159list_a (F A)) C2))))) of role axiom named fact_155_order__le__less__subst2
% 0.66/0.85 A new axiom: (forall (A:prefix1027212443list_a) (B:prefix1027212443list_a) (F:(prefix1027212443list_a->prefix1027212443list_a)) (C2:prefix1027212443list_a), (((ord_le699472955list_a A) B)->(((ord_le887097159list_a (F B)) C2)->((forall (X2:prefix1027212443list_a) (Y2:prefix1027212443list_a), (((ord_le699472955list_a X2) Y2)->((ord_le699472955list_a (F X2)) (F Y2))))->((ord_le887097159list_a (F A)) C2)))))
% 0.66/0.85 FOF formula (forall (A:nat) (B:nat) (F:(nat->nat)) (C2:nat), (((ord_less_eq_nat A) B)->(((ord_less_nat (F B)) C2)->((forall (X2:nat) (Y2:nat), (((ord_less_eq_nat X2) Y2)->((ord_less_eq_nat (F X2)) (F Y2))))->((ord_less_nat (F A)) C2))))) of role axiom named fact_156_order__le__less__subst2
% 0.66/0.85 A new axiom: (forall (A:nat) (B:nat) (F:(nat->nat)) (C2:nat), (((ord_less_eq_nat A) B)->(((ord_less_nat (F B)) C2)->((forall (X2:nat) (Y2:nat), (((ord_less_eq_nat X2) Y2)->((ord_less_eq_nat (F X2)) (F Y2))))->((ord_less_nat (F A)) C2)))))
% 0.66/0.85 FOF formula (forall (A:prefix1027212443list_a) (F:(nat->prefix1027212443list_a)) (B:nat) (C2:nat), (((ord_le887097159list_a A) (F B))->(((ord_less_eq_nat B) C2)->((forall (X2:nat) (Y2:nat), (((ord_less_eq_nat X2) Y2)->((ord_le699472955list_a (F X2)) (F Y2))))->((ord_le887097159list_a A) (F C2)))))) of role axiom named fact_157_order__less__le__subst1
% 0.69/0.86 A new axiom: (forall (A:prefix1027212443list_a) (F:(nat->prefix1027212443list_a)) (B:nat) (C2:nat), (((ord_le887097159list_a A) (F B))->(((ord_less_eq_nat B) C2)->((forall (X2:nat) (Y2:nat), (((ord_less_eq_nat X2) Y2)->((ord_le699472955list_a (F X2)) (F Y2))))->((ord_le887097159list_a A) (F C2))))))
% 0.69/0.86 FOF formula (forall (A:nat) (F:(prefix1027212443list_a->nat)) (B:prefix1027212443list_a) (C2:prefix1027212443list_a), (((ord_less_nat A) (F B))->(((ord_le699472955list_a B) C2)->((forall (X2:prefix1027212443list_a) (Y2:prefix1027212443list_a), (((ord_le699472955list_a X2) Y2)->((ord_less_eq_nat (F X2)) (F Y2))))->((ord_less_nat A) (F C2)))))) of role axiom named fact_158_order__less__le__subst1
% 0.69/0.86 A new axiom: (forall (A:nat) (F:(prefix1027212443list_a->nat)) (B:prefix1027212443list_a) (C2:prefix1027212443list_a), (((ord_less_nat A) (F B))->(((ord_le699472955list_a B) C2)->((forall (X2:prefix1027212443list_a) (Y2:prefix1027212443list_a), (((ord_le699472955list_a X2) Y2)->((ord_less_eq_nat (F X2)) (F Y2))))->((ord_less_nat A) (F C2))))))
% 0.69/0.86 FOF formula (forall (A:prefix1027212443list_a) (F:(prefix1027212443list_a->prefix1027212443list_a)) (B:prefix1027212443list_a) (C2:prefix1027212443list_a), (((ord_le887097159list_a A) (F B))->(((ord_le699472955list_a B) C2)->((forall (X2:prefix1027212443list_a) (Y2:prefix1027212443list_a), (((ord_le699472955list_a X2) Y2)->((ord_le699472955list_a (F X2)) (F Y2))))->((ord_le887097159list_a A) (F C2)))))) of role axiom named fact_159_order__less__le__subst1
% 0.69/0.86 A new axiom: (forall (A:prefix1027212443list_a) (F:(prefix1027212443list_a->prefix1027212443list_a)) (B:prefix1027212443list_a) (C2:prefix1027212443list_a), (((ord_le887097159list_a A) (F B))->(((ord_le699472955list_a B) C2)->((forall (X2:prefix1027212443list_a) (Y2:prefix1027212443list_a), (((ord_le699472955list_a X2) Y2)->((ord_le699472955list_a (F X2)) (F Y2))))->((ord_le887097159list_a A) (F C2))))))
% 0.69/0.86 FOF formula (forall (A:nat) (F:(nat->nat)) (B:nat) (C2:nat), (((ord_less_nat A) (F B))->(((ord_less_eq_nat B) C2)->((forall (X2:nat) (Y2:nat), (((ord_less_eq_nat X2) Y2)->((ord_less_eq_nat (F X2)) (F Y2))))->((ord_less_nat A) (F C2)))))) of role axiom named fact_160_order__less__le__subst1
% 0.69/0.86 A new axiom: (forall (A:nat) (F:(nat->nat)) (B:nat) (C2:nat), (((ord_less_nat A) (F B))->(((ord_less_eq_nat B) C2)->((forall (X2:nat) (Y2:nat), (((ord_less_eq_nat X2) Y2)->((ord_less_eq_nat (F X2)) (F Y2))))->((ord_less_nat A) (F C2))))))
% 0.69/0.86 FOF formula (forall (A:nat) (B:nat) (F:(nat->prefix1027212443list_a)) (C2:prefix1027212443list_a), (((ord_less_nat A) B)->(((ord_le699472955list_a (F B)) C2)->((forall (X2:nat) (Y2:nat), (((ord_less_nat X2) Y2)->((ord_le887097159list_a (F X2)) (F Y2))))->((ord_le887097159list_a (F A)) C2))))) of role axiom named fact_161_order__less__le__subst2
% 0.69/0.86 A new axiom: (forall (A:nat) (B:nat) (F:(nat->prefix1027212443list_a)) (C2:prefix1027212443list_a), (((ord_less_nat A) B)->(((ord_le699472955list_a (F B)) C2)->((forall (X2:nat) (Y2:nat), (((ord_less_nat X2) Y2)->((ord_le887097159list_a (F X2)) (F Y2))))->((ord_le887097159list_a (F A)) C2)))))
% 0.69/0.86 FOF formula (forall (A:nat) (B:nat) (F:(nat->nat)) (C2:nat), (((ord_less_nat A) B)->(((ord_less_eq_nat (F B)) C2)->((forall (X2:nat) (Y2:nat), (((ord_less_nat X2) Y2)->((ord_less_nat (F X2)) (F Y2))))->((ord_less_nat (F A)) C2))))) of role axiom named fact_162_order__less__le__subst2
% 0.69/0.86 A new axiom: (forall (A:nat) (B:nat) (F:(nat->nat)) (C2:nat), (((ord_less_nat A) B)->(((ord_less_eq_nat (F B)) C2)->((forall (X2:nat) (Y2:nat), (((ord_less_nat X2) Y2)->((ord_less_nat (F X2)) (F Y2))))->((ord_less_nat (F A)) C2)))))
% 0.69/0.86 FOF formula (forall (X:nat) (Y:nat), (((eq Prop) (((ord_less_eq_nat X) Y)->False)) ((ord_less_nat Y) X))) of role axiom named fact_163_not__le
% 0.69/0.86 A new axiom: (forall (X:nat) (Y:nat), (((eq Prop) (((ord_less_eq_nat X) Y)->False)) ((ord_less_nat Y) X)))
% 0.69/0.87 FOF formula (forall (X:nat) (Y:nat), (((eq Prop) (((ord_less_nat X) Y)->False)) ((ord_less_eq_nat Y) X))) of role axiom named fact_164_not__less
% 0.69/0.87 A new axiom: (forall (X:nat) (Y:nat), (((eq Prop) (((ord_less_nat X) Y)->False)) ((ord_less_eq_nat Y) X)))
% 0.69/0.87 FOF formula (forall (A:prefix1027212443list_a) (B:prefix1027212443list_a), (((ord_le699472955list_a A) B)->((not (((eq prefix1027212443list_a) A) B))->((ord_le887097159list_a A) B)))) of role axiom named fact_165_le__neq__trans
% 0.69/0.87 A new axiom: (forall (A:prefix1027212443list_a) (B:prefix1027212443list_a), (((ord_le699472955list_a A) B)->((not (((eq prefix1027212443list_a) A) B))->((ord_le887097159list_a A) B))))
% 0.69/0.87 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_166_le__neq__trans
% 0.69/0.87 A new axiom: (forall (A:nat) (B:nat), (((ord_less_eq_nat A) B)->((not (((eq nat) A) B))->((ord_less_nat A) B))))
% 0.69/0.87 FOF formula (forall (X:prefix1027212443list_a) (Y:prefix1027212443list_a), ((((ord_le887097159list_a X) Y)->False)->(((eq Prop) ((ord_le699472955list_a X) Y)) (((eq prefix1027212443list_a) X) Y)))) of role axiom named fact_167_antisym__conv1
% 0.69/0.87 A new axiom: (forall (X:prefix1027212443list_a) (Y:prefix1027212443list_a), ((((ord_le887097159list_a X) Y)->False)->(((eq Prop) ((ord_le699472955list_a X) Y)) (((eq prefix1027212443list_a) X) Y))))
% 0.69/0.87 FOF formula (forall (X:nat) (Y:nat), ((((ord_less_nat X) Y)->False)->(((eq Prop) ((ord_less_eq_nat X) Y)) (((eq nat) X) Y)))) of role axiom named fact_168_antisym__conv1
% 0.69/0.87 A new axiom: (forall (X:nat) (Y:nat), ((((ord_less_nat X) Y)->False)->(((eq Prop) ((ord_less_eq_nat X) Y)) (((eq nat) X) Y))))
% 0.69/0.87 FOF formula (forall (X:prefix1027212443list_a) (Y:prefix1027212443list_a), (((ord_le699472955list_a X) Y)->(((eq Prop) (((ord_le887097159list_a X) Y)->False)) (((eq prefix1027212443list_a) X) Y)))) of role axiom named fact_169_antisym__conv2
% 0.69/0.87 A new axiom: (forall (X:prefix1027212443list_a) (Y:prefix1027212443list_a), (((ord_le699472955list_a X) Y)->(((eq Prop) (((ord_le887097159list_a X) Y)->False)) (((eq prefix1027212443list_a) X) Y))))
% 0.69/0.87 FOF formula (forall (X:nat) (Y:nat), (((ord_less_eq_nat X) Y)->(((eq Prop) (((ord_less_nat X) Y)->False)) (((eq nat) X) Y)))) of role axiom named fact_170_antisym__conv2
% 0.69/0.87 A new axiom: (forall (X:nat) (Y:nat), (((ord_less_eq_nat X) Y)->(((eq Prop) (((ord_less_nat X) Y)->False)) (((eq nat) X) Y))))
% 0.69/0.87 FOF formula (forall (X:prefix1027212443list_a) (Y:prefix1027212443list_a), (((ord_le887097159list_a X) Y)->((ord_le699472955list_a X) Y))) of role axiom named fact_171_less__imp__le
% 0.69/0.87 A new axiom: (forall (X:prefix1027212443list_a) (Y:prefix1027212443list_a), (((ord_le887097159list_a X) Y)->((ord_le699472955list_a X) Y)))
% 0.69/0.87 FOF formula (forall (X:nat) (Y:nat), (((ord_less_nat X) Y)->((ord_less_eq_nat X) Y))) of role axiom named fact_172_less__imp__le
% 0.69/0.87 A new axiom: (forall (X:nat) (Y:nat), (((ord_less_nat X) Y)->((ord_less_eq_nat X) Y)))
% 0.69/0.87 FOF formula (forall (X:prefix1027212443list_a) (Y:prefix1027212443list_a) (Z4:prefix1027212443list_a), (((ord_le699472955list_a X) Y)->(((ord_le887097159list_a Y) Z4)->((ord_le887097159list_a X) Z4)))) of role axiom named fact_173_le__less__trans
% 0.69/0.87 A new axiom: (forall (X:prefix1027212443list_a) (Y:prefix1027212443list_a) (Z4:prefix1027212443list_a), (((ord_le699472955list_a X) Y)->(((ord_le887097159list_a Y) Z4)->((ord_le887097159list_a X) Z4))))
% 0.69/0.87 FOF formula (forall (X:nat) (Y:nat) (Z4:nat), (((ord_less_eq_nat X) Y)->(((ord_less_nat Y) Z4)->((ord_less_nat X) Z4)))) of role axiom named fact_174_le__less__trans
% 0.69/0.87 A new axiom: (forall (X:nat) (Y:nat) (Z4:nat), (((ord_less_eq_nat X) Y)->(((ord_less_nat Y) Z4)->((ord_less_nat X) Z4))))
% 0.69/0.87 FOF formula (forall (X:prefix1027212443list_a) (Y:prefix1027212443list_a) (Z4:prefix1027212443list_a), (((ord_le887097159list_a X) Y)->(((ord_le699472955list_a Y) Z4)->((ord_le887097159list_a X) Z4)))) of role axiom named fact_175_less__le__trans
% 0.69/0.87 A new axiom: (forall (X:prefix1027212443list_a) (Y:prefix1027212443list_a) (Z4:prefix1027212443list_a), (((ord_le887097159list_a X) Y)->(((ord_le699472955list_a Y) Z4)->((ord_le887097159list_a X) Z4))))
% 0.69/0.88 FOF formula (forall (X:nat) (Y:nat) (Z4:nat), (((ord_less_nat X) Y)->(((ord_less_eq_nat Y) Z4)->((ord_less_nat X) Z4)))) of role axiom named fact_176_less__le__trans
% 0.69/0.88 A new axiom: (forall (X:nat) (Y:nat) (Z4:nat), (((ord_less_nat X) Y)->(((ord_less_eq_nat Y) Z4)->((ord_less_nat X) Z4))))
% 0.69/0.88 FOF formula (forall (X:nat) (Y:nat), ((or ((ord_less_eq_nat X) Y)) ((ord_less_nat Y) X))) of role axiom named fact_177_le__less__linear
% 0.69/0.88 A new axiom: (forall (X:nat) (Y:nat), ((or ((ord_less_eq_nat X) Y)) ((ord_less_nat Y) X)))
% 0.69/0.88 FOF formula (forall (X:prefix1027212443list_a) (Y:prefix1027212443list_a), (((ord_le699472955list_a X) Y)->((or ((ord_le887097159list_a X) Y)) (((eq prefix1027212443list_a) X) Y)))) of role axiom named fact_178_le__imp__less__or__eq
% 0.69/0.88 A new axiom: (forall (X:prefix1027212443list_a) (Y:prefix1027212443list_a), (((ord_le699472955list_a X) Y)->((or ((ord_le887097159list_a X) Y)) (((eq prefix1027212443list_a) X) Y))))
% 0.69/0.88 FOF formula (forall (X:nat) (Y:nat), (((ord_less_eq_nat X) Y)->((or ((ord_less_nat X) Y)) (((eq nat) X) Y)))) of role axiom named fact_179_le__imp__less__or__eq
% 0.69/0.88 A new axiom: (forall (X:nat) (Y:nat), (((ord_less_eq_nat X) Y)->((or ((ord_less_nat X) Y)) (((eq nat) X) Y))))
% 0.69/0.88 FOF formula (((eq (prefix1027212443list_a->(prefix1027212443list_a->Prop))) ord_le887097159list_a) (fun (X4:prefix1027212443list_a) (Y5:prefix1027212443list_a)=> ((and ((ord_le699472955list_a X4) Y5)) (((ord_le699472955list_a Y5) X4)->False)))) of role axiom named fact_180_less__le__not__le
% 0.69/0.88 A new axiom: (((eq (prefix1027212443list_a->(prefix1027212443list_a->Prop))) ord_le887097159list_a) (fun (X4:prefix1027212443list_a) (Y5:prefix1027212443list_a)=> ((and ((ord_le699472955list_a X4) Y5)) (((ord_le699472955list_a Y5) X4)->False))))
% 0.69/0.88 FOF formula (((eq (nat->(nat->Prop))) ord_less_nat) (fun (X4:nat) (Y5:nat)=> ((and ((ord_less_eq_nat X4) Y5)) (((ord_less_eq_nat Y5) X4)->False)))) of role axiom named fact_181_less__le__not__le
% 0.69/0.88 A new axiom: (((eq (nat->(nat->Prop))) ord_less_nat) (fun (X4:nat) (Y5:nat)=> ((and ((ord_less_eq_nat X4) Y5)) (((ord_less_eq_nat Y5) X4)->False))))
% 0.69/0.88 FOF formula (forall (Y:nat) (X:nat), ((((ord_less_eq_nat Y) X)->False)->((ord_less_nat X) Y))) of role axiom named fact_182_not__le__imp__less
% 0.69/0.88 A new axiom: (forall (Y:nat) (X:nat), ((((ord_less_eq_nat Y) X)->False)->((ord_less_nat X) Y)))
% 0.69/0.88 FOF formula (forall (A:prefix1027212443list_a) (B:prefix1027212443list_a) (C2:prefix1027212443list_a), (((ord_le699472955list_a A) B)->(((ord_le887097159list_a B) C2)->((ord_le887097159list_a A) C2)))) of role axiom named fact_183_order_Ostrict__trans1
% 0.69/0.88 A new axiom: (forall (A:prefix1027212443list_a) (B:prefix1027212443list_a) (C2:prefix1027212443list_a), (((ord_le699472955list_a A) B)->(((ord_le887097159list_a B) C2)->((ord_le887097159list_a A) C2))))
% 0.69/0.88 FOF formula (forall (A:nat) (B:nat) (C2:nat), (((ord_less_eq_nat A) B)->(((ord_less_nat B) C2)->((ord_less_nat A) C2)))) of role axiom named fact_184_order_Ostrict__trans1
% 0.69/0.88 A new axiom: (forall (A:nat) (B:nat) (C2:nat), (((ord_less_eq_nat A) B)->(((ord_less_nat B) C2)->((ord_less_nat A) C2))))
% 0.69/0.88 FOF formula (forall (A:prefix1027212443list_a) (B:prefix1027212443list_a) (C2:prefix1027212443list_a), (((ord_le887097159list_a A) B)->(((ord_le699472955list_a B) C2)->((ord_le887097159list_a A) C2)))) of role axiom named fact_185_order_Ostrict__trans2
% 0.69/0.88 A new axiom: (forall (A:prefix1027212443list_a) (B:prefix1027212443list_a) (C2:prefix1027212443list_a), (((ord_le887097159list_a A) B)->(((ord_le699472955list_a B) C2)->((ord_le887097159list_a A) C2))))
% 0.69/0.88 FOF formula (forall (A:nat) (B:nat) (C2:nat), (((ord_less_nat A) B)->(((ord_less_eq_nat B) C2)->((ord_less_nat A) C2)))) of role axiom named fact_186_order_Ostrict__trans2
% 0.69/0.88 A new axiom: (forall (A:nat) (B:nat) (C2:nat), (((ord_less_nat A) B)->(((ord_less_eq_nat B) C2)->((ord_less_nat A) C2))))
% 0.69/0.88 FOF formula (((eq (prefix1027212443list_a->(prefix1027212443list_a->Prop))) ord_le699472955list_a) (fun (A2:prefix1027212443list_a) (B2:prefix1027212443list_a)=> ((or ((ord_le887097159list_a A2) B2)) (((eq prefix1027212443list_a) A2) B2)))) of role axiom named fact_187_order_Oorder__iff__strict
% 0.69/0.88 A new axiom: (((eq (prefix1027212443list_a->(prefix1027212443list_a->Prop))) ord_le699472955list_a) (fun (A2:prefix1027212443list_a) (B2:prefix1027212443list_a)=> ((or ((ord_le887097159list_a A2) B2)) (((eq prefix1027212443list_a) A2) B2))))
% 0.69/0.88 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_188_order_Oorder__iff__strict
% 0.69/0.88 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))))
% 0.69/0.88 FOF formula (((eq (prefix1027212443list_a->(prefix1027212443list_a->Prop))) ord_le887097159list_a) (fun (A2:prefix1027212443list_a) (B2:prefix1027212443list_a)=> ((and ((ord_le699472955list_a A2) B2)) (not (((eq prefix1027212443list_a) A2) B2))))) of role axiom named fact_189_order_Ostrict__iff__order
% 0.69/0.88 A new axiom: (((eq (prefix1027212443list_a->(prefix1027212443list_a->Prop))) ord_le887097159list_a) (fun (A2:prefix1027212443list_a) (B2:prefix1027212443list_a)=> ((and ((ord_le699472955list_a A2) B2)) (not (((eq prefix1027212443list_a) A2) B2)))))
% 0.69/0.88 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_190_order_Ostrict__iff__order
% 0.69/0.88 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)))))
% 0.69/0.88 FOF formula (forall (B:prefix1027212443list_a) (A:prefix1027212443list_a) (C2:prefix1027212443list_a), (((ord_le699472955list_a B) A)->(((ord_le887097159list_a C2) B)->((ord_le887097159list_a C2) A)))) of role axiom named fact_191_dual__order_Ostrict__trans1
% 0.69/0.88 A new axiom: (forall (B:prefix1027212443list_a) (A:prefix1027212443list_a) (C2:prefix1027212443list_a), (((ord_le699472955list_a B) A)->(((ord_le887097159list_a C2) B)->((ord_le887097159list_a C2) A))))
% 0.69/0.88 FOF formula (forall (B:nat) (A:nat) (C2:nat), (((ord_less_eq_nat B) A)->(((ord_less_nat C2) B)->((ord_less_nat C2) A)))) of role axiom named fact_192_dual__order_Ostrict__trans1
% 0.69/0.88 A new axiom: (forall (B:nat) (A:nat) (C2:nat), (((ord_less_eq_nat B) A)->(((ord_less_nat C2) B)->((ord_less_nat C2) A))))
% 0.69/0.88 FOF formula (forall (B:prefix1027212443list_a) (A:prefix1027212443list_a) (C2:prefix1027212443list_a), (((ord_le887097159list_a B) A)->(((ord_le699472955list_a C2) B)->((ord_le887097159list_a C2) A)))) of role axiom named fact_193_dual__order_Ostrict__trans2
% 0.69/0.88 A new axiom: (forall (B:prefix1027212443list_a) (A:prefix1027212443list_a) (C2:prefix1027212443list_a), (((ord_le887097159list_a B) A)->(((ord_le699472955list_a C2) B)->((ord_le887097159list_a C2) A))))
% 0.69/0.88 FOF formula (forall (B:nat) (A:nat) (C2:nat), (((ord_less_nat B) A)->(((ord_less_eq_nat C2) B)->((ord_less_nat C2) A)))) of role axiom named fact_194_dual__order_Ostrict__trans2
% 0.69/0.88 A new axiom: (forall (B:nat) (A:nat) (C2:nat), (((ord_less_nat B) A)->(((ord_less_eq_nat C2) B)->((ord_less_nat C2) A))))
% 0.69/0.88 FOF formula ((ord_less_nat ia) (((monito1457594016ress_a sigma) (((until_a phi_1) i2) phi_2)) (plen_P694648887list_a pi))) of role axiom named fact_195_Until_Oprems
% 0.69/0.88 A new axiom: ((ord_less_nat ia) (((monito1457594016ress_a sigma) (((until_a phi_1) i2) phi_2)) (plen_P694648887list_a pi)))
% 0.69/0.88 FOF formula (forall (Pi:prefix1027212443list_a) (Pi2:prefix1027212443list_a), (((ord_le699472955list_a Pi) Pi2)->((ord_less_eq_nat (plen_P694648887list_a Pi)) (plen_P694648887list_a Pi2)))) of role axiom named fact_196_plen__mono
% 0.69/0.88 A new axiom: (forall (Pi:prefix1027212443list_a) (Pi2:prefix1027212443list_a), (((ord_le699472955list_a Pi) Pi2)->((ord_less_eq_nat (plen_P694648887list_a Pi)) (plen_P694648887list_a Pi2))))
% 0.69/0.88 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_197_verit__comp__simplify1_I3_J
% 0.69/0.88 A new axiom: (forall (B4:nat) (A4:nat), (((eq Prop) (((ord_less_eq_nat B4) A4)->False)) ((ord_less_nat A4) B4)))
% 0.69/0.89 FOF formula ((ord_less_nat ia) (((monito1457594016ress_a sigma2) (((until_a phi_1) i2) phi_2)) (plen_P694648887list_a pi))) of role axiom named fact_198__092_060open_062i_A_060_AMonitor__Mirabelle__prbptmgypa_Oprogress_A_092_060sigma_062_H_A_Iformula_OUntil_A_092_060phi_0621_AI_A_092_060phi_0622_J_A_Iplen_A_092_060pi_062_J_092_060close_062
% 0.69/0.89 A new axiom: ((ord_less_nat ia) (((monito1457594016ress_a sigma2) (((until_a phi_1) i2) phi_2)) (plen_P694648887list_a pi)))
% 0.69/0.89 FOF formula (((eq (prefix1027212443list_a->(prefix1027212443list_a->Prop))) ord_le887097159list_a) (fun (X4:prefix1027212443list_a) (Y5:prefix1027212443list_a)=> ((and ((ord_le699472955list_a X4) Y5)) (((ord_le699472955list_a Y5) X4)->False)))) of role axiom named fact_199_less__prefix__def
% 0.69/0.89 A new axiom: (((eq (prefix1027212443list_a->(prefix1027212443list_a->Prop))) ord_le887097159list_a) (fun (X4:prefix1027212443list_a) (Y5:prefix1027212443list_a)=> ((and ((ord_le699472955list_a X4) Y5)) (((ord_le699472955list_a Y5) X4)->False))))
% 0.69/0.89 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_200_verit__la__disequality
% 0.69/0.89 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)))
% 0.69/0.89 FOF formula (forall (A:nat), (((ord_less_nat A) A)->False)) of role axiom named fact_201_verit__comp__simplify1_I1_J
% 0.69/0.89 A new axiom: (forall (A:nat), (((ord_less_nat A) A)->False))
% 0.69/0.89 FOF formula (forall (P5:prefix1027212443list_a), ((ex trace_1367752404list_a) (fun (X_1:trace_1367752404list_a)=> ((prefix1041802747list_a P5) X_1)))) of role axiom named fact_202_ex__prefix__of
% 0.69/0.89 A new axiom: (forall (P5:prefix1027212443list_a), ((ex trace_1367752404list_a) (fun (X_1:trace_1367752404list_a)=> ((prefix1041802747list_a P5) X_1))))
% 0.69/0.89 FOF formula (forall (Pi:prefix1027212443list_a) (Pi2:prefix1027212443list_a) (S:trace_1367752404list_a), (((ord_le699472955list_a Pi) Pi2)->(((prefix1041802747list_a Pi2) S)->((prefix1041802747list_a Pi) S)))) of role axiom named fact_203_prefix__of__antimono
% 0.69/0.89 A new axiom: (forall (Pi:prefix1027212443list_a) (Pi2:prefix1027212443list_a) (S:trace_1367752404list_a), (((ord_le699472955list_a Pi) Pi2)->(((prefix1041802747list_a Pi2) S)->((prefix1041802747list_a Pi) S))))
% 0.69/0.89 FOF formula (forall (Pi:prefix1027212443list_a) (Sigma:trace_1367752404list_a) (Pi2:prefix1027212443list_a), (((prefix1041802747list_a Pi) Sigma)->(((prefix1041802747list_a Pi2) Sigma)->((or ((ord_le699472955list_a Pi) Pi2)) ((ord_le699472955list_a Pi2) Pi))))) of role axiom named fact_204_prefix__of__imp__linear
% 0.69/0.89 A new axiom: (forall (Pi:prefix1027212443list_a) (Sigma:trace_1367752404list_a) (Pi2:prefix1027212443list_a), (((prefix1041802747list_a Pi) Sigma)->(((prefix1041802747list_a Pi2) Sigma)->((or ((ord_le699472955list_a Pi) Pi2)) ((ord_le699472955list_a Pi2) Pi)))))
% 0.69/0.89 FOF formula (forall (X91:formula_a) (X92:i) (X93:formula_a) (Y91:formula_a) (Y92:i) (Y93:formula_a), (((eq Prop) (((eq formula_a) (((until_a X91) X92) X93)) (((until_a Y91) Y92) Y93))) ((and ((and (((eq formula_a) X91) Y91)) (((eq i) X92) Y92))) (((eq formula_a) X93) Y93)))) of role axiom named fact_205_formula_Oinject_I9_J
% 0.69/0.89 A new axiom: (forall (X91:formula_a) (X92:i) (X93:formula_a) (Y91:formula_a) (Y92:i) (Y93:formula_a), (((eq Prop) (((eq formula_a) (((until_a X91) X92) X93)) (((until_a Y91) Y92) Y93))) ((and ((and (((eq formula_a) X91) Y91)) (((eq i) X92) Y92))) (((eq formula_a) X93) Y93))))
% 0.69/0.89 FOF formula (forall (K:nat), (((ord_less_eq_nat ((tau_Pr257024512list_a sigma2) K)) ((plus_plus_nat ((tau_Pr257024512list_a sigma2) ia)) b))->((ord_less_nat K) (((monito1457594016ress_a sigma) phi_2) (plen_P694648887list_a pi))))) of role axiom named fact_206__C21_C
% 0.69/0.89 A new axiom: (forall (K:nat), (((ord_less_eq_nat ((tau_Pr257024512list_a sigma2) K)) ((plus_plus_nat ((tau_Pr257024512list_a sigma2) ia)) b))->((ord_less_nat K) (((monito1457594016ress_a sigma) phi_2) (plen_P694648887list_a pi)))))
% 0.69/0.89 FOF formula (forall (K:nat), (((ord_less_eq_nat ((tau_Pr257024512list_a sigma2) K)) ((plus_plus_nat ((tau_Pr257024512list_a sigma2) ia)) b))->((ord_less_nat K) (((monito1457594016ress_a sigma) phi_1) (plen_P694648887list_a pi))))) of role axiom named fact_207__C11_C
% 0.69/0.90 A new axiom: (forall (K:nat), (((ord_less_eq_nat ((tau_Pr257024512list_a sigma2) K)) ((plus_plus_nat ((tau_Pr257024512list_a sigma2) ia)) b))->((ord_less_nat K) (((monito1457594016ress_a sigma) phi_1) (plen_P694648887list_a pi)))))
% 0.69/0.90 FOF formula ((ord_less_eq_nat ((tau_Pr257024512list_a sigma2) k)) ((plus_plus_nat ((tau_Pr257024512list_a sigma2) ia)) b)) of role axiom named fact_208_that
% 0.69/0.90 A new axiom: ((ord_less_eq_nat ((tau_Pr257024512list_a sigma2) k)) ((plus_plus_nat ((tau_Pr257024512list_a sigma2) ia)) b))
% 0.69/0.90 FOF formula (forall (K:nat) (M:nat) (N:nat), (((eq Prop) ((ord_less_nat ((plus_plus_nat K) M)) ((plus_plus_nat K) N))) ((ord_less_nat M) N))) of role axiom named fact_209_nat__add__left__cancel__less
% 0.69/0.90 A new axiom: (forall (K:nat) (M:nat) (N:nat), (((eq Prop) ((ord_less_nat ((plus_plus_nat K) M)) ((plus_plus_nat K) N))) ((ord_less_nat M) N)))
% 0.69/0.90 FOF formula (forall (K:nat) (M:nat) (N:nat), (((eq Prop) ((ord_less_eq_nat ((plus_plus_nat K) M)) ((plus_plus_nat K) N))) ((ord_less_eq_nat M) N))) of role axiom named fact_210_nat__add__left__cancel__le
% 0.69/0.90 A new axiom: (forall (K:nat) (M:nat) (N:nat), (((eq Prop) ((ord_less_eq_nat ((plus_plus_nat K) M)) ((plus_plus_nat K) N))) ((ord_less_eq_nat M) N)))
% 0.69/0.90 FOF formula (forall (K:nat), (((ord_less_eq_nat ((tau_Pr257024512list_a sigma) K)) ((plus_plus_nat ((tau_Pr257024512list_a sigma) ia)) b))->((ord_less_nat K) (plen_P694648887list_a pi)))) of role axiom named fact_211__C3_C
% 0.69/0.90 A new axiom: (forall (K:nat), (((ord_less_eq_nat ((tau_Pr257024512list_a sigma) K)) ((plus_plus_nat ((tau_Pr257024512list_a sigma) ia)) b))->((ord_less_nat K) (plen_P694648887list_a pi))))
% 0.69/0.90 FOF formula (forall (K:nat), (((ord_less_eq_nat ((tau_Pr257024512list_a sigma) K)) ((plus_plus_nat ((tau_Pr257024512list_a sigma) ia)) b))->((ord_less_nat K) (((monito1457594016ress_a sigma) phi_1) (plen_P694648887list_a pi))))) of role axiom named fact_212__C1_C
% 0.69/0.90 A new axiom: (forall (K:nat), (((ord_less_eq_nat ((tau_Pr257024512list_a sigma) K)) ((plus_plus_nat ((tau_Pr257024512list_a sigma) ia)) b))->((ord_less_nat K) (((monito1457594016ress_a sigma) phi_1) (plen_P694648887list_a pi)))))
% 0.69/0.90 FOF formula (forall (K:nat), (((ord_less_eq_nat ((tau_Pr257024512list_a sigma) K)) ((plus_plus_nat ((tau_Pr257024512list_a sigma) ia)) b))->((ord_less_nat K) (((monito1457594016ress_a sigma) phi_2) (plen_P694648887list_a pi))))) of role axiom named fact_213__C2_C
% 0.69/0.90 A new axiom: (forall (K:nat), (((ord_less_eq_nat ((tau_Pr257024512list_a sigma) K)) ((plus_plus_nat ((tau_Pr257024512list_a sigma) ia)) b))->((ord_less_nat K) (((monito1457594016ress_a sigma) phi_2) (plen_P694648887list_a pi)))))
% 0.69/0.90 FOF formula ((ord_less_eq_nat ((plus_plus_nat ((plus_plus_nat ((tau_Pr257024512list_a sigma) ia)) b)) one_one_nat)) ((tau_Pr257024512list_a sigma) j)) of role axiom named fact_214__092_060open_062_092_060tau_062_A_092_060sigma_062_Ai_A_L_Ab_A_L_A1_A_092_060le_062_A_092_060tau_062_A_092_060sigma_062_Aj_____092_060close_062
% 0.69/0.90 A new axiom: ((ord_less_eq_nat ((plus_plus_nat ((plus_plus_nat ((tau_Pr257024512list_a sigma) ia)) b)) one_one_nat)) ((tau_Pr257024512list_a sigma) j))
% 0.69/0.90 FOF formula ((ord_less_eq_nat ((plus_plus_nat ((plus_plus_nat ((tau_Pr257024512list_a sigma2) ia)) b)) one_one_nat)) ((tau_Pr257024512list_a sigma2) ja)) of role axiom named fact_215__092_060open_062_092_060tau_062_A_092_060sigma_062_H_Ai_A_L_Ab_A_L_A1_A_092_060le_062_A_092_060tau_062_A_092_060sigma_062_H_Aj_092_060close_062
% 0.69/0.90 A new axiom: ((ord_less_eq_nat ((plus_plus_nat ((plus_plus_nat ((tau_Pr257024512list_a sigma2) ia)) b)) one_one_nat)) ((tau_Pr257024512list_a sigma2) ja))
% 0.69/0.90 FOF formula (forall (Sigma:trace_1367752404list_a) (_TPTP_I:nat) (J:nat), (((ord_less_nat ((tau_Pr257024512list_a Sigma) _TPTP_I)) ((tau_Pr257024512list_a Sigma) J))->((ord_less_nat _TPTP_I) J))) of role axiom named fact_216_less___092_060tau_062D
% 0.69/0.90 A new axiom: (forall (Sigma:trace_1367752404list_a) (_TPTP_I:nat) (J:nat), (((ord_less_nat ((tau_Pr257024512list_a Sigma) _TPTP_I)) ((tau_Pr257024512list_a Sigma) J))->((ord_less_nat _TPTP_I) J)))
% 0.69/0.91 FOF formula (forall (_TPTP_I:nat) (X:nat) (S:trace_1367752404list_a), ((ex nat) (fun (J3:nat)=> ((and ((ord_less_eq_nat _TPTP_I) J3)) ((ord_less_eq_nat X) ((tau_Pr257024512list_a S) J3)))))) of role axiom named fact_217_ex__le___092_060tau_062
% 0.69/0.91 A new axiom: (forall (_TPTP_I:nat) (X:nat) (S:trace_1367752404list_a), ((ex nat) (fun (J3:nat)=> ((and ((ord_less_eq_nat _TPTP_I) J3)) ((ord_less_eq_nat X) ((tau_Pr257024512list_a S) J3))))))
% 0.69/0.91 FOF formula (forall (_TPTP_I:nat) (J:nat) (S:trace_1367752404list_a), (((ord_less_eq_nat _TPTP_I) J)->((ord_less_eq_nat ((tau_Pr257024512list_a S) _TPTP_I)) ((tau_Pr257024512list_a S) J)))) of role axiom named fact_218__092_060tau_062__mono
% 0.69/0.91 A new axiom: (forall (_TPTP_I:nat) (J:nat) (S:trace_1367752404list_a), (((ord_less_eq_nat _TPTP_I) J)->((ord_less_eq_nat ((tau_Pr257024512list_a S) _TPTP_I)) ((tau_Pr257024512list_a S) J))))
% 0.69/0.91 FOF formula (forall (K:nat) (L:nat) (M:nat) (N:nat), (((ord_less_nat K) L)->((((eq nat) ((plus_plus_nat M) L)) ((plus_plus_nat K) N))->((ord_less_nat M) N)))) of role axiom named fact_219_less__add__eq__less
% 0.69/0.91 A new axiom: (forall (K:nat) (L:nat) (M:nat) (N:nat), (((ord_less_nat K) L)->((((eq nat) ((plus_plus_nat M) L)) ((plus_plus_nat K) N))->((ord_less_nat M) N))))
% 0.69/0.91 FOF formula (forall (_TPTP_I:nat) (J:nat) (M:nat), (((ord_less_nat _TPTP_I) J)->((ord_less_nat _TPTP_I) ((plus_plus_nat M) J)))) of role axiom named fact_220_trans__less__add2
% 0.69/0.91 A new axiom: (forall (_TPTP_I:nat) (J:nat) (M:nat), (((ord_less_nat _TPTP_I) J)->((ord_less_nat _TPTP_I) ((plus_plus_nat M) J))))
% 0.69/0.91 FOF formula (forall (_TPTP_I:nat) (J:nat) (M:nat), (((ord_less_nat _TPTP_I) J)->((ord_less_nat _TPTP_I) ((plus_plus_nat J) M)))) of role axiom named fact_221_trans__less__add1
% 0.69/0.91 A new axiom: (forall (_TPTP_I:nat) (J:nat) (M:nat), (((ord_less_nat _TPTP_I) J)->((ord_less_nat _TPTP_I) ((plus_plus_nat J) M))))
% 0.69/0.91 FOF formula (forall (_TPTP_I:nat) (J:nat) (K:nat), (((ord_less_nat _TPTP_I) J)->((ord_less_nat ((plus_plus_nat _TPTP_I) K)) ((plus_plus_nat J) K)))) of role axiom named fact_222_add__less__mono1
% 0.69/0.91 A new axiom: (forall (_TPTP_I:nat) (J:nat) (K:nat), (((ord_less_nat _TPTP_I) J)->((ord_less_nat ((plus_plus_nat _TPTP_I) K)) ((plus_plus_nat J) K))))
% 0.69/0.91 FOF formula (forall (J:nat) (_TPTP_I:nat), (((ord_less_nat ((plus_plus_nat J) _TPTP_I)) _TPTP_I)->False)) of role axiom named fact_223_not__add__less2
% 0.69/0.91 A new axiom: (forall (J:nat) (_TPTP_I:nat), (((ord_less_nat ((plus_plus_nat J) _TPTP_I)) _TPTP_I)->False))
% 0.69/0.91 FOF formula (forall (_TPTP_I:nat) (J:nat), (((ord_less_nat ((plus_plus_nat _TPTP_I) J)) _TPTP_I)->False)) of role axiom named fact_224_not__add__less1
% 0.69/0.91 A new axiom: (forall (_TPTP_I:nat) (J:nat), (((ord_less_nat ((plus_plus_nat _TPTP_I) J)) _TPTP_I)->False))
% 0.69/0.91 FOF formula (forall (_TPTP_I:nat) (J:nat) (K:nat) (L:nat), (((ord_less_nat _TPTP_I) J)->(((ord_less_nat K) L)->((ord_less_nat ((plus_plus_nat _TPTP_I) K)) ((plus_plus_nat J) L))))) of role axiom named fact_225_add__less__mono
% 0.69/0.91 A new axiom: (forall (_TPTP_I:nat) (J:nat) (K:nat) (L:nat), (((ord_less_nat _TPTP_I) J)->(((ord_less_nat K) L)->((ord_less_nat ((plus_plus_nat _TPTP_I) K)) ((plus_plus_nat J) L)))))
% 0.69/0.91 FOF formula (forall (_TPTP_I:nat) (J:nat) (K:nat), (((ord_less_nat ((plus_plus_nat _TPTP_I) J)) K)->((ord_less_nat _TPTP_I) K))) of role axiom named fact_226_add__lessD1
% 0.69/0.91 A new axiom: (forall (_TPTP_I:nat) (J:nat) (K:nat), (((ord_less_nat ((plus_plus_nat _TPTP_I) J)) K)->((ord_less_nat _TPTP_I) K)))
% 0.69/0.91 FOF formula (forall (M:nat) (K:nat) (N:nat), (((ord_less_eq_nat ((plus_plus_nat M) K)) N)->((((ord_less_eq_nat M) N)->(((ord_less_eq_nat K) N)->False))->False))) of role axiom named fact_227_add__leE
% 0.69/0.91 A new axiom: (forall (M:nat) (K:nat) (N:nat), (((ord_less_eq_nat ((plus_plus_nat M) K)) N)->((((ord_less_eq_nat M) N)->(((ord_less_eq_nat K) N)->False))->False)))
% 0.69/0.91 FOF formula (forall (N:nat) (M:nat), ((ord_less_eq_nat N) ((plus_plus_nat N) M))) of role axiom named fact_228_le__add1
% 0.69/0.91 A new axiom: (forall (N:nat) (M:nat), ((ord_less_eq_nat N) ((plus_plus_nat N) M)))
% 0.69/0.91 FOF formula (forall (N:nat) (M:nat), ((ord_less_eq_nat N) ((plus_plus_nat M) N))) of role axiom named fact_229_le__add2
% 0.69/0.92 A new axiom: (forall (N:nat) (M:nat), ((ord_less_eq_nat N) ((plus_plus_nat M) N)))
% 0.69/0.92 FOF formula (forall (M:nat) (K:nat) (N:nat), (((ord_less_eq_nat ((plus_plus_nat M) K)) N)->((ord_less_eq_nat M) N))) of role axiom named fact_230_add__leD1
% 0.69/0.92 A new axiom: (forall (M:nat) (K:nat) (N:nat), (((ord_less_eq_nat ((plus_plus_nat M) K)) N)->((ord_less_eq_nat M) N)))
% 0.69/0.92 FOF formula (forall (M:nat) (K:nat) (N:nat), (((ord_less_eq_nat ((plus_plus_nat M) K)) N)->((ord_less_eq_nat K) N))) of role axiom named fact_231_add__leD2
% 0.69/0.92 A new axiom: (forall (M:nat) (K:nat) (N:nat), (((ord_less_eq_nat ((plus_plus_nat M) K)) N)->((ord_less_eq_nat K) N)))
% 0.69/0.92 FOF formula (forall (K:nat) (L:nat), (((ord_less_eq_nat K) L)->((ex nat) (fun (N2:nat)=> (((eq nat) L) ((plus_plus_nat K) N2)))))) of role axiom named fact_232_le__Suc__ex
% 0.69/0.92 A new axiom: (forall (K:nat) (L:nat), (((ord_less_eq_nat K) L)->((ex nat) (fun (N2:nat)=> (((eq nat) L) ((plus_plus_nat K) N2))))))
% 0.69/0.92 FOF formula (forall (_TPTP_I:nat) (J:nat) (K:nat) (L:nat), (((ord_less_eq_nat _TPTP_I) J)->(((ord_less_eq_nat K) L)->((ord_less_eq_nat ((plus_plus_nat _TPTP_I) K)) ((plus_plus_nat J) L))))) of role axiom named fact_233_add__le__mono
% 0.69/0.92 A new axiom: (forall (_TPTP_I:nat) (J:nat) (K:nat) (L:nat), (((ord_less_eq_nat _TPTP_I) J)->(((ord_less_eq_nat K) L)->((ord_less_eq_nat ((plus_plus_nat _TPTP_I) K)) ((plus_plus_nat J) L)))))
% 0.69/0.92 FOF formula (forall (_TPTP_I:nat) (J:nat) (K:nat), (((ord_less_eq_nat _TPTP_I) J)->((ord_less_eq_nat ((plus_plus_nat _TPTP_I) K)) ((plus_plus_nat J) K)))) of role axiom named fact_234_add__le__mono1
% 0.69/0.92 A new axiom: (forall (_TPTP_I:nat) (J:nat) (K:nat), (((ord_less_eq_nat _TPTP_I) J)->((ord_less_eq_nat ((plus_plus_nat _TPTP_I) K)) ((plus_plus_nat J) K))))
% 0.69/0.92 FOF formula (forall (_TPTP_I:nat) (J:nat) (M:nat), (((ord_less_eq_nat _TPTP_I) J)->((ord_less_eq_nat _TPTP_I) ((plus_plus_nat J) M)))) of role axiom named fact_235_trans__le__add1
% 0.69/0.92 A new axiom: (forall (_TPTP_I:nat) (J:nat) (M:nat), (((ord_less_eq_nat _TPTP_I) J)->((ord_less_eq_nat _TPTP_I) ((plus_plus_nat J) M))))
% 0.69/0.92 FOF formula (forall (_TPTP_I:nat) (J:nat) (M:nat), (((ord_less_eq_nat _TPTP_I) J)->((ord_less_eq_nat _TPTP_I) ((plus_plus_nat M) J)))) of role axiom named fact_236_trans__le__add2
% 0.69/0.92 A new axiom: (forall (_TPTP_I:nat) (J:nat) (M:nat), (((ord_less_eq_nat _TPTP_I) J)->((ord_less_eq_nat _TPTP_I) ((plus_plus_nat M) J))))
% 0.69/0.92 FOF formula (((eq (nat->(nat->Prop))) ord_less_eq_nat) (fun (M3:nat) (N3:nat)=> ((ex nat) (fun (K3:nat)=> (((eq nat) N3) ((plus_plus_nat M3) K3)))))) of role axiom named fact_237_nat__le__iff__add
% 0.69/0.92 A new axiom: (((eq (nat->(nat->Prop))) ord_less_eq_nat) (fun (M3:nat) (N3:nat)=> ((ex nat) (fun (K3:nat)=> (((eq nat) N3) ((plus_plus_nat M3) K3))))))
% 0.69/0.92 FOF formula (forall (F:(nat->nat)) (M:nat) (K:nat), ((forall (M4:nat) (N2:nat), (((ord_less_nat M4) N2)->((ord_less_nat (F M4)) (F N2))))->((ord_less_eq_nat ((plus_plus_nat (F M)) K)) (F ((plus_plus_nat M) K))))) of role axiom named fact_238_mono__nat__linear__lb
% 0.69/0.92 A new axiom: (forall (F:(nat->nat)) (M:nat) (K:nat), ((forall (M4:nat) (N2:nat), (((ord_less_nat M4) N2)->((ord_less_nat (F M4)) (F N2))))->((ord_less_eq_nat ((plus_plus_nat (F M)) K)) (F ((plus_plus_nat M) K)))))
% 0.69/0.92 FOF formula (forall (J:nat) (Sigma:trace_1367752404list_a) (Sigma2:trace_1367752404list_a) (Phi:formula_a), ((forall (I2:nat), (((ord_less_nat I2) J)->(((eq nat) ((tau_Pr257024512list_a Sigma) I2)) ((tau_Pr257024512list_a Sigma2) I2))))->(((eq nat) (((monito1457594016ress_a Sigma) Phi) J)) (((monito1457594016ress_a Sigma2) Phi) J)))) of role axiom named fact_239_progress__time__conv
% 0.69/0.92 A new axiom: (forall (J:nat) (Sigma:trace_1367752404list_a) (Sigma2:trace_1367752404list_a) (Phi:formula_a), ((forall (I2:nat), (((ord_less_nat I2) J)->(((eq nat) ((tau_Pr257024512list_a Sigma) I2)) ((tau_Pr257024512list_a Sigma2) I2))))->(((eq nat) (((monito1457594016ress_a Sigma) Phi) J)) (((monito1457594016ress_a Sigma2) Phi) J))))
% 0.69/0.92 FOF formula (forall (Sigma:trace_1367752404list_a) (_TPTP_I:nat) (J:nat), (((ord_less_eq_nat ((tau_Pr257024512list_a Sigma) _TPTP_I)) ((tau_Pr257024512list_a Sigma) J))->(((ord_less_nat J) _TPTP_I)->(((eq nat) ((tau_Pr257024512list_a Sigma) _TPTP_I)) ((tau_Pr257024512list_a Sigma) J))))) of role axiom named fact_240_le___092_060tau_062__less
% 0.69/0.92 A new axiom: (forall (Sigma:trace_1367752404list_a) (_TPTP_I:nat) (J:nat), (((ord_less_eq_nat ((tau_Pr257024512list_a Sigma) _TPTP_I)) ((tau_Pr257024512list_a Sigma) J))->(((ord_less_nat J) _TPTP_I)->(((eq nat) ((tau_Pr257024512list_a Sigma) _TPTP_I)) ((tau_Pr257024512list_a Sigma) J)))))
% 0.69/0.92 FOF formula (forall (P5:prefix1027212443list_a) (S:trace_1367752404list_a) (S2:trace_1367752404list_a) (_TPTP_I:nat), (((prefix1041802747list_a P5) S)->(((prefix1041802747list_a P5) S2)->(((ord_less_nat _TPTP_I) (plen_P694648887list_a P5))->(((eq nat) ((tau_Pr257024512list_a S) _TPTP_I)) ((tau_Pr257024512list_a S2) _TPTP_I)))))) of role axiom named fact_241__092_060tau_062__prefix__conv
% 0.69/0.92 A new axiom: (forall (P5:prefix1027212443list_a) (S:trace_1367752404list_a) (S2:trace_1367752404list_a) (_TPTP_I:nat), (((prefix1041802747list_a P5) S)->(((prefix1041802747list_a P5) S2)->(((ord_less_nat _TPTP_I) (plen_P694648887list_a P5))->(((eq nat) ((tau_Pr257024512list_a S) _TPTP_I)) ((tau_Pr257024512list_a S2) _TPTP_I))))))
% 0.69/0.92 <<<htarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,(
% 0.69/0.92 ~ !>>>!!!<<< [J3: nat] :
% 0.69/0.92 ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( tau_Pr257>>>
% 0.69/0.92 statestack=[0, 1, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 11, 22, 30, 36, 43, 50, 99, 124]
% 0.69/0.92 symstack=[$end, TPTP_file_pre, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, 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TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, LexToken(THF,'thf',1,66904), LexToken(LPAR,'(',1,66907), name, LexToken(COMMA,',',1,67477), formula_role, LexToken(COMMA,',',1,67483), LexToken(LPAR,'(',1,67484), unary_connective]
% 0.69/0.92 Unexpected exception Syntax error at '!':BANG
% 0.69/0.92 Traceback (most recent call last):
% 0.69/0.92 File "CASC.py", line 79, in <module>
% 0.69/0.92 problem=TPTP.TPTPproblem(env=environment,debug=1,file=file)
% 0.69/0.92 File "/export/starexec/sandbox/solver/bin/TPTP.py", line 38, in __init__
% 0.69/0.92 parser.parse(file.read(),debug=0,lexer=lexer)
% 0.69/0.92 File "/export/starexec/sandbox/solver/bin/ply/yacc.py", line 265, in parse
% 0.69/0.92 return self.parseopt_notrack(input,lexer,debug,tracking,tokenfunc)
% 0.69/0.92 File "/export/starexec/sandbox/solver/bin/ply/yacc.py", line 1047, in parseopt_notrack
% 0.69/0.92 tok = self.errorfunc(errtoken)
% 0.69/0.92 File "/export/starexec/sandbox/solver/bin/TPTPparser.py", line 2099, in p_error
% 0.69/0.92 raise TPTPParsingError("Syntax error at '%s':%s" % (t.value,t.type))
% 0.69/0.92 TPTPparser.TPTPParsingError: Syntax error at '!':BANG
%------------------------------------------------------------------------------