TSTP Solution File: SCT169^1 by cocATP---0.2.0
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%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SCT169^1 : TPTP v6.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n091.star.cs.uiowa.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz
% Memory : 32286.75MB
% OS : Linux 2.6.32-431.20.3.el6.x86_64
% CPULimit : 300s
% DateTime : Thu Jul 17 13:29:44 EDT 2014
% Result : Timeout 300.05s
% Output : None
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : SCT169^1 : TPTP v6.1.0. Released v5.3.0.
% % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n091.star.cs.uiowa.edu
% % Model : x86_64 x86_64
% % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% % Memory : 32286.75MB
% % OS : Linux 2.6.32-431.20.3.el6.x86_64
% % CPULimit : 300
% % DateTime : Thu Jul 17 08:21:51 CDT 2014
% % CPUTime : 300.05
% Python 2.7.5
% Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% FOF formula (<kernel.Constant object at 0x1d34440>, <kernel.Type object at 0x1d34950>) of role type named ty_ty_tc__Arrow____Order____Mirabelle____sdiojnqkdh__Oalt
% Using role type
% Declaring arrow_1346734812le_alt:Type
% FOF formula (<kernel.Constant object at 0x1a1fcb0>, <kernel.Type object at 0x1d34998>) of role type named ty_ty_tc__List__Olist_Itc__Arrow____Order____Mirabelle____sdiojnqkdh__Oalt_J
% Using role type
% Declaring list_A1528105233le_alt:Type
% FOF formula (<kernel.Constant object at 0x1d34a70>, <kernel.Type object at 0x1d34b00>) of role type named ty_ty_tc__Nat__Onat
% Using role type
% Declaring nat:Type
% FOF formula (<kernel.Constant object at 0x1d344d0>, <kernel.DependentProduct object at 0x1d32200>) of role type named sy_c_HOL_Oequal__class_Oequal_000tc__List__Olist_Itc__Arrow____Order____Mirabell
% Using role type
% Declaring equal_2044961839le_alt:(list_A1528105233le_alt->(list_A1528105233le_alt->Prop))
% FOF formula (<kernel.Constant object at 0x1d348c0>, <kernel.DependentProduct object at 0x1d32b48>) of role type named sy_c_List_Oappend_000tc__Arrow____Order____Mirabelle____sdiojnqkdh__Oalt
% Using role type
% Declaring append1050458273le_alt:(list_A1528105233le_alt->(list_A1528105233le_alt->list_A1528105233le_alt))
% FOF formula (<kernel.Constant object at 0x1d347a0>, <kernel.DependentProduct object at 0x1d32050>) of role type named sy_c_List_Obutlast_000tc__Arrow____Order____Mirabelle____sdiojnqkdh__Oalt
% Using role type
% Declaring butlas1146323672le_alt:(list_A1528105233le_alt->list_A1528105233le_alt)
% FOF formula (<kernel.Constant object at 0x1d348c0>, <kernel.DependentProduct object at 0x1d325a8>) of role type named sy_c_List_Odistinct_000tc__Arrow____Order____Mirabelle____sdiojnqkdh__Oalt
% Using role type
% Declaring distin1107700095le_alt:(list_A1528105233le_alt->Prop)
% FOF formula (<kernel.Constant object at 0x1d347a0>, <kernel.DependentProduct object at 0x1d32050>) of role type named sy_c_List_OdropWhile_000tc__Arrow____Order____Mirabelle____sdiojnqkdh__Oalt
% Using role type
% Declaring dropWh40674093le_alt:((arrow_1346734812le_alt->Prop)->(list_A1528105233le_alt->list_A1528105233le_alt))
% FOF formula (<kernel.Constant object at 0x1d348c0>, <kernel.DependentProduct object at 0x1d32638>) of role type named sy_c_List_Ohd_000tc__Arrow____Order____Mirabelle____sdiojnqkdh__Oalt
% Using role type
% Declaring hd_Arr689575519le_alt:(list_A1528105233le_alt->arrow_1346734812le_alt)
% FOF formula (<kernel.Constant object at 0x1d348c0>, <kernel.DependentProduct object at 0x1d32128>) of role type named sy_c_List_Oinsert_000tc__Arrow____Order____Mirabelle____sdiojnqkdh__Oalt
% Using role type
% Declaring insert844458914le_alt:(arrow_1346734812le_alt->(list_A1528105233le_alt->list_A1528105233le_alt))
% FOF formula (<kernel.Constant object at 0x1d32050>, <kernel.DependentProduct object at 0x1d32488>) of role type named sy_c_List_Olast_000tc__Arrow____Order____Mirabelle____sdiojnqkdh__Oalt
% Using role type
% Declaring last_A2088691109le_alt:(list_A1528105233le_alt->arrow_1346734812le_alt)
% FOF formula (<kernel.Constant object at 0x1d32638>, <kernel.DependentProduct object at 0x1d32c68>) of role type named sy_c_List_Olist_OCons_000tc__Arrow____Order____Mirabelle____sdiojnqkdh__Oalt
% Using role type
% Declaring cons_A1100118844le_alt:(arrow_1346734812le_alt->(list_A1528105233le_alt->list_A1528105233le_alt))
% FOF formula (<kernel.Constant object at 0x1d32128>, <kernel.Constant object at 0x1d32c68>) of role type named sy_c_List_Olist_ONil_000tc__Arrow____Order____Mirabelle____sdiojnqkdh__Oalt
% Using role type
% Declaring nil_Ar10086284le_alt:list_A1528105233le_alt
% FOF formula (<kernel.Constant object at 0x1d32050>, <kernel.DependentProduct object at 0x1d32638>) of role type named sy_c_List_Omaps_000tc__Arrow____Order____Mirabelle____sdiojnqkdh__Oalt_000tc__Ar
% Using role type
% Declaring maps_A51637569le_alt:((arrow_1346734812le_alt->list_A1528105233le_alt)->(list_A1528105233le_alt->list_A1528105233le_alt))
% FOF formula (<kernel.Constant object at 0x1d32680>, <kernel.DependentProduct object at 0x1d32830>) of role type named sy_c_List_Onull_000tc__Arrow____Order____Mirabelle____sdiojnqkdh__Oalt
% Using role type
% Declaring null_A244857236le_alt:(list_A1528105233le_alt->Prop)
% FOF formula (<kernel.Constant object at 0x1d32cb0>, <kernel.DependentProduct object at 0x1d32488>) of role type named sy_c_List_Oreplicate_000tc__Arrow____Order____Mirabelle____sdiojnqkdh__Oalt
% Using role type
% Declaring replic235430982le_alt:(nat->(arrow_1346734812le_alt->list_A1528105233le_alt))
% FOF formula (<kernel.Constant object at 0x1d32638>, <kernel.DependentProduct object at 0x1d32758>) of role type named sy_c_List_Orev_000tc__Arrow____Order____Mirabelle____sdiojnqkdh__Oalt
% Using role type
% Declaring rev_Ar1977782764le_alt:(list_A1528105233le_alt->list_A1528105233le_alt)
% FOF formula (<kernel.Constant object at 0x1d32830>, <kernel.DependentProduct object at 0x1d32050>) of role type named sy_c_List_Orotate1_000tc__Arrow____Order____Mirabelle____sdiojnqkdh__Oalt
% Using role type
% Declaring rotate1206725081le_alt:(list_A1528105233le_alt->list_A1528105233le_alt)
% FOF formula (<kernel.Constant object at 0x1d32488>, <kernel.DependentProduct object at 0x1d32cb0>) of role type named sy_c_List_Osplice_000tc__Arrow____Order____Mirabelle____sdiojnqkdh__Oalt
% Using role type
% Declaring splice244790623le_alt:(list_A1528105233le_alt->(list_A1528105233le_alt->list_A1528105233le_alt))
% FOF formula (<kernel.Constant object at 0x1d32758>, <kernel.DependentProduct object at 0x1d327a0>) of role type named sy_c_List_Otl_000tc__Arrow____Order____Mirabelle____sdiojnqkdh__Oalt
% Using role type
% Declaring tl_Arr1336826979le_alt:(list_A1528105233le_alt->list_A1528105233le_alt)
% FOF formula (<kernel.Constant object at 0x1d32050>, <kernel.DependentProduct object at 0x1d32830>) of role type named sy_c_fequal_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____sdiojnqkdh__O
% Using role type
% Declaring fequal194154450le_alt:(list_A1528105233le_alt->(list_A1528105233le_alt->Prop))
% FOF formula (<kernel.Constant object at 0x1d32cb0>, <kernel.Constant object at 0x1d32830>) of role type named sy_v_a
% Using role type
% Declaring a:arrow_1346734812le_alt
% FOF formula (<kernel.Constant object at 0x1d32758>, <kernel.Constant object at 0x1d32830>) of role type named sy_v_b
% Using role type
% Declaring b:arrow_1346734812le_alt
% FOF formula ((ex arrow_1346734812le_alt) (fun (A_2:arrow_1346734812le_alt)=> ((ex arrow_1346734812le_alt) (fun (B:arrow_1346734812le_alt)=> ((ex arrow_1346734812le_alt) (fun (C:arrow_1346734812le_alt)=> (distin1107700095le_alt ((cons_A1100118844le_alt A_2) ((cons_A1100118844le_alt B) ((cons_A1100118844le_alt C) nil_Ar10086284le_alt)))))))))) of role axiom named fact_0_alt3
% A new axiom: ((ex arrow_1346734812le_alt) (fun (A_2:arrow_1346734812le_alt)=> ((ex arrow_1346734812le_alt) (fun (B:arrow_1346734812le_alt)=> ((ex arrow_1346734812le_alt) (fun (C:arrow_1346734812le_alt)=> (distin1107700095le_alt ((cons_A1100118844le_alt A_2) ((cons_A1100118844le_alt B) ((cons_A1100118844le_alt C) nil_Ar10086284le_alt))))))))))
% FOF formula (distin1107700095le_alt nil_Ar10086284le_alt) of role axiom named fact_1_distinct_Osimps_I1_J
% A new axiom: (distin1107700095le_alt nil_Ar10086284le_alt)
% FOF formula (forall (A_4:arrow_1346734812le_alt) (List_4:list_A1528105233le_alt), (not (((eq list_A1528105233le_alt) nil_Ar10086284le_alt) ((cons_A1100118844le_alt A_4) List_4)))) of role axiom named fact_2_list_Osimps_I2_J
% A new axiom: (forall (A_4:arrow_1346734812le_alt) (List_4:list_A1528105233le_alt), (not (((eq list_A1528105233le_alt) nil_Ar10086284le_alt) ((cons_A1100118844le_alt A_4) List_4))))
% FOF formula (forall (A_3:arrow_1346734812le_alt) (List_3:list_A1528105233le_alt), (not (((eq list_A1528105233le_alt) ((cons_A1100118844le_alt A_3) List_3)) nil_Ar10086284le_alt))) of role axiom named fact_3_list_Osimps_I3_J
% A new axiom: (forall (A_3:arrow_1346734812le_alt) (List_3:list_A1528105233le_alt), (not (((eq list_A1528105233le_alt) ((cons_A1100118844le_alt A_3) List_3)) nil_Ar10086284le_alt)))
% FOF formula (forall (Xs_71:list_A1528105233le_alt), ((iff (not (((eq list_A1528105233le_alt) Xs_71) nil_Ar10086284le_alt))) ((ex arrow_1346734812le_alt) (fun (Y_3:arrow_1346734812le_alt)=> ((ex list_A1528105233le_alt) (fun (Ys_7:list_A1528105233le_alt)=> (((eq list_A1528105233le_alt) Xs_71) ((cons_A1100118844le_alt Y_3) Ys_7)))))))) of role axiom named fact_4_neq__Nil__conv
% A new axiom: (forall (Xs_71:list_A1528105233le_alt), ((iff (not (((eq list_A1528105233le_alt) Xs_71) nil_Ar10086284le_alt))) ((ex arrow_1346734812le_alt) (fun (Y_3:arrow_1346734812le_alt)=> ((ex list_A1528105233le_alt) (fun (Ys_7:list_A1528105233le_alt)=> (((eq list_A1528105233le_alt) Xs_71) ((cons_A1100118844le_alt Y_3) Ys_7))))))))
% FOF formula (forall (Y_7:list_A1528105233le_alt), ((not (((eq list_A1528105233le_alt) Y_7) nil_Ar10086284le_alt))->((forall (A_2:arrow_1346734812le_alt) (List_2:list_A1528105233le_alt), (not (((eq list_A1528105233le_alt) Y_7) ((cons_A1100118844le_alt A_2) List_2))))->False))) of role axiom named fact_5_list_Oexhaust
% A new axiom: (forall (Y_7:list_A1528105233le_alt), ((not (((eq list_A1528105233le_alt) Y_7) nil_Ar10086284le_alt))->((forall (A_2:arrow_1346734812le_alt) (List_2:list_A1528105233le_alt), (not (((eq list_A1528105233le_alt) Y_7) ((cons_A1100118844le_alt A_2) List_2))))->False)))
% FOF formula (forall (Xs_70:list_A1528105233le_alt) (X_33:arrow_1346734812le_alt), (not (((eq list_A1528105233le_alt) Xs_70) ((cons_A1100118844le_alt X_33) Xs_70)))) of role axiom named fact_6_not__Cons__self
% A new axiom: (forall (Xs_70:list_A1528105233le_alt) (X_33:arrow_1346734812le_alt), (not (((eq list_A1528105233le_alt) Xs_70) ((cons_A1100118844le_alt X_33) Xs_70))))
% FOF formula (forall (X_32:arrow_1346734812le_alt) (Xs_69:list_A1528105233le_alt), (not (((eq list_A1528105233le_alt) ((cons_A1100118844le_alt X_32) Xs_69)) Xs_69))) of role axiom named fact_7_not__Cons__self2
% A new axiom: (forall (X_32:arrow_1346734812le_alt) (Xs_69:list_A1528105233le_alt), (not (((eq list_A1528105233le_alt) ((cons_A1100118844le_alt X_32) Xs_69)) Xs_69)))
% FOF formula (forall (A_1:arrow_1346734812le_alt) (List_1:list_A1528105233le_alt) (A:arrow_1346734812le_alt) (List:list_A1528105233le_alt), ((iff (((eq list_A1528105233le_alt) ((cons_A1100118844le_alt A_1) List_1)) ((cons_A1100118844le_alt A) List))) ((and (((eq arrow_1346734812le_alt) A_1) A)) (((eq list_A1528105233le_alt) List_1) List)))) of role axiom named fact_8_list_Oinject
% A new axiom: (forall (A_1:arrow_1346734812le_alt) (List_1:list_A1528105233le_alt) (A:arrow_1346734812le_alt) (List:list_A1528105233le_alt), ((iff (((eq list_A1528105233le_alt) ((cons_A1100118844le_alt A_1) List_1)) ((cons_A1100118844le_alt A) List))) ((and (((eq arrow_1346734812le_alt) A_1) A)) (((eq list_A1528105233le_alt) List_1) List))))
% FOF formula (forall (V:arrow_1346734812le_alt) (Va:list_A1528105233le_alt), (((eq list_A1528105233le_alt) ((splice244790623le_alt ((cons_A1100118844le_alt V) Va)) nil_Ar10086284le_alt)) ((cons_A1100118844le_alt V) Va))) of role axiom named fact_9_splice_Osimps_I2_J
% A new axiom: (forall (V:arrow_1346734812le_alt) (Va:list_A1528105233le_alt), (((eq list_A1528105233le_alt) ((splice244790623le_alt ((cons_A1100118844le_alt V) Va)) nil_Ar10086284le_alt)) ((cons_A1100118844le_alt V) Va)))
% FOF formula (forall (X_31:arrow_1346734812le_alt), (((eq list_A1528105233le_alt) ((insert844458914le_alt X_31) nil_Ar10086284le_alt)) ((cons_A1100118844le_alt X_31) nil_Ar10086284le_alt))) of role axiom named fact_10_insert__Nil
% A new axiom: (forall (X_31:arrow_1346734812le_alt), (((eq list_A1528105233le_alt) ((insert844458914le_alt X_31) nil_Ar10086284le_alt)) ((cons_A1100118844le_alt X_31) nil_Ar10086284le_alt)))
% FOF formula (forall (P_5:(list_A1528105233le_alt->Prop)) (Xs_68:list_A1528105233le_alt), ((not (((eq list_A1528105233le_alt) Xs_68) nil_Ar10086284le_alt))->((forall (X_20:arrow_1346734812le_alt), (P_5 ((cons_A1100118844le_alt X_20) nil_Ar10086284le_alt)))->((forall (X_20:arrow_1346734812le_alt) (Xs_23:list_A1528105233le_alt), ((not (((eq list_A1528105233le_alt) Xs_23) nil_Ar10086284le_alt))->((P_5 Xs_23)->(P_5 ((cons_A1100118844le_alt X_20) Xs_23)))))->(P_5 Xs_68))))) of role axiom named fact_11_list__nonempty__induct
% A new axiom: (forall (P_5:(list_A1528105233le_alt->Prop)) (Xs_68:list_A1528105233le_alt), ((not (((eq list_A1528105233le_alt) Xs_68) nil_Ar10086284le_alt))->((forall (X_20:arrow_1346734812le_alt), (P_5 ((cons_A1100118844le_alt X_20) nil_Ar10086284le_alt)))->((forall (X_20:arrow_1346734812le_alt) (Xs_23:list_A1528105233le_alt), ((not (((eq list_A1528105233le_alt) Xs_23) nil_Ar10086284le_alt))->((P_5 Xs_23)->(P_5 ((cons_A1100118844le_alt X_20) Xs_23)))))->(P_5 Xs_68)))))
% FOF formula (forall (Xs_67:list_A1528105233le_alt), ((not (((eq list_A1528105233le_alt) Xs_67) nil_Ar10086284le_alt))->((distin1107700095le_alt Xs_67)->(distin1107700095le_alt (butlas1146323672le_alt Xs_67))))) of role axiom named fact_12_distinct__butlast
% A new axiom: (forall (Xs_67:list_A1528105233le_alt), ((not (((eq list_A1528105233le_alt) Xs_67) nil_Ar10086284le_alt))->((distin1107700095le_alt Xs_67)->(distin1107700095le_alt (butlas1146323672le_alt Xs_67)))))
% FOF formula (((eq list_A1528105233le_alt) (butlas1146323672le_alt nil_Ar10086284le_alt)) nil_Ar10086284le_alt) of role axiom named fact_13_butlast_Osimps_I1_J
% A new axiom: (((eq list_A1528105233le_alt) (butlas1146323672le_alt nil_Ar10086284le_alt)) nil_Ar10086284le_alt)
% FOF formula (forall (X_30:arrow_1346734812le_alt) (Xs_66:list_A1528105233le_alt), ((distin1107700095le_alt Xs_66)->(distin1107700095le_alt ((insert844458914le_alt X_30) Xs_66)))) of role axiom named fact_14_distinct__insert
% A new axiom: (forall (X_30:arrow_1346734812le_alt) (Xs_66:list_A1528105233le_alt), ((distin1107700095le_alt Xs_66)->(distin1107700095le_alt ((insert844458914le_alt X_30) Xs_66))))
% FOF formula (forall (X_29:arrow_1346734812le_alt) (Xs_65:list_A1528105233le_alt) (Y_6:arrow_1346734812le_alt) (Ys_33:list_A1528105233le_alt), (((eq list_A1528105233le_alt) ((splice244790623le_alt ((cons_A1100118844le_alt X_29) Xs_65)) ((cons_A1100118844le_alt Y_6) Ys_33))) ((cons_A1100118844le_alt X_29) ((cons_A1100118844le_alt Y_6) ((splice244790623le_alt Xs_65) Ys_33))))) of role axiom named fact_15_splice_Osimps_I3_J
% A new axiom: (forall (X_29:arrow_1346734812le_alt) (Xs_65:list_A1528105233le_alt) (Y_6:arrow_1346734812le_alt) (Ys_33:list_A1528105233le_alt), (((eq list_A1528105233le_alt) ((splice244790623le_alt ((cons_A1100118844le_alt X_29) Xs_65)) ((cons_A1100118844le_alt Y_6) Ys_33))) ((cons_A1100118844le_alt X_29) ((cons_A1100118844le_alt Y_6) ((splice244790623le_alt Xs_65) Ys_33)))))
% FOF formula (forall (Xs_64:list_A1528105233le_alt), (((eq list_A1528105233le_alt) ((splice244790623le_alt Xs_64) nil_Ar10086284le_alt)) Xs_64)) of role axiom named fact_16_splice__Nil2
% A new axiom: (forall (Xs_64:list_A1528105233le_alt), (((eq list_A1528105233le_alt) ((splice244790623le_alt Xs_64) nil_Ar10086284le_alt)) Xs_64))
% FOF formula (forall (Ys_32:list_A1528105233le_alt), (((eq list_A1528105233le_alt) ((splice244790623le_alt nil_Ar10086284le_alt) Ys_32)) Ys_32)) of role axiom named fact_17_splice_Osimps_I1_J
% A new axiom: (forall (Ys_32:list_A1528105233le_alt), (((eq list_A1528105233le_alt) ((splice244790623le_alt nil_Ar10086284le_alt) Ys_32)) Ys_32))
% FOF formula (forall (X_28:arrow_1346734812le_alt) (Xs_63:list_A1528105233le_alt), ((and ((((eq list_A1528105233le_alt) Xs_63) nil_Ar10086284le_alt)->(((eq list_A1528105233le_alt) (butlas1146323672le_alt ((cons_A1100118844le_alt X_28) Xs_63))) nil_Ar10086284le_alt))) ((not (((eq list_A1528105233le_alt) Xs_63) nil_Ar10086284le_alt))->(((eq list_A1528105233le_alt) (butlas1146323672le_alt ((cons_A1100118844le_alt X_28) Xs_63))) ((cons_A1100118844le_alt X_28) (butlas1146323672le_alt Xs_63)))))) of role axiom named fact_18_butlast_Osimps_I2_J
% A new axiom: (forall (X_28:arrow_1346734812le_alt) (Xs_63:list_A1528105233le_alt), ((and ((((eq list_A1528105233le_alt) Xs_63) nil_Ar10086284le_alt)->(((eq list_A1528105233le_alt) (butlas1146323672le_alt ((cons_A1100118844le_alt X_28) Xs_63))) nil_Ar10086284le_alt))) ((not (((eq list_A1528105233le_alt) Xs_63) nil_Ar10086284le_alt))->(((eq list_A1528105233le_alt) (butlas1146323672le_alt ((cons_A1100118844le_alt X_28) Xs_63))) ((cons_A1100118844le_alt X_28) (butlas1146323672le_alt Xs_63))))))
% FOF formula (forall (Xs_62:list_A1528105233le_alt), ((iff (((eq list_A1528105233le_alt) Xs_62) nil_Ar10086284le_alt)) (null_A244857236le_alt Xs_62))) of role axiom named fact_19_eq__Nil__null
% A new axiom: (forall (Xs_62:list_A1528105233le_alt), ((iff (((eq list_A1528105233le_alt) Xs_62) nil_Ar10086284le_alt)) (null_A244857236le_alt Xs_62)))
% FOF formula (forall (Xs_61:list_A1528105233le_alt), ((iff (null_A244857236le_alt Xs_61)) (((eq list_A1528105233le_alt) Xs_61) nil_Ar10086284le_alt))) of role axiom named fact_20_List_Onull__def
% A new axiom: (forall (Xs_61:list_A1528105233le_alt), ((iff (null_A244857236le_alt Xs_61)) (((eq list_A1528105233le_alt) Xs_61) nil_Ar10086284le_alt)))
% FOF formula (null_A244857236le_alt nil_Ar10086284le_alt) of role axiom named fact_21_null__rec_I2_J
% A new axiom: (null_A244857236le_alt nil_Ar10086284le_alt)
% FOF formula (forall (X_27:arrow_1346734812le_alt) (Xs_60:list_A1528105233le_alt), ((null_A244857236le_alt ((cons_A1100118844le_alt X_27) Xs_60))->False)) of role axiom named fact_22_null__rec_I1_J
% A new axiom: (forall (X_27:arrow_1346734812le_alt) (Xs_60:list_A1528105233le_alt), ((null_A244857236le_alt ((cons_A1100118844le_alt X_27) Xs_60))->False))
% FOF formula (forall (Xs_59:list_A1528105233le_alt) (X_26:arrow_1346734812le_alt), (((eq list_A1528105233le_alt) (butlas1146323672le_alt ((append1050458273le_alt Xs_59) ((cons_A1100118844le_alt X_26) nil_Ar10086284le_alt)))) Xs_59)) of role axiom named fact_23_butlast__snoc
% A new axiom: (forall (Xs_59:list_A1528105233le_alt) (X_26:arrow_1346734812le_alt), (((eq list_A1528105233le_alt) (butlas1146323672le_alt ((append1050458273le_alt Xs_59) ((cons_A1100118844le_alt X_26) nil_Ar10086284le_alt)))) Xs_59))
% FOF formula (forall (Xs_58:list_A1528105233le_alt) (Ys_31:list_A1528105233le_alt) (Zs_8:list_A1528105233le_alt), (((eq list_A1528105233le_alt) ((append1050458273le_alt ((append1050458273le_alt Xs_58) Ys_31)) Zs_8)) ((append1050458273le_alt Xs_58) ((append1050458273le_alt Ys_31) Zs_8)))) of role axiom named fact_24_append__assoc
% A new axiom: (forall (Xs_58:list_A1528105233le_alt) (Ys_31:list_A1528105233le_alt) (Zs_8:list_A1528105233le_alt), (((eq list_A1528105233le_alt) ((append1050458273le_alt ((append1050458273le_alt Xs_58) Ys_31)) Zs_8)) ((append1050458273le_alt Xs_58) ((append1050458273le_alt Ys_31) Zs_8))))
% FOF formula (forall (Xs_57:list_A1528105233le_alt) (Ys_30:list_A1528105233le_alt) (Zs_7:list_A1528105233le_alt) (Ts:list_A1528105233le_alt), ((iff (((eq list_A1528105233le_alt) ((append1050458273le_alt Xs_57) Ys_30)) ((append1050458273le_alt Zs_7) Ts))) ((ex list_A1528105233le_alt) (fun (Us_1:list_A1528105233le_alt)=> ((or ((and (((eq list_A1528105233le_alt) Xs_57) ((append1050458273le_alt Zs_7) Us_1))) (((eq list_A1528105233le_alt) ((append1050458273le_alt Us_1) Ys_30)) Ts))) ((and (((eq list_A1528105233le_alt) ((append1050458273le_alt Xs_57) Us_1)) Zs_7)) (((eq list_A1528105233le_alt) Ys_30) ((append1050458273le_alt Us_1) Ts)))))))) of role axiom named fact_25_append__eq__append__conv2
% A new axiom: (forall (Xs_57:list_A1528105233le_alt) (Ys_30:list_A1528105233le_alt) (Zs_7:list_A1528105233le_alt) (Ts:list_A1528105233le_alt), ((iff (((eq list_A1528105233le_alt) ((append1050458273le_alt Xs_57) Ys_30)) ((append1050458273le_alt Zs_7) Ts))) ((ex list_A1528105233le_alt) (fun (Us_1:list_A1528105233le_alt)=> ((or ((and (((eq list_A1528105233le_alt) Xs_57) ((append1050458273le_alt Zs_7) Us_1))) (((eq list_A1528105233le_alt) ((append1050458273le_alt Us_1) Ys_30)) Ts))) ((and (((eq list_A1528105233le_alt) ((append1050458273le_alt Xs_57) Us_1)) Zs_7)) (((eq list_A1528105233le_alt) Ys_30) ((append1050458273le_alt Us_1) Ts))))))))
% FOF formula (forall (Xs_56:list_A1528105233le_alt) (Ys_29:list_A1528105233le_alt) (Zs_6:list_A1528105233le_alt), ((iff (((eq list_A1528105233le_alt) ((append1050458273le_alt Xs_56) Ys_29)) ((append1050458273le_alt Xs_56) Zs_6))) (((eq list_A1528105233le_alt) Ys_29) Zs_6))) of role axiom named fact_26_same__append__eq
% A new axiom: (forall (Xs_56:list_A1528105233le_alt) (Ys_29:list_A1528105233le_alt) (Zs_6:list_A1528105233le_alt), ((iff (((eq list_A1528105233le_alt) ((append1050458273le_alt Xs_56) Ys_29)) ((append1050458273le_alt Xs_56) Zs_6))) (((eq list_A1528105233le_alt) Ys_29) Zs_6)))
% FOF formula (forall (Ys_28:list_A1528105233le_alt) (Xs_55:list_A1528105233le_alt) (Zs_5:list_A1528105233le_alt), ((iff (((eq list_A1528105233le_alt) ((append1050458273le_alt Ys_28) Xs_55)) ((append1050458273le_alt Zs_5) Xs_55))) (((eq list_A1528105233le_alt) Ys_28) Zs_5))) of role axiom named fact_27_append__same__eq
% A new axiom: (forall (Ys_28:list_A1528105233le_alt) (Xs_55:list_A1528105233le_alt) (Zs_5:list_A1528105233le_alt), ((iff (((eq list_A1528105233le_alt) ((append1050458273le_alt Ys_28) Xs_55)) ((append1050458273le_alt Zs_5) Xs_55))) (((eq list_A1528105233le_alt) Ys_28) Zs_5)))
% FOF formula (forall (Ys_27:list_A1528105233le_alt) (Us:list_A1528105233le_alt) (Xs_54:list_A1528105233le_alt) (Xs1_1:list_A1528105233le_alt) (Zs_4:list_A1528105233le_alt), ((((eq list_A1528105233le_alt) ((append1050458273le_alt Xs_54) Xs1_1)) Zs_4)->((((eq list_A1528105233le_alt) Ys_27) ((append1050458273le_alt Xs1_1) Us))->(((eq list_A1528105233le_alt) ((append1050458273le_alt Xs_54) Ys_27)) ((append1050458273le_alt Zs_4) Us))))) of role axiom named fact_28_append__eq__appendI
% A new axiom: (forall (Ys_27:list_A1528105233le_alt) (Us:list_A1528105233le_alt) (Xs_54:list_A1528105233le_alt) (Xs1_1:list_A1528105233le_alt) (Zs_4:list_A1528105233le_alt), ((((eq list_A1528105233le_alt) ((append1050458273le_alt Xs_54) Xs1_1)) Zs_4)->((((eq list_A1528105233le_alt) Ys_27) ((append1050458273le_alt Xs1_1) Us))->(((eq list_A1528105233le_alt) ((append1050458273le_alt Xs_54) Ys_27)) ((append1050458273le_alt Zs_4) Us)))))
% FOF formula (forall (X_25:arrow_1346734812le_alt) (Xs_53:list_A1528105233le_alt) (Ys_26:list_A1528105233le_alt), (((eq list_A1528105233le_alt) ((append1050458273le_alt ((cons_A1100118844le_alt X_25) Xs_53)) Ys_26)) ((cons_A1100118844le_alt X_25) ((append1050458273le_alt Xs_53) Ys_26)))) of role axiom named fact_29_append__Cons
% A new axiom: (forall (X_25:arrow_1346734812le_alt) (Xs_53:list_A1528105233le_alt) (Ys_26:list_A1528105233le_alt), (((eq list_A1528105233le_alt) ((append1050458273le_alt ((cons_A1100118844le_alt X_25) Xs_53)) Ys_26)) ((cons_A1100118844le_alt X_25) ((append1050458273le_alt Xs_53) Ys_26))))
% FOF formula (forall (Xs_52:list_A1528105233le_alt) (Zs_3:list_A1528105233le_alt) (X_24:arrow_1346734812le_alt) (Xs1:list_A1528105233le_alt) (Ys_25:list_A1528105233le_alt), ((((eq list_A1528105233le_alt) ((cons_A1100118844le_alt X_24) Xs1)) Ys_25)->((((eq list_A1528105233le_alt) Xs_52) ((append1050458273le_alt Xs1) Zs_3))->(((eq list_A1528105233le_alt) ((cons_A1100118844le_alt X_24) Xs_52)) ((append1050458273le_alt Ys_25) Zs_3))))) of role axiom named fact_30_Cons__eq__appendI
% A new axiom: (forall (Xs_52:list_A1528105233le_alt) (Zs_3:list_A1528105233le_alt) (X_24:arrow_1346734812le_alt) (Xs1:list_A1528105233le_alt) (Ys_25:list_A1528105233le_alt), ((((eq list_A1528105233le_alt) ((cons_A1100118844le_alt X_24) Xs1)) Ys_25)->((((eq list_A1528105233le_alt) Xs_52) ((append1050458273le_alt Xs1) Zs_3))->(((eq list_A1528105233le_alt) ((cons_A1100118844le_alt X_24) Xs_52)) ((append1050458273le_alt Ys_25) Zs_3)))))
% FOF formula (forall (Ys_24:list_A1528105233le_alt), (((eq list_A1528105233le_alt) ((append1050458273le_alt nil_Ar10086284le_alt) Ys_24)) Ys_24)) of role axiom named fact_31_append__Nil
% A new axiom: (forall (Ys_24:list_A1528105233le_alt), (((eq list_A1528105233le_alt) ((append1050458273le_alt nil_Ar10086284le_alt) Ys_24)) Ys_24))
% FOF formula (forall (Xs_51:list_A1528105233le_alt) (Ys_23:list_A1528105233le_alt), ((iff (((eq list_A1528105233le_alt) nil_Ar10086284le_alt) ((append1050458273le_alt Xs_51) Ys_23))) ((and (((eq list_A1528105233le_alt) Xs_51) nil_Ar10086284le_alt)) (((eq list_A1528105233le_alt) Ys_23) nil_Ar10086284le_alt)))) of role axiom named fact_32_Nil__is__append__conv
% A new axiom: (forall (Xs_51:list_A1528105233le_alt) (Ys_23:list_A1528105233le_alt), ((iff (((eq list_A1528105233le_alt) nil_Ar10086284le_alt) ((append1050458273le_alt Xs_51) Ys_23))) ((and (((eq list_A1528105233le_alt) Xs_51) nil_Ar10086284le_alt)) (((eq list_A1528105233le_alt) Ys_23) nil_Ar10086284le_alt))))
% FOF formula (forall (Xs_50:list_A1528105233le_alt), (((eq list_A1528105233le_alt) ((append1050458273le_alt Xs_50) nil_Ar10086284le_alt)) Xs_50)) of role axiom named fact_33_append__Nil2
% A new axiom: (forall (Xs_50:list_A1528105233le_alt), (((eq list_A1528105233le_alt) ((append1050458273le_alt Xs_50) nil_Ar10086284le_alt)) Xs_50))
% FOF formula (forall (Xs_49:list_A1528105233le_alt) (Ys_22:list_A1528105233le_alt), ((iff (((eq list_A1528105233le_alt) Xs_49) ((append1050458273le_alt Xs_49) Ys_22))) (((eq list_A1528105233le_alt) Ys_22) nil_Ar10086284le_alt))) of role axiom named fact_34_self__append__conv
% A new axiom: (forall (Xs_49:list_A1528105233le_alt) (Ys_22:list_A1528105233le_alt), ((iff (((eq list_A1528105233le_alt) Xs_49) ((append1050458273le_alt Xs_49) Ys_22))) (((eq list_A1528105233le_alt) Ys_22) nil_Ar10086284le_alt)))
% FOF formula (forall (Ys_21:list_A1528105233le_alt) (Xs_48:list_A1528105233le_alt), ((iff (((eq list_A1528105233le_alt) Ys_21) ((append1050458273le_alt Xs_48) Ys_21))) (((eq list_A1528105233le_alt) Xs_48) nil_Ar10086284le_alt))) of role axiom named fact_35_self__append__conv2
% A new axiom: (forall (Ys_21:list_A1528105233le_alt) (Xs_48:list_A1528105233le_alt), ((iff (((eq list_A1528105233le_alt) Ys_21) ((append1050458273le_alt Xs_48) Ys_21))) (((eq list_A1528105233le_alt) Xs_48) nil_Ar10086284le_alt)))
% FOF formula (forall (Xs_47:list_A1528105233le_alt) (Ys_20:list_A1528105233le_alt), ((iff (((eq list_A1528105233le_alt) ((append1050458273le_alt Xs_47) Ys_20)) nil_Ar10086284le_alt)) ((and (((eq list_A1528105233le_alt) Xs_47) nil_Ar10086284le_alt)) (((eq list_A1528105233le_alt) Ys_20) nil_Ar10086284le_alt)))) of role axiom named fact_36_append__is__Nil__conv
% A new axiom: (forall (Xs_47:list_A1528105233le_alt) (Ys_20:list_A1528105233le_alt), ((iff (((eq list_A1528105233le_alt) ((append1050458273le_alt Xs_47) Ys_20)) nil_Ar10086284le_alt)) ((and (((eq list_A1528105233le_alt) Xs_47) nil_Ar10086284le_alt)) (((eq list_A1528105233le_alt) Ys_20) nil_Ar10086284le_alt))))
% FOF formula (forall (Xs_46:list_A1528105233le_alt) (Ys_19:list_A1528105233le_alt), ((iff (((eq list_A1528105233le_alt) ((append1050458273le_alt Xs_46) Ys_19)) Xs_46)) (((eq list_A1528105233le_alt) Ys_19) nil_Ar10086284le_alt))) of role axiom named fact_37_append__self__conv
% A new axiom: (forall (Xs_46:list_A1528105233le_alt) (Ys_19:list_A1528105233le_alt), ((iff (((eq list_A1528105233le_alt) ((append1050458273le_alt Xs_46) Ys_19)) Xs_46)) (((eq list_A1528105233le_alt) Ys_19) nil_Ar10086284le_alt)))
% FOF formula (forall (Xs_45:list_A1528105233le_alt) (Ys_18:list_A1528105233le_alt), ((iff (((eq list_A1528105233le_alt) ((append1050458273le_alt Xs_45) Ys_18)) Ys_18)) (((eq list_A1528105233le_alt) Xs_45) nil_Ar10086284le_alt))) of role axiom named fact_38_append__self__conv2
% A new axiom: (forall (Xs_45:list_A1528105233le_alt) (Ys_18:list_A1528105233le_alt), ((iff (((eq list_A1528105233le_alt) ((append1050458273le_alt Xs_45) Ys_18)) Ys_18)) (((eq list_A1528105233le_alt) Xs_45) nil_Ar10086284le_alt)))
% FOF formula (forall (Xs_44:list_A1528105233le_alt) (Ys_17:list_A1528105233le_alt), ((((eq list_A1528105233le_alt) Xs_44) Ys_17)->(((eq list_A1528105233le_alt) Xs_44) ((append1050458273le_alt nil_Ar10086284le_alt) Ys_17)))) of role axiom named fact_39_eq__Nil__appendI
% A new axiom: (forall (Xs_44:list_A1528105233le_alt) (Ys_17:list_A1528105233le_alt), ((((eq list_A1528105233le_alt) Xs_44) Ys_17)->(((eq list_A1528105233le_alt) Xs_44) ((append1050458273le_alt nil_Ar10086284le_alt) Ys_17))))
% FOF formula (forall (Ys_16:list_A1528105233le_alt) (Zs_2:list_A1528105233le_alt) (X_23:arrow_1346734812le_alt) (Xs_43:list_A1528105233le_alt), ((iff (((eq list_A1528105233le_alt) ((append1050458273le_alt Ys_16) Zs_2)) ((cons_A1100118844le_alt X_23) Xs_43))) ((or ((and (((eq list_A1528105233le_alt) Ys_16) nil_Ar10086284le_alt)) (((eq list_A1528105233le_alt) Zs_2) ((cons_A1100118844le_alt X_23) Xs_43)))) ((ex list_A1528105233le_alt) (fun (Ys_15:list_A1528105233le_alt)=> ((and (((eq list_A1528105233le_alt) Ys_16) ((cons_A1100118844le_alt X_23) Ys_15))) (((eq list_A1528105233le_alt) ((append1050458273le_alt Ys_15) Zs_2)) Xs_43))))))) of role axiom named fact_40_append__eq__Cons__conv
% A new axiom: (forall (Ys_16:list_A1528105233le_alt) (Zs_2:list_A1528105233le_alt) (X_23:arrow_1346734812le_alt) (Xs_43:list_A1528105233le_alt), ((iff (((eq list_A1528105233le_alt) ((append1050458273le_alt Ys_16) Zs_2)) ((cons_A1100118844le_alt X_23) Xs_43))) ((or ((and (((eq list_A1528105233le_alt) Ys_16) nil_Ar10086284le_alt)) (((eq list_A1528105233le_alt) Zs_2) ((cons_A1100118844le_alt X_23) Xs_43)))) ((ex list_A1528105233le_alt) (fun (Ys_15:list_A1528105233le_alt)=> ((and (((eq list_A1528105233le_alt) Ys_16) ((cons_A1100118844le_alt X_23) Ys_15))) (((eq list_A1528105233le_alt) ((append1050458273le_alt Ys_15) Zs_2)) Xs_43)))))))
% FOF formula (forall (X_22:arrow_1346734812le_alt) (Xs_42:list_A1528105233le_alt) (Ys_14:list_A1528105233le_alt) (Zs_1:list_A1528105233le_alt), ((iff (((eq list_A1528105233le_alt) ((cons_A1100118844le_alt X_22) Xs_42)) ((append1050458273le_alt Ys_14) Zs_1))) ((or ((and (((eq list_A1528105233le_alt) Ys_14) nil_Ar10086284le_alt)) (((eq list_A1528105233le_alt) ((cons_A1100118844le_alt X_22) Xs_42)) Zs_1))) ((ex list_A1528105233le_alt) (fun (Ys_15:list_A1528105233le_alt)=> ((and (((eq list_A1528105233le_alt) ((cons_A1100118844le_alt X_22) Ys_15)) Ys_14)) (((eq list_A1528105233le_alt) Xs_42) ((append1050458273le_alt Ys_15) Zs_1)))))))) of role axiom named fact_41_Cons__eq__append__conv
% A new axiom: (forall (X_22:arrow_1346734812le_alt) (Xs_42:list_A1528105233le_alt) (Ys_14:list_A1528105233le_alt) (Zs_1:list_A1528105233le_alt), ((iff (((eq list_A1528105233le_alt) ((cons_A1100118844le_alt X_22) Xs_42)) ((append1050458273le_alt Ys_14) Zs_1))) ((or ((and (((eq list_A1528105233le_alt) Ys_14) nil_Ar10086284le_alt)) (((eq list_A1528105233le_alt) ((cons_A1100118844le_alt X_22) Xs_42)) Zs_1))) ((ex list_A1528105233le_alt) (fun (Ys_15:list_A1528105233le_alt)=> ((and (((eq list_A1528105233le_alt) ((cons_A1100118844le_alt X_22) Ys_15)) Ys_14)) (((eq list_A1528105233le_alt) Xs_42) ((append1050458273le_alt Ys_15) Zs_1))))))))
% FOF formula (forall (Xs_41:list_A1528105233le_alt) (X_21:arrow_1346734812le_alt) (Ys_13:list_A1528105233le_alt) (Y_5:arrow_1346734812le_alt), ((iff (((eq list_A1528105233le_alt) ((append1050458273le_alt Xs_41) ((cons_A1100118844le_alt X_21) nil_Ar10086284le_alt))) ((append1050458273le_alt Ys_13) ((cons_A1100118844le_alt Y_5) nil_Ar10086284le_alt)))) ((and (((eq list_A1528105233le_alt) Xs_41) Ys_13)) (((eq arrow_1346734812le_alt) X_21) Y_5)))) of role axiom named fact_42_append1__eq__conv
% A new axiom: (forall (Xs_41:list_A1528105233le_alt) (X_21:arrow_1346734812le_alt) (Ys_13:list_A1528105233le_alt) (Y_5:arrow_1346734812le_alt), ((iff (((eq list_A1528105233le_alt) ((append1050458273le_alt Xs_41) ((cons_A1100118844le_alt X_21) nil_Ar10086284le_alt))) ((append1050458273le_alt Ys_13) ((cons_A1100118844le_alt Y_5) nil_Ar10086284le_alt)))) ((and (((eq list_A1528105233le_alt) Xs_41) Ys_13)) (((eq arrow_1346734812le_alt) X_21) Y_5))))
% FOF formula (forall (Xs_40:list_A1528105233le_alt) (Ys_12:list_A1528105233le_alt), ((and ((((eq list_A1528105233le_alt) Ys_12) nil_Ar10086284le_alt)->(((eq list_A1528105233le_alt) (butlas1146323672le_alt ((append1050458273le_alt Xs_40) Ys_12))) (butlas1146323672le_alt Xs_40)))) ((not (((eq list_A1528105233le_alt) Ys_12) nil_Ar10086284le_alt))->(((eq list_A1528105233le_alt) (butlas1146323672le_alt ((append1050458273le_alt Xs_40) Ys_12))) ((append1050458273le_alt Xs_40) (butlas1146323672le_alt Ys_12)))))) of role axiom named fact_43_butlast__append
% A new axiom: (forall (Xs_40:list_A1528105233le_alt) (Ys_12:list_A1528105233le_alt), ((and ((((eq list_A1528105233le_alt) Ys_12) nil_Ar10086284le_alt)->(((eq list_A1528105233le_alt) (butlas1146323672le_alt ((append1050458273le_alt Xs_40) Ys_12))) (butlas1146323672le_alt Xs_40)))) ((not (((eq list_A1528105233le_alt) Ys_12) nil_Ar10086284le_alt))->(((eq list_A1528105233le_alt) (butlas1146323672le_alt ((append1050458273le_alt Xs_40) Ys_12))) ((append1050458273le_alt Xs_40) (butlas1146323672le_alt Ys_12))))))
% FOF formula (forall (Xs_39:list_A1528105233le_alt) (P_4:(list_A1528105233le_alt->Prop)), ((P_4 nil_Ar10086284le_alt)->((forall (X_20:arrow_1346734812le_alt) (Xs_23:list_A1528105233le_alt), ((P_4 Xs_23)->(P_4 ((append1050458273le_alt Xs_23) ((cons_A1100118844le_alt X_20) nil_Ar10086284le_alt)))))->(P_4 Xs_39)))) of role axiom named fact_44_rev__induct
% A new axiom: (forall (Xs_39:list_A1528105233le_alt) (P_4:(list_A1528105233le_alt->Prop)), ((P_4 nil_Ar10086284le_alt)->((forall (X_20:arrow_1346734812le_alt) (Xs_23:list_A1528105233le_alt), ((P_4 Xs_23)->(P_4 ((append1050458273le_alt Xs_23) ((cons_A1100118844le_alt X_20) nil_Ar10086284le_alt)))))->(P_4 Xs_39))))
% FOF formula (forall (Xs_38:list_A1528105233le_alt), ((not (((eq list_A1528105233le_alt) Xs_38) nil_Ar10086284le_alt))->((forall (Ys_7:list_A1528105233le_alt) (Y_3:arrow_1346734812le_alt), (not (((eq list_A1528105233le_alt) Xs_38) ((append1050458273le_alt Ys_7) ((cons_A1100118844le_alt Y_3) nil_Ar10086284le_alt)))))->False))) of role axiom named fact_45_rev__cases
% A new axiom: (forall (Xs_38:list_A1528105233le_alt), ((not (((eq list_A1528105233le_alt) Xs_38) nil_Ar10086284le_alt))->((forall (Ys_7:list_A1528105233le_alt) (Y_3:arrow_1346734812le_alt), (not (((eq list_A1528105233le_alt) Xs_38) ((append1050458273le_alt Ys_7) ((cons_A1100118844le_alt Y_3) nil_Ar10086284le_alt)))))->False)))
% FOF formula (forall (Xs_37:list_A1528105233le_alt), ((iff ((equal_2044961839le_alt Xs_37) nil_Ar10086284le_alt)) (null_A244857236le_alt Xs_37))) of role axiom named fact_46_equal__Nil__null
% A new axiom: (forall (Xs_37:list_A1528105233le_alt), ((iff ((equal_2044961839le_alt Xs_37) nil_Ar10086284le_alt)) (null_A244857236le_alt Xs_37)))
% FOF formula (forall (Xs_36:list_A1528105233le_alt) (X_19:arrow_1346734812le_alt) (Ys_11:list_A1528105233le_alt), ((iff (((eq list_A1528105233le_alt) ((append1050458273le_alt Xs_36) ((cons_A1100118844le_alt X_19) nil_Ar10086284le_alt))) Ys_11)) ((and ((and (not (((eq list_A1528105233le_alt) Ys_11) nil_Ar10086284le_alt))) (((eq list_A1528105233le_alt) (butlas1146323672le_alt Ys_11)) Xs_36))) (((eq arrow_1346734812le_alt) (last_A2088691109le_alt Ys_11)) X_19)))) of role axiom named fact_47_snoc__eq__iff__butlast
% A new axiom: (forall (Xs_36:list_A1528105233le_alt) (X_19:arrow_1346734812le_alt) (Ys_11:list_A1528105233le_alt), ((iff (((eq list_A1528105233le_alt) ((append1050458273le_alt Xs_36) ((cons_A1100118844le_alt X_19) nil_Ar10086284le_alt))) Ys_11)) ((and ((and (not (((eq list_A1528105233le_alt) Ys_11) nil_Ar10086284le_alt))) (((eq list_A1528105233le_alt) (butlas1146323672le_alt Ys_11)) Xs_36))) (((eq arrow_1346734812le_alt) (last_A2088691109le_alt Ys_11)) X_19))))
% FOF formula (forall (Xs_35:list_A1528105233le_alt), ((not (((eq list_A1528105233le_alt) Xs_35) nil_Ar10086284le_alt))->(((eq list_A1528105233le_alt) ((append1050458273le_alt (butlas1146323672le_alt Xs_35)) ((cons_A1100118844le_alt (last_A2088691109le_alt Xs_35)) nil_Ar10086284le_alt))) Xs_35))) of role axiom named fact_48_append__butlast__last__id
% A new axiom: (forall (Xs_35:list_A1528105233le_alt), ((not (((eq list_A1528105233le_alt) Xs_35) nil_Ar10086284le_alt))->(((eq list_A1528105233le_alt) ((append1050458273le_alt (butlas1146323672le_alt Xs_35)) ((cons_A1100118844le_alt (last_A2088691109le_alt Xs_35)) nil_Ar10086284le_alt))) Xs_35)))
% FOF formula (forall (X_18:arrow_1346734812le_alt) (Xs_34:list_A1528105233le_alt), ((and (((eq list_A1528105233le_alt) (rotate1206725081le_alt nil_Ar10086284le_alt)) nil_Ar10086284le_alt)) (((eq list_A1528105233le_alt) (rotate1206725081le_alt ((cons_A1100118844le_alt X_18) Xs_34))) ((append1050458273le_alt Xs_34) ((cons_A1100118844le_alt X_18) nil_Ar10086284le_alt))))) of role axiom named fact_49_rotate__simps
% A new axiom: (forall (X_18:arrow_1346734812le_alt) (Xs_34:list_A1528105233le_alt), ((and (((eq list_A1528105233le_alt) (rotate1206725081le_alt nil_Ar10086284le_alt)) nil_Ar10086284le_alt)) (((eq list_A1528105233le_alt) (rotate1206725081le_alt ((cons_A1100118844le_alt X_18) Xs_34))) ((append1050458273le_alt Xs_34) ((cons_A1100118844le_alt X_18) nil_Ar10086284le_alt)))))
% FOF formula (forall (X_17:list_A1528105233le_alt) (Y_4:list_A1528105233le_alt), ((iff ((equal_2044961839le_alt X_17) Y_4)) (((eq list_A1528105233le_alt) X_17) Y_4))) of role axiom named fact_50_equal__list__def
% A new axiom: (forall (X_17:list_A1528105233le_alt) (Y_4:list_A1528105233le_alt), ((iff ((equal_2044961839le_alt X_17) Y_4)) (((eq list_A1528105233le_alt) X_17) Y_4)))
% FOF formula (forall (Xs_33:list_A1528105233le_alt), ((iff (((eq list_A1528105233le_alt) (rotate1206725081le_alt Xs_33)) nil_Ar10086284le_alt)) (((eq list_A1528105233le_alt) Xs_33) nil_Ar10086284le_alt))) of role axiom named fact_51_rotate1__is__Nil__conv
% A new axiom: (forall (Xs_33:list_A1528105233le_alt), ((iff (((eq list_A1528105233le_alt) (rotate1206725081le_alt Xs_33)) nil_Ar10086284le_alt)) (((eq list_A1528105233le_alt) Xs_33) nil_Ar10086284le_alt)))
% FOF formula (forall (Xs_32:list_A1528105233le_alt), ((iff (distin1107700095le_alt (rotate1206725081le_alt Xs_32))) (distin1107700095le_alt Xs_32))) of role axiom named fact_52_distinct1__rotate
% A new axiom: (forall (Xs_32:list_A1528105233le_alt), ((iff (distin1107700095le_alt (rotate1206725081le_alt Xs_32))) (distin1107700095le_alt Xs_32)))
% FOF formula (forall (X_16:arrow_1346734812le_alt) (Xs_31:list_A1528105233le_alt), ((((eq list_A1528105233le_alt) Xs_31) nil_Ar10086284le_alt)->(((eq arrow_1346734812le_alt) (last_A2088691109le_alt ((cons_A1100118844le_alt X_16) Xs_31))) X_16))) of role axiom named fact_53_last__ConsL
% A new axiom: (forall (X_16:arrow_1346734812le_alt) (Xs_31:list_A1528105233le_alt), ((((eq list_A1528105233le_alt) Xs_31) nil_Ar10086284le_alt)->(((eq arrow_1346734812le_alt) (last_A2088691109le_alt ((cons_A1100118844le_alt X_16) Xs_31))) X_16)))
% FOF formula (forall (X_15:arrow_1346734812le_alt) (Xs_30:list_A1528105233le_alt), ((not (((eq list_A1528105233le_alt) Xs_30) nil_Ar10086284le_alt))->(((eq arrow_1346734812le_alt) (last_A2088691109le_alt ((cons_A1100118844le_alt X_15) Xs_30))) (last_A2088691109le_alt Xs_30)))) of role axiom named fact_54_last__ConsR
% A new axiom: (forall (X_15:arrow_1346734812le_alt) (Xs_30:list_A1528105233le_alt), ((not (((eq list_A1528105233le_alt) Xs_30) nil_Ar10086284le_alt))->(((eq arrow_1346734812le_alt) (last_A2088691109le_alt ((cons_A1100118844le_alt X_15) Xs_30))) (last_A2088691109le_alt Xs_30))))
% FOF formula (forall (X_14:arrow_1346734812le_alt) (Xs_29:list_A1528105233le_alt), ((and ((((eq list_A1528105233le_alt) Xs_29) nil_Ar10086284le_alt)->(((eq arrow_1346734812le_alt) (last_A2088691109le_alt ((cons_A1100118844le_alt X_14) Xs_29))) X_14))) ((not (((eq list_A1528105233le_alt) Xs_29) nil_Ar10086284le_alt))->(((eq arrow_1346734812le_alt) (last_A2088691109le_alt ((cons_A1100118844le_alt X_14) Xs_29))) (last_A2088691109le_alt Xs_29))))) of role axiom named fact_55_last_Osimps
% A new axiom: (forall (X_14:arrow_1346734812le_alt) (Xs_29:list_A1528105233le_alt), ((and ((((eq list_A1528105233le_alt) Xs_29) nil_Ar10086284le_alt)->(((eq arrow_1346734812le_alt) (last_A2088691109le_alt ((cons_A1100118844le_alt X_14) Xs_29))) X_14))) ((not (((eq list_A1528105233le_alt) Xs_29) nil_Ar10086284le_alt))->(((eq arrow_1346734812le_alt) (last_A2088691109le_alt ((cons_A1100118844le_alt X_14) Xs_29))) (last_A2088691109le_alt Xs_29)))))
% FOF formula (forall (Xs_28:list_A1528105233le_alt) (Ys_10:list_A1528105233le_alt), ((((eq list_A1528105233le_alt) Ys_10) nil_Ar10086284le_alt)->(((eq arrow_1346734812le_alt) (last_A2088691109le_alt ((append1050458273le_alt Xs_28) Ys_10))) (last_A2088691109le_alt Xs_28)))) of role axiom named fact_56_last__appendL
% A new axiom: (forall (Xs_28:list_A1528105233le_alt) (Ys_10:list_A1528105233le_alt), ((((eq list_A1528105233le_alt) Ys_10) nil_Ar10086284le_alt)->(((eq arrow_1346734812le_alt) (last_A2088691109le_alt ((append1050458273le_alt Xs_28) Ys_10))) (last_A2088691109le_alt Xs_28))))
% FOF formula (forall (Xs_27:list_A1528105233le_alt) (Ys_9:list_A1528105233le_alt), ((not (((eq list_A1528105233le_alt) Ys_9) nil_Ar10086284le_alt))->(((eq arrow_1346734812le_alt) (last_A2088691109le_alt ((append1050458273le_alt Xs_27) Ys_9))) (last_A2088691109le_alt Ys_9)))) of role axiom named fact_57_last__appendR
% A new axiom: (forall (Xs_27:list_A1528105233le_alt) (Ys_9:list_A1528105233le_alt), ((not (((eq list_A1528105233le_alt) Ys_9) nil_Ar10086284le_alt))->(((eq arrow_1346734812le_alt) (last_A2088691109le_alt ((append1050458273le_alt Xs_27) Ys_9))) (last_A2088691109le_alt Ys_9))))
% FOF formula (forall (Xs_26:list_A1528105233le_alt) (Ys_8:list_A1528105233le_alt), ((and ((((eq list_A1528105233le_alt) Ys_8) nil_Ar10086284le_alt)->(((eq arrow_1346734812le_alt) (last_A2088691109le_alt ((append1050458273le_alt Xs_26) Ys_8))) (last_A2088691109le_alt Xs_26)))) ((not (((eq list_A1528105233le_alt) Ys_8) nil_Ar10086284le_alt))->(((eq arrow_1346734812le_alt) (last_A2088691109le_alt ((append1050458273le_alt Xs_26) Ys_8))) (last_A2088691109le_alt Ys_8))))) of role axiom named fact_58_last__append
% A new axiom: (forall (Xs_26:list_A1528105233le_alt) (Ys_8:list_A1528105233le_alt), ((and ((((eq list_A1528105233le_alt) Ys_8) nil_Ar10086284le_alt)->(((eq arrow_1346734812le_alt) (last_A2088691109le_alt ((append1050458273le_alt Xs_26) Ys_8))) (last_A2088691109le_alt Xs_26)))) ((not (((eq list_A1528105233le_alt) Ys_8) nil_Ar10086284le_alt))->(((eq arrow_1346734812le_alt) (last_A2088691109le_alt ((append1050458273le_alt Xs_26) Ys_8))) (last_A2088691109le_alt Ys_8)))))
% FOF formula (forall (Xs_25:list_A1528105233le_alt) (X_13:arrow_1346734812le_alt), (((eq arrow_1346734812le_alt) (last_A2088691109le_alt ((append1050458273le_alt Xs_25) ((cons_A1100118844le_alt X_13) nil_Ar10086284le_alt)))) X_13)) of role axiom named fact_59_last__snoc
% A new axiom: (forall (Xs_25:list_A1528105233le_alt) (X_13:arrow_1346734812le_alt), (((eq arrow_1346734812le_alt) (last_A2088691109le_alt ((append1050458273le_alt Xs_25) ((cons_A1100118844le_alt X_13) nil_Ar10086284le_alt)))) X_13))
% FOF formula (forall (F:(arrow_1346734812le_alt->list_A1528105233le_alt)) (X_12:arrow_1346734812le_alt) (Xs_24:list_A1528105233le_alt), (((eq list_A1528105233le_alt) ((maps_A51637569le_alt F) ((cons_A1100118844le_alt X_12) Xs_24))) ((append1050458273le_alt (F X_12)) ((maps_A51637569le_alt F) Xs_24)))) of role axiom named fact_60_maps__simps_I1_J
% A new axiom: (forall (F:(arrow_1346734812le_alt->list_A1528105233le_alt)) (X_12:arrow_1346734812le_alt) (Xs_24:list_A1528105233le_alt), (((eq list_A1528105233le_alt) ((maps_A51637569le_alt F) ((cons_A1100118844le_alt X_12) Xs_24))) ((append1050458273le_alt (F X_12)) ((maps_A51637569le_alt F) Xs_24))))
% FOF formula (forall (Ws:list_A1528105233le_alt), (((distin1107700095le_alt Ws)->False)->((ex list_A1528105233le_alt) (fun (Xs_23:list_A1528105233le_alt)=> ((ex list_A1528105233le_alt) (fun (Ys_7:list_A1528105233le_alt)=> ((ex list_A1528105233le_alt) (fun (Zs:list_A1528105233le_alt)=> ((ex arrow_1346734812le_alt) (fun (Y_3:arrow_1346734812le_alt)=> (((eq list_A1528105233le_alt) Ws) ((append1050458273le_alt Xs_23) ((append1050458273le_alt ((cons_A1100118844le_alt Y_3) nil_Ar10086284le_alt)) ((append1050458273le_alt Ys_7) ((append1050458273le_alt ((cons_A1100118844le_alt Y_3) nil_Ar10086284le_alt)) Zs))))))))))))))) of role axiom named fact_61_not__distinct__decomp
% A new axiom: (forall (Ws:list_A1528105233le_alt), (((distin1107700095le_alt Ws)->False)->((ex list_A1528105233le_alt) (fun (Xs_23:list_A1528105233le_alt)=> ((ex list_A1528105233le_alt) (fun (Ys_7:list_A1528105233le_alt)=> ((ex list_A1528105233le_alt) (fun (Zs:list_A1528105233le_alt)=> ((ex arrow_1346734812le_alt) (fun (Y_3:arrow_1346734812le_alt)=> (((eq list_A1528105233le_alt) Ws) ((append1050458273le_alt Xs_23) ((append1050458273le_alt ((cons_A1100118844le_alt Y_3) nil_Ar10086284le_alt)) ((append1050458273le_alt Ys_7) ((append1050458273le_alt ((cons_A1100118844le_alt Y_3) nil_Ar10086284le_alt)) Zs)))))))))))))))
% FOF formula (((eq (list_A1528105233le_alt->(list_A1528105233le_alt->Prop))) equal_2044961839le_alt) fequal194154450le_alt) of role axiom named fact_62_equal
% A new axiom: (((eq (list_A1528105233le_alt->(list_A1528105233le_alt->Prop))) equal_2044961839le_alt) fequal194154450le_alt)
% FOF formula (forall (X_11:list_A1528105233le_alt), ((equal_2044961839le_alt X_11) X_11)) of role axiom named fact_63_equal__refl
% A new axiom: (forall (X_11:list_A1528105233le_alt), ((equal_2044961839le_alt X_11) X_11))
% FOF formula (((eq (list_A1528105233le_alt->(list_A1528105233le_alt->Prop))) fequal194154450le_alt) equal_2044961839le_alt) of role axiom named fact_64_eq__equal
% A new axiom: (((eq (list_A1528105233le_alt->(list_A1528105233le_alt->Prop))) fequal194154450le_alt) equal_2044961839le_alt)
% FOF formula (forall (X_10:list_A1528105233le_alt) (Y_2:list_A1528105233le_alt), ((iff ((equal_2044961839le_alt X_10) Y_2)) (((eq list_A1528105233le_alt) X_10) Y_2))) of role axiom named fact_65_equal__eq
% A new axiom: (forall (X_10:list_A1528105233le_alt) (Y_2:list_A1528105233le_alt), ((iff ((equal_2044961839le_alt X_10) Y_2)) (((eq list_A1528105233le_alt) X_10) Y_2)))
% FOF formula (forall (_TPTP_I:nat) (X_9:arrow_1346734812le_alt), (((eq list_A1528105233le_alt) ((append1050458273le_alt ((replic235430982le_alt _TPTP_I) X_9)) ((cons_A1100118844le_alt X_9) nil_Ar10086284le_alt))) ((cons_A1100118844le_alt X_9) ((replic235430982le_alt _TPTP_I) X_9)))) of role axiom named fact_66_replicate__append__same
% A new axiom: (forall (_TPTP_I:nat) (X_9:arrow_1346734812le_alt), (((eq list_A1528105233le_alt) ((append1050458273le_alt ((replic235430982le_alt _TPTP_I) X_9)) ((cons_A1100118844le_alt X_9) nil_Ar10086284le_alt))) ((cons_A1100118844le_alt X_9) ((replic235430982le_alt _TPTP_I) X_9))))
% FOF formula (forall (X_8:arrow_1346734812le_alt) (Xs_22:list_A1528105233le_alt), (((eq list_A1528105233le_alt) (rev_Ar1977782764le_alt ((cons_A1100118844le_alt X_8) Xs_22))) ((append1050458273le_alt (rev_Ar1977782764le_alt Xs_22)) ((cons_A1100118844le_alt X_8) nil_Ar10086284le_alt)))) of role axiom named fact_67_rev_Osimps_I2_J
% A new axiom: (forall (X_8:arrow_1346734812le_alt) (Xs_22:list_A1528105233le_alt), (((eq list_A1528105233le_alt) (rev_Ar1977782764le_alt ((cons_A1100118844le_alt X_8) Xs_22))) ((append1050458273le_alt (rev_Ar1977782764le_alt Xs_22)) ((cons_A1100118844le_alt X_8) nil_Ar10086284le_alt))))
% FOF formula (forall (Xs_21:list_A1528105233le_alt) (Y_1:arrow_1346734812le_alt) (Ys_6:list_A1528105233le_alt), ((iff (((eq list_A1528105233le_alt) (rev_Ar1977782764le_alt Xs_21)) ((cons_A1100118844le_alt Y_1) Ys_6))) (((eq list_A1528105233le_alt) Xs_21) ((append1050458273le_alt (rev_Ar1977782764le_alt Ys_6)) ((cons_A1100118844le_alt Y_1) nil_Ar10086284le_alt))))) of role axiom named fact_68_rev__eq__Cons__iff
% A new axiom: (forall (Xs_21:list_A1528105233le_alt) (Y_1:arrow_1346734812le_alt) (Ys_6:list_A1528105233le_alt), ((iff (((eq list_A1528105233le_alt) (rev_Ar1977782764le_alt Xs_21)) ((cons_A1100118844le_alt Y_1) Ys_6))) (((eq list_A1528105233le_alt) Xs_21) ((append1050458273le_alt (rev_Ar1977782764le_alt Ys_6)) ((cons_A1100118844le_alt Y_1) nil_Ar10086284le_alt)))))
% FOF formula (forall (Xs_20:list_A1528105233le_alt) (Ys_5:list_A1528105233le_alt), ((iff (((eq list_A1528105233le_alt) (rev_Ar1977782764le_alt Xs_20)) (rev_Ar1977782764le_alt Ys_5))) (((eq list_A1528105233le_alt) Xs_20) Ys_5))) of role axiom named fact_69_rev__is__rev__conv
% A new axiom: (forall (Xs_20:list_A1528105233le_alt) (Ys_5:list_A1528105233le_alt), ((iff (((eq list_A1528105233le_alt) (rev_Ar1977782764le_alt Xs_20)) (rev_Ar1977782764le_alt Ys_5))) (((eq list_A1528105233le_alt) Xs_20) Ys_5)))
% FOF formula (forall (Xs_19:list_A1528105233le_alt) (Ys_4:list_A1528105233le_alt), ((iff (((eq list_A1528105233le_alt) (rev_Ar1977782764le_alt Xs_19)) Ys_4)) (((eq list_A1528105233le_alt) Xs_19) (rev_Ar1977782764le_alt Ys_4)))) of role axiom named fact_70_rev__swap
% A new axiom: (forall (Xs_19:list_A1528105233le_alt) (Ys_4:list_A1528105233le_alt), ((iff (((eq list_A1528105233le_alt) (rev_Ar1977782764le_alt Xs_19)) Ys_4)) (((eq list_A1528105233le_alt) Xs_19) (rev_Ar1977782764le_alt Ys_4))))
% FOF formula (forall (N_2:nat) (X_7:arrow_1346734812le_alt), (((eq list_A1528105233le_alt) (rev_Ar1977782764le_alt ((replic235430982le_alt N_2) X_7))) ((replic235430982le_alt N_2) X_7))) of role axiom named fact_71_rev__replicate
% A new axiom: (forall (N_2:nat) (X_7:arrow_1346734812le_alt), (((eq list_A1528105233le_alt) (rev_Ar1977782764le_alt ((replic235430982le_alt N_2) X_7))) ((replic235430982le_alt N_2) X_7)))
% FOF formula (forall (Xs_18:list_A1528105233le_alt), (((eq list_A1528105233le_alt) (rev_Ar1977782764le_alt (rev_Ar1977782764le_alt Xs_18))) Xs_18)) of role axiom named fact_72_rev__rev__ident
% A new axiom: (forall (Xs_18:list_A1528105233le_alt), (((eq list_A1528105233le_alt) (rev_Ar1977782764le_alt (rev_Ar1977782764le_alt Xs_18))) Xs_18))
% FOF formula (forall (N_1:nat) (X_6:arrow_1346734812le_alt) (K:nat), (((eq list_A1528105233le_alt) ((append1050458273le_alt ((replic235430982le_alt N_1) X_6)) ((replic235430982le_alt K) X_6))) ((append1050458273le_alt ((replic235430982le_alt K) X_6)) ((replic235430982le_alt N_1) X_6)))) of role axiom named fact_73_append__replicate__commute
% A new axiom: (forall (N_1:nat) (X_6:arrow_1346734812le_alt) (K:nat), (((eq list_A1528105233le_alt) ((append1050458273le_alt ((replic235430982le_alt N_1) X_6)) ((replic235430982le_alt K) X_6))) ((append1050458273le_alt ((replic235430982le_alt K) X_6)) ((replic235430982le_alt N_1) X_6))))
% FOF formula (forall (Xs_17:list_A1528105233le_alt), ((iff (distin1107700095le_alt (rev_Ar1977782764le_alt Xs_17))) (distin1107700095le_alt Xs_17))) of role axiom named fact_74_distinct__rev
% A new axiom: (forall (Xs_17:list_A1528105233le_alt), ((iff (distin1107700095le_alt (rev_Ar1977782764le_alt Xs_17))) (distin1107700095le_alt Xs_17)))
% FOF formula (forall (Xs_16:list_A1528105233le_alt) (Ys_3:list_A1528105233le_alt), (((eq list_A1528105233le_alt) (rev_Ar1977782764le_alt ((append1050458273le_alt Xs_16) Ys_3))) ((append1050458273le_alt (rev_Ar1977782764le_alt Ys_3)) (rev_Ar1977782764le_alt Xs_16)))) of role axiom named fact_75_rev__append
% A new axiom: (forall (Xs_16:list_A1528105233le_alt) (Ys_3:list_A1528105233le_alt), (((eq list_A1528105233le_alt) (rev_Ar1977782764le_alt ((append1050458273le_alt Xs_16) Ys_3))) ((append1050458273le_alt (rev_Ar1977782764le_alt Ys_3)) (rev_Ar1977782764le_alt Xs_16))))
% FOF formula (((eq list_A1528105233le_alt) (rev_Ar1977782764le_alt nil_Ar10086284le_alt)) nil_Ar10086284le_alt) of role axiom named fact_76_rev_Osimps_I1_J
% A new axiom: (((eq list_A1528105233le_alt) (rev_Ar1977782764le_alt nil_Ar10086284le_alt)) nil_Ar10086284le_alt)
% FOF formula (forall (Xs_15:list_A1528105233le_alt), ((iff (((eq list_A1528105233le_alt) nil_Ar10086284le_alt) (rev_Ar1977782764le_alt Xs_15))) (((eq list_A1528105233le_alt) Xs_15) nil_Ar10086284le_alt))) of role axiom named fact_77_Nil__is__rev__conv
% A new axiom: (forall (Xs_15:list_A1528105233le_alt), ((iff (((eq list_A1528105233le_alt) nil_Ar10086284le_alt) (rev_Ar1977782764le_alt Xs_15))) (((eq list_A1528105233le_alt) Xs_15) nil_Ar10086284le_alt)))
% FOF formula (forall (Xs_14:list_A1528105233le_alt), ((iff (((eq list_A1528105233le_alt) (rev_Ar1977782764le_alt Xs_14)) nil_Ar10086284le_alt)) (((eq list_A1528105233le_alt) Xs_14) nil_Ar10086284le_alt))) of role axiom named fact_78_rev__is__Nil__conv
% A new axiom: (forall (Xs_14:list_A1528105233le_alt), ((iff (((eq list_A1528105233le_alt) (rev_Ar1977782764le_alt Xs_14)) nil_Ar10086284le_alt)) (((eq list_A1528105233le_alt) Xs_14) nil_Ar10086284le_alt)))
% FOF formula (forall (X_5:arrow_1346734812le_alt) (Xs_13:list_A1528105233le_alt), ((iff (((eq list_A1528105233le_alt) ((cons_A1100118844le_alt X_5) nil_Ar10086284le_alt)) (rev_Ar1977782764le_alt Xs_13))) (((eq list_A1528105233le_alt) Xs_13) ((cons_A1100118844le_alt X_5) nil_Ar10086284le_alt)))) of role axiom named fact_79_singleton__rev__conv
% A new axiom: (forall (X_5:arrow_1346734812le_alt) (Xs_13:list_A1528105233le_alt), ((iff (((eq list_A1528105233le_alt) ((cons_A1100118844le_alt X_5) nil_Ar10086284le_alt)) (rev_Ar1977782764le_alt Xs_13))) (((eq list_A1528105233le_alt) Xs_13) ((cons_A1100118844le_alt X_5) nil_Ar10086284le_alt))))
% FOF formula (forall (Xs_12:list_A1528105233le_alt) (X_4:arrow_1346734812le_alt), ((iff (((eq list_A1528105233le_alt) (rev_Ar1977782764le_alt Xs_12)) ((cons_A1100118844le_alt X_4) nil_Ar10086284le_alt))) (((eq list_A1528105233le_alt) Xs_12) ((cons_A1100118844le_alt X_4) nil_Ar10086284le_alt)))) of role axiom named fact_80_rev__singleton__conv
% A new axiom: (forall (Xs_12:list_A1528105233le_alt) (X_4:arrow_1346734812le_alt), ((iff (((eq list_A1528105233le_alt) (rev_Ar1977782764le_alt Xs_12)) ((cons_A1100118844le_alt X_4) nil_Ar10086284le_alt))) (((eq list_A1528105233le_alt) Xs_12) ((cons_A1100118844le_alt X_4) nil_Ar10086284le_alt))))
% FOF formula (forall (N:nat) (X_3:arrow_1346734812le_alt) (Xs_11:list_A1528105233le_alt), (((eq list_A1528105233le_alt) ((append1050458273le_alt ((replic235430982le_alt N) X_3)) ((cons_A1100118844le_alt X_3) Xs_11))) ((cons_A1100118844le_alt X_3) ((append1050458273le_alt ((replic235430982le_alt N) X_3)) Xs_11)))) of role axiom named fact_81_replicate__app__Cons__same
% A new axiom: (forall (N:nat) (X_3:arrow_1346734812le_alt) (Xs_11:list_A1528105233le_alt), (((eq list_A1528105233le_alt) ((append1050458273le_alt ((replic235430982le_alt N) X_3)) ((cons_A1100118844le_alt X_3) Xs_11))) ((cons_A1100118844le_alt X_3) ((append1050458273le_alt ((replic235430982le_alt N) X_3)) Xs_11))))
% FOF formula (forall (Xs_10:list_A1528105233le_alt), ((not (((eq list_A1528105233le_alt) Xs_10) nil_Ar10086284le_alt))->(((eq arrow_1346734812le_alt) (hd_Arr689575519le_alt (rev_Ar1977782764le_alt Xs_10))) (last_A2088691109le_alt Xs_10)))) of role axiom named fact_82_hd__rev
% A new axiom: (forall (Xs_10:list_A1528105233le_alt), ((not (((eq list_A1528105233le_alt) Xs_10) nil_Ar10086284le_alt))->(((eq arrow_1346734812le_alt) (hd_Arr689575519le_alt (rev_Ar1977782764le_alt Xs_10))) (last_A2088691109le_alt Xs_10))))
% FOF formula (forall (Xs_9:list_A1528105233le_alt), ((not (((eq list_A1528105233le_alt) Xs_9) nil_Ar10086284le_alt))->(((eq arrow_1346734812le_alt) (last_A2088691109le_alt (rev_Ar1977782764le_alt Xs_9))) (hd_Arr689575519le_alt Xs_9)))) of role axiom named fact_83_last__rev
% A new axiom: (forall (Xs_9:list_A1528105233le_alt), ((not (((eq list_A1528105233le_alt) Xs_9) nil_Ar10086284le_alt))->(((eq arrow_1346734812le_alt) (last_A2088691109le_alt (rev_Ar1977782764le_alt Xs_9))) (hd_Arr689575519le_alt Xs_9))))
% FOF formula (forall (X_2:arrow_1346734812le_alt) (Xs_8:list_A1528105233le_alt), (((eq arrow_1346734812le_alt) (hd_Arr689575519le_alt ((cons_A1100118844le_alt X_2) Xs_8))) X_2)) of role axiom named fact_84_hd_Osimps
% A new axiom: (forall (X_2:arrow_1346734812le_alt) (Xs_8:list_A1528105233le_alt), (((eq arrow_1346734812le_alt) (hd_Arr689575519le_alt ((cons_A1100118844le_alt X_2) Xs_8))) X_2))
% FOF formula (forall (Ys_2:list_A1528105233le_alt) (Xs_7:list_A1528105233le_alt), ((and ((((eq list_A1528105233le_alt) Xs_7) nil_Ar10086284le_alt)->(((eq arrow_1346734812le_alt) (hd_Arr689575519le_alt ((append1050458273le_alt Xs_7) Ys_2))) (hd_Arr689575519le_alt Ys_2)))) ((not (((eq list_A1528105233le_alt) Xs_7) nil_Ar10086284le_alt))->(((eq arrow_1346734812le_alt) (hd_Arr689575519le_alt ((append1050458273le_alt Xs_7) Ys_2))) (hd_Arr689575519le_alt Xs_7))))) of role axiom named fact_85_hd__append
% A new axiom: (forall (Ys_2:list_A1528105233le_alt) (Xs_7:list_A1528105233le_alt), ((and ((((eq list_A1528105233le_alt) Xs_7) nil_Ar10086284le_alt)->(((eq arrow_1346734812le_alt) (hd_Arr689575519le_alt ((append1050458273le_alt Xs_7) Ys_2))) (hd_Arr689575519le_alt Ys_2)))) ((not (((eq list_A1528105233le_alt) Xs_7) nil_Ar10086284le_alt))->(((eq arrow_1346734812le_alt) (hd_Arr689575519le_alt ((append1050458273le_alt Xs_7) Ys_2))) (hd_Arr689575519le_alt Xs_7)))))
% FOF formula (forall (Ys_1:list_A1528105233le_alt) (Xs_6:list_A1528105233le_alt), ((not (((eq list_A1528105233le_alt) Xs_6) nil_Ar10086284le_alt))->(((eq arrow_1346734812le_alt) (hd_Arr689575519le_alt ((append1050458273le_alt Xs_6) Ys_1))) (hd_Arr689575519le_alt Xs_6)))) of role axiom named fact_86_hd__append2
% A new axiom: (forall (Ys_1:list_A1528105233le_alt) (Xs_6:list_A1528105233le_alt), ((not (((eq list_A1528105233le_alt) Xs_6) nil_Ar10086284le_alt))->(((eq arrow_1346734812le_alt) (hd_Arr689575519le_alt ((append1050458273le_alt Xs_6) Ys_1))) (hd_Arr689575519le_alt Xs_6))))
% FOF formula (forall (Xs_5:list_A1528105233le_alt), ((not (((eq list_A1528105233le_alt) Xs_5) nil_Ar10086284le_alt))->(((eq list_A1528105233le_alt) (rotate1206725081le_alt Xs_5)) ((append1050458273le_alt (tl_Arr1336826979le_alt Xs_5)) ((cons_A1100118844le_alt (hd_Arr689575519le_alt Xs_5)) nil_Ar10086284le_alt))))) of role axiom named fact_87_rotate1__hd__tl
% A new axiom: (forall (Xs_5:list_A1528105233le_alt), ((not (((eq list_A1528105233le_alt) Xs_5) nil_Ar10086284le_alt))->(((eq list_A1528105233le_alt) (rotate1206725081le_alt Xs_5)) ((append1050458273le_alt (tl_Arr1336826979le_alt Xs_5)) ((cons_A1100118844le_alt (hd_Arr689575519le_alt Xs_5)) nil_Ar10086284le_alt)))))
% FOF formula (forall (P_3:(arrow_1346734812le_alt->Prop)) (Xs_4:list_A1528105233le_alt), ((not (((eq list_A1528105233le_alt) ((dropWh40674093le_alt P_3) Xs_4)) nil_Ar10086284le_alt))->((P_3 (hd_Arr689575519le_alt ((dropWh40674093le_alt P_3) Xs_4)))->False))) of role axiom named fact_88_hd__dropWhile
% A new axiom: (forall (P_3:(arrow_1346734812le_alt->Prop)) (Xs_4:list_A1528105233le_alt), ((not (((eq list_A1528105233le_alt) ((dropWh40674093le_alt P_3) Xs_4)) nil_Ar10086284le_alt))->((P_3 (hd_Arr689575519le_alt ((dropWh40674093le_alt P_3) Xs_4)))->False)))
% FOF formula (forall (Ys:list_A1528105233le_alt) (Xs_3:list_A1528105233le_alt), ((not (((eq list_A1528105233le_alt) Xs_3) nil_Ar10086284le_alt))->(((eq list_A1528105233le_alt) (tl_Arr1336826979le_alt ((append1050458273le_alt Xs_3) Ys))) ((append1050458273le_alt (tl_Arr1336826979le_alt Xs_3)) Ys)))) of role axiom named fact_89_tl__append2
% A new axiom: (forall (Ys:list_A1528105233le_alt) (Xs_3:list_A1528105233le_alt), ((not (((eq list_A1528105233le_alt) Xs_3) nil_Ar10086284le_alt))->(((eq list_A1528105233le_alt) (tl_Arr1336826979le_alt ((append1050458273le_alt Xs_3) Ys))) ((append1050458273le_alt (tl_Arr1336826979le_alt Xs_3)) Ys))))
% FOF formula (forall (Xs_2:list_A1528105233le_alt), ((distin1107700095le_alt Xs_2)->(distin1107700095le_alt (tl_Arr1336826979le_alt Xs_2)))) of role axiom named fact_90_distinct__tl
% A new axiom: (forall (Xs_2:list_A1528105233le_alt), ((distin1107700095le_alt Xs_2)->(distin1107700095le_alt (tl_Arr1336826979le_alt Xs_2))))
% FOF formula (forall (P_2:(arrow_1346734812le_alt->Prop)) (Xs_1:list_A1528105233le_alt), ((distin1107700095le_alt Xs_1)->(distin1107700095le_alt ((dropWh40674093le_alt P_2) Xs_1)))) of role axiom named fact_91_distinct__dropWhile
% A new axiom: (forall (P_2:(arrow_1346734812le_alt->Prop)) (Xs_1:list_A1528105233le_alt), ((distin1107700095le_alt Xs_1)->(distin1107700095le_alt ((dropWh40674093le_alt P_2) Xs_1))))
% FOF formula (forall (P_1:(arrow_1346734812le_alt->Prop)), (((eq list_A1528105233le_alt) ((dropWh40674093le_alt P_1) nil_Ar10086284le_alt)) nil_Ar10086284le_alt)) of role axiom named fact_92_dropWhile_Osimps_I1_J
% A new axiom: (forall (P_1:(arrow_1346734812le_alt->Prop)), (((eq list_A1528105233le_alt) ((dropWh40674093le_alt P_1) nil_Ar10086284le_alt)) nil_Ar10086284le_alt))
% FOF formula (forall (Xs:list_A1528105233le_alt) (P:(arrow_1346734812le_alt->Prop)) (X_1:arrow_1346734812le_alt), ((and ((P X_1)->(((eq list_A1528105233le_alt) ((dropWh40674093le_alt P) ((cons_A1100118844le_alt X_1) Xs))) ((dropWh40674093le_alt P) Xs)))) (((P X_1)->False)->(((eq list_A1528105233le_alt) ((dropWh40674093le_alt P) ((cons_A1100118844le_alt X_1) Xs))) ((cons_A1100118844le_alt X_1) Xs))))) of role axiom named fact_93_dropWhile_Osimps_I2_J
% A new axiom: (forall (Xs:list_A1528105233le_alt) (P:(arrow_1346734812le_alt->Prop)) (X_1:arrow_1346734812le_alt), ((and ((P X_1)->(((eq list_A1528105233le_alt) ((dropWh40674093le_alt P) ((cons_A1100118844le_alt X_1) Xs))) ((dropWh40674093le_alt P) Xs)))) (((P X_1)->False)->(((eq list_A1528105233le_alt) ((dropWh40674093le_alt P) ((cons_A1100118844le_alt X_1) Xs))) ((cons_A1100118844le_alt X_1) Xs)))))
% FOF formula (forall (X:list_A1528105233le_alt) (Y:list_A1528105233le_alt), ((or (((fequal194154450le_alt X) Y)->False)) (((eq list_A1528105233le_alt) X) Y))) of role axiom named help_fequal_1_1_fequal_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____sd
% A new axiom: (forall (X:list_A1528105233le_alt) (Y:list_A1528105233le_alt), ((or (((fequal194154450le_alt X) Y)->False)) (((eq list_A1528105233le_alt) X) Y)))
% FOF formula (forall (X:list_A1528105233le_alt) (Y:list_A1528105233le_alt), ((or (not (((eq list_A1528105233le_alt) X) Y))) ((fequal194154450le_alt X) Y))) of role axiom named help_fequal_2_1_fequal_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____sd
% A new axiom: (forall (X:list_A1528105233le_alt) (Y:list_A1528105233le_alt), ((or (not (((eq list_A1528105233le_alt) X) Y))) ((fequal194154450le_alt X) Y)))
% FOF formula (not (((eq arrow_1346734812le_alt) a) b)) of role hypothesis named conj_0
% A new axiom: (not (((eq arrow_1346734812le_alt) a) b))
% FOF formula ((ex arrow_1346734812le_alt) (fun (C:arrow_1346734812le_alt)=> (distin1107700095le_alt ((cons_A1100118844le_alt a) ((cons_A1100118844le_alt b) ((cons_A1100118844le_alt C) nil_Ar10086284le_alt)))))) of role conjecture named conj_1
% Conjecture to prove = ((ex arrow_1346734812le_alt) (fun (C:arrow_1346734812le_alt)=> (distin1107700095le_alt ((cons_A1100118844le_alt a) ((cons_A1100118844le_alt b) ((cons_A1100118844le_alt C) nil_Ar10086284le_alt)))))):Prop
% Parameter nat_DUMMY:nat.
% We need to prove ['((ex arrow_1346734812le_alt) (fun (C:arrow_1346734812le_alt)=> (distin1107700095le_alt ((cons_A1100118844le_alt a) ((cons_A1100118844le_alt b) ((cons_A1100118844le_alt C) nil_Ar10086284le_alt))))))']
% Parameter arrow_1346734812le_alt:Type.
% Parameter list_A1528105233le_alt:Type.
% Parameter nat:Type.
% Parameter equal_2044961839le_alt:(list_A1528105233le_alt->(list_A1528105233le_alt->Prop)).
% Parameter append1050458273le_alt:(list_A1528105233le_alt->(list_A1528105233le_alt->list_A1528105233le_alt)).
% Parameter butlas1146323672le_alt:(list_A1528105233le_alt->list_A1528105233le_alt).
% Parameter distin1107700095le_alt:(list_A1528105233le_alt->Prop).
% Parameter dropWh40674093le_alt:((arrow_1346734812le_alt->Prop)->(list_A1528105233le_alt->list_A1528105233le_alt)).
% Parameter hd_Arr689575519le_alt:(list_A1528105233le_alt->arrow_1346734812le_alt).
% Parameter insert844458914le_alt:(arrow_1346734812le_alt->(list_A1528105233le_alt->list_A1528105233le_alt)).
% Parameter last_A2088691109le_alt:(list_A1528105233le_alt->arrow_1346734812le_alt).
% Parameter cons_A1100118844le_alt:(arrow_1346734812le_alt->(list_A1528105233le_alt->list_A1528105233le_alt)).
% Parameter nil_Ar10086284le_alt:list_A1528105233le_alt.
% Parameter maps_A51637569le_alt:((arrow_1346734812le_alt->list_A1528105233le_alt)->(list_A1528105233le_alt->list_A1528105233le_alt)).
% Parameter null_A244857236le_alt:(list_A1528105233le_alt->Prop).
% Parameter replic235430982le_alt:(nat->(arrow_1346734812le_alt->list_A1528105233le_alt)).
% Parameter rev_Ar1977782764le_alt:(list_A1528105233le_alt->list_A1528105233le_alt).
% Parameter rotate1206725081le_alt:(list_A1528105233le_alt->list_A1528105233le_alt).
% Parameter splice244790623le_alt:(list_A1528105233le_alt->(list_A1528105233le_alt->list_A1528105233le_alt)).
% Parameter tl_Arr1336826979le_alt:(list_A1528105233le_alt->list_A1528105233le_alt).
% Parameter fequal194154450le_alt:(list_A1528105233le_alt->(list_A1528105233le_alt->Prop)).
% Parameter a:arrow_1346734812le_alt.
% Parameter b:arrow_1346734812le_alt.
% Axiom fact_0_alt3:((ex arrow_1346734812le_alt) (fun (A_2:arrow_1346734812le_alt)=> ((ex arrow_1346734812le_alt) (fun (B:arrow_1346734812le_alt)=> ((ex arrow_1346734812le_alt) (fun (C:arrow_1346734812le_alt)=> (distin1107700095le_alt ((cons_A1100118844le_alt A_2) ((cons_A1100118844le_alt B) ((cons_A1100118844le_alt C) nil_Ar10086284le_alt)))))))))).
% Axiom fact_1_distinct_Osimps_I1_J:(distin1107700095le_alt nil_Ar10086284le_alt).
% Axiom fact_2_list_Osimps_I2_J:(forall (A_4:arrow_1346734812le_alt) (List_4:list_A1528105233le_alt), (not (((eq list_A1528105233le_alt) nil_Ar10086284le_alt) ((cons_A1100118844le_alt A_4) List_4)))).
% Axiom fact_3_list_Osimps_I3_J:(forall (A_3:arrow_1346734812le_alt) (List_3:list_A1528105233le_alt), (not (((eq list_A1528105233le_alt) ((cons_A1100118844le_alt A_3) List_3)) nil_Ar10086284le_alt))).
% Axiom fact_4_neq__Nil__conv:(forall (Xs_71:list_A1528105233le_alt), ((iff (not (((eq list_A1528105233le_alt) Xs_71) nil_Ar10086284le_alt))) ((ex arrow_1346734812le_alt) (fun (Y_3:arrow_1346734812le_alt)=> ((ex list_A1528105233le_alt) (fun (Ys_7:list_A1528105233le_alt)=> (((eq list_A1528105233le_alt) Xs_71) ((cons_A1100118844le_alt Y_3) Ys_7)))))))).
% Axiom fact_5_list_Oexhaust:(forall (Y_7:list_A1528105233le_alt), ((not (((eq list_A1528105233le_alt) Y_7) nil_Ar10086284le_alt))->((forall (A_2:arrow_1346734812le_alt) (List_2:list_A1528105233le_alt), (not (((eq list_A1528105233le_alt) Y_7) ((cons_A1100118844le_alt A_2) List_2))))->False))).
% Axiom fact_6_not__Cons__self:(forall (Xs_70:list_A1528105233le_alt) (X_33:arrow_1346734812le_alt), (not (((eq list_A1528105233le_alt) Xs_70) ((cons_A1100118844le_alt X_33) Xs_70)))).
% Axiom fact_7_not__Cons__self2:(forall (X_32:arrow_1346734812le_alt) (Xs_69:list_A1528105233le_alt), (not (((eq list_A1528105233le_alt) ((cons_A1100118844le_alt X_32) Xs_69)) Xs_69))).
% Axiom fact_8_list_Oinject:(forall (A_1:arrow_1346734812le_alt) (List_1:list_A1528105233le_alt) (A:arrow_1346734812le_alt) (List:list_A1528105233le_alt), ((iff (((eq list_A1528105233le_alt) ((cons_A1100118844le_alt A_1) List_1)) ((cons_A1100118844le_alt A) List))) ((and (((eq arrow_1346734812le_alt) A_1) A)) (((eq list_A1528105233le_alt) List_1) List)))).
% Axiom fact_9_splice_Osimps_I2_J:(forall (V:arrow_1346734812le_alt) (Va:list_A1528105233le_alt), (((eq list_A1528105233le_alt) ((splice244790623le_alt ((cons_A1100118844le_alt V) Va)) nil_Ar10086284le_alt)) ((cons_A1100118844le_alt V) Va))).
% Axiom fact_10_insert__Nil:(forall (X_31:arrow_1346734812le_alt), (((eq list_A1528105233le_alt) ((insert844458914le_alt X_31) nil_Ar10086284le_alt)) ((cons_A1100118844le_alt X_31) nil_Ar10086284le_alt))).
% Axiom fact_11_list__nonempty__induct:(forall (P_5:(list_A1528105233le_alt->Prop)) (Xs_68:list_A1528105233le_alt), ((not (((eq list_A1528105233le_alt) Xs_68) nil_Ar10086284le_alt))->((forall (X_20:arrow_1346734812le_alt), (P_5 ((cons_A1100118844le_alt X_20) nil_Ar10086284le_alt)))->((forall (X_20:arrow_1346734812le_alt) (Xs_23:list_A1528105233le_alt), ((not (((eq list_A1528105233le_alt) Xs_23) nil_Ar10086284le_alt))->((P_5 Xs_23)->(P_5 ((cons_A1100118844le_alt X_20) Xs_23)))))->(P_5 Xs_68))))).
% Axiom fact_12_distinct__butlast:(forall (Xs_67:list_A1528105233le_alt), ((not (((eq list_A1528105233le_alt) Xs_67) nil_Ar10086284le_alt))->((distin1107700095le_alt Xs_67)->(distin1107700095le_alt (butlas1146323672le_alt Xs_67))))).
% Axiom fact_13_butlast_Osimps_I1_J:(((eq list_A1528105233le_alt) (butlas1146323672le_alt nil_Ar10086284le_alt)) nil_Ar10086284le_alt).
% Axiom fact_14_distinct__insert:(forall (X_30:arrow_1346734812le_alt) (Xs_66:list_A1528105233le_alt), ((distin1107700095le_alt Xs_66)->(distin1107700095le_alt ((insert844458914le_alt X_30) Xs_66)))).
% Axiom fact_15_splice_Osimps_I3_J:(forall (X_29:arrow_1346734812le_alt) (Xs_65:list_A1528105233le_alt) (Y_6:arrow_1346734812le_alt) (Ys_33:list_A1528105233le_alt), (((eq list_A1528105233le_alt) ((splice244790623le_alt ((cons_A1100118844le_alt X_29) Xs_65)) ((cons_A1100118844le_alt Y_6) Ys_33))) ((cons_A1100118844le_alt X_29) ((cons_A1100118844le_alt Y_6) ((splice244790623le_alt Xs_65) Ys_33))))).
% Axiom fact_16_splice__Nil2:(forall (Xs_64:list_A1528105233le_alt), (((eq list_A1528105233le_alt) ((splice244790623le_alt Xs_64) nil_Ar10086284le_alt)) Xs_64)).
% Axiom fact_17_splice_Osimps_I1_J:(forall (Ys_32:list_A1528105233le_alt), (((eq list_A1528105233le_alt) ((splice244790623le_alt nil_Ar10086284le_alt) Ys_32)) Ys_32)).
% Axiom fact_18_butlast_Osimps_I2_J:(forall (X_28:arrow_1346734812le_alt) (Xs_63:list_A1528105233le_alt), ((and ((((eq list_A1528105233le_alt) Xs_63) nil_Ar10086284le_alt)->(((eq list_A1528105233le_alt) (butlas1146323672le_alt ((cons_A1100118844le_alt X_28) Xs_63))) nil_Ar10086284le_alt))) ((not (((eq list_A1528105233le_alt) Xs_63) nil_Ar10086284le_alt))->(((eq list_A1528105233le_alt) (butlas1146323672le_alt ((cons_A1100118844le_alt X_28) Xs_63))) ((cons_A1100118844le_alt X_28) (butlas1146323672le_alt Xs_63)))))).
% Axiom fact_19_eq__Nil__null:(forall (Xs_62:list_A1528105233le_alt), ((iff (((eq list_A1528105233le_alt) Xs_62) nil_Ar10086284le_alt)) (null_A244857236le_alt Xs_62))).
% Axiom fact_20_List_Onull__def:(forall (Xs_61:list_A1528105233le_alt), ((iff (null_A244857236le_alt Xs_61)) (((eq list_A1528105233le_alt) Xs_61) nil_Ar10086284le_alt))).
% Axiom fact_21_null__rec_I2_J:(null_A244857236le_alt nil_Ar10086284le_alt).
% Axiom fact_22_null__rec_I1_J:(forall (X_27:arrow_1346734812le_alt) (Xs_60:list_A1528105233le_alt), ((null_A244857236le_alt ((cons_A1100118844le_alt X_27) Xs_60))->False)).
% Axiom fact_23_butlast__snoc:(forall (Xs_59:list_A1528105233le_alt) (X_26:arrow_1346734812le_alt), (((eq list_A1528105233le_alt) (butlas1146323672le_alt ((append1050458273le_alt Xs_59) ((cons_A1100118844le_alt X_26) nil_Ar10086284le_alt)))) Xs_59)).
% Axiom fact_24_append__assoc:(forall (Xs_58:list_A1528105233le_alt) (Ys_31:list_A1528105233le_alt) (Zs_8:list_A1528105233le_alt), (((eq list_A1528105233le_alt) ((append1050458273le_alt ((append1050458273le_alt Xs_58) Ys_31)) Zs_8)) ((append1050458273le_alt Xs_58) ((append1050458273le_alt Ys_31) Zs_8)))).
% Axiom fact_25_append__eq__append__conv2:(forall (Xs_57:list_A1528105233le_alt) (Ys_30:list_A1528105233le_alt) (Zs_7:list_A1528105233le_alt) (Ts:list_A1528105233le_alt), ((iff (((eq list_A1528105233le_alt) ((append1050458273le_alt Xs_57) Ys_30)) ((append1050458273le_alt Zs_7) Ts))) ((ex list_A1528105233le_alt) (fun (Us_1:list_A1528105233le_alt)=> ((or ((and (((eq list_A1528105233le_alt) Xs_57) ((append1050458273le_alt Zs_7) Us_1))) (((eq list_A1528105233le_alt) ((append1050458273le_alt Us_1) Ys_30)) Ts))) ((and (((eq list_A1528105233le_alt) ((append1050458273le_alt Xs_57) Us_1)) Zs_7)) (((eq list_A1528105233le_alt) Ys_30) ((append1050458273le_alt Us_1) Ts)))))))).
% Axiom fact_26_same__append__eq:(forall (Xs_56:list_A1528105233le_alt) (Ys_29:list_A1528105233le_alt) (Zs_6:list_A1528105233le_alt), ((iff (((eq list_A1528105233le_alt) ((append1050458273le_alt Xs_56) Ys_29)) ((append1050458273le_alt Xs_56) Zs_6))) (((eq list_A1528105233le_alt) Ys_29) Zs_6))).
% Axiom fact_27_append__same__eq:(forall (Ys_28:list_A1528105233le_alt) (Xs_55:list_A1528105233le_alt) (Zs_5:list_A1528105233le_alt), ((iff (((eq list_A1528105233le_alt) ((append1050458273le_alt Ys_28) Xs_55)) ((append1050458273le_alt Zs_5) Xs_55))) (((eq list_A1528105233le_alt) Ys_28) Zs_5))).
% Axiom fact_28_append__eq__appendI:(forall (Ys_27:list_A1528105233le_alt) (Us:list_A1528105233le_alt) (Xs_54:list_A1528105233le_alt) (Xs1_1:list_A1528105233le_alt) (Zs_4:list_A1528105233le_alt), ((((eq list_A1528105233le_alt) ((append1050458273le_alt Xs_54) Xs1_1)) Zs_4)->((((eq list_A1528105233le_alt) Ys_27) ((append1050458273le_alt Xs1_1) Us))->(((eq list_A1528105233le_alt) ((append1050458273le_alt Xs_54) Ys_27)) ((append1050458273le_alt Zs_4) Us))))).
% Axiom fact_29_append__Cons:(forall (X_25:arrow_1346734812le_alt) (Xs_53:list_A1528105233le_alt) (Ys_26:list_A1528105233le_alt), (((eq list_A1528105233le_alt) ((append1050458273le_alt ((cons_A1100118844le_alt X_25) Xs_53)) Ys_26)) ((cons_A1100118844le_alt X_25) ((append1050458273le_alt Xs_53) Ys_26)))).
% Axiom fact_30_Cons__eq__appendI:(forall (Xs_52:list_A1528105233le_alt) (Zs_3:list_A1528105233le_alt) (X_24:arrow_1346734812le_alt) (Xs1:list_A1528105233le_alt) (Ys_25:list_A1528105233le_alt), ((((eq list_A1528105233le_alt) ((cons_A1100118844le_alt X_24) Xs1)) Ys_25)->((((eq list_A1528105233le_alt) Xs_52) ((append1050458273le_alt Xs1) Zs_3))->(((eq list_A1528105233le_alt) ((cons_A1100118844le_alt X_24) Xs_52)) ((append1050458273le_alt Ys_25) Zs_3))))).
% Axiom fact_31_append__Nil:(forall (Ys_24:list_A1528105233le_alt), (((eq list_A1528105233le_alt) ((append1050458273le_alt nil_Ar10086284le_alt) Ys_24)) Ys_24)).
% Axiom fact_32_Nil__is__append__conv:(forall (Xs_51:list_A1528105233le_alt) (Ys_23:list_A1528105233le_alt), ((iff (((eq list_A1528105233le_alt) nil_Ar10086284le_alt) ((append1050458273le_alt Xs_51) Ys_23))) ((and (((eq list_A1528105233le_alt) Xs_51) nil_Ar10086284le_alt)) (((eq list_A1528105233le_alt) Ys_23) nil_Ar10086284le_alt)))).
% Axiom fact_33_append__Nil2:(forall (Xs_50:list_A1528105233le_alt), (((eq list_A1528105233le_alt) ((append1050458273le_alt Xs_50) nil_Ar10086284le_alt)) Xs_50)).
% Axiom fact_34_self__append__conv:(forall (Xs_49:list_A1528105233le_alt) (Ys_22:list_A1528105233le_alt), ((iff (((eq list_A1528105233le_alt) Xs_49) ((append1050458273le_alt Xs_49) Ys_22))) (((eq list_A1528105233le_alt) Ys_22) nil_Ar10086284le_alt))).
% Axiom fact_35_self__append__conv2:(forall (Ys_21:list_A1528105233le_alt) (Xs_48:list_A1528105233le_alt), ((iff (((eq list_A1528105233le_alt) Ys_21) ((append1050458273le_alt Xs_48) Ys_21))) (((eq list_A1528105233le_alt) Xs_48) nil_Ar10086284le_alt))).
% Axiom fact_36_append__is__Nil__conv:(forall (Xs_47:list_A1528105233le_alt) (Ys_20:list_A1528105233le_alt), ((iff (((eq list_A1528105233le_alt) ((append1050458273le_alt Xs_47) Ys_20)) nil_Ar10086284le_alt)) ((and (((eq list_A1528105233le_alt) Xs_47) nil_Ar10086284le_alt)) (((eq list_A1528105233le_alt) Ys_20) nil_Ar10086284le_alt)))).
% Axiom fact_37_append__self__conv:(forall (Xs_46:list_A1528105233le_alt) (Ys_19:list_A1528105233le_alt), ((iff (((eq list_A1528105233le_alt) ((append1050458273le_alt Xs_46) Ys_19)) Xs_46)) (((eq list_A1528105233le_alt) Ys_19) nil_Ar10086284le_alt))).
% Axiom fact_38_append__self__conv2:(forall (Xs_45:list_A1528105233le_alt) (Ys_18:list_A1528105233le_alt), ((iff (((eq list_A1528105233le_alt) ((append1050458273le_alt Xs_45) Ys_18)) Ys_18)) (((eq list_A1528105233le_alt) Xs_45) nil_Ar10086284le_alt))).
% Axiom fact_39_eq__Nil__appendI:(forall (Xs_44:list_A1528105233le_alt) (Ys_17:list_A1528105233le_alt), ((((eq list_A1528105233le_alt) Xs_44) Ys_17)->(((eq list_A1528105233le_alt) Xs_44) ((append1050458273le_alt nil_Ar10086284le_alt) Ys_17)))).
% Axiom fact_40_append__eq__Cons__conv:(forall (Ys_16:list_A1528105233le_alt) (Zs_2:list_A1528105233le_alt) (X_23:arrow_1346734812le_alt) (Xs_43:list_A1528105233le_alt), ((iff (((eq list_A1528105233le_alt) ((append1050458273le_alt Ys_16) Zs_2)) ((cons_A1100118844le_alt X_23) Xs_43))) ((or ((and (((eq list_A1528105233le_alt) Ys_16) nil_Ar10086284le_alt)) (((eq list_A1528105233le_alt) Zs_2) ((cons_A1100118844le_alt X_23) Xs_43)))) ((ex list_A1528105233le_alt) (fun (Ys_15:list_A1528105233le_alt)=> ((and (((eq list_A1528105233le_alt) Ys_16) ((cons_A1100118844le_alt X_23) Ys_15))) (((eq list_A1528105233le_alt) ((append1050458273le_alt Ys_15) Zs_2)) Xs_43))))))).
% Axiom fact_41_Cons__eq__append__conv:(forall (X_22:arrow_1346734812le_alt) (Xs_42:list_A1528105233le_alt) (Ys_14:list_A1528105233le_alt) (Zs_1:list_A1528105233le_alt), ((iff (((eq list_A1528105233le_alt) ((cons_A1100118844le_alt X_22) Xs_42)) ((append1050458273le_alt Ys_14) Zs_1))) ((or ((and (((eq list_A1528105233le_alt) Ys_14) nil_Ar10086284le_alt)) (((eq list_A1528105233le_alt) ((cons_A1100118844le_alt X_22) Xs_42)) Zs_1))) ((ex list_A1528105233le_alt) (fun (Ys_15:list_A1528105233le_alt)=> ((and (((eq list_A1528105233le_alt) ((cons_A1100118844le_alt X_22) Ys_15)) Ys_14)) (((eq list_A1528105233le_alt) Xs_42) ((append1050458273le_alt Ys_15) Zs_1)))))))).
% Axiom fact_42_append1__eq__conv:(forall (Xs_41:list_A1528105233le_alt) (X_21:arrow_1346734812le_alt) (Ys_13:list_A1528105233le_alt) (Y_5:arrow_1346734812le_alt), ((iff (((eq list_A1528105233le_alt) ((append1050458273le_alt Xs_41) ((cons_A1100118844le_alt X_21) nil_Ar10086284le_alt))) ((append1050458273le_alt Ys_13) ((cons_A1100118844le_alt Y_5) nil_Ar10086284le_alt)))) ((and (((eq list_A1528105233le_alt) Xs_41) Ys_13)) (((eq arrow_1346734812le_alt) X_21) Y_5)))).
% Axiom fact_43_butlast__append:(forall (Xs_40:list_A1528105233le_alt) (Ys_12:list_A1528105233le_alt), ((and ((((eq list_A1528105233le_alt) Ys_12) nil_Ar10086284le_alt)->(((eq list_A1528105233le_alt) (butlas1146323672le_alt ((append1050458273le_alt Xs_40) Ys_12))) (butlas1146323672le_alt Xs_40)))) ((not (((eq list_A1528105233le_alt) Ys_12) nil_Ar10086284le_alt))->(((eq list_A1528105233le_alt) (butlas1146323672le_alt ((append1050458273le_alt Xs_40) Ys_12))) ((append1050458273le_alt Xs_40) (butlas1146323672le_alt Ys_12)))))).
% Axiom fact_44_rev__induct:(forall (Xs_39:list_A1528105233le_alt) (P_4:(list_A1528105233le_alt->Prop)), ((P_4 nil_Ar10086284le_alt)->((forall (X_20:arrow_1346734812le_alt) (Xs_23:list_A1528105233le_alt), ((P_4 Xs_23)->(P_4 ((append1050458273le_alt Xs_23) ((cons_A1100118844le_alt X_20) nil_Ar10086284le_alt)))))->(P_4 Xs_39)))).
% Axiom fact_45_rev__cases:(forall (Xs_38:list_A1528105233le_alt), ((not (((eq list_A1528105233le_alt) Xs_38) nil_Ar10086284le_alt))->((forall (Ys_7:list_A1528105233le_alt) (Y_3:arrow_1346734812le_alt), (not (((eq list_A1528105233le_alt) Xs_38) ((append1050458273le_alt Ys_7) ((cons_A1100118844le_alt Y_3) nil_Ar10086284le_alt)))))->False))).
% Axiom fact_46_equal__Nil__null:(forall (Xs_37:list_A1528105233le_alt), ((iff ((equal_2044961839le_alt Xs_37) nil_Ar10086284le_alt)) (null_A244857236le_alt Xs_37))).
% Axiom fact_47_snoc__eq__iff__butlast:(forall (Xs_36:list_A1528105233le_alt) (X_19:arrow_1346734812le_alt) (Ys_11:list_A1528105233le_alt), ((iff (((eq list_A1528105233le_alt) ((append1050458273le_alt Xs_36) ((cons_A1100118844le_alt X_19) nil_Ar10086284le_alt))) Ys_11)) ((and ((and (not (((eq list_A1528105233le_alt) Ys_11) nil_Ar10086284le_alt))) (((eq list_A1528105233le_alt) (butlas1146323672le_alt Ys_11)) Xs_36))) (((eq arrow_1346734812le_alt) (last_A2088691109le_alt Ys_11)) X_19)))).
% Axiom fact_48_append__butlast__last__id:(forall (Xs_35:list_A1528105233le_alt), ((not (((eq list_A1528105233le_alt) Xs_35) nil_Ar10086284le_alt))->(((eq list_A1528105233le_alt) ((append1050458273le_alt (butlas1146323672le_alt Xs_35)) ((cons_A1100118844le_alt (last_A2088691109le_alt Xs_35)) nil_Ar10086284le_alt))) Xs_35))).
% Axiom fact_49_rotate__simps:(forall (X_18:arrow_1346734812le_alt) (Xs_34:list_A1528105233le_alt), ((and (((eq list_A1528105233le_alt) (rotate1206725081le_alt nil_Ar10086284le_alt)) nil_Ar10086284le_alt)) (((eq list_A1528105233le_alt) (rotate1206725081le_alt ((cons_A1100118844le_alt X_18) Xs_34))) ((append1050458273le_alt Xs_34) ((cons_A1100118844le_alt X_18) nil_Ar10086284le_alt))))).
% Axiom fact_50_equal__list__def:(forall (X_17:list_A1528105233le_alt) (Y_4:list_A1528105233le_alt), ((iff ((equal_2044961839le_alt X_17) Y_4)) (((eq list_A1528105233le_alt) X_17) Y_4))).
% Axiom fact_51_rotate1__is__Nil__conv:(forall (Xs_33:list_A1528105233le_alt), ((iff (((eq list_A1528105233le_alt) (rotate1206725081le_alt Xs_33)) nil_Ar10086284le_alt)) (((eq list_A1528105233le_alt) Xs_33) nil_Ar10086284le_alt))).
% Axiom fact_52_distinct1__rotate:(forall (Xs_32:list_A1528105233le_alt), ((iff (distin1107700095le_alt (rotate1206725081le_alt Xs_32))) (distin1107700095le_alt Xs_32))).
% Axiom fact_53_last__ConsL:(forall (X_16:arrow_1346734812le_alt) (Xs_31:list_A1528105233le_alt), ((((eq list_A1528105233le_alt) Xs_31) nil_Ar10086284le_alt)->(((eq arrow_1346734812le_alt) (last_A2088691109le_alt ((cons_A1100118844le_alt X_16) Xs_31))) X_16))).
% Axiom fact_54_last__ConsR:(forall (X_15:arrow_1346734812le_alt) (Xs_30:list_A1528105233le_alt), ((not (((eq list_A1528105233le_alt) Xs_30) nil_Ar10086284le_alt))->(((eq arrow_1346734812le_alt) (last_A2088691109le_alt ((cons_A1100118844le_alt X_15) Xs_30))) (last_A2088691109le_alt Xs_30)))).
% Axiom fact_55_last_Osimps:(forall (X_14:arrow_1346734812le_alt) (Xs_29:list_A1528105233le_alt), ((and ((((eq list_A1528105233le_alt) Xs_29) nil_Ar10086284le_alt)->(((eq arrow_1346734812le_alt) (last_A2088691109le_alt ((cons_A1100118844le_alt X_14) Xs_29))) X_14))) ((not (((eq list_A1528105233le_alt) Xs_29) nil_Ar10086284le_alt))->(((eq arrow_1346734812le_alt) (last_A2088691109le_alt ((cons_A1100118844le_alt X_14) Xs_29))) (last_A2088691109le_alt Xs_29))))).
% Axiom fact_56_last__appendL:(forall (Xs_28:list_A1528105233le_alt) (Ys_10:list_A1528105233le_alt), ((((eq list_A1528105233le_alt) Ys_10) nil_Ar10086284le_alt)->(((eq arrow_1346734812le_alt) (last_A2088691109le_alt ((append1050458273le_alt Xs_28) Ys_10))) (last_A2088691109le_alt Xs_28)))).
% Axiom fact_57_last__appendR:(forall (Xs_27:list_A1528105233le_alt) (Ys_9:list_A1528105233le_alt), ((not (((eq list_A1528105233le_alt) Ys_9) nil_Ar10086284le_alt))->(((eq arrow_1346734812le_alt) (last_A2088691109le_alt ((append1050458273le_alt Xs_27) Ys_9))) (last_A2088691109le_alt Ys_9)))).
% Axiom fact_58_last__append:(forall (Xs_26:list_A1528105233le_alt) (Ys_8:list_A1528105233le_alt), ((and ((((eq list_A1528105233le_alt) Ys_8) nil_Ar10086284le_alt)->(((eq arrow_1346734812le_alt) (last_A2088691109le_alt ((append1050458273le_alt Xs_26) Ys_8))) (last_A2088691109le_alt Xs_26)))) ((not (((eq list_A1528105233le_alt) Ys_8) nil_Ar10086284le_alt))->(((eq arrow_1346734812le_alt) (last_A2088691109le_alt ((append1050458273le_alt Xs_26) Ys_8))) (last_A2088691109le_alt Ys_8))))).
% Axiom fact_59_last__snoc:(forall (Xs_25:list_A1528105233le_alt) (X_13:arrow_1346734812le_alt), (((eq arrow_1346734812le_alt) (last_A2088691109le_alt ((append1050458273le_alt Xs_25) ((cons_A1100118844le_alt X_13) nil_Ar10086284le_alt)))) X_13)).
% Axiom fact_60_maps__simps_I1_J:(forall (F:(arrow_1346734812le_alt->list_A1528105233le_alt)) (X_12:arrow_1346734812le_alt) (Xs_24:list_A1528105233le_alt), (((eq list_A1528105233le_alt) ((maps_A51637569le_alt F) ((cons_A1100118844le_alt X_12) Xs_24))) ((append1050458273le_alt (F X_12)) ((maps_A51637569le_alt F) Xs_24)))).
% Axiom fact_61_not__distinct__decomp:(forall (Ws:list_A1528105233le_alt), (((distin1107700095le_alt Ws)->False)->((ex list_A1528105233le_alt) (fun (Xs_23:list_A1528105233le_alt)=> ((ex list_A1528105233le_alt) (fun (Ys_7:list_A1528105233le_alt)=> ((ex list_A1528105233le_alt) (fun (Zs:list_A1528105233le_alt)=> ((ex arrow_1346734812le_alt) (fun (Y_3:arrow_1346734812le_alt)=> (((eq list_A1528105233le_alt) Ws) ((append1050458273le_alt Xs_23) ((append1050458273le_alt ((cons_A1100118844le_alt Y_3) nil_Ar10086284le_alt)) ((append1050458273le_alt Ys_7) ((append1050458273le_alt ((cons_A1100118844le_alt Y_3) nil_Ar10086284le_alt)) Zs))))))))))))))).
% Axiom fact_62_equal:(((eq (list_A1528105233le_alt->(list_A1528105233le_alt->Prop))) equal_2044961839le_alt) fequal194154450le_alt).
% Axiom fact_63_equal__refl:(forall (X_11:list_A1528105233le_alt), ((equal_2044961839le_alt X_11) X_11)).
% Axiom fact_64_eq__equal:(((eq (list_A1528105233le_alt->(list_A1528105233le_alt->Prop))) fequal194154450le_alt) equal_2044961839le_alt).
% Axiom fact_65_equal__eq:(forall (X_10:list_A1528105233le_alt) (Y_2:list_A1528105233le_alt), ((iff ((equal_2044961839le_alt X_10) Y_2)) (((eq list_A1528105233le_alt) X_10) Y_2))).
% Axiom fact_66_replicate__append__same:(forall (_TPTP_I:nat) (X_9:arrow_1346734812le_alt), (((eq list_A1528105233le_alt) ((append1050458273le_alt ((replic235430982le_alt _TPTP_I) X_9)) ((cons_A1100118844le_alt X_9) nil_Ar10086284le_alt))) ((cons_A1100118844le_alt X_9) ((replic235430982le_alt _TPTP_I) X_9)))).
% Axiom fact_67_rev_Osimps_I2_J:(forall (X_8:arrow_1346734812le_alt) (Xs_22:list_A1528105233le_alt), (((eq list_A1528105233le_alt) (rev_Ar1977782764le_alt ((cons_A1100118844le_alt X_8) Xs_22))) ((append1050458273le_alt (rev_Ar1977782764le_alt Xs_22)) ((cons_A1100118844le_alt X_8) nil_Ar10086284le_alt)))).
% Axiom fact_68_rev__eq__Cons__iff:(forall (Xs_21:list_A1528105233le_alt) (Y_1:arrow_1346734812le_alt) (Ys_6:list_A1528105233le_alt), ((iff (((eq list_A1528105233le_alt) (rev_Ar1977782764le_alt Xs_21)) ((cons_A1100118844le_alt Y_1) Ys_6))) (((eq list_A1528105233le_alt) Xs_21) ((append1050458273le_alt (rev_Ar1977782764le_alt Ys_6)) ((cons_A1100118844le_alt Y_1) nil_Ar10086284le_alt))))).
% Axiom fact_69_rev__is__rev__conv:(forall (Xs_20:list_A1528105233le_alt) (Ys_5:list_A1528105233le_alt), ((iff (((eq list_A1528105233le_alt) (rev_Ar1977782764le_alt Xs_20)) (rev_Ar1977782764le_alt Ys_5))) (((eq list_A1528105233le_alt) Xs_20) Ys_5))).
% Axiom fact_70_rev__swap:(forall (Xs_19:list_A1528105233le_alt) (Ys_4:list_A1528105233le_alt), ((iff (((eq list_A1528105233le_alt) (rev_Ar1977782764le_alt Xs_19)) Ys_4)) (((eq list_A1528105233le_alt) Xs_19) (rev_Ar1977782764le_alt Ys_4)))).
% Axiom fact_71_rev__replicate:(forall (N_2:nat) (X_7:arrow_1346734812le_alt), (((eq list_A1528105233le_alt) (rev_Ar1977782764le_alt ((replic235430982le_alt N_2) X_7))) ((replic235430982le_alt N_2) X_7))).
% Axiom fact_72_rev__rev__ident:(forall (Xs_18:list_A1528105233le_alt), (((eq list_A1528105233le_alt) (rev_Ar1977782764le_alt (rev_Ar1977782764le_alt Xs_18))) Xs_18)).
% Axiom fact_73_append__replicate__commute:(forall (N_1:nat) (X_6:arrow_1346734812le_alt) (K:nat), (((eq list_A1528105233le_alt) ((append1050458273le_alt ((replic235430982le_alt N_1) X_6)) ((replic235430982le_alt K) X_6))) ((append1050458273le_alt ((replic235430982le_alt K) X_6)) ((replic235430982le_alt N_1) X_6)))).
% Axiom fact_74_distinct__rev:(forall (Xs_17:list_A1528105233le_alt), ((iff (distin1107700095le_alt (rev_Ar1977782764le_alt Xs_17))) (distin1107700095le_alt Xs_17))).
% Axiom fact_75_rev__append:(forall (Xs_16:list_A1528105233le_alt) (Ys_3:list_A1528105233le_alt), (((eq list_A1528105233le_alt) (rev_Ar1977782764le_alt ((append1050458273le_alt Xs_16) Ys_3))) ((append1050458273le_alt (rev_Ar1977782764le_alt Ys_3)) (rev_Ar1977782764le_alt Xs_16)))).
% Axiom fact_76_rev_Osimps_I1_J:(((eq list_A1528105233le_alt) (rev_Ar1977782764le_alt nil_Ar10086284le_alt)) nil_Ar10086284le_alt).
% Axiom fact_77_Nil__is__rev__conv:(forall (Xs_15:list_A1528105233le_alt), ((iff (((eq list_A1528105233le_alt) nil_Ar10086284le_alt) (rev_Ar1977782764le_alt Xs_15))) (((eq list_A1528105233le_alt) Xs_15) nil_Ar10086284le_alt))).
% Axiom fact_78_rev__is__Nil__conv:(forall (Xs_14:list_A1528105233le_alt), ((iff (((eq list_A1528105233le_alt) (rev_Ar1977782764le_alt Xs_14)) nil_Ar10086284le_alt)) (((eq list_A1528105233le_alt) Xs_14) nil_Ar10086284le_alt))).
% Axiom fact_79_singleton__rev__conv:(forall (X_5:arrow_1346734812le_alt) (Xs_13:list_A1528105233le_alt), ((iff (((eq list_A1528105233le_alt) ((cons_A1100118844le_alt X_5) nil_Ar10086284le_alt)) (rev_Ar1977782764le_alt Xs_13))) (((eq list_A1528105233le_alt) Xs_13) ((cons_A1100118844le_alt X_5) nil_Ar10086284le_alt)))).
% Axiom fact_80_rev__singleton__conv:(forall (Xs_12:list_A1528105233le_alt) (X_4:arrow_1346734812le_alt), ((iff (((eq list_A1528105233le_alt) (rev_Ar1977782764le_alt Xs_12)) ((cons_A1100118844le_alt X_4) nil_Ar10086284le_alt))) (((eq list_A1528105233le_alt) Xs_12) ((cons_A1100118844le_alt X_4) nil_Ar10086284le_alt)))).
% Axiom fact_81_replicate__app__Cons__same:(forall (N:nat) (X_3:arrow_1346734812le_alt) (Xs_11:list_A1528105233le_alt), (((eq list_A1528105233le_alt) ((append1050458273le_alt ((replic235430982le_alt N) X_3)) ((cons_A1100118844le_alt X_3) Xs_11))) ((cons_A1100118844le_alt X_3) ((append1050458273le_alt ((replic235430982le_alt N) X_3)) Xs_11)))).
% Axiom fact_82_hd__rev:(forall (Xs_10:list_A1528105233le_alt), ((not (((eq list_A1528105233le_alt) Xs_10) nil_Ar10086284le_alt))->(((eq arrow_1346734812le_alt) (hd_Arr689575519le_alt (rev_Ar1977782764le_alt Xs_10))) (last_A2088691109le_alt Xs_10)))).
% Axiom fact_83_last__rev:(forall (Xs_9:list_A1528105233le_alt), ((not (((eq list_A1528105233le_alt) Xs_9) nil_Ar10086284le_alt))->(((eq arrow_1346734812le_alt) (last_A2088691109le_alt (rev_Ar1977782764le_alt Xs_9))) (hd_Arr689575519le_alt Xs_9)))).
% Axiom fact_84_hd_Osimps:(forall (X_2:arrow_1346734812le_alt) (Xs_8:list_A1528105233le_alt), (((eq arrow_1346734812le_alt) (hd_Arr689575519le_alt ((cons_A1100118844le_alt X_2) Xs_8))) X_2)).
% Axiom fact_85_hd__append:(forall (Ys_2:list_A1528105233le_alt) (Xs_7:list_A1528105233le_alt), ((and ((((eq list_A1528105233le_alt) Xs_7) nil_Ar10086284le_alt)->(((eq arrow_1346734812le_alt) (hd_Arr689575519le_alt ((append1050458273le_alt Xs_7) Ys_2))) (hd_Arr689575519le_alt Ys_2)))) ((not (((eq list_A1528105233le_alt) Xs_7) nil_Ar10086284le_alt))->(((eq arrow_1346734812le_alt) (hd_Arr689575519le_alt ((append1050458273le_alt Xs_7) Ys_2))) (hd_Arr689575519le_alt Xs_7))))).
% Axiom fact_86_hd__append2:(forall (Ys_1:list_A1528105233le_alt) (Xs_6:list_A1528105233le_alt), ((not (((eq list_A1528105233le_alt) Xs_6) nil_Ar10086284le_alt))->(((eq arrow_1346734812le_alt) (hd_Arr689575519le_alt ((append1050458273le_alt Xs_6) Ys_1))) (hd_Arr689575519le_alt Xs_6)))).
% Axiom fact_87_rotate1__hd__tl:(forall (Xs_5:list_A1528105233le_alt), (
% EOF
%------------------------------------------------------------------------------