TPTP Problem File: SCT169+2.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : SCT169+2 : TPTP v8.2.0. Released v5.3.0.
% Domain : Social Choice Theory
% Problem : Arrow's Impossibility Theorem line 29, 500 axioms selected
% Version : Especial.
% English :
% Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe
% Source : [Bla11]
% Names : arrow_500_fofmg_l29 [Bla11]
% Status : Theorem
% Rating : 1.00 v5.3.0
% Syntax : Number of formulae : 734 ( 297 unt; 0 def)
% Number of atoms : 1505 ( 813 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 1006 ( 235 ~; 38 |; 105 &)
% ( 161 <=>; 467 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 0 prp; 1-2 aty)
% Number of functors : 144 ( 144 usr; 43 con; 0-2 aty)
% Number of variables : 1592 (1537 !; 55 ?)
% SPC : FOF_THM_RFO_SEQ
% Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 2011-08-09 14:00:31
% : Encoded with monomorphized guards.
%------------------------------------------------------------------------------
%----Explicit typings (18)
fof(gsy_c_HOL_Oundefined_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt,axiom,
is_Arr723427730le_alt(undefi1471133025le_alt(arrow_1486210539le_alt)) ).
fof(gsy_c_List_Ohd_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt,axiom,
! [B_1_1] : is_Arr723427730le_alt(hd_Arr1814706386le_alt(B_1_1)) ).
fof(gsy_c_List_Olast_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt,axiom,
! [B_1_1] : is_Arr723427730le_alt(last_A1066338328le_alt(B_1_1)) ).
fof(gsy_c_Orderings_Obot__class_Obot_000tc__HOL__Obool,axiom,
is_bool(bot_bot_bool) ).
fof(gsy_c_fFalse,axiom,
is_bool(fFalse) ).
fof(gsy_c_fTrue,axiom,
is_bool(fTrue) ).
fof(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_000tc__HOL__Ob,axiom,
! [B_1_1,B_2_1] :
( is_Arr723427730le_alt(B_2_1)
=> is_bool(hAPP_A1120018583t_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__HOL__Obool_000tc__HOL__Obool,axiom,
! [B_1_1,B_2_1] :
( is_bool(B_2_1)
=> is_bool(hAPP_bool_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__Int__Oint_000tc__HOL__Obool,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_int_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oa,hypothesis,
! [B_1_1,B_2_1] : is_bool(hAPP_l300482276t_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__List__Olist_Itc__Int__Oint_J_000tc__HOL__Obool,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_list_int_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__List__Olist_Itc__Nat__Onat_J_000tc__HOL__Obool,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_list_nat_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__Nat__Onat_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oa,axiom,
! [B_1_1,B_2_1] : is_Arr723427730le_alt(hAPP_n1410269210le_alt(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__Nat__Onat_000tc__HOL__Obool,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_nat_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_000tc__HOL__Obool,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f448129468l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__HOL__Obool,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f54304608l_bool(B_1_1,B_2_1)) ).
fof(gsy_v_a,hypothesis,
is_Arr723427730le_alt(a) ).
fof(gsy_v_b,hypothesis,
is_Arr723427730le_alt(b) ).
%----Relevant facts (700)
fof(fact_0_alt3,axiom,
? [A_47,B_30,C] :
( is_Arr723427730le_alt(A_47)
& is_Arr723427730le_alt(B_30)
& is_Arr723427730le_alt(C)
& hBOOL(hAPP_l300482276t_bool(distin85347314le_alt,cons_A77766063le_alt(A_47,cons_A77766063le_alt(B_30,cons_A77766063le_alt(C,nil_Ar1135217151le_alt))))) ) ).
fof(fact_1_distinct_Osimps_I1_J,axiom,
hBOOL(hAPP_l300482276t_bool(distin85347314le_alt,nil_Ar1135217151le_alt)) ).
fof(fact_2_distinct_Osimps_I1_J,axiom,
hBOOL(hAPP_list_nat_bool(distinct_nat,nil_nat)) ).
fof(fact_3_list_Osimps_I2_J,axiom,
! [A_48,List_4] : nil_Ar1135217151le_alt != cons_A77766063le_alt(A_48,List_4) ).
fof(fact_4_list_Osimps_I2_J,axiom,
! [A_48,List_4] : nil_nat != cons_nat(A_48,List_4) ).
fof(fact_5_list_Osimps_I3_J,axiom,
! [A_46,List_2] : cons_A77766063le_alt(A_46,List_2) != nil_Ar1135217151le_alt ).
fof(fact_6_list_Osimps_I3_J,axiom,
! [A_46,List_2] : cons_nat(A_46,List_2) != nil_nat ).
fof(fact_7_neq__Nil__conv,axiom,
! [Xs_22] :
( Xs_22 != nil_Ar1135217151le_alt
<=> ? [Y_3,Ys_5] :
( is_Arr723427730le_alt(Y_3)
& Xs_22 = cons_A77766063le_alt(Y_3,Ys_5) ) ) ).
fof(fact_8_neq__Nil__conv,axiom,
! [Xs_22] :
( Xs_22 != nil_nat
<=> ? [Y_3,Ys_5] : Xs_22 = cons_nat(Y_3,Ys_5) ) ).
fof(fact_9_list_Oexhaust,axiom,
! [Y_30] :
( Y_30 != nil_Ar1135217151le_alt
=> ~ ! [A_47,List_3] :
( is_Arr723427730le_alt(A_47)
=> Y_30 != cons_A77766063le_alt(A_47,List_3) ) ) ).
fof(fact_10_list_Oexhaust,axiom,
! [Y_30] :
( Y_30 != nil_nat
=> ~ ! [A_47,List_3] : Y_30 != cons_nat(A_47,List_3) ) ).
fof(fact_11_not__Cons__self,axiom,
! [Xs_114,X_84] : Xs_114 != cons_A77766063le_alt(X_84,Xs_114) ).
fof(fact_12_not__Cons__self2,axiom,
! [X_83,Xs_113] : cons_A77766063le_alt(X_83,Xs_113) != Xs_113 ).
fof(fact_13_list_Oinject,axiom,
! [Aa,List,A_46,List_2] :
( ( is_Arr723427730le_alt(Aa)
& is_Arr723427730le_alt(A_46) )
=> ( cons_A77766063le_alt(Aa,List) = cons_A77766063le_alt(A_46,List_2)
<=> ( Aa = A_46
& List = List_2 ) ) ) ).
fof(fact_14_splice_Osimps_I2_J,axiom,
! [V_4,Va] : splice1369921490le_alt(cons_A77766063le_alt(V_4,Va),nil_Ar1135217151le_alt) = cons_A77766063le_alt(V_4,Va) ).
fof(fact_15_splice_Osimps_I2_J,axiom,
! [V_4,Va] : splice_nat(cons_nat(V_4,Va),nil_nat) = cons_nat(V_4,Va) ).
fof(fact_16_insert__Nil,axiom,
! [X_82] : insert1969589781le_alt(X_82,nil_Ar1135217151le_alt) = cons_A77766063le_alt(X_82,nil_Ar1135217151le_alt) ).
fof(fact_17_insert__Nil,axiom,
! [X_82] : insert_nat(X_82,nil_nat) = cons_nat(X_82,nil_nat) ).
fof(fact_18_list__nonempty__induct,axiom,
! [P_1,Xs_22] :
( Xs_22 != nil_Ar1135217151le_alt
=> ( ! [X_52] :
( is_Arr723427730le_alt(X_52)
=> hBOOL(hAPP_l300482276t_bool(P_1,cons_A77766063le_alt(X_52,nil_Ar1135217151le_alt))) )
=> ( ! [X_52,Xs_44] :
( is_Arr723427730le_alt(X_52)
=> ( Xs_44 != nil_Ar1135217151le_alt
=> ( hBOOL(hAPP_l300482276t_bool(P_1,Xs_44))
=> hBOOL(hAPP_l300482276t_bool(P_1,cons_A77766063le_alt(X_52,Xs_44))) ) ) )
=> hBOOL(hAPP_l300482276t_bool(P_1,Xs_22)) ) ) ) ).
fof(fact_19_list__nonempty__induct,axiom,
! [P_1,Xs_22] :
( Xs_22 != nil_nat
=> ( ! [X_52] : hBOOL(hAPP_list_nat_bool(P_1,cons_nat(X_52,nil_nat)))
=> ( ! [X_52,Xs_44] :
( Xs_44 != nil_nat
=> ( hBOOL(hAPP_list_nat_bool(P_1,Xs_44))
=> hBOOL(hAPP_list_nat_bool(P_1,cons_nat(X_52,Xs_44))) ) )
=> hBOOL(hAPP_list_nat_bool(P_1,Xs_22)) ) ) ) ).
fof(fact_20_distinct__butlast,axiom,
! [Xs_112] :
( Xs_112 != nil_Ar1135217151le_alt
=> ( hBOOL(hAPP_l300482276t_bool(distin85347314le_alt,Xs_112))
=> hBOOL(hAPP_l300482276t_bool(distin85347314le_alt,butlas123970891le_alt(Xs_112))) ) ) ).
fof(fact_21_distinct__butlast,axiom,
! [Xs_112] :
( Xs_112 != nil_nat
=> ( hBOOL(hAPP_list_nat_bool(distinct_nat,Xs_112))
=> hBOOL(hAPP_list_nat_bool(distinct_nat,butlast_nat(Xs_112))) ) ) ).
fof(fact_22_butlast_Osimps_I1_J,axiom,
butlas123970891le_alt(nil_Ar1135217151le_alt) = nil_Ar1135217151le_alt ).
fof(fact_23_butlast_Osimps_I1_J,axiom,
butlast_nat(nil_nat) = nil_nat ).
fof(fact_24_distinct__insert,axiom,
! [X_81,Xs_111] :
( hBOOL(hAPP_l300482276t_bool(distin85347314le_alt,Xs_111))
=> hBOOL(hAPP_l300482276t_bool(distin85347314le_alt,insert1969589781le_alt(X_81,Xs_111))) ) ).
fof(fact_25_splice_Osimps_I3_J,axiom,
! [X_80,Xs_110,Y_29,Ys_31] : splice1369921490le_alt(cons_A77766063le_alt(X_80,Xs_110),cons_A77766063le_alt(Y_29,Ys_31)) = cons_A77766063le_alt(X_80,cons_A77766063le_alt(Y_29,splice1369921490le_alt(Xs_110,Ys_31))) ).
fof(fact_26_splice__Nil2,axiom,
! [Xs_109] : splice1369921490le_alt(Xs_109,nil_Ar1135217151le_alt) = Xs_109 ).
fof(fact_27_splice__Nil2,axiom,
! [Xs_109] : splice_nat(Xs_109,nil_nat) = Xs_109 ).
fof(fact_28_splice_Osimps_I1_J,axiom,
! [Ys_30] : splice1369921490le_alt(nil_Ar1135217151le_alt,Ys_30) = Ys_30 ).
fof(fact_29_splice_Osimps_I1_J,axiom,
! [Ys_30] : splice_nat(nil_nat,Ys_30) = Ys_30 ).
fof(fact_30_butlast_Osimps_I2_J,axiom,
! [X_79,Xs_108] :
( ( Xs_108 = nil_Ar1135217151le_alt
=> butlas123970891le_alt(cons_A77766063le_alt(X_79,Xs_108)) = nil_Ar1135217151le_alt )
& ( Xs_108 != nil_Ar1135217151le_alt
=> butlas123970891le_alt(cons_A77766063le_alt(X_79,Xs_108)) = cons_A77766063le_alt(X_79,butlas123970891le_alt(Xs_108)) ) ) ).
fof(fact_31_butlast_Osimps_I2_J,axiom,
! [X_79,Xs_108] :
( ( Xs_108 = nil_nat
=> butlast_nat(cons_nat(X_79,Xs_108)) = nil_nat )
& ( Xs_108 != nil_nat
=> butlast_nat(cons_nat(X_79,Xs_108)) = cons_nat(X_79,butlast_nat(Xs_108)) ) ) ).
fof(fact_32_eq__Nil__null,axiom,
! [Xs_22] :
( Xs_22 = nil_Ar1135217151le_alt
<=> hBOOL(hAPP_l300482276t_bool(null_A1369988103le_alt,Xs_22)) ) ).
fof(fact_33_eq__Nil__null,axiom,
! [Xs_22] :
( Xs_22 = nil_nat
<=> hBOOL(hAPP_list_nat_bool(null_nat,Xs_22)) ) ).
fof(fact_34_List_Onull__def,axiom,
! [Xs_22] :
( hBOOL(hAPP_l300482276t_bool(null_A1369988103le_alt,Xs_22))
<=> Xs_22 = nil_Ar1135217151le_alt ) ).
fof(fact_35_List_Onull__def,axiom,
! [Xs_22] :
( hBOOL(hAPP_list_nat_bool(null_nat,Xs_22))
<=> Xs_22 = nil_nat ) ).
fof(fact_36_null__rec_I2_J,axiom,
hBOOL(hAPP_l300482276t_bool(null_A1369988103le_alt,nil_Ar1135217151le_alt)) ).
fof(fact_37_null__rec_I2_J,axiom,
hBOOL(hAPP_list_nat_bool(null_nat,nil_nat)) ).
fof(fact_38_null__rec_I1_J,axiom,
! [X_78,Xs_107] : ~ hBOOL(hAPP_l300482276t_bool(null_A1369988103le_alt,cons_A77766063le_alt(X_78,Xs_107))) ).
fof(fact_39_butlast__snoc,axiom,
! [Xs_106,X_77] : butlas123970891le_alt(append28105492le_alt(Xs_106,cons_A77766063le_alt(X_77,nil_Ar1135217151le_alt))) = Xs_106 ).
fof(fact_40_butlast__snoc,axiom,
! [Xs_106,X_77] : butlast_nat(append_nat(Xs_106,cons_nat(X_77,nil_nat))) = Xs_106 ).
fof(fact_41_maps__simps_I2_J,axiom,
! [F] : maps_n976979462le_alt(F,nil_nat) = nil_Ar1135217151le_alt ).
fof(fact_42_maps__simps_I2_J,axiom,
! [F] : maps_A99719484lt_nat(F,nil_Ar1135217151le_alt) = nil_nat ).
fof(fact_43_maps__simps_I2_J,axiom,
! [F] : maps_A517286529le_alt(F,nil_Ar1135217151le_alt) = nil_Ar1135217151le_alt ).
fof(fact_44_sorted__single,axiom,
! [X_76] : hBOOL(hAPP_list_nat_bool(linorder_sorted_nat,cons_nat(X_76,nil_nat))) ).
fof(fact_45_sorted_ONil,axiom,
hBOOL(hAPP_list_nat_bool(linorder_sorted_nat,nil_nat)) ).
fof(fact_46_append__assoc,axiom,
! [Xs_105,Ys_29,Zs_4] : append28105492le_alt(append28105492le_alt(Xs_105,Ys_29),Zs_4) = append28105492le_alt(Xs_105,append28105492le_alt(Ys_29,Zs_4)) ).
fof(fact_47_append__eq__append__conv2,axiom,
! [Xs_22,Ys_4,Zs,Ts] :
( append28105492le_alt(Xs_22,Ys_4) = append28105492le_alt(Zs,Ts)
<=> ? [Us_1] :
( ( Xs_22 = append28105492le_alt(Zs,Us_1)
& append28105492le_alt(Us_1,Ys_4) = Ts )
| ( append28105492le_alt(Xs_22,Us_1) = Zs
& Ys_4 = append28105492le_alt(Us_1,Ts) ) ) ) ).
fof(fact_48_same__append__eq,axiom,
! [Xs_22,Ys_4,Zs] :
( append28105492le_alt(Xs_22,Ys_4) = append28105492le_alt(Xs_22,Zs)
<=> Ys_4 = Zs ) ).
fof(fact_49_append__same__eq,axiom,
! [Ys_4,Xs_22,Zs] :
( append28105492le_alt(Ys_4,Xs_22) = append28105492le_alt(Zs,Xs_22)
<=> Ys_4 = Zs ) ).
fof(fact_50_append__eq__appendI,axiom,
! [Ys_28,Us,Xs_104,Xs1_1,Zs_3] :
( append28105492le_alt(Xs_104,Xs1_1) = Zs_3
=> ( Ys_28 = append28105492le_alt(Xs1_1,Us)
=> append28105492le_alt(Xs_104,Ys_28) = append28105492le_alt(Zs_3,Us) ) ) ).
fof(fact_51_maps__simps_I1_J,axiom,
! [F,X_9,Xs_22] : maps_A517286529le_alt(F,cons_A77766063le_alt(X_9,Xs_22)) = append28105492le_alt(hAPP_A1849759038le_alt(F,X_9),maps_A517286529le_alt(F,Xs_22)) ).
fof(fact_52_append__Cons,axiom,
! [X_75,Xs_103,Ys_27] : append28105492le_alt(cons_A77766063le_alt(X_75,Xs_103),Ys_27) = cons_A77766063le_alt(X_75,append28105492le_alt(Xs_103,Ys_27)) ).
fof(fact_53_Cons__eq__appendI,axiom,
! [Xs_102,Zs_2,X_74,Xs1,Ys_26] :
( cons_A77766063le_alt(X_74,Xs1) = Ys_26
=> ( Xs_102 = append28105492le_alt(Xs1,Zs_2)
=> cons_A77766063le_alt(X_74,Xs_102) = append28105492le_alt(Ys_26,Zs_2) ) ) ).
fof(fact_54_append__Nil,axiom,
! [Ys_25] : append28105492le_alt(nil_Ar1135217151le_alt,Ys_25) = Ys_25 ).
fof(fact_55_append__Nil,axiom,
! [Ys_25] : append_nat(nil_nat,Ys_25) = Ys_25 ).
fof(fact_56_Nil__is__append__conv,axiom,
! [Xs_22,Ys_4] :
( nil_Ar1135217151le_alt = append28105492le_alt(Xs_22,Ys_4)
<=> ( Xs_22 = nil_Ar1135217151le_alt
& Ys_4 = nil_Ar1135217151le_alt ) ) ).
fof(fact_57_Nil__is__append__conv,axiom,
! [Xs_22,Ys_4] :
( nil_nat = append_nat(Xs_22,Ys_4)
<=> ( Xs_22 = nil_nat
& Ys_4 = nil_nat ) ) ).
fof(fact_58_append__Nil2,axiom,
! [Xs_101] : append28105492le_alt(Xs_101,nil_Ar1135217151le_alt) = Xs_101 ).
fof(fact_59_append__Nil2,axiom,
! [Xs_101] : append_nat(Xs_101,nil_nat) = Xs_101 ).
fof(fact_60_self__append__conv,axiom,
! [Xs_22,Ys_4] :
( Xs_22 = append28105492le_alt(Xs_22,Ys_4)
<=> Ys_4 = nil_Ar1135217151le_alt ) ).
fof(fact_61_self__append__conv,axiom,
! [Xs_22,Ys_4] :
( Xs_22 = append_nat(Xs_22,Ys_4)
<=> Ys_4 = nil_nat ) ).
fof(fact_62_self__append__conv2,axiom,
! [Ys_4,Xs_22] :
( Ys_4 = append28105492le_alt(Xs_22,Ys_4)
<=> Xs_22 = nil_Ar1135217151le_alt ) ).
fof(fact_63_self__append__conv2,axiom,
! [Ys_4,Xs_22] :
( Ys_4 = append_nat(Xs_22,Ys_4)
<=> Xs_22 = nil_nat ) ).
fof(fact_64_append__is__Nil__conv,axiom,
! [Xs_22,Ys_4] :
( append28105492le_alt(Xs_22,Ys_4) = nil_Ar1135217151le_alt
<=> ( Xs_22 = nil_Ar1135217151le_alt
& Ys_4 = nil_Ar1135217151le_alt ) ) ).
fof(fact_65_append__is__Nil__conv,axiom,
! [Xs_22,Ys_4] :
( append_nat(Xs_22,Ys_4) = nil_nat
<=> ( Xs_22 = nil_nat
& Ys_4 = nil_nat ) ) ).
fof(fact_66_append__self__conv,axiom,
! [Xs_22,Ys_4] :
( append28105492le_alt(Xs_22,Ys_4) = Xs_22
<=> Ys_4 = nil_Ar1135217151le_alt ) ).
fof(fact_67_append__self__conv,axiom,
! [Xs_22,Ys_4] :
( append_nat(Xs_22,Ys_4) = Xs_22
<=> Ys_4 = nil_nat ) ).
fof(fact_68_append__self__conv2,axiom,
! [Xs_22,Ys_4] :
( append28105492le_alt(Xs_22,Ys_4) = Ys_4
<=> Xs_22 = nil_Ar1135217151le_alt ) ).
fof(fact_69_append__self__conv2,axiom,
! [Xs_22,Ys_4] :
( append_nat(Xs_22,Ys_4) = Ys_4
<=> Xs_22 = nil_nat ) ).
fof(fact_70_eq__Nil__appendI,axiom,
! [Xs_100,Ys_24] :
( Xs_100 = Ys_24
=> Xs_100 = append28105492le_alt(nil_Ar1135217151le_alt,Ys_24) ) ).
fof(fact_71_eq__Nil__appendI,axiom,
! [Xs_100,Ys_24] :
( Xs_100 = Ys_24
=> Xs_100 = append_nat(nil_nat,Ys_24) ) ).
fof(fact_72_append__eq__Cons__conv,axiom,
! [Ys_4,Zs,X_9,Xs_22] :
( append28105492le_alt(Ys_4,Zs) = cons_A77766063le_alt(X_9,Xs_22)
<=> ( ( Ys_4 = nil_Ar1135217151le_alt
& Zs = cons_A77766063le_alt(X_9,Xs_22) )
| ? [Ys_23] :
( Ys_4 = cons_A77766063le_alt(X_9,Ys_23)
& append28105492le_alt(Ys_23,Zs) = Xs_22 ) ) ) ).
fof(fact_73_append__eq__Cons__conv,axiom,
! [Ys_4,Zs,X_9,Xs_22] :
( append_nat(Ys_4,Zs) = cons_nat(X_9,Xs_22)
<=> ( ( Ys_4 = nil_nat
& Zs = cons_nat(X_9,Xs_22) )
| ? [Ys_23] :
( Ys_4 = cons_nat(X_9,Ys_23)
& append_nat(Ys_23,Zs) = Xs_22 ) ) ) ).
fof(fact_74_Cons__eq__append__conv,axiom,
! [X_9,Xs_22,Ys_4,Zs] :
( cons_A77766063le_alt(X_9,Xs_22) = append28105492le_alt(Ys_4,Zs)
<=> ( ( Ys_4 = nil_Ar1135217151le_alt
& cons_A77766063le_alt(X_9,Xs_22) = Zs )
| ? [Ys_23] :
( cons_A77766063le_alt(X_9,Ys_23) = Ys_4
& Xs_22 = append28105492le_alt(Ys_23,Zs) ) ) ) ).
fof(fact_75_Cons__eq__append__conv,axiom,
! [X_9,Xs_22,Ys_4,Zs] :
( cons_nat(X_9,Xs_22) = append_nat(Ys_4,Zs)
<=> ( ( Ys_4 = nil_nat
& cons_nat(X_9,Xs_22) = Zs )
| ? [Ys_23] :
( cons_nat(X_9,Ys_23) = Ys_4
& Xs_22 = append_nat(Ys_23,Zs) ) ) ) ).
fof(fact_76_append1__eq__conv,axiom,
! [Xs_22,X_9,Ys_4,Y_9] :
( ( is_Arr723427730le_alt(X_9)
& is_Arr723427730le_alt(Y_9) )
=> ( append28105492le_alt(Xs_22,cons_A77766063le_alt(X_9,nil_Ar1135217151le_alt)) = append28105492le_alt(Ys_4,cons_A77766063le_alt(Y_9,nil_Ar1135217151le_alt))
<=> ( Xs_22 = Ys_4
& X_9 = Y_9 ) ) ) ).
fof(fact_77_append1__eq__conv,axiom,
! [Xs_22,X_9,Ys_4,Y_9] :
( append_nat(Xs_22,cons_nat(X_9,nil_nat)) = append_nat(Ys_4,cons_nat(Y_9,nil_nat))
<=> ( Xs_22 = Ys_4
& X_9 = Y_9 ) ) ).
fof(fact_78_butlast__append,axiom,
! [Xs_99,Ys_22] :
( ( Ys_22 = nil_Ar1135217151le_alt
=> butlas123970891le_alt(append28105492le_alt(Xs_99,Ys_22)) = butlas123970891le_alt(Xs_99) )
& ( Ys_22 != nil_Ar1135217151le_alt
=> butlas123970891le_alt(append28105492le_alt(Xs_99,Ys_22)) = append28105492le_alt(Xs_99,butlas123970891le_alt(Ys_22)) ) ) ).
fof(fact_79_butlast__append,axiom,
! [Xs_99,Ys_22] :
( ( Ys_22 = nil_nat
=> butlast_nat(append_nat(Xs_99,Ys_22)) = butlast_nat(Xs_99) )
& ( Ys_22 != nil_nat
=> butlast_nat(append_nat(Xs_99,Ys_22)) = append_nat(Xs_99,butlast_nat(Ys_22)) ) ) ).
fof(fact_80_sorted__butlast,axiom,
! [Xs_98] :
( Xs_98 != nil_nat
=> ( hBOOL(hAPP_list_nat_bool(linorder_sorted_nat,Xs_98))
=> hBOOL(hAPP_list_nat_bool(linorder_sorted_nat,butlast_nat(Xs_98))) ) ) ).
fof(fact_81_rev__induct,axiom,
! [Xs_22,P_1] :
( hBOOL(hAPP_l300482276t_bool(P_1,nil_Ar1135217151le_alt))
=> ( ! [X_52,Xs_44] :
( is_Arr723427730le_alt(X_52)
=> ( hBOOL(hAPP_l300482276t_bool(P_1,Xs_44))
=> hBOOL(hAPP_l300482276t_bool(P_1,append28105492le_alt(Xs_44,cons_A77766063le_alt(X_52,nil_Ar1135217151le_alt)))) ) )
=> hBOOL(hAPP_l300482276t_bool(P_1,Xs_22)) ) ) ).
fof(fact_82_rev__induct,axiom,
! [Xs_22,P_1] :
( hBOOL(hAPP_list_nat_bool(P_1,nil_nat))
=> ( ! [X_52,Xs_44] :
( hBOOL(hAPP_list_nat_bool(P_1,Xs_44))
=> hBOOL(hAPP_list_nat_bool(P_1,append_nat(Xs_44,cons_nat(X_52,nil_nat)))) )
=> hBOOL(hAPP_list_nat_bool(P_1,Xs_22)) ) ) ).
fof(fact_83_rev__cases,axiom,
! [Xs_97] :
( Xs_97 != nil_Ar1135217151le_alt
=> ~ ! [Ys_5,Y_3] :
( is_Arr723427730le_alt(Y_3)
=> Xs_97 != append28105492le_alt(Ys_5,cons_A77766063le_alt(Y_3,nil_Ar1135217151le_alt)) ) ) ).
fof(fact_84_rev__cases,axiom,
! [Xs_97] :
( Xs_97 != nil_nat
=> ~ ! [Ys_5,Y_3] : Xs_97 != append_nat(Ys_5,cons_nat(Y_3,nil_nat)) ) ).
fof(fact_85_equal__Nil__null,axiom,
! [Xs_22] :
( hBOOL(hAPP_l300482276t_bool(hAPP_l2066632447t_bool(equal_732151074le_alt,Xs_22),nil_Ar1135217151le_alt))
<=> hBOOL(hAPP_l300482276t_bool(null_A1369988103le_alt,Xs_22)) ) ).
fof(fact_86_equal__Nil__null,axiom,
! [Xs_22] :
( hBOOL(hAPP_list_nat_bool(hAPP_l120351551t_bool(equal_equal_list_nat,Xs_22),nil_nat))
<=> hBOOL(hAPP_list_nat_bool(null_nat,Xs_22)) ) ).
fof(fact_87_snoc__eq__iff__butlast,axiom,
! [Xs_22,X_9,Ys_4] :
( is_Arr723427730le_alt(X_9)
=> ( append28105492le_alt(Xs_22,cons_A77766063le_alt(X_9,nil_Ar1135217151le_alt)) = Ys_4
<=> ( Ys_4 != nil_Ar1135217151le_alt
& butlas123970891le_alt(Ys_4) = Xs_22
& last_A1066338328le_alt(Ys_4) = X_9 ) ) ) ).
fof(fact_88_snoc__eq__iff__butlast,axiom,
! [Xs_22,X_9,Ys_4] :
( append_nat(Xs_22,cons_nat(X_9,nil_nat)) = Ys_4
<=> ( Ys_4 != nil_nat
& butlast_nat(Ys_4) = Xs_22
& last_nat(Ys_4) = X_9 ) ) ).
fof(fact_89_append__butlast__last__id,axiom,
! [Xs_96] :
( Xs_96 != nil_Ar1135217151le_alt
=> append28105492le_alt(butlas123970891le_alt(Xs_96),cons_A77766063le_alt(last_A1066338328le_alt(Xs_96),nil_Ar1135217151le_alt)) = Xs_96 ) ).
fof(fact_90_append__butlast__last__id,axiom,
! [Xs_96] :
( Xs_96 != nil_nat
=> append_nat(butlast_nat(Xs_96),cons_nat(last_nat(Xs_96),nil_nat)) = Xs_96 ) ).
fof(fact_91_rotate__simps,axiom,
! [X_73,Xs_95] :
( rotate1_nat(nil_nat) = nil_nat
& rotate184372300le_alt(cons_A77766063le_alt(X_73,Xs_95)) = append28105492le_alt(Xs_95,cons_A77766063le_alt(X_73,nil_Ar1135217151le_alt)) ) ).
fof(fact_92_rotate__simps,axiom,
! [X_73,Xs_95] :
( rotate184372300le_alt(nil_Ar1135217151le_alt) = nil_Ar1135217151le_alt
& rotate184372300le_alt(cons_A77766063le_alt(X_73,Xs_95)) = append28105492le_alt(Xs_95,cons_A77766063le_alt(X_73,nil_Ar1135217151le_alt)) ) ).
fof(fact_93_rotate__simps,axiom,
! [X_73,Xs_95] :
( rotate184372300le_alt(nil_Ar1135217151le_alt) = nil_Ar1135217151le_alt
& rotate1_nat(cons_nat(X_73,Xs_95)) = append_nat(Xs_95,cons_nat(X_73,nil_nat)) ) ).
fof(fact_94_last__snoc,axiom,
! [Xs_94,X_72] :
( is_Arr723427730le_alt(X_72)
=> last_A1066338328le_alt(append28105492le_alt(Xs_94,cons_A77766063le_alt(X_72,nil_Ar1135217151le_alt))) = X_72 ) ).
fof(fact_95_last__snoc,axiom,
! [Xs_94,X_72] : last_nat(append_nat(Xs_94,cons_nat(X_72,nil_nat))) = X_72 ).
fof(fact_96_not__distinct__decomp,axiom,
! [Ws] :
( ~ hBOOL(hAPP_l300482276t_bool(distin85347314le_alt,Ws))
=> ? [Xs_44,Ys_5,Zs_1,Y_3] :
( is_Arr723427730le_alt(Y_3)
& Ws = append28105492le_alt(Xs_44,append28105492le_alt(cons_A77766063le_alt(Y_3,nil_Ar1135217151le_alt),append28105492le_alt(Ys_5,append28105492le_alt(cons_A77766063le_alt(Y_3,nil_Ar1135217151le_alt),Zs_1)))) ) ) ).
fof(fact_97_not__distinct__decomp,axiom,
! [Ws] :
( ~ hBOOL(hAPP_list_nat_bool(distinct_nat,Ws))
=> ? [Xs_44,Ys_5,Zs_1,Y_3] : Ws = append_nat(Xs_44,append_nat(cons_nat(Y_3,nil_nat),append_nat(Ys_5,append_nat(cons_nat(Y_3,nil_nat),Zs_1)))) ) ).
fof(fact_98_replicate__append__same,axiom,
! [I_27,X_71] : append28105492le_alt(hAPP_A1849759038le_alt(replic1360561849le_alt(I_27),X_71),cons_A77766063le_alt(X_71,nil_Ar1135217151le_alt)) = cons_A77766063le_alt(X_71,hAPP_A1849759038le_alt(replic1360561849le_alt(I_27),X_71)) ).
fof(fact_99_replicate__append__same,axiom,
! [I_27,X_71] : append_nat(hAPP_nat_list_nat(replicate_nat(I_27),X_71),cons_nat(X_71,nil_nat)) = cons_nat(X_71,hAPP_nat_list_nat(replicate_nat(I_27),X_71)) ).
fof(fact_100_rev_Osimps_I2_J,axiom,
! [X_70,Xs_93] : rev_Ar955429983le_alt(cons_A77766063le_alt(X_70,Xs_93)) = append28105492le_alt(rev_Ar955429983le_alt(Xs_93),cons_A77766063le_alt(X_70,nil_Ar1135217151le_alt)) ).
fof(fact_101_rev_Osimps_I2_J,axiom,
! [X_70,Xs_93] : rev_nat(cons_nat(X_70,Xs_93)) = append_nat(rev_nat(Xs_93),cons_nat(X_70,nil_nat)) ).
fof(fact_102_rev__is__rev__conv,axiom,
! [Xs_22,Ys_4] :
( rev_nat(Xs_22) = rev_nat(Ys_4)
<=> Xs_22 = Ys_4 ) ).
fof(fact_103_rev__is__rev__conv,axiom,
! [Xs_22,Ys_4] :
( rev_Ar955429983le_alt(Xs_22) = rev_Ar955429983le_alt(Ys_4)
<=> Xs_22 = Ys_4 ) ).
fof(fact_104_rev__swap,axiom,
! [Xs_22,Ys_4] :
( rev_nat(Xs_22) = Ys_4
<=> Xs_22 = rev_nat(Ys_4) ) ).
fof(fact_105_rev__swap,axiom,
! [Xs_22,Ys_4] :
( rev_Ar955429983le_alt(Xs_22) = Ys_4
<=> Xs_22 = rev_Ar955429983le_alt(Ys_4) ) ).
fof(fact_106_rev__replicate,axiom,
! [N_45,X_69] : rev_nat(hAPP_nat_list_nat(replicate_nat(N_45),X_69)) = hAPP_nat_list_nat(replicate_nat(N_45),X_69) ).
fof(fact_107_rev__replicate,axiom,
! [N_45,X_69] : rev_Ar955429983le_alt(hAPP_A1849759038le_alt(replic1360561849le_alt(N_45),X_69)) = hAPP_A1849759038le_alt(replic1360561849le_alt(N_45),X_69) ).
fof(fact_108_rev__rev__ident,axiom,
! [Xs_92] : rev_nat(rev_nat(Xs_92)) = Xs_92 ).
fof(fact_109_rev__rev__ident,axiom,
! [Xs_92] : rev_Ar955429983le_alt(rev_Ar955429983le_alt(Xs_92)) = Xs_92 ).
fof(fact_110_equal__list__def,axiom,
! [X_9,Y_9] :
( hBOOL(hAPP_l300482276t_bool(hAPP_l2066632447t_bool(equal_732151074le_alt,X_9),Y_9))
<=> X_9 = Y_9 ) ).
fof(fact_111_rev__is__Nil__conv,axiom,
! [Xs_22] :
( rev_Ar955429983le_alt(Xs_22) = nil_Ar1135217151le_alt
<=> Xs_22 = nil_Ar1135217151le_alt ) ).
fof(fact_112_rev__is__Nil__conv,axiom,
! [Xs_22] :
( rev_nat(Xs_22) = nil_nat
<=> Xs_22 = nil_nat ) ).
fof(fact_113_Nil__is__rev__conv,axiom,
! [Xs_22] :
( nil_Ar1135217151le_alt = rev_Ar955429983le_alt(Xs_22)
<=> Xs_22 = nil_Ar1135217151le_alt ) ).
fof(fact_114_Nil__is__rev__conv,axiom,
! [Xs_22] :
( nil_nat = rev_nat(Xs_22)
<=> Xs_22 = nil_nat ) ).
fof(fact_115_rev_Osimps_I1_J,axiom,
rev_Ar955429983le_alt(nil_Ar1135217151le_alt) = nil_Ar1135217151le_alt ).
fof(fact_116_rev_Osimps_I1_J,axiom,
rev_nat(nil_nat) = nil_nat ).
fof(fact_117_rev__append,axiom,
! [Xs_91,Ys_21] : rev_nat(append_nat(Xs_91,Ys_21)) = append_nat(rev_nat(Ys_21),rev_nat(Xs_91)) ).
fof(fact_118_rev__append,axiom,
! [Xs_91,Ys_21] : rev_Ar955429983le_alt(append28105492le_alt(Xs_91,Ys_21)) = append28105492le_alt(rev_Ar955429983le_alt(Ys_21),rev_Ar955429983le_alt(Xs_91)) ).
fof(fact_119_distinct__rev,axiom,
! [Xs_22] :
( hBOOL(hAPP_l300482276t_bool(distin85347314le_alt,rev_Ar955429983le_alt(Xs_22)))
<=> hBOOL(hAPP_l300482276t_bool(distin85347314le_alt,Xs_22)) ) ).
fof(fact_120_distinct__rev,axiom,
! [Xs_22] :
( hBOOL(hAPP_list_nat_bool(distinct_nat,rev_nat(Xs_22)))
<=> hBOOL(hAPP_list_nat_bool(distinct_nat,Xs_22)) ) ).
fof(fact_121_append__replicate__commute,axiom,
! [N_44,X_68,K_7] : append28105492le_alt(hAPP_A1849759038le_alt(replic1360561849le_alt(N_44),X_68),hAPP_A1849759038le_alt(replic1360561849le_alt(K_7),X_68)) = append28105492le_alt(hAPP_A1849759038le_alt(replic1360561849le_alt(K_7),X_68),hAPP_A1849759038le_alt(replic1360561849le_alt(N_44),X_68)) ).
fof(fact_122_rotate1__is__Nil__conv,axiom,
! [Xs_22] :
( rotate184372300le_alt(Xs_22) = nil_Ar1135217151le_alt
<=> Xs_22 = nil_Ar1135217151le_alt ) ).
fof(fact_123_rotate1__is__Nil__conv,axiom,
! [Xs_22] :
( rotate1_nat(Xs_22) = nil_nat
<=> Xs_22 = nil_nat ) ).
fof(fact_124_mem__def,axiom,
! [X_9,A] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_9),A))
<=> hBOOL(hAPP_nat_bool(A,X_9)) ) ).
fof(fact_125_mem__def,axiom,
! [X_9,A] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_9),A))
<=> hBOOL(hAPP_int_bool(A,X_9)) ) ).
fof(fact_126_Collect__def,axiom,
! [P_1] : collect_nat(P_1) = P_1 ).
fof(fact_127_distinct1__rotate,axiom,
! [Xs_22] :
( hBOOL(hAPP_l300482276t_bool(distin85347314le_alt,rotate184372300le_alt(Xs_22)))
<=> hBOOL(hAPP_l300482276t_bool(distin85347314le_alt,Xs_22)) ) ).
fof(fact_128_singleton__rev__conv,axiom,
! [X_9,Xs_22] :
( cons_A77766063le_alt(X_9,nil_Ar1135217151le_alt) = rev_Ar955429983le_alt(Xs_22)
<=> Xs_22 = cons_A77766063le_alt(X_9,nil_Ar1135217151le_alt) ) ).
fof(fact_129_singleton__rev__conv,axiom,
! [X_9,Xs_22] :
( cons_nat(X_9,nil_nat) = rev_nat(Xs_22)
<=> Xs_22 = cons_nat(X_9,nil_nat) ) ).
fof(fact_130_rev__singleton__conv,axiom,
! [Xs_22,X_9] :
( rev_Ar955429983le_alt(Xs_22) = cons_A77766063le_alt(X_9,nil_Ar1135217151le_alt)
<=> Xs_22 = cons_A77766063le_alt(X_9,nil_Ar1135217151le_alt) ) ).
fof(fact_131_rev__singleton__conv,axiom,
! [Xs_22,X_9] :
( rev_nat(Xs_22) = cons_nat(X_9,nil_nat)
<=> Xs_22 = cons_nat(X_9,nil_nat) ) ).
fof(fact_132_replicate__app__Cons__same,axiom,
! [N_43,X_67,Xs_90] : append28105492le_alt(hAPP_A1849759038le_alt(replic1360561849le_alt(N_43),X_67),cons_A77766063le_alt(X_67,Xs_90)) = cons_A77766063le_alt(X_67,append28105492le_alt(hAPP_A1849759038le_alt(replic1360561849le_alt(N_43),X_67),Xs_90)) ).
fof(fact_133_last__ConsL,axiom,
! [X_66,Xs_89] :
( is_Arr723427730le_alt(X_66)
=> ( Xs_89 = nil_Ar1135217151le_alt
=> last_A1066338328le_alt(cons_A77766063le_alt(X_66,Xs_89)) = X_66 ) ) ).
fof(fact_134_last__ConsL,axiom,
! [X_66,Xs_89] :
( Xs_89 = nil_nat
=> last_nat(cons_nat(X_66,Xs_89)) = X_66 ) ).
fof(fact_135_last__ConsR,axiom,
! [X_65,Xs_88] :
( Xs_88 != nil_Ar1135217151le_alt
=> last_A1066338328le_alt(cons_A77766063le_alt(X_65,Xs_88)) = last_A1066338328le_alt(Xs_88) ) ).
fof(fact_136_last__ConsR,axiom,
! [X_65,Xs_88] :
( Xs_88 != nil_nat
=> last_nat(cons_nat(X_65,Xs_88)) = last_nat(Xs_88) ) ).
fof(fact_137_last_Osimps,axiom,
! [X_64,Xs_87] :
( is_Arr723427730le_alt(X_64)
=> ( ( Xs_87 = nil_Ar1135217151le_alt
=> last_A1066338328le_alt(cons_A77766063le_alt(X_64,Xs_87)) = X_64 )
& ( Xs_87 != nil_Ar1135217151le_alt
=> last_A1066338328le_alt(cons_A77766063le_alt(X_64,Xs_87)) = last_A1066338328le_alt(Xs_87) ) ) ) ).
fof(fact_138_last_Osimps,axiom,
! [X_64,Xs_87] :
( ( Xs_87 = nil_nat
=> last_nat(cons_nat(X_64,Xs_87)) = X_64 )
& ( Xs_87 != nil_nat
=> last_nat(cons_nat(X_64,Xs_87)) = last_nat(Xs_87) ) ) ).
fof(fact_139_last__append,axiom,
! [Xs_86,Ys_20] :
( ( Ys_20 = nil_Ar1135217151le_alt
=> last_A1066338328le_alt(append28105492le_alt(Xs_86,Ys_20)) = last_A1066338328le_alt(Xs_86) )
& ( Ys_20 != nil_Ar1135217151le_alt
=> last_A1066338328le_alt(append28105492le_alt(Xs_86,Ys_20)) = last_A1066338328le_alt(Ys_20) ) ) ).
fof(fact_140_last__append,axiom,
! [Xs_86,Ys_20] :
( ( Ys_20 = nil_nat
=> last_nat(append_nat(Xs_86,Ys_20)) = last_nat(Xs_86) )
& ( Ys_20 != nil_nat
=> last_nat(append_nat(Xs_86,Ys_20)) = last_nat(Ys_20) ) ) ).
fof(fact_141_last__appendR,axiom,
! [Xs_85,Ys_19] :
( Ys_19 != nil_Ar1135217151le_alt
=> last_A1066338328le_alt(append28105492le_alt(Xs_85,Ys_19)) = last_A1066338328le_alt(Ys_19) ) ).
fof(fact_142_last__appendR,axiom,
! [Xs_85,Ys_19] :
( Ys_19 != nil_nat
=> last_nat(append_nat(Xs_85,Ys_19)) = last_nat(Ys_19) ) ).
fof(fact_143_last__appendL,axiom,
! [Xs_84,Ys_18] :
( Ys_18 = nil_Ar1135217151le_alt
=> last_A1066338328le_alt(append28105492le_alt(Xs_84,Ys_18)) = last_A1066338328le_alt(Xs_84) ) ).
fof(fact_144_last__appendL,axiom,
! [Xs_84,Ys_18] :
( Ys_18 = nil_nat
=> last_nat(append_nat(Xs_84,Ys_18)) = last_nat(Xs_84) ) ).
fof(fact_145_rev__eq__Cons__iff,axiom,
! [Xs_22,Y_9,Ys_4] :
( rev_Ar955429983le_alt(Xs_22) = cons_A77766063le_alt(Y_9,Ys_4)
<=> Xs_22 = append28105492le_alt(rev_Ar955429983le_alt(Ys_4),cons_A77766063le_alt(Y_9,nil_Ar1135217151le_alt)) ) ).
fof(fact_146_rev__eq__Cons__iff,axiom,
! [Xs_22,Y_9,Ys_4] :
( rev_nat(Xs_22) = cons_nat(Y_9,Ys_4)
<=> Xs_22 = append_nat(rev_nat(Ys_4),cons_nat(Y_9,nil_nat)) ) ).
fof(fact_147_last__rev,axiom,
! [Xs_83] :
( Xs_83 != nil_Ar1135217151le_alt
=> last_A1066338328le_alt(rev_Ar955429983le_alt(Xs_83)) = hd_Arr1814706386le_alt(Xs_83) ) ).
fof(fact_148_last__rev,axiom,
! [Xs_83] :
( Xs_83 != nil_nat
=> last_nat(rev_nat(Xs_83)) = hd_nat(Xs_83) ) ).
fof(fact_149_hd__rev,axiom,
! [Xs_82] :
( Xs_82 != nil_Ar1135217151le_alt
=> hd_Arr1814706386le_alt(rev_Ar955429983le_alt(Xs_82)) = last_A1066338328le_alt(Xs_82) ) ).
fof(fact_150_hd__rev,axiom,
! [Xs_82] :
( Xs_82 != nil_nat
=> hd_nat(rev_nat(Xs_82)) = last_nat(Xs_82) ) ).
fof(fact_151_equal,axiom,
equal_732151074le_alt = fequal1028827333le_alt ).
fof(fact_152_equal__refl,axiom,
! [X_63] : hBOOL(hAPP_l300482276t_bool(hAPP_l2066632447t_bool(equal_732151074le_alt,X_63),X_63)) ).
fof(fact_153_equal__eq,axiom,
! [X_9,Y_9] :
( hBOOL(hAPP_l300482276t_bool(hAPP_l2066632447t_bool(equal_732151074le_alt,X_9),Y_9))
<=> X_9 = Y_9 ) ).
fof(fact_154_eq__equal,axiom,
fequal1028827333le_alt = equal_732151074le_alt ).
fof(fact_155_hd__append,axiom,
! [Ys_17,Xs_81] :
( ( Xs_81 = nil_Ar1135217151le_alt
=> hd_Arr1814706386le_alt(append28105492le_alt(Xs_81,Ys_17)) = hd_Arr1814706386le_alt(Ys_17) )
& ( Xs_81 != nil_Ar1135217151le_alt
=> hd_Arr1814706386le_alt(append28105492le_alt(Xs_81,Ys_17)) = hd_Arr1814706386le_alt(Xs_81) ) ) ).
fof(fact_156_hd__append,axiom,
! [Ys_17,Xs_81] :
( ( Xs_81 = nil_nat
=> hd_nat(append_nat(Xs_81,Ys_17)) = hd_nat(Ys_17) )
& ( Xs_81 != nil_nat
=> hd_nat(append_nat(Xs_81,Ys_17)) = hd_nat(Xs_81) ) ) ).
fof(fact_157_hd__append2,axiom,
! [Ys_16,Xs_80] :
( Xs_80 != nil_Ar1135217151le_alt
=> hd_Arr1814706386le_alt(append28105492le_alt(Xs_80,Ys_16)) = hd_Arr1814706386le_alt(Xs_80) ) ).
fof(fact_158_hd__append2,axiom,
! [Ys_16,Xs_80] :
( Xs_80 != nil_nat
=> hd_nat(append_nat(Xs_80,Ys_16)) = hd_nat(Xs_80) ) ).
fof(fact_159_rotate1__hd__tl,axiom,
! [Xs_79] :
( Xs_79 != nil_Ar1135217151le_alt
=> rotate184372300le_alt(Xs_79) = append28105492le_alt(tl_Arr314474198le_alt(Xs_79),cons_A77766063le_alt(hd_Arr1814706386le_alt(Xs_79),nil_Ar1135217151le_alt)) ) ).
fof(fact_160_rotate1__hd__tl,axiom,
! [Xs_79] :
( Xs_79 != nil_nat
=> rotate1_nat(Xs_79) = append_nat(tl_nat(Xs_79),cons_nat(hd_nat(Xs_79),nil_nat)) ) ).
fof(fact_161_tl_Osimps_I2_J,axiom,
! [X_62,Xs_78] : tl_Arr314474198le_alt(cons_A77766063le_alt(X_62,Xs_78)) = Xs_78 ).
fof(fact_162_tl_Osimps_I1_J,axiom,
tl_Arr314474198le_alt(nil_Ar1135217151le_alt) = nil_Ar1135217151le_alt ).
fof(fact_163_tl_Osimps_I1_J,axiom,
tl_nat(nil_nat) = nil_nat ).
fof(fact_164_hd_Osimps,axiom,
! [X_61,Xs_77] :
( is_Arr723427730le_alt(X_61)
=> hd_Arr1814706386le_alt(cons_A77766063le_alt(X_61,Xs_77)) = X_61 ) ).
fof(fact_165_distinct__tl,axiom,
! [Xs_76] :
( hBOOL(hAPP_l300482276t_bool(distin85347314le_alt,Xs_76))
=> hBOOL(hAPP_l300482276t_bool(distin85347314le_alt,tl_Arr314474198le_alt(Xs_76))) ) ).
fof(fact_166_sorted__tl,axiom,
! [Xs_75] :
( hBOOL(hAPP_list_nat_bool(linorder_sorted_nat,Xs_75))
=> hBOOL(hAPP_list_nat_bool(linorder_sorted_nat,tl_nat(Xs_75))) ) ).
fof(fact_167_tl__append2,axiom,
! [Ys_15,Xs_74] :
( Xs_74 != nil_Ar1135217151le_alt
=> tl_Arr314474198le_alt(append28105492le_alt(Xs_74,Ys_15)) = append28105492le_alt(tl_Arr314474198le_alt(Xs_74),Ys_15) ) ).
fof(fact_168_tl__append2,axiom,
! [Ys_15,Xs_74] :
( Xs_74 != nil_nat
=> tl_nat(append_nat(Xs_74,Ys_15)) = append_nat(tl_nat(Xs_74),Ys_15) ) ).
fof(fact_169_hd__dropWhile,axiom,
! [P_1,Xs_22] :
( dropWh1165804960le_alt(P_1,Xs_22) != nil_Ar1135217151le_alt
=> ~ hBOOL(hAPP_A1120018583t_bool(P_1,hd_Arr1814706386le_alt(dropWh1165804960le_alt(P_1,Xs_22)))) ) ).
fof(fact_170_hd__dropWhile,axiom,
! [P_1,Xs_22] :
( dropWhile_nat(P_1,Xs_22) != nil_nat
=> ~ hBOOL(hAPP_nat_bool(P_1,hd_nat(dropWhile_nat(P_1,Xs_22)))) ) ).
fof(fact_171_member__rec_I2_J,axiom,
! [Y_28] : ~ hBOOL(hAPP_A1120018583t_bool(member1353991188le_alt(nil_Ar1135217151le_alt),Y_28)) ).
fof(fact_172_member__rec_I2_J,axiom,
! [Y_28] : ~ hBOOL(hAPP_nat_bool(member_nat_1(nil_nat),Y_28)) ).
fof(fact_173_list__ex1__simps_I1_J,axiom,
! [P_1] : ~ hBOOL(hAPP_l300482276t_bool(list_e88267970le_alt(P_1),nil_Ar1135217151le_alt)) ).
fof(fact_174_list__ex1__simps_I1_J,axiom,
! [P_1] : ~ hBOOL(hAPP_list_nat_bool(list_ex1_nat(P_1),nil_nat)) ).
fof(fact_175_elem,axiom,
! [X_60,Xs_73] : hBOOL(hAPP_l300482276t_bool(listMe2074553835le_alt(X_60),cons_A77766063le_alt(X_60,Xs_73))) ).
fof(fact_176_member__rec_I1_J,axiom,
! [X_9,Xs_22,Y_9] :
( ( is_Arr723427730le_alt(X_9)
& is_Arr723427730le_alt(Y_9) )
=> ( hBOOL(hAPP_A1120018583t_bool(member1353991188le_alt(cons_A77766063le_alt(X_9,Xs_22)),Y_9))
<=> ( X_9 = Y_9
| hBOOL(hAPP_A1120018583t_bool(member1353991188le_alt(Xs_22),Y_9)) ) ) ) ).
fof(fact_177_insert,axiom,
! [Y_27,X_59,Xs_72] :
( hBOOL(hAPP_l300482276t_bool(listMe2074553835le_alt(X_59),Xs_72))
=> hBOOL(hAPP_l300482276t_bool(listMe2074553835le_alt(X_59),cons_A77766063le_alt(Y_27,Xs_72))) ) ).
fof(fact_178_hd__replicate,axiom,
! [X_58,N_42] :
( is_Arr723427730le_alt(X_58)
=> ( N_42 != zero_zero_nat
=> hd_Arr1814706386le_alt(hAPP_A1849759038le_alt(replic1360561849le_alt(N_42),X_58)) = X_58 ) ) ).
fof(fact_179_last__replicate,axiom,
! [X_57,N_41] :
( is_Arr723427730le_alt(X_57)
=> ( N_41 != zero_zero_nat
=> last_A1066338328le_alt(hAPP_A1849759038le_alt(replic1360561849le_alt(N_41),X_57)) = X_57 ) ) ).
fof(fact_180_replicate__eq__replicate,axiom,
! [M_1,X_9,N_12,Y_9] :
( ( is_Arr723427730le_alt(X_9)
& is_Arr723427730le_alt(Y_9) )
=> ( hAPP_A1849759038le_alt(replic1360561849le_alt(M_1),X_9) = hAPP_A1849759038le_alt(replic1360561849le_alt(N_12),Y_9)
<=> ( M_1 = N_12
& ( M_1 != zero_zero_nat
=> X_9 = Y_9 ) ) ) ) ).
fof(fact_181_dropWhile_Osimps_I2_J,axiom,
! [Xs_22,P_1,X_9] :
( ( hBOOL(hAPP_A1120018583t_bool(P_1,X_9))
=> dropWh1165804960le_alt(P_1,cons_A77766063le_alt(X_9,Xs_22)) = dropWh1165804960le_alt(P_1,Xs_22) )
& ( ~ hBOOL(hAPP_A1120018583t_bool(P_1,X_9))
=> dropWh1165804960le_alt(P_1,cons_A77766063le_alt(X_9,Xs_22)) = cons_A77766063le_alt(X_9,Xs_22) ) ) ).
fof(fact_182_dropWhile_Osimps_I1_J,axiom,
! [P_1] : dropWh1165804960le_alt(P_1,nil_Ar1135217151le_alt) = nil_Ar1135217151le_alt ).
fof(fact_183_dropWhile_Osimps_I1_J,axiom,
! [P_1] : dropWhile_nat(P_1,nil_nat) = nil_nat ).
fof(fact_184_distinct__dropWhile,axiom,
! [P_1,Xs_22] :
( hBOOL(hAPP_l300482276t_bool(distin85347314le_alt,Xs_22))
=> hBOOL(hAPP_l300482276t_bool(distin85347314le_alt,dropWh1165804960le_alt(P_1,Xs_22))) ) ).
fof(fact_185_sorted__dropWhile,axiom,
! [P_1,Xs_22] :
( hBOOL(hAPP_list_nat_bool(linorder_sorted_nat,Xs_22))
=> hBOOL(hAPP_list_nat_bool(linorder_sorted_nat,dropWhile_nat(P_1,Xs_22))) ) ).
fof(fact_186_replicate__0,axiom,
! [X_56] : hAPP_A1849759038le_alt(replic1360561849le_alt(zero_zero_nat),X_56) = nil_Ar1135217151le_alt ).
fof(fact_187_replicate__0,axiom,
! [X_56] : hAPP_nat_list_nat(replicate_nat(zero_zero_nat),X_56) = nil_nat ).
fof(fact_188_empty__replicate,axiom,
! [N_12,X_9] :
( nil_Ar1135217151le_alt = hAPP_A1849759038le_alt(replic1360561849le_alt(N_12),X_9)
<=> N_12 = zero_zero_nat ) ).
fof(fact_189_empty__replicate,axiom,
! [N_12,X_9] :
( nil_nat = hAPP_nat_list_nat(replicate_nat(N_12),X_9)
<=> N_12 = zero_zero_nat ) ).
fof(fact_190_replicate__empty,axiom,
! [N_12,X_9] :
( hAPP_A1849759038le_alt(replic1360561849le_alt(N_12),X_9) = nil_Ar1135217151le_alt
<=> N_12 = zero_zero_nat ) ).
fof(fact_191_replicate__empty,axiom,
! [N_12,X_9] :
( hAPP_nat_list_nat(replicate_nat(N_12),X_9) = nil_nat
<=> N_12 = zero_zero_nat ) ).
fof(fact_192_sublist__singleton,axiom,
! [X_9,A] :
( ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,zero_zero_nat),A))
=> sublis1896976644le_alt(cons_A77766063le_alt(X_9,nil_Ar1135217151le_alt),A) = cons_A77766063le_alt(X_9,nil_Ar1135217151le_alt) )
& ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,zero_zero_nat),A))
=> sublis1896976644le_alt(cons_A77766063le_alt(X_9,nil_Ar1135217151le_alt),A) = nil_Ar1135217151le_alt ) ) ).
fof(fact_193_sublist__singleton,axiom,
! [X_9,A] :
( ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,zero_zero_nat),A))
=> sublist_nat(cons_nat(X_9,nil_nat),A) = cons_nat(X_9,nil_nat) )
& ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,zero_zero_nat),A))
=> sublist_nat(cons_nat(X_9,nil_nat),A) = nil_nat ) ) ).
fof(fact_194_dropWhile__eq__Cons__conv,axiom,
! [P_1,Xs_22,Y_9,Ys_4] :
( dropWh1165804960le_alt(P_1,Xs_22) = cons_A77766063le_alt(Y_9,Ys_4)
<=> ( Xs_22 = append28105492le_alt(takeWh1545314552le_alt(P_1,Xs_22),cons_A77766063le_alt(Y_9,Ys_4))
& ~ hBOOL(hAPP_A1120018583t_bool(P_1,Y_9)) ) ) ).
fof(fact_195_list_Osize_I1_J,axiom,
! [Fa] : list_s99318913le_alt(Fa,nil_Ar1135217151le_alt) = zero_zero_nat ).
fof(fact_196_list_Osize_I1_J,axiom,
! [Fa] : list_size_nat(Fa,nil_nat) = zero_zero_nat ).
fof(fact_197_ListMem_Osimps,axiom,
! [A1,A2] :
( is_Arr723427730le_alt(A1)
=> ( hBOOL(hAPP_l300482276t_bool(listMe2074553835le_alt(A1),A2))
<=> ( ? [X_52,Xs_44] :
( is_Arr723427730le_alt(X_52)
& A1 = X_52
& A2 = cons_A77766063le_alt(X_52,Xs_44) )
| ? [X_52,Xs_44,Y_3] :
( is_Arr723427730le_alt(X_52)
& is_Arr723427730le_alt(Y_3)
& A1 = X_52
& A2 = cons_A77766063le_alt(Y_3,Xs_44)
& hBOOL(hAPP_l300482276t_bool(listMe2074553835le_alt(X_52),Xs_44)) ) ) ) ) ).
fof(fact_198_zero__reorient,axiom,
! [X_9] :
( zero_zero_int = X_9
<=> X_9 = zero_zero_int ) ).
fof(fact_199_zero__reorient,axiom,
! [X_9] :
( zero_zero_nat = X_9
<=> X_9 = zero_zero_nat ) ).
fof(fact_200_hd__conv__nth,axiom,
! [Xs_71] :
( Xs_71 != nil_nat
=> hd_nat(Xs_71) = hAPP_nat_nat(nth_nat(Xs_71),zero_zero_nat) ) ).
fof(fact_201_hd__conv__nth,axiom,
! [Xs_71] :
( Xs_71 != nil_Ar1135217151le_alt
=> hd_Arr1814706386le_alt(Xs_71) = hAPP_n1410269210le_alt(nth_Ar2122385664le_alt(Xs_71),zero_zero_nat) ) ).
fof(fact_202_takeWhile_Osimps_I1_J,axiom,
! [P_1] : takeWhile_nat(P_1,nil_nat) = nil_nat ).
fof(fact_203_takeWhile_Osimps_I1_J,axiom,
! [P_1] : takeWh1545314552le_alt(P_1,nil_Ar1135217151le_alt) = nil_Ar1135217151le_alt ).
fof(fact_204_distinct__takeWhile,axiom,
! [P_1,Xs_22] :
( hBOOL(hAPP_l300482276t_bool(distin85347314le_alt,Xs_22))
=> hBOOL(hAPP_l300482276t_bool(distin85347314le_alt,takeWh1545314552le_alt(P_1,Xs_22))) ) ).
fof(fact_205_sorted__takeWhile,axiom,
! [P_1,Xs_22] :
( hBOOL(hAPP_list_nat_bool(linorder_sorted_nat,Xs_22))
=> hBOOL(hAPP_list_nat_bool(linorder_sorted_nat,takeWhile_nat(P_1,Xs_22))) ) ).
fof(fact_206_sublist__nil,axiom,
! [A] : sublist_nat(nil_nat,A) = nil_nat ).
fof(fact_207_sublist__nil,axiom,
! [A] : sublis1896976644le_alt(nil_Ar1135217151le_alt,A) = nil_Ar1135217151le_alt ).
fof(fact_208_distinct__sublistI,axiom,
! [I_26,Xs_22] :
( hBOOL(hAPP_l300482276t_bool(distin85347314le_alt,Xs_22))
=> hBOOL(hAPP_l300482276t_bool(distin85347314le_alt,sublis1896976644le_alt(Xs_22,I_26))) ) ).
fof(fact_209_nth__Cons__0,axiom,
! [X_55,Xs_70] : hAPP_nat_nat(nth_nat(cons_nat(X_55,Xs_70)),zero_zero_nat) = X_55 ).
fof(fact_210_nth__Cons__0,axiom,
! [X_55,Xs_70] :
( is_Arr723427730le_alt(X_55)
=> hAPP_n1410269210le_alt(nth_Ar2122385664le_alt(cons_A77766063le_alt(X_55,Xs_70)),zero_zero_nat) = X_55 ) ).
fof(fact_211_takeWhile_Osimps_I2_J,axiom,
! [Xs_22,P_1,X_9] :
( ( hBOOL(hAPP_nat_bool(P_1,X_9))
=> takeWhile_nat(P_1,cons_nat(X_9,Xs_22)) = cons_nat(X_9,takeWhile_nat(P_1,Xs_22)) )
& ( ~ hBOOL(hAPP_nat_bool(P_1,X_9))
=> takeWhile_nat(P_1,cons_nat(X_9,Xs_22)) = nil_nat ) ) ).
fof(fact_212_takeWhile_Osimps_I2_J,axiom,
! [Xs_22,P_1,X_9] :
( ( hBOOL(hAPP_A1120018583t_bool(P_1,X_9))
=> takeWh1545314552le_alt(P_1,cons_A77766063le_alt(X_9,Xs_22)) = cons_A77766063le_alt(X_9,takeWh1545314552le_alt(P_1,Xs_22)) )
& ( ~ hBOOL(hAPP_A1120018583t_bool(P_1,X_9))
=> takeWh1545314552le_alt(P_1,cons_A77766063le_alt(X_9,Xs_22)) = nil_Ar1135217151le_alt ) ) ).
fof(fact_213_takeWhile__tail,axiom,
! [Xs_22,L_1,P_1,X_9] :
( ~ hBOOL(hAPP_A1120018583t_bool(P_1,X_9))
=> takeWh1545314552le_alt(P_1,append28105492le_alt(Xs_22,cons_A77766063le_alt(X_9,L_1))) = takeWh1545314552le_alt(P_1,Xs_22) ) ).
fof(fact_214_takeWhile__dropWhile__id,axiom,
! [P_1,Xs_22] : append28105492le_alt(takeWh1545314552le_alt(P_1,Xs_22),dropWh1165804960le_alt(P_1,Xs_22)) = Xs_22 ).
fof(fact_215_nth__append__length,axiom,
! [Xs_69,X_54,Ys_14] : hAPP_nat_nat(nth_nat(append_nat(Xs_69,cons_nat(X_54,Ys_14))),size_size_list_nat(Xs_69)) = X_54 ).
fof(fact_216_nth__append__length,axiom,
! [Xs_69,X_54,Ys_14] :
( is_Arr723427730le_alt(X_54)
=> hAPP_n1410269210le_alt(nth_Ar2122385664le_alt(append28105492le_alt(Xs_69,cons_A77766063le_alt(X_54,Ys_14))),size_s2106320494le_alt(Xs_69)) = X_54 ) ).
fof(fact_217_foldr__max__sorted,axiom,
! [Y_9,Xs_22] :
( hBOOL(hAPP_list_int_bool(linorder_sorted_int,rev_int(Xs_22)))
=> ( ( Xs_22 = nil_int
=> hAPP_int_int(foldr_int_int(ord_max_int,Xs_22),Y_9) = Y_9 )
& ( Xs_22 != nil_int
=> hAPP_int_int(foldr_int_int(ord_max_int,Xs_22),Y_9) = hAPP_int_int(hAPP_int_fun_int_int(ord_max_int,hAPP_nat_int(nth_int(Xs_22),zero_zero_nat)),Y_9) ) ) ) ).
fof(fact_218_foldr__max__sorted,axiom,
! [Y_9,Xs_22] :
( hBOOL(hAPP_list_nat_bool(linorder_sorted_nat,rev_nat(Xs_22)))
=> ( ( Xs_22 = nil_nat
=> hAPP_nat_nat(foldr_nat_nat(ord_max_nat,Xs_22),Y_9) = Y_9 )
& ( Xs_22 != nil_nat
=> hAPP_nat_nat(foldr_nat_nat(ord_max_nat,Xs_22),Y_9) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,hAPP_nat_nat(nth_nat(Xs_22),zero_zero_nat)),Y_9) ) ) ) ).
fof(fact_219_list__induct2_H,axiom,
! [Xs_22,Ys_4,P_1] :
( hBOOL(hAPP_list_nat_bool(hAPP_l1595748666t_bool(P_1,nil_Ar1135217151le_alt),nil_nat))
=> ( ! [X_52,Xs_44] :
( is_Arr723427730le_alt(X_52)
=> hBOOL(hAPP_list_nat_bool(hAPP_l1595748666t_bool(P_1,cons_A77766063le_alt(X_52,Xs_44)),nil_nat)) )
=> ( ! [Y_3,Ys_5] : hBOOL(hAPP_list_nat_bool(hAPP_l1595748666t_bool(P_1,nil_Ar1135217151le_alt),cons_nat(Y_3,Ys_5)))
=> ( ! [X_52,Xs_44,Y_3,Ys_5] :
( is_Arr723427730le_alt(X_52)
=> ( hBOOL(hAPP_list_nat_bool(hAPP_l1595748666t_bool(P_1,Xs_44),Ys_5))
=> hBOOL(hAPP_list_nat_bool(hAPP_l1595748666t_bool(P_1,cons_A77766063le_alt(X_52,Xs_44)),cons_nat(Y_3,Ys_5))) ) )
=> hBOOL(hAPP_list_nat_bool(hAPP_l1595748666t_bool(P_1,Xs_22),Ys_4)) ) ) ) ) ).
fof(fact_220_list__induct2_H,axiom,
! [Xs_22,Ys_4,P_1] :
( hBOOL(hAPP_l300482276t_bool(hAPP_l411306372t_bool(P_1,nil_nat),nil_Ar1135217151le_alt))
=> ( ! [X_52,Xs_44] : hBOOL(hAPP_l300482276t_bool(hAPP_l411306372t_bool(P_1,cons_nat(X_52,Xs_44)),nil_Ar1135217151le_alt))
=> ( ! [Y_3,Ys_5] :
( is_Arr723427730le_alt(Y_3)
=> hBOOL(hAPP_l300482276t_bool(hAPP_l411306372t_bool(P_1,nil_nat),cons_A77766063le_alt(Y_3,Ys_5))) )
=> ( ! [X_52,Xs_44,Y_3,Ys_5] :
( is_Arr723427730le_alt(Y_3)
=> ( hBOOL(hAPP_l300482276t_bool(hAPP_l411306372t_bool(P_1,Xs_44),Ys_5))
=> hBOOL(hAPP_l300482276t_bool(hAPP_l411306372t_bool(P_1,cons_nat(X_52,Xs_44)),cons_A77766063le_alt(Y_3,Ys_5))) ) )
=> hBOOL(hAPP_l300482276t_bool(hAPP_l411306372t_bool(P_1,Xs_22),Ys_4)) ) ) ) ) ).
fof(fact_221_map__filter__simps_I2_J,axiom,
! [F] : map_fi434460357lt_nat(F,nil_Ar1135217151le_alt) = nil_nat ).
fof(fact_222_map__filter__simps_I2_J,axiom,
! [F] : map_fi1311720335le_alt(F,nil_nat) = nil_Ar1135217151le_alt ).
fof(fact_223_listrelp_ONil,axiom,
! [R_1] : hBOOL(hAPP_list_nat_bool(hAPP_l120351551t_bool(listrelp_nat(R_1),nil_nat),nil_nat)) ).
fof(fact_224_listrelp_ONil,axiom,
! [R_1] : hBOOL(hAPP_l300482276t_bool(hAPP_l2066632447t_bool(listre1062185049le_alt(R_1),nil_Ar1135217151le_alt),nil_Ar1135217151le_alt)) ).
fof(fact_225_listrelp_OCons,axiom,
! [Xs_22,Ys_4,R_1,X_9,Y_9] :
( hBOOL(hAPP_A1120018583t_bool(hAPP_A1781286015t_bool(R_1,X_9),Y_9))
=> ( hBOOL(hAPP_l300482276t_bool(hAPP_l2066632447t_bool(listre1062185049le_alt(R_1),Xs_22),Ys_4))
=> hBOOL(hAPP_l300482276t_bool(hAPP_l2066632447t_bool(listre1062185049le_alt(R_1),cons_A77766063le_alt(X_9,Xs_22)),cons_A77766063le_alt(Y_9,Ys_4))) ) ) ).
fof(fact_226_sublist__empty,axiom,
! [Xs_22] : sublist_nat(Xs_22,bot_bot_fun_nat_bool) = nil_nat ).
fof(fact_227_sublist__empty,axiom,
! [Xs_22] : sublis1896976644le_alt(Xs_22,bot_bot_fun_nat_bool) = nil_Ar1135217151le_alt ).
fof(fact_228_neq__if__length__neq,axiom,
! [Xs_68,Ys_13] :
( size_s2106320494le_alt(Xs_68) != size_s2106320494le_alt(Ys_13)
=> Xs_68 != Ys_13 ) ).
fof(fact_229_length__rev,axiom,
! [Xs_67] : size_size_list_nat(rev_nat(Xs_67)) = size_size_list_nat(Xs_67) ).
fof(fact_230_length__rev,axiom,
! [Xs_67] : size_s2106320494le_alt(rev_Ar955429983le_alt(Xs_67)) = size_s2106320494le_alt(Xs_67) ).
fof(fact_231_length__replicate,axiom,
! [N_40,X_53] : size_s2106320494le_alt(hAPP_A1849759038le_alt(replic1360561849le_alt(N_40),X_53)) = N_40 ).
fof(fact_232_length__rotate1,axiom,
! [Xs_66] : size_s2106320494le_alt(rotate184372300le_alt(Xs_66)) = size_s2106320494le_alt(Xs_66) ).
fof(fact_233_foldr_Osimps_I2_J,axiom,
! [F,X_9,Xs_22,Aa] : hAPP_nat_nat(foldr_nat_nat(F,cons_nat(X_9,Xs_22)),Aa) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,X_9),hAPP_nat_nat(foldr_nat_nat(F,Xs_22),Aa)) ).
fof(fact_234_foldr_Osimps_I1_J,axiom,
! [F,Aa] : hAPP_nat_nat(foldr_nat_nat(F,nil_nat),Aa) = Aa ).
fof(fact_235_foldr__append,axiom,
! [F,Xs_22,Ys_4,Aa] : hAPP_nat_nat(foldr_nat_nat(F,append_nat(Xs_22,Ys_4)),Aa) = hAPP_nat_nat(foldr_nat_nat(F,Xs_22),hAPP_nat_nat(foldr_nat_nat(F,Ys_4),Aa)) ).
fof(fact_236_length__0__conv,axiom,
! [Xs_22] :
( size_size_list_nat(Xs_22) = zero_zero_nat
<=> Xs_22 = nil_nat ) ).
fof(fact_237_length__0__conv,axiom,
! [Xs_22] :
( size_s2106320494le_alt(Xs_22) = zero_zero_nat
<=> Xs_22 = nil_Ar1135217151le_alt ) ).
fof(fact_238_list_Osize_I3_J,axiom,
size_size_list_nat(nil_nat) = zero_zero_nat ).
fof(fact_239_list_Osize_I3_J,axiom,
size_s2106320494le_alt(nil_Ar1135217151le_alt) = zero_zero_nat ).
fof(fact_240_list__induct2,axiom,
! [P_1,Xs_22,Ys_4] :
( size_s2106320494le_alt(Xs_22) = size_size_list_nat(Ys_4)
=> ( hBOOL(hAPP_list_nat_bool(hAPP_l1595748666t_bool(P_1,nil_Ar1135217151le_alt),nil_nat))
=> ( ! [X_52,Xs_44,Y_3,Ys_5] :
( is_Arr723427730le_alt(X_52)
=> ( size_s2106320494le_alt(Xs_44) = size_size_list_nat(Ys_5)
=> ( hBOOL(hAPP_list_nat_bool(hAPP_l1595748666t_bool(P_1,Xs_44),Ys_5))
=> hBOOL(hAPP_list_nat_bool(hAPP_l1595748666t_bool(P_1,cons_A77766063le_alt(X_52,Xs_44)),cons_nat(Y_3,Ys_5))) ) ) )
=> hBOOL(hAPP_list_nat_bool(hAPP_l1595748666t_bool(P_1,Xs_22),Ys_4)) ) ) ) ).
fof(fact_241_list__induct2,axiom,
! [P_1,Xs_22,Ys_4] :
( size_size_list_nat(Xs_22) = size_s2106320494le_alt(Ys_4)
=> ( hBOOL(hAPP_l300482276t_bool(hAPP_l411306372t_bool(P_1,nil_nat),nil_Ar1135217151le_alt))
=> ( ! [X_52,Xs_44,Y_3,Ys_5] :
( is_Arr723427730le_alt(Y_3)
=> ( size_size_list_nat(Xs_44) = size_s2106320494le_alt(Ys_5)
=> ( hBOOL(hAPP_l300482276t_bool(hAPP_l411306372t_bool(P_1,Xs_44),Ys_5))
=> hBOOL(hAPP_l300482276t_bool(hAPP_l411306372t_bool(P_1,cons_nat(X_52,Xs_44)),cons_A77766063le_alt(Y_3,Ys_5))) ) ) )
=> hBOOL(hAPP_l300482276t_bool(hAPP_l411306372t_bool(P_1,Xs_22),Ys_4)) ) ) ) ).
fof(fact_242_list__induct2,axiom,
! [P_1,Xs_22,Ys_4] :
( size_s2106320494le_alt(Xs_22) = size_s2106320494le_alt(Ys_4)
=> ( hBOOL(hAPP_l300482276t_bool(hAPP_l2066632447t_bool(P_1,nil_Ar1135217151le_alt),nil_Ar1135217151le_alt))
=> ( ! [X_52,Xs_44,Y_3,Ys_5] :
( ( is_Arr723427730le_alt(X_52)
& is_Arr723427730le_alt(Y_3) )
=> ( size_s2106320494le_alt(Xs_44) = size_s2106320494le_alt(Ys_5)
=> ( hBOOL(hAPP_l300482276t_bool(hAPP_l2066632447t_bool(P_1,Xs_44),Ys_5))
=> hBOOL(hAPP_l300482276t_bool(hAPP_l2066632447t_bool(P_1,cons_A77766063le_alt(X_52,Xs_44)),cons_A77766063le_alt(Y_3,Ys_5))) ) ) )
=> hBOOL(hAPP_l300482276t_bool(hAPP_l2066632447t_bool(P_1,Xs_22),Ys_4)) ) ) ) ).
fof(fact_243_emptyE,axiom,
! [Aa] : ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Aa),bot_bot_fun_int_bool)) ).
fof(fact_244_emptyE,axiom,
! [Aa] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Aa),bot_bot_fun_nat_bool)) ).
fof(fact_245_bot__fun__def,axiom,
! [X_52] :
( hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,X_52))
<=> hBOOL(bot_bot_bool) ) ).
fof(fact_246_bot__apply,axiom,
! [X_9] :
( hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,X_9))
<=> hBOOL(bot_bot_bool) ) ).
fof(fact_247_Ex__list__of__length,axiom,
! [N_39] :
? [Xs_44] : size_s2106320494le_alt(Xs_44) = N_39 ).
fof(fact_248_listrelp_Osimps,axiom,
! [R_1,A1,A2] :
( hBOOL(hAPP_list_nat_bool(hAPP_l120351551t_bool(listrelp_nat(R_1),A1),A2))
<=> ( ( A1 = nil_nat
& A2 = nil_nat )
| ? [X_52,Y_3,Xs_44,Ys_5] :
( A1 = cons_nat(X_52,Xs_44)
& A2 = cons_nat(Y_3,Ys_5)
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(R_1,X_52),Y_3))
& hBOOL(hAPP_list_nat_bool(hAPP_l120351551t_bool(listrelp_nat(R_1),Xs_44),Ys_5)) ) ) ) ).
fof(fact_249_listrelp_Osimps,axiom,
! [R_1,A1,A2] :
( hBOOL(hAPP_l300482276t_bool(hAPP_l2066632447t_bool(listre1062185049le_alt(R_1),A1),A2))
<=> ( ( A1 = nil_Ar1135217151le_alt
& A2 = nil_Ar1135217151le_alt )
| ? [X_52,Y_3,Xs_44,Ys_5] :
( is_Arr723427730le_alt(X_52)
& is_Arr723427730le_alt(Y_3)
& A1 = cons_A77766063le_alt(X_52,Xs_44)
& A2 = cons_A77766063le_alt(Y_3,Ys_5)
& hBOOL(hAPP_A1120018583t_bool(hAPP_A1781286015t_bool(R_1,X_52),Y_3))
& hBOOL(hAPP_l300482276t_bool(hAPP_l2066632447t_bool(listre1062185049le_alt(R_1),Xs_44),Ys_5)) ) ) ) ).
fof(fact_250_equals0D,axiom,
! [Aa,A] :
( A = bot_bot_fun_int_bool
=> ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Aa),A)) ) ).
fof(fact_251_equals0D,axiom,
! [Aa,A] :
( A = bot_bot_fun_nat_bool
=> ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Aa),A)) ) ).
fof(fact_252_Collect__empty__eq,axiom,
! [P_1] :
( collect_nat(P_1) = bot_bot_fun_nat_bool
<=> ! [X_52] : ~ hBOOL(hAPP_nat_bool(P_1,X_52)) ) ).
fof(fact_253_empty__iff,axiom,
! [C_1] : ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,C_1),bot_bot_fun_int_bool)) ).
fof(fact_254_empty__iff,axiom,
! [C_1] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_1),bot_bot_fun_nat_bool)) ).
fof(fact_255_empty__Collect__eq,axiom,
! [P_1] :
( bot_bot_fun_nat_bool = collect_nat(P_1)
<=> ! [X_52] : ~ hBOOL(hAPP_nat_bool(P_1,X_52)) ) ).
fof(fact_256_ex__in__conv,axiom,
! [A] :
( ? [X_52] : hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_52),A))
<=> A != bot_bot_fun_int_bool ) ).
fof(fact_257_ex__in__conv,axiom,
! [A] :
( ? [X_52] : hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_52),A))
<=> A != bot_bot_fun_nat_bool ) ).
fof(fact_258_all__not__in__conv,axiom,
! [A] :
( ! [X_52] : ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_52),A))
<=> A = bot_bot_fun_int_bool ) ).
fof(fact_259_all__not__in__conv,axiom,
! [A] :
( ! [X_52] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_52),A))
<=> A = bot_bot_fun_nat_bool ) ).
fof(fact_260_empty__def,axiom,
bot_bot_fun_nat_bool = collect_nat(cOMBK_bool_nat(fFalse)) ).
fof(fact_261_equals0I,axiom,
! [A] :
( ! [Y_3] : ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Y_3),A))
=> A = bot_bot_fun_int_bool ) ).
fof(fact_262_equals0I,axiom,
! [A] :
( ! [Y_3] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Y_3),A))
=> A = bot_bot_fun_nat_bool ) ).
fof(fact_263_sorted__list__of__set__empty,axiom,
linord810813188et_nat(bot_bot_fun_nat_bool) = nil_nat ).
fof(fact_264_min__max_Osup__assoc,axiom,
! [X_51,Y_26,Z_7] : hAPP_int_int(hAPP_int_fun_int_int(ord_max_int,hAPP_int_int(hAPP_int_fun_int_int(ord_max_int,X_51),Y_26)),Z_7) = hAPP_int_int(hAPP_int_fun_int_int(ord_max_int,X_51),hAPP_int_int(hAPP_int_fun_int_int(ord_max_int,Y_26),Z_7)) ).
fof(fact_265_min__max_Osup__assoc,axiom,
! [X_51,Y_26,Z_7] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,X_51),Y_26)),Z_7) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,X_51),hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,Y_26),Z_7)) ).
fof(fact_266_min__max_Osup_Oassoc,axiom,
! [A_45,B_29,C_24] : hAPP_int_int(hAPP_int_fun_int_int(ord_max_int,hAPP_int_int(hAPP_int_fun_int_int(ord_max_int,A_45),B_29)),C_24) = hAPP_int_int(hAPP_int_fun_int_int(ord_max_int,A_45),hAPP_int_int(hAPP_int_fun_int_int(ord_max_int,B_29),C_24)) ).
fof(fact_267_min__max_Osup_Oassoc,axiom,
! [A_45,B_29,C_24] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,A_45),B_29)),C_24) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,A_45),hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,B_29),C_24)) ).
fof(fact_268_min__max_Osup__left__commute,axiom,
! [X_50,Y_25,Z_6] : hAPP_int_int(hAPP_int_fun_int_int(ord_max_int,X_50),hAPP_int_int(hAPP_int_fun_int_int(ord_max_int,Y_25),Z_6)) = hAPP_int_int(hAPP_int_fun_int_int(ord_max_int,Y_25),hAPP_int_int(hAPP_int_fun_int_int(ord_max_int,X_50),Z_6)) ).
fof(fact_269_min__max_Osup__left__commute,axiom,
! [X_50,Y_25,Z_6] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,X_50),hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,Y_25),Z_6)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,Y_25),hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,X_50),Z_6)) ).
fof(fact_270_min__max_Osup_Oleft__commute,axiom,
! [B_28,A_44,C_23] : hAPP_int_int(hAPP_int_fun_int_int(ord_max_int,B_28),hAPP_int_int(hAPP_int_fun_int_int(ord_max_int,A_44),C_23)) = hAPP_int_int(hAPP_int_fun_int_int(ord_max_int,A_44),hAPP_int_int(hAPP_int_fun_int_int(ord_max_int,B_28),C_23)) ).
fof(fact_271_min__max_Osup_Oleft__commute,axiom,
! [B_28,A_44,C_23] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,B_28),hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,A_44),C_23)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,A_44),hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,B_28),C_23)) ).
fof(fact_272_min__max_Osup_Oidem,axiom,
! [A_43] : hAPP_int_int(hAPP_int_fun_int_int(ord_max_int,A_43),A_43) = A_43 ).
fof(fact_273_min__max_Osup_Oidem,axiom,
! [A_43] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,A_43),A_43) = A_43 ).
fof(fact_274_min__max_Osup_Ocommute,axiom,
! [A_42,B_27] : hAPP_int_int(hAPP_int_fun_int_int(ord_max_int,A_42),B_27) = hAPP_int_int(hAPP_int_fun_int_int(ord_max_int,B_27),A_42) ).
fof(fact_275_min__max_Osup_Ocommute,axiom,
! [A_42,B_27] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,A_42),B_27) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,B_27),A_42) ).
fof(fact_276_min__max_Osup__commute,axiom,
! [X_49,Y_24] : hAPP_int_int(hAPP_int_fun_int_int(ord_max_int,X_49),Y_24) = hAPP_int_int(hAPP_int_fun_int_int(ord_max_int,Y_24),X_49) ).
fof(fact_277_min__max_Osup__commute,axiom,
! [X_49,Y_24] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,X_49),Y_24) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,Y_24),X_49) ).
fof(fact_278_min__max_Osup_Oleft__idem,axiom,
! [A_41,B_26] : hAPP_int_int(hAPP_int_fun_int_int(ord_max_int,A_41),hAPP_int_int(hAPP_int_fun_int_int(ord_max_int,A_41),B_26)) = hAPP_int_int(hAPP_int_fun_int_int(ord_max_int,A_41),B_26) ).
fof(fact_279_min__max_Osup_Oleft__idem,axiom,
! [A_41,B_26] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,A_41),hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,A_41),B_26)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,A_41),B_26) ).
fof(fact_280_min__max_Osup__left__idem,axiom,
! [X_48,Y_23] : hAPP_int_int(hAPP_int_fun_int_int(ord_max_int,X_48),hAPP_int_int(hAPP_int_fun_int_int(ord_max_int,X_48),Y_23)) = hAPP_int_int(hAPP_int_fun_int_int(ord_max_int,X_48),Y_23) ).
fof(fact_281_min__max_Osup__left__idem,axiom,
! [X_48,Y_23] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,X_48),hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,X_48),Y_23)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,X_48),Y_23) ).
fof(fact_282_Max_Oidem,axiom,
! [X_47] : hAPP_int_int(hAPP_int_fun_int_int(ord_max_int,X_47),X_47) = X_47 ).
fof(fact_283_Max_Oidem,axiom,
! [X_47] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,X_47),X_47) = X_47 ).
fof(fact_284_dropWhile__eq__drop,axiom,
! [P_1,Xs_22] : dropWh1165804960le_alt(P_1,Xs_22) = drop_A1195732799le_alt(size_s2106320494le_alt(takeWh1545314552le_alt(P_1,Xs_22)),Xs_22) ).
fof(fact_285_nth__length__takeWhile,axiom,
! [P_1,Xs_22] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,size_size_list_nat(takeWhile_nat(P_1,Xs_22))),size_size_list_nat(Xs_22)))
=> ~ hBOOL(hAPP_nat_bool(P_1,hAPP_nat_nat(nth_nat(Xs_22),size_size_list_nat(takeWhile_nat(P_1,Xs_22))))) ) ).
fof(fact_286_nth__length__takeWhile,axiom,
! [P_1,Xs_22] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,size_s2106320494le_alt(takeWh1545314552le_alt(P_1,Xs_22))),size_s2106320494le_alt(Xs_22)))
=> ~ hBOOL(hAPP_A1120018583t_bool(P_1,hAPP_n1410269210le_alt(nth_Ar2122385664le_alt(Xs_22),size_s2106320494le_alt(takeWh1545314552le_alt(P_1,Xs_22))))) ) ).
fof(fact_287_takeWhile__nth,axiom,
! [J_1,P_1,Xs_22] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,J_1),size_size_list_nat(takeWhile_nat(P_1,Xs_22))))
=> hAPP_nat_nat(nth_nat(takeWhile_nat(P_1,Xs_22)),J_1) = hAPP_nat_nat(nth_nat(Xs_22),J_1) ) ).
fof(fact_288_takeWhile__nth,axiom,
! [J_1,P_1,Xs_22] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,J_1),size_s2106320494le_alt(takeWh1545314552le_alt(P_1,Xs_22))))
=> hAPP_n1410269210le_alt(nth_Ar2122385664le_alt(takeWh1545314552le_alt(P_1,Xs_22)),J_1) = hAPP_n1410269210le_alt(nth_Ar2122385664le_alt(Xs_22),J_1) ) ).
fof(fact_289_list__update__length,axiom,
! [Xs_65,X_46,Ys_12,Y_22] : hAPP_A1849759038le_alt(list_u2058984551le_alt(append28105492le_alt(Xs_65,cons_A77766063le_alt(X_46,Ys_12)),size_s2106320494le_alt(Xs_65)),Y_22) = append28105492le_alt(Xs_65,cons_A77766063le_alt(Y_22,Ys_12)) ).
fof(fact_290_max__0L,axiom,
! [N_5] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,zero_zero_nat),N_5) = N_5 ).
fof(fact_291_less__zeroE,axiom,
! [N_5] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_5),zero_zero_nat)) ).
fof(fact_292_list__update__overwrite,axiom,
! [Xs_64,I_25,X_45,Y_21] : hAPP_A1849759038le_alt(list_u2058984551le_alt(hAPP_A1849759038le_alt(list_u2058984551le_alt(Xs_64,I_25),X_45),I_25),Y_21) = hAPP_A1849759038le_alt(list_u2058984551le_alt(Xs_64,I_25),Y_21) ).
fof(fact_293_list__update__swap,axiom,
! [Xs_63,X_44,X_43,I_24,I_23] :
( I_24 != I_23
=> hAPP_A1849759038le_alt(list_u2058984551le_alt(hAPP_A1849759038le_alt(list_u2058984551le_alt(Xs_63,I_24),X_44),I_23),X_43) = hAPP_A1849759038le_alt(list_u2058984551le_alt(hAPP_A1849759038le_alt(list_u2058984551le_alt(Xs_63,I_23),X_43),I_24),X_44) ) ).
fof(fact_294_nat__less__cases,axiom,
! [P_1,M_1,N_12] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_12))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(P_1,N_12),M_1)) )
=> ( ( M_1 = N_12
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(P_1,N_12),M_1)) )
=> ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_12),M_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(P_1,N_12),M_1)) )
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(P_1,N_12),M_1)) ) ) ) ).
fof(fact_295_less__not__refl3,axiom,
! [S,T] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,S),T))
=> S != T ) ).
fof(fact_296_less__not__refl2,axiom,
! [N_5,M] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_5),M))
=> M != N_5 ) ).
fof(fact_297_less__irrefl__nat,axiom,
! [N_5] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_5),N_5)) ).
fof(fact_298_linorder__neqE__nat,axiom,
! [X,Y] :
( X != Y
=> ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X),Y))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y),X)) ) ) ).
fof(fact_299_nat__neq__iff,axiom,
! [M_1,N_12] :
( M_1 != N_12
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_12))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_12),M_1)) ) ) ).
fof(fact_300_less__not__refl,axiom,
! [N_5] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_5),N_5)) ).
fof(fact_301_gr0I,axiom,
! [N_5] :
( N_5 != zero_zero_nat
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_5)) ) ).
fof(fact_302_gr__implies__not0,axiom,
! [M,N_5] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N_5))
=> N_5 != zero_zero_nat ) ).
fof(fact_303_less__nat__zero__code,axiom,
! [N_5] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_5),zero_zero_nat)) ).
fof(fact_304_neq0__conv,axiom,
! [N_12] :
( N_12 != zero_zero_nat
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_12)) ) ).
fof(fact_305_not__less0,axiom,
! [N_5] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_5),zero_zero_nat)) ).
fof(fact_306_order__less__irrefl,axiom,
! [X_42] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_42),X_42)) ).
fof(fact_307_order__less__irrefl,axiom,
! [X_9] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_9),X_9)) ).
fof(fact_308_order__less__irrefl,axiom,
! [X_42] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_42),X_42)) ).
fof(fact_309_linorder__neq__iff,axiom,
! [X_9,Y_9] :
( X_9 != Y_9
<=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_9),Y_9))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_9),X_9)) ) ) ).
fof(fact_310_linorder__neq__iff,axiom,
! [X_9,Y_9] :
( X_9 != Y_9
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_9),Y_9))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_9),X_9)) ) ) ).
fof(fact_311_not__less__iff__gr__or__eq,axiom,
! [X_9,Y_9] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_9),Y_9))
<=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_9),X_9))
| X_9 = Y_9 ) ) ).
fof(fact_312_not__less__iff__gr__or__eq,axiom,
! [X_9,Y_9] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_9),Y_9))
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_9),X_9))
| X_9 = Y_9 ) ) ).
fof(fact_313_linorder__less__linear,axiom,
! [X_41,Y_20] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_41),Y_20))
| X_41 = Y_20
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_20),X_41)) ) ).
fof(fact_314_linorder__less__linear,axiom,
! [X_41,Y_20] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_41),Y_20))
| X_41 = Y_20
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_20),X_41)) ) ).
fof(fact_315_linorder__antisym__conv3,axiom,
! [Y_9,X_9] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_9),X_9))
=> ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_9),Y_9))
<=> X_9 = Y_9 ) ) ).
fof(fact_316_linorder__antisym__conv3,axiom,
! [Y_9,X_9] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_9),X_9))
=> ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_9),Y_9))
<=> X_9 = Y_9 ) ) ).
fof(fact_317_linorder__neqE,axiom,
! [X_40,Y_19] :
( X_40 != Y_19
=> ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_40),Y_19))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_19),X_40)) ) ) ).
fof(fact_318_linorder__neqE,axiom,
! [X_40,Y_19] :
( X_40 != Y_19
=> ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_40),Y_19))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_19),X_40)) ) ) ).
fof(fact_319_less__imp__neq,axiom,
! [X_39,Y_18] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_39),Y_18))
=> X_39 != Y_18 ) ).
fof(fact_320_less__imp__neq,axiom,
! [X_9,Y_9] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_9),Y_9))
=> X_9 != Y_9 ) ).
fof(fact_321_less__imp__neq,axiom,
! [X_39,Y_18] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_39),Y_18))
=> X_39 != Y_18 ) ).
fof(fact_322_order__less__not__sym,axiom,
! [X_38,Y_17] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_38),Y_17))
=> ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_17),X_38)) ) ).
fof(fact_323_order__less__not__sym,axiom,
! [X_9,Y_9] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_9),Y_9))
=> ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Y_9),X_9)) ) ).
fof(fact_324_order__less__not__sym,axiom,
! [X_38,Y_17] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_38),Y_17))
=> ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_17),X_38)) ) ).
fof(fact_325_order__less__imp__not__less,axiom,
! [X_37,Y_16] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_37),Y_16))
=> ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_16),X_37)) ) ).
fof(fact_326_order__less__imp__not__less,axiom,
! [X_9,Y_9] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_9),Y_9))
=> ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Y_9),X_9)) ) ).
fof(fact_327_order__less__imp__not__less,axiom,
! [X_37,Y_16] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_37),Y_16))
=> ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_16),X_37)) ) ).
fof(fact_328_order__less__imp__not__eq,axiom,
! [X_36,Y_15] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_36),Y_15))
=> X_36 != Y_15 ) ).
fof(fact_329_order__less__imp__not__eq,axiom,
! [X_9,Y_9] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_9),Y_9))
=> X_9 != Y_9 ) ).
fof(fact_330_order__less__imp__not__eq,axiom,
! [X_36,Y_15] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_36),Y_15))
=> X_36 != Y_15 ) ).
fof(fact_331_order__less__imp__not__eq2,axiom,
! [X_35,Y_14] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_35),Y_14))
=> Y_14 != X_35 ) ).
fof(fact_332_order__less__imp__not__eq2,axiom,
! [X_9,Y_9] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_9),Y_9))
=> Y_9 != X_9 ) ).
fof(fact_333_order__less__imp__not__eq2,axiom,
! [X_35,Y_14] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_35),Y_14))
=> Y_14 != X_35 ) ).
fof(fact_334_order__less__imp__triv,axiom,
! [P_1,X_9,Y_9] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_9),Y_9))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_9),X_9))
=> hBOOL(P_1) ) ) ).
fof(fact_335_order__less__imp__triv,axiom,
! [P_1,X_9,Y_9] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_9),Y_9))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Y_9),X_9))
=> hBOOL(P_1) ) ) ).
fof(fact_336_order__less__imp__triv,axiom,
! [P_1,X_9,Y_9] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_9),Y_9))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_9),X_9))
=> hBOOL(P_1) ) ) ).
fof(fact_337_order__less__asym_H,axiom,
! [A_40,B_25] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_40),B_25))
=> ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_25),A_40)) ) ).
fof(fact_338_order__less__asym_H,axiom,
! [Aa,Ba] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),Ba))
=> ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ba),Aa)) ) ).
fof(fact_339_order__less__asym_H,axiom,
! [A_40,B_25] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_40),B_25))
=> ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_25),A_40)) ) ).
fof(fact_340_xt1_I9_J,axiom,
! [B_24,A_39] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_24),A_39))
=> ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_39),B_24)) ) ).
fof(fact_341_xt1_I9_J,axiom,
! [Ba,Aa] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ba),Aa))
=> ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),Ba)) ) ).
fof(fact_342_xt1_I9_J,axiom,
! [B_24,A_39] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_24),A_39))
=> ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_39),B_24)) ) ).
fof(fact_343_ord__eq__less__trans,axiom,
! [C_22,A_38,B_23] :
( A_38 = B_23
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_23),C_22))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_38),C_22)) ) ) ).
fof(fact_344_ord__eq__less__trans,axiom,
! [C_1,Aa,Ba] :
( Aa = Ba
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ba),C_1))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),C_1)) ) ) ).
fof(fact_345_ord__eq__less__trans,axiom,
! [C_22,A_38,B_23] :
( A_38 = B_23
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_23),C_22))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_38),C_22)) ) ) ).
fof(fact_346_xt1_I1_J,axiom,
! [C_21,A_37,B_22] :
( A_37 = B_22
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,C_21),B_22))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,C_21),A_37)) ) ) ).
fof(fact_347_xt1_I1_J,axiom,
! [C_1,Aa,Ba] :
( Aa = Ba
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,C_1),Ba))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,C_1),Aa)) ) ) ).
fof(fact_348_xt1_I1_J,axiom,
! [C_21,A_37,B_22] :
( A_37 = B_22
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,C_21),B_22))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,C_21),A_37)) ) ) ).
fof(fact_349_ord__less__eq__trans,axiom,
! [C_20,A_36,B_21] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_36),B_21))
=> ( B_21 = C_20
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_36),C_20)) ) ) ).
fof(fact_350_ord__less__eq__trans,axiom,
! [C_1,Aa,Ba] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),Ba))
=> ( Ba = C_1
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),C_1)) ) ) ).
fof(fact_351_ord__less__eq__trans,axiom,
! [C_20,A_36,B_21] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_36),B_21))
=> ( B_21 = C_20
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_36),C_20)) ) ) ).
fof(fact_352_xt1_I2_J,axiom,
! [C_19,B_20,A_35] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_20),A_35))
=> ( B_20 = C_19
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,C_19),A_35)) ) ) ).
fof(fact_353_xt1_I2_J,axiom,
! [C_1,Ba,Aa] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ba),Aa))
=> ( Ba = C_1
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,C_1),Aa)) ) ) ).
fof(fact_354_xt1_I2_J,axiom,
! [C_19,B_20,A_35] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_20),A_35))
=> ( B_20 = C_19
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,C_19),A_35)) ) ) ).
fof(fact_355_order__less__trans,axiom,
! [Z_5,X_34,Y_13] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_34),Y_13))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_13),Z_5))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_34),Z_5)) ) ) ).
fof(fact_356_order__less__trans,axiom,
! [Z_3,X_9,Y_9] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_9),Y_9))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Y_9),Z_3))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_9),Z_3)) ) ) ).
fof(fact_357_order__less__trans,axiom,
! [Z_5,X_34,Y_13] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_34),Y_13))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_13),Z_5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_34),Z_5)) ) ) ).
fof(fact_358_xt1_I10_J,axiom,
! [Z_4,Y_12,X_33] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_12),X_33))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Z_4),Y_12))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Z_4),X_33)) ) ) ).
fof(fact_359_xt1_I10_J,axiom,
! [Z_3,Y_9,X_9] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Y_9),X_9))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Z_3),Y_9))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Z_3),X_9)) ) ) ).
fof(fact_360_xt1_I10_J,axiom,
! [Z_4,Y_12,X_33] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_12),X_33))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Z_4),Y_12))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Z_4),X_33)) ) ) ).
fof(fact_361_order__less__asym,axiom,
! [X_32,Y_11] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_32),Y_11))
=> ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_11),X_32)) ) ).
fof(fact_362_order__less__asym,axiom,
! [X_9,Y_9] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_9),Y_9))
=> ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Y_9),X_9)) ) ).
fof(fact_363_order__less__asym,axiom,
! [X_32,Y_11] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_32),Y_11))
=> ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_11),X_32)) ) ).
fof(fact_364_linorder__cases,axiom,
! [X_31,Y_10] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_31),Y_10))
=> ( X_31 != Y_10
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_10),X_31)) ) ) ).
fof(fact_365_linorder__cases,axiom,
! [X_31,Y_10] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_31),Y_10))
=> ( X_31 != Y_10
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_10),X_31)) ) ) ).
fof(fact_366_list__update__append1,axiom,
! [Ys_11,X_30,I_22,Xs_62] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_22),size_s2106320494le_alt(Xs_62)))
=> hAPP_A1849759038le_alt(list_u2058984551le_alt(append28105492le_alt(Xs_62,Ys_11),I_22),X_30) = append28105492le_alt(hAPP_A1849759038le_alt(list_u2058984551le_alt(Xs_62,I_22),X_30),Ys_11) ) ).
fof(fact_367_nth__list__update,axiom,
! [X_29,J_5,I_21,Xs_61] :
( is_Arr723427730le_alt(X_29)
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_21),size_s2106320494le_alt(Xs_61)))
=> ( ( I_21 = J_5
=> hAPP_n1410269210le_alt(nth_Ar2122385664le_alt(hAPP_A1849759038le_alt(list_u2058984551le_alt(Xs_61,I_21),X_29)),J_5) = X_29 )
& ( I_21 != J_5
=> hAPP_n1410269210le_alt(nth_Ar2122385664le_alt(hAPP_A1849759038le_alt(list_u2058984551le_alt(Xs_61,I_21),X_29)),J_5) = hAPP_n1410269210le_alt(nth_Ar2122385664le_alt(Xs_61),J_5) ) ) ) ) ).
fof(fact_368_nth__list__update,axiom,
! [X_29,J_5,I_21,Xs_61] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_21),size_size_list_nat(Xs_61)))
=> ( ( I_21 = J_5
=> hAPP_nat_nat(nth_nat(hAPP_nat_list_nat(list_update_nat(Xs_61,I_21),X_29)),J_5) = X_29 )
& ( I_21 != J_5
=> hAPP_nat_nat(nth_nat(hAPP_nat_list_nat(list_update_nat(Xs_61,I_21),X_29)),J_5) = hAPP_nat_nat(nth_nat(Xs_61),J_5) ) ) ) ).
fof(fact_369_list__update__same__conv,axiom,
! [X_9,I,Xs_22] :
( is_Arr723427730le_alt(X_9)
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),size_s2106320494le_alt(Xs_22)))
=> ( hAPP_A1849759038le_alt(list_u2058984551le_alt(Xs_22,I),X_9) = Xs_22
<=> hAPP_n1410269210le_alt(nth_Ar2122385664le_alt(Xs_22),I) = X_9 ) ) ) ).
fof(fact_370_list__update__same__conv,axiom,
! [X_9,I,Xs_22] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),size_size_list_nat(Xs_22)))
=> ( hAPP_nat_list_nat(list_update_nat(Xs_22,I),X_9) = Xs_22
<=> hAPP_nat_nat(nth_nat(Xs_22),I) = X_9 ) ) ).
fof(fact_371_nth__list__update__eq,axiom,
! [X_28,I_20,Xs_60] :
( is_Arr723427730le_alt(X_28)
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_20),size_s2106320494le_alt(Xs_60)))
=> hAPP_n1410269210le_alt(nth_Ar2122385664le_alt(hAPP_A1849759038le_alt(list_u2058984551le_alt(Xs_60,I_20),X_28)),I_20) = X_28 ) ) ).
fof(fact_372_nth__list__update__eq,axiom,
! [X_28,I_20,Xs_60] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_20),size_size_list_nat(Xs_60)))
=> hAPP_nat_nat(nth_nat(hAPP_nat_list_nat(list_update_nat(Xs_60,I_20),X_28)),I_20) = X_28 ) ).
fof(fact_373_last__drop,axiom,
! [N_38,Xs_59] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_38),size_s2106320494le_alt(Xs_59)))
=> last_A1066338328le_alt(drop_A1195732799le_alt(N_38,Xs_59)) = last_A1066338328le_alt(Xs_59) ) ).
fof(fact_374_not__less__bot,axiom,
! [Aa] : ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Aa),bot_bot_bool)) ).
fof(fact_375_not__less__bot,axiom,
! [A_34] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_34),bot_bot_nat)) ).
fof(fact_376_not__less__bot,axiom,
! [Aa] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),bot_bot_fun_nat_bool)) ).
fof(fact_377_bot__less,axiom,
! [Aa] :
( ~ ( hBOOL(Aa)
<=> hBOOL(bot_bot_bool) )
<=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,bot_bot_bool),Aa)) ) ).
fof(fact_378_bot__less,axiom,
! [Aa] :
( Aa != bot_bot_nat
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,bot_bot_nat),Aa)) ) ).
fof(fact_379_bot__less,axiom,
! [Aa] :
( Aa != bot_bot_fun_nat_bool
<=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,bot_bot_fun_nat_bool),Aa)) ) ).
fof(fact_380_drop__0,axiom,
! [Xs_58] : drop_A1195732799le_alt(zero_zero_nat,Xs_58) = Xs_58 ).
fof(fact_381_drop__Nil,axiom,
! [N_37] : drop_nat(N_37,nil_nat) = nil_nat ).
fof(fact_382_drop__Nil,axiom,
! [N_37] : drop_A1195732799le_alt(N_37,nil_Ar1135217151le_alt) = nil_Ar1135217151le_alt ).
fof(fact_383_less__max__iff__disj,axiom,
! [Z_3,X_9,Y_9] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Z_3),hAPP_int_int(hAPP_int_fun_int_int(ord_max_int,X_9),Y_9)))
<=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Z_3),X_9))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Z_3),Y_9)) ) ) ).
fof(fact_384_less__max__iff__disj,axiom,
! [Z_3,X_9,Y_9] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Z_3),hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,X_9),Y_9)))
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Z_3),X_9))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Z_3),Y_9)) ) ) ).
fof(fact_385_max__less__iff__conj,axiom,
! [X_9,Y_9,Z_3] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(ord_max_int,X_9),Y_9)),Z_3))
<=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_9),Z_3))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y_9),Z_3)) ) ) ).
fof(fact_386_max__less__iff__conj,axiom,
! [X_9,Y_9,Z_3] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,X_9),Y_9)),Z_3))
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_9),Z_3))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_9),Z_3)) ) ) ).
fof(fact_387_min__max_Oless__supI1,axiom,
! [B_19,X_27,A_33] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_27),A_33))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_27),hAPP_int_int(hAPP_int_fun_int_int(ord_max_int,A_33),B_19))) ) ).
fof(fact_388_min__max_Oless__supI1,axiom,
! [B_19,X_27,A_33] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_27),A_33))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_27),hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,A_33),B_19))) ) ).
fof(fact_389_min__max_Oless__supI2,axiom,
! [A_32,X_26,B_18] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_26),B_18))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_26),hAPP_int_int(hAPP_int_fun_int_int(ord_max_int,A_32),B_18))) ) ).
fof(fact_390_min__max_Oless__supI2,axiom,
! [A_32,X_26,B_18] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_26),B_18))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_26),hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,A_32),B_18))) ) ).
fof(fact_391_distinct__drop,axiom,
! [I_19,Xs_57] :
( hBOOL(hAPP_l300482276t_bool(distin85347314le_alt,Xs_57))
=> hBOOL(hAPP_l300482276t_bool(distin85347314le_alt,drop_A1195732799le_alt(I_19,Xs_57))) ) ).
fof(fact_392_sorted__drop,axiom,
! [N_36,Xs_56] :
( hBOOL(hAPP_list_nat_bool(linorder_sorted_nat,Xs_56))
=> hBOOL(hAPP_list_nat_bool(linorder_sorted_nat,drop_nat(N_36,Xs_56))) ) ).
fof(fact_393_list__update__nonempty,axiom,
! [Xs_22,K_3,X_9] :
( hAPP_nat_list_nat(list_update_nat(Xs_22,K_3),X_9) = nil_nat
<=> Xs_22 = nil_nat ) ).
fof(fact_394_list__update__nonempty,axiom,
! [Xs_22,K_3,X_9] :
( hAPP_A1849759038le_alt(list_u2058984551le_alt(Xs_22,K_3),X_9) = nil_Ar1135217151le_alt
<=> Xs_22 = nil_Ar1135217151le_alt ) ).
fof(fact_395_list__update_Osimps_I1_J,axiom,
! [I_18,V_3] : hAPP_nat_list_nat(list_update_nat(nil_nat,I_18),V_3) = nil_nat ).
fof(fact_396_list__update_Osimps_I1_J,axiom,
! [I_18,V_3] : hAPP_A1849759038le_alt(list_u2058984551le_alt(nil_Ar1135217151le_alt,I_18),V_3) = nil_Ar1135217151le_alt ).
fof(fact_397_list__update__code_I1_J,axiom,
! [I_17,Y_8] : hAPP_nat_list_nat(list_update_nat(nil_nat,I_17),Y_8) = nil_nat ).
fof(fact_398_list__update__code_I1_J,axiom,
! [I_17,Y_8] : hAPP_A1849759038le_alt(list_u2058984551le_alt(nil_Ar1135217151le_alt,I_17),Y_8) = nil_Ar1135217151le_alt ).
fof(fact_399_length__list__update,axiom,
! [Xs_55,I_16,X_25] : size_s2106320494le_alt(hAPP_A1849759038le_alt(list_u2058984551le_alt(Xs_55,I_16),X_25)) = size_s2106320494le_alt(Xs_55) ).
fof(fact_400_list__update__id,axiom,
! [Xs_54,I_15] : hAPP_A1849759038le_alt(list_u2058984551le_alt(Xs_54,I_15),hAPP_n1410269210le_alt(nth_Ar2122385664le_alt(Xs_54),I_15)) = Xs_54 ).
fof(fact_401_list__update__id,axiom,
! [Xs_54,I_15] : hAPP_nat_list_nat(list_update_nat(Xs_54,I_15),hAPP_nat_nat(nth_nat(Xs_54),I_15)) = Xs_54 ).
fof(fact_402_nth__list__update__neq,axiom,
! [Xs_53,X_24,I_14,J_4] :
( I_14 != J_4
=> hAPP_n1410269210le_alt(nth_Ar2122385664le_alt(hAPP_A1849759038le_alt(list_u2058984551le_alt(Xs_53,I_14),X_24)),J_4) = hAPP_n1410269210le_alt(nth_Ar2122385664le_alt(Xs_53),J_4) ) ).
fof(fact_403_nth__list__update__neq,axiom,
! [Xs_53,X_24,I_14,J_4] :
( I_14 != J_4
=> hAPP_nat_nat(nth_nat(hAPP_nat_list_nat(list_update_nat(Xs_53,I_14),X_24)),J_4) = hAPP_nat_nat(nth_nat(Xs_53),J_4) ) ).
fof(fact_404_drop__butlast,axiom,
! [N_35,Xs_52] : drop_A1195732799le_alt(N_35,butlas123970891le_alt(Xs_52)) = butlas123970891le_alt(drop_A1195732799le_alt(N_35,Xs_52)) ).
fof(fact_405_butlast__drop,axiom,
! [N_34,Xs_51] : butlas123970891le_alt(drop_A1195732799le_alt(N_34,Xs_51)) = drop_A1195732799le_alt(N_34,butlas123970891le_alt(Xs_51)) ).
fof(fact_406_tl__drop,axiom,
! [N_33,Xs_50] : tl_Arr314474198le_alt(drop_A1195732799le_alt(N_33,Xs_50)) = drop_A1195732799le_alt(N_33,tl_Arr314474198le_alt(Xs_50)) ).
fof(fact_407_drop__tl,axiom,
! [N_32,Xs_49] : drop_A1195732799le_alt(N_32,tl_Arr314474198le_alt(Xs_49)) = tl_Arr314474198le_alt(drop_A1195732799le_alt(N_32,Xs_49)) ).
fof(fact_408_hd__drop__conv__nth,axiom,
! [N_31,Xs_48] :
( Xs_48 != nil_nat
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_31),size_size_list_nat(Xs_48)))
=> hd_nat(drop_nat(N_31,Xs_48)) = hAPP_nat_nat(nth_nat(Xs_48),N_31) ) ) ).
fof(fact_409_hd__drop__conv__nth,axiom,
! [N_31,Xs_48] :
( Xs_48 != nil_Ar1135217151le_alt
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_31),size_s2106320494le_alt(Xs_48)))
=> hd_Arr1814706386le_alt(drop_A1195732799le_alt(N_31,Xs_48)) = hAPP_n1410269210le_alt(nth_Ar2122385664le_alt(Xs_48),N_31) ) ) ).
fof(fact_410_nth__via__drop,axiom,
! [N_30,Xs_47,Y_7,Ys_10] :
( drop_nat(N_30,Xs_47) = cons_nat(Y_7,Ys_10)
=> hAPP_nat_nat(nth_nat(Xs_47),N_30) = Y_7 ) ).
fof(fact_411_nth__via__drop,axiom,
! [N_30,Xs_47,Y_7,Ys_10] :
( is_Arr723427730le_alt(Y_7)
=> ( drop_A1195732799le_alt(N_30,Xs_47) = cons_A77766063le_alt(Y_7,Ys_10)
=> hAPP_n1410269210le_alt(nth_Ar2122385664le_alt(Xs_47),N_30) = Y_7 ) ) ).
fof(fact_412_list__eq__iff__nth__eq,axiom,
! [Xs_22,Ys_4] :
( Xs_22 = Ys_4
<=> ( size_s2106320494le_alt(Xs_22) = size_s2106320494le_alt(Ys_4)
& ! [I_5] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_5),size_s2106320494le_alt(Xs_22)))
=> hAPP_n1410269210le_alt(nth_Ar2122385664le_alt(Xs_22),I_5) = hAPP_n1410269210le_alt(nth_Ar2122385664le_alt(Ys_4),I_5) ) ) ) ).
fof(fact_413_list__eq__iff__nth__eq,axiom,
! [Xs_22,Ys_4] :
( Xs_22 = Ys_4
<=> ( size_size_list_nat(Xs_22) = size_size_list_nat(Ys_4)
& ! [I_5] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_5),size_size_list_nat(Xs_22)))
=> hAPP_nat_nat(nth_nat(Xs_22),I_5) = hAPP_nat_nat(nth_nat(Ys_4),I_5) ) ) ) ).
fof(fact_414_list__update__code_I2_J,axiom,
! [X_23,Xs_46,Y_6] : hAPP_A1849759038le_alt(list_u2058984551le_alt(cons_A77766063le_alt(X_23,Xs_46),zero_zero_nat),Y_6) = cons_A77766063le_alt(Y_6,Xs_46) ).
fof(fact_415_nth__replicate,axiom,
! [X_22,I_13,N_29] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_13),N_29))
=> hAPP_nat_nat(nth_nat(hAPP_nat_list_nat(replicate_nat(N_29),X_22)),I_13) = X_22 ) ).
fof(fact_416_nth__replicate,axiom,
! [X_22,I_13,N_29] :
( is_Arr723427730le_alt(X_22)
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_13),N_29))
=> hAPP_n1410269210le_alt(nth_Ar2122385664le_alt(hAPP_A1849759038le_alt(replic1360561849le_alt(N_29),X_22)),I_13) = X_22 ) ) ).
fof(fact_417_length__greater__0__conv,axiom,
! [Xs_22] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),size_size_list_nat(Xs_22)))
<=> Xs_22 != nil_nat ) ).
fof(fact_418_length__greater__0__conv,axiom,
! [Xs_22] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),size_s2106320494le_alt(Xs_22)))
<=> Xs_22 != nil_Ar1135217151le_alt ) ).
fof(fact_419_distinct__conv__nth,axiom,
! [Xs_22] :
( hBOOL(hAPP_list_nat_bool(distinct_nat,Xs_22))
<=> ! [I_5] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_5),size_size_list_nat(Xs_22)))
=> ! [J_3] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,J_3),size_size_list_nat(Xs_22)))
=> ( I_5 != J_3
=> hAPP_nat_nat(nth_nat(Xs_22),I_5) != hAPP_nat_nat(nth_nat(Xs_22),J_3) ) ) ) ) ).
fof(fact_420_distinct__conv__nth,axiom,
! [Xs_22] :
( hBOOL(hAPP_l300482276t_bool(distin85347314le_alt,Xs_22))
<=> ! [I_5] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_5),size_s2106320494le_alt(Xs_22)))
=> ! [J_3] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,J_3),size_s2106320494le_alt(Xs_22)))
=> ( I_5 != J_3
=> hAPP_n1410269210le_alt(nth_Ar2122385664le_alt(Xs_22),I_5) != hAPP_n1410269210le_alt(nth_Ar2122385664le_alt(Xs_22),J_3) ) ) ) ) ).
fof(fact_421_nth__eq__iff__index__eq,axiom,
! [J_1,I,Xs_22] :
( hBOOL(hAPP_list_nat_bool(distinct_nat,Xs_22))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),size_size_list_nat(Xs_22)))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,J_1),size_size_list_nat(Xs_22)))
=> ( hAPP_nat_nat(nth_nat(Xs_22),I) = hAPP_nat_nat(nth_nat(Xs_22),J_1)
<=> I = J_1 ) ) ) ) ).
fof(fact_422_nth__eq__iff__index__eq,axiom,
! [J_1,I,Xs_22] :
( hBOOL(hAPP_l300482276t_bool(distin85347314le_alt,Xs_22))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),size_s2106320494le_alt(Xs_22)))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,J_1),size_s2106320494le_alt(Xs_22)))
=> ( hAPP_n1410269210le_alt(nth_Ar2122385664le_alt(Xs_22),I) = hAPP_n1410269210le_alt(nth_Ar2122385664le_alt(Xs_22),J_1)
<=> I = J_1 ) ) ) ) ).
fof(fact_423_bot__nat__def,axiom,
bot_bot_nat = zero_zero_nat ).
fof(fact_424_max__0R,axiom,
! [N_5] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,N_5),zero_zero_nat) = N_5 ).
fof(fact_425_nth__equalityI,axiom,
! [Xs_45,Ys_9] :
( size_s2106320494le_alt(Xs_45) = size_s2106320494le_alt(Ys_9)
=> ( ! [I_5] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_5),size_s2106320494le_alt(Xs_45)))
=> hAPP_n1410269210le_alt(nth_Ar2122385664le_alt(Xs_45),I_5) = hAPP_n1410269210le_alt(nth_Ar2122385664le_alt(Ys_9),I_5) )
=> Xs_45 = Ys_9 ) ) ).
fof(fact_426_nth__equalityI,axiom,
! [Xs_45,Ys_9] :
( size_size_list_nat(Xs_45) = size_size_list_nat(Ys_9)
=> ( ! [I_5] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_5),size_size_list_nat(Xs_45)))
=> hAPP_nat_nat(nth_nat(Xs_45),I_5) = hAPP_nat_nat(nth_nat(Ys_9),I_5) )
=> Xs_45 = Ys_9 ) ) ).
fof(fact_427_Skolem__list__nth,axiom,
! [P_1,K_3] :
( ! [I_5] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_5),K_3))
=> ? [X1] :
( is_Arr723427730le_alt(X1)
& hBOOL(hAPP_A1120018583t_bool(hAPP_n572947642t_bool(P_1,I_5),X1)) ) )
<=> ? [Xs_44] :
( size_s2106320494le_alt(Xs_44) = K_3
& ! [I_5] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_5),K_3))
=> hBOOL(hAPP_A1120018583t_bool(hAPP_n572947642t_bool(P_1,I_5),hAPP_n1410269210le_alt(nth_Ar2122385664le_alt(Xs_44),I_5))) ) ) ) ).
fof(fact_428_Skolem__list__nth,axiom,
! [P_1,K_3] :
( ! [I_5] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_5),K_3))
=> ? [X1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(P_1,I_5),X1)) )
<=> ? [Xs_44] :
( size_size_list_nat(Xs_44) = K_3
& ! [I_5] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_5),K_3))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(P_1,I_5),hAPP_nat_nat(nth_nat(Xs_44),I_5))) ) ) ) ).
fof(fact_429_dropWhile__nth,axiom,
! [J_1,P_1,Xs_22] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,J_1),size_size_list_nat(dropWhile_nat(P_1,Xs_22))))
=> hAPP_nat_nat(nth_nat(dropWhile_nat(P_1,Xs_22)),J_1) = hAPP_nat_nat(nth_nat(Xs_22),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J_1),size_size_list_nat(takeWhile_nat(P_1,Xs_22)))) ) ).
fof(fact_430_dropWhile__nth,axiom,
! [J_1,P_1,Xs_22] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,J_1),size_s2106320494le_alt(dropWh1165804960le_alt(P_1,Xs_22))))
=> hAPP_n1410269210le_alt(nth_Ar2122385664le_alt(dropWh1165804960le_alt(P_1,Xs_22)),J_1) = hAPP_n1410269210le_alt(nth_Ar2122385664le_alt(Xs_22),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J_1),size_s2106320494le_alt(takeWh1545314552le_alt(P_1,Xs_22)))) ) ).
fof(fact_431_nth__drop_H,axiom,
! [I_12,Xs_43] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_12),size_size_list_nat(Xs_43)))
=> cons_nat(hAPP_nat_nat(nth_nat(Xs_43),I_12),drop_nat(hAPP_nat_nat(suc,I_12),Xs_43)) = drop_nat(I_12,Xs_43) ) ).
fof(fact_432_nth__drop_H,axiom,
! [I_12,Xs_43] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_12),size_s2106320494le_alt(Xs_43)))
=> cons_A77766063le_alt(hAPP_n1410269210le_alt(nth_Ar2122385664le_alt(Xs_43),I_12),drop_A1195732799le_alt(hAPP_nat_nat(suc,I_12),Xs_43)) = drop_A1195732799le_alt(I_12,Xs_43) ) ).
fof(fact_433_list__ex__length,axiom,
! [P_1,Xs_22] :
( hBOOL(hAPP_l300482276t_bool(list_e1101825597le_alt(P_1),Xs_22))
<=> ? [N_7] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_7),size_s2106320494le_alt(Xs_22)))
& hBOOL(hAPP_A1120018583t_bool(P_1,hAPP_n1410269210le_alt(nth_Ar2122385664le_alt(Xs_22),N_7))) ) ) ).
fof(fact_434_list__ex__length,axiom,
! [P_1,Xs_22] :
( hBOOL(hAPP_list_nat_bool(list_ex_nat(P_1),Xs_22))
<=> ? [N_7] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_7),size_size_list_nat(Xs_22)))
& hBOOL(hAPP_nat_bool(P_1,hAPP_nat_nat(nth_nat(Xs_22),N_7))) ) ) ).
fof(fact_435_lessI,axiom,
! [N_5] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_5),hAPP_nat_nat(suc,N_5))) ).
fof(fact_436_Suc__mono,axiom,
! [M,N_5] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N_5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M)),hAPP_nat_nat(suc,N_5))) ) ).
fof(fact_437_zero__less__Suc,axiom,
! [N_5] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(suc,N_5))) ).
fof(fact_438_Suc__inject,axiom,
! [X,Y] :
( hAPP_nat_nat(suc,X) = hAPP_nat_nat(suc,Y)
=> X = Y ) ).
fof(fact_439_nat__add__right__cancel,axiom,
! [M_1,K_3,N_12] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),K_3) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_12),K_3)
<=> M_1 = N_12 ) ).
fof(fact_440_nat__add__left__cancel,axiom,
! [K_3,M_1,N_12] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K_3),M_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K_3),N_12)
<=> M_1 = N_12 ) ).
fof(fact_441_nat__add__assoc,axiom,
! [M,N_5,K_4] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),N_5)),K_4) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_5),K_4)) ).
fof(fact_442_nat_Oinject,axiom,
! [Nat_4,Nat_3] :
( hAPP_nat_nat(suc,Nat_4) = hAPP_nat_nat(suc,Nat_3)
<=> Nat_4 = Nat_3 ) ).
fof(fact_443_add__Suc__shift,axiom,
! [M,N_5] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(suc,M)),N_5) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),hAPP_nat_nat(suc,N_5)) ).
fof(fact_444_add__Suc,axiom,
! [M,N_5] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(suc,M)),N_5) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),N_5)) ).
fof(fact_445_nat__add__left__commute,axiom,
! [X,Y,Z_1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Y),Z_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Y),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X),Z_1)) ).
fof(fact_446_add__Suc__right,axiom,
! [M,N_5] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),hAPP_nat_nat(suc,N_5)) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),N_5)) ).
fof(fact_447_nat__add__commute,axiom,
! [M,N_5] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),N_5) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_5),M) ).
fof(fact_448_less__iff__Suc__add,axiom,
! [M_1,N_12] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_12))
<=> ? [K_6] : N_12 = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),K_6)) ) ).
fof(fact_449_less__add__Suc2,axiom,
! [I_3,M] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_3),hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),I_3)))) ).
fof(fact_450_less__add__Suc1,axiom,
! [I_3,M] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_3),hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_3),M)))) ).
fof(fact_451_Suc__n__not__n,axiom,
! [N_5] : hAPP_nat_nat(suc,N_5) != N_5 ).
fof(fact_452_n__not__Suc__n,axiom,
! [N_5] : N_5 != hAPP_nat_nat(suc,N_5) ).
fof(fact_453_add__is__1,axiom,
! [M_1,N_12] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),N_12) = hAPP_nat_nat(suc,zero_zero_nat)
<=> ( ( M_1 = hAPP_nat_nat(suc,zero_zero_nat)
& N_12 = zero_zero_nat )
| ( M_1 = zero_zero_nat
& N_12 = hAPP_nat_nat(suc,zero_zero_nat) ) ) ) ).
fof(fact_454_one__is__add,axiom,
! [M_1,N_12] :
( hAPP_nat_nat(suc,zero_zero_nat) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),N_12)
<=> ( ( M_1 = hAPP_nat_nat(suc,zero_zero_nat)
& N_12 = zero_zero_nat )
| ( M_1 = zero_zero_nat
& N_12 = hAPP_nat_nat(suc,zero_zero_nat) ) ) ) ).
fof(fact_455_add__right__imp__eq,axiom,
! [B_17,A_31,C_18] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_17),A_31) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_18),A_31)
=> B_17 = C_18 ) ).
fof(fact_456_add__right__imp__eq,axiom,
! [B_17,A_31,C_18] :
( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,B_17),A_31) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,C_18),A_31)
=> B_17 = C_18 ) ).
fof(fact_457_add__imp__eq,axiom,
! [A_30,B_16,C_17] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_30),B_16) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_30),C_17)
=> B_16 = C_17 ) ).
fof(fact_458_add__imp__eq,axiom,
! [A_30,B_16,C_17] :
( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_30),B_16) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_30),C_17)
=> B_16 = C_17 ) ).
fof(fact_459_add__left__imp__eq,axiom,
! [A_29,B_15,C_16] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_29),B_15) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_29),C_16)
=> B_15 = C_16 ) ).
fof(fact_460_add__left__imp__eq,axiom,
! [A_29,B_15,C_16] :
( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_29),B_15) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_29),C_16)
=> B_15 = C_16 ) ).
fof(fact_461_add__right__cancel,axiom,
! [Ba,Aa,C_1] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Ba),Aa) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_1),Aa)
<=> Ba = C_1 ) ).
fof(fact_462_add__right__cancel,axiom,
! [Ba,Aa,C_1] :
( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Ba),Aa) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,C_1),Aa)
<=> Ba = C_1 ) ).
fof(fact_463_add__left__cancel,axiom,
! [Aa,Ba,C_1] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Aa),Ba) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Aa),C_1)
<=> Ba = C_1 ) ).
fof(fact_464_add__left__cancel,axiom,
! [Aa,Ba,C_1] :
( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Aa),Ba) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Aa),C_1)
<=> Ba = C_1 ) ).
fof(fact_465_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
! [A_28,B_14,C_15] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_28),B_14)),C_15) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_28),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_14),C_15)) ).
fof(fact_466_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
! [A_28,B_14,C_15] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_28),B_14)),C_15) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_28),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,B_14),C_15)) ).
fof(fact_467_add_Ocomm__neutral,axiom,
! [A_27] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_27),zero_zero_nat) = A_27 ).
fof(fact_468_add_Ocomm__neutral,axiom,
! [A_27] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_27),zero_zero_int) = A_27 ).
fof(fact_469_add__0__right,axiom,
! [A_26] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_26),zero_zero_nat) = A_26 ).
fof(fact_470_add__0__right,axiom,
! [A_26] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_26),zero_zero_int) = A_26 ).
fof(fact_471_double__zero__sym,axiom,
! [Aa] :
( zero_zero_int = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Aa),Aa)
<=> Aa = zero_zero_int ) ).
fof(fact_472_add__0,axiom,
! [A_25] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,zero_zero_nat),A_25) = A_25 ).
fof(fact_473_add__0,axiom,
! [A_25] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,zero_zero_int),A_25) = A_25 ).
fof(fact_474_add__0__left,axiom,
! [A_24] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,zero_zero_nat),A_24) = A_24 ).
fof(fact_475_add__0__left,axiom,
! [A_24] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,zero_zero_int),A_24) = A_24 ).
fof(fact_476_add__less__imp__less__left,axiom,
! [C_14,A_23,B_13] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_14),A_23)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_14),B_13)))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_23),B_13)) ) ).
fof(fact_477_add__less__imp__less__left,axiom,
! [C_14,A_23,B_13] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,C_14),A_23)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,C_14),B_13)))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_23),B_13)) ) ).
fof(fact_478_add__less__imp__less__right,axiom,
! [A_22,C_13,B_12] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_22),C_13)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_12),C_13)))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_22),B_12)) ) ).
fof(fact_479_add__less__imp__less__right,axiom,
! [A_22,C_13,B_12] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_22),C_13)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,B_12),C_13)))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_22),B_12)) ) ).
fof(fact_480_add__strict__mono,axiom,
! [C_12,D_5,A_21,B_11] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_21),B_11))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,C_12),D_5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_21),C_12)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_11),D_5))) ) ) ).
fof(fact_481_add__strict__mono,axiom,
! [C_12,D_5,A_21,B_11] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_21),B_11))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,C_12),D_5))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_21),C_12)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,B_11),D_5))) ) ) ).
fof(fact_482_add__strict__left__mono,axiom,
! [C_11,A_20,B_10] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_20),B_10))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_11),A_20)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_11),B_10))) ) ).
fof(fact_483_add__strict__left__mono,axiom,
! [C_11,A_20,B_10] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_20),B_10))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,C_11),A_20)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,C_11),B_10))) ) ).
fof(fact_484_add__strict__right__mono,axiom,
! [C_10,A_19,B_9] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_19),B_9))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_19),C_10)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_9),C_10))) ) ).
fof(fact_485_add__strict__right__mono,axiom,
! [C_10,A_19,B_9] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_19),B_9))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_19),C_10)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,B_9),C_10))) ) ).
fof(fact_486_add__less__cancel__left,axiom,
! [C_1,Aa,Ba] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_1),Aa)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_1),Ba)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),Ba)) ) ).
fof(fact_487_add__less__cancel__left,axiom,
! [C_1,Aa,Ba] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,C_1),Aa)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,C_1),Ba)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Aa),Ba)) ) ).
fof(fact_488_add__less__cancel__right,axiom,
! [Aa,C_1,Ba] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Aa),C_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Ba),C_1)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),Ba)) ) ).
fof(fact_489_add__less__cancel__right,axiom,
! [Aa,C_1,Ba] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Aa),C_1)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Ba),C_1)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Aa),Ba)) ) ).
fof(fact_490_Zero__not__Suc,axiom,
! [M] : zero_zero_nat != hAPP_nat_nat(suc,M) ).
fof(fact_491_nat_Osimps_I2_J,axiom,
! [Nat_2] : zero_zero_nat != hAPP_nat_nat(suc,Nat_2) ).
fof(fact_492_Suc__not__Zero,axiom,
! [M] : hAPP_nat_nat(suc,M) != zero_zero_nat ).
fof(fact_493_nat_Osimps_I3_J,axiom,
! [Nat_1] : hAPP_nat_nat(suc,Nat_1) != zero_zero_nat ).
fof(fact_494_Zero__neq__Suc,axiom,
! [M] : zero_zero_nat != hAPP_nat_nat(suc,M) ).
fof(fact_495_Suc__neq__Zero,axiom,
! [M] : hAPP_nat_nat(suc,M) != zero_zero_nat ).
fof(fact_496_not__less__eq,axiom,
! [M_1,N_12] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_12))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_12),hAPP_nat_nat(suc,M_1))) ) ).
fof(fact_497_less__Suc__eq,axiom,
! [M_1,N_12] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),hAPP_nat_nat(suc,N_12)))
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_12))
| M_1 = N_12 ) ) ).
fof(fact_498_Suc__less__eq,axiom,
! [M_1,N_12] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M_1)),hAPP_nat_nat(suc,N_12)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_12)) ) ).
fof(fact_499_not__less__less__Suc__eq,axiom,
! [N_12,M_1] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_12),M_1))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_12),hAPP_nat_nat(suc,M_1)))
<=> N_12 = M_1 ) ) ).
fof(fact_500_less__antisym,axiom,
! [N_5,M] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_5),M))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_5),hAPP_nat_nat(suc,M)))
=> M = N_5 ) ) ).
fof(fact_501_less__SucI,axiom,
! [M,N_5] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N_5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),hAPP_nat_nat(suc,N_5))) ) ).
fof(fact_502_Suc__lessI,axiom,
! [M,N_5] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N_5))
=> ( hAPP_nat_nat(suc,M) != N_5
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M)),N_5)) ) ) ).
fof(fact_503_less__trans__Suc,axiom,
! [K_4,I_3,J] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_3),J))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,J),K_4))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,I_3)),K_4)) ) ) ).
fof(fact_504_less__SucE,axiom,
! [M,N_5] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),hAPP_nat_nat(suc,N_5)))
=> ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N_5))
=> M = N_5 ) ) ).
fof(fact_505_Suc__lessD,axiom,
! [M,N_5] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M)),N_5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N_5)) ) ).
fof(fact_506_Suc__less__SucD,axiom,
! [M,N_5] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M)),hAPP_nat_nat(suc,N_5)))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N_5)) ) ).
fof(fact_507_not__psubset__empty,axiom,
! [A] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,A),bot_bot_fun_nat_bool)) ).
fof(fact_508_plus__nat_Oadd__0,axiom,
! [N_5] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,zero_zero_nat),N_5) = N_5 ).
fof(fact_509_Nat_Oadd__0__right,axiom,
! [M] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),zero_zero_nat) = M ).
fof(fact_510_add__is__0,axiom,
! [M_1,N_12] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),N_12) = zero_zero_nat
<=> ( M_1 = zero_zero_nat
& N_12 = zero_zero_nat ) ) ).
fof(fact_511_add__eq__self__zero,axiom,
! [M,N_5] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),N_5) = M
=> N_5 = zero_zero_nat ) ).
fof(fact_512_not__add__less1,axiom,
! [I_3,J] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_3),J)),I_3)) ).
fof(fact_513_not__add__less2,axiom,
! [J,I_3] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J),I_3)),I_3)) ).
fof(fact_514_nat__add__left__cancel__less,axiom,
! [K_3,M_1,N_12] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K_3),M_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K_3),N_12)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_12)) ) ).
fof(fact_515_trans__less__add1,axiom,
! [M,I_3,J] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_3),J))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_3),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J),M))) ) ).
fof(fact_516_trans__less__add2,axiom,
! [M,I_3,J] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_3),J))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_3),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),J))) ) ).
fof(fact_517_add__less__mono1,axiom,
! [K_4,I_3,J] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_3),J))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_3),K_4)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J),K_4))) ) ).
fof(fact_518_add__less__mono,axiom,
! [K_4,L,I_3,J] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_3),J))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,K_4),L))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_3),K_4)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J),L))) ) ) ).
fof(fact_519_less__add__eq__less,axiom,
! [M,N_5,K_4,L] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,K_4),L))
=> ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),L) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K_4),N_5)
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N_5)) ) ) ).
fof(fact_520_add__lessD1,axiom,
! [I_3,J,K_4] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_3),J)),K_4))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_3),K_4)) ) ).
fof(fact_521_max__add__distrib__left,axiom,
! [X_21,Y_5,Z_2] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,X_21),Y_5)),Z_2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X_21),Z_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Y_5),Z_2)) ).
fof(fact_522_max__add__distrib__left,axiom,
! [X_21,Y_5,Z_2] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(ord_max_int,X_21),Y_5)),Z_2) = hAPP_int_int(hAPP_int_fun_int_int(ord_max_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X_21),Z_2)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Y_5),Z_2)) ).
fof(fact_523_drop__drop,axiom,
! [N_28,M_4,Xs_42] : drop_A1195732799le_alt(N_28,drop_A1195732799le_alt(M_4,Xs_42)) = drop_A1195732799le_alt(hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_28),M_4),Xs_42) ).
fof(fact_524_max__Suc__Suc,axiom,
! [M,N_5] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,hAPP_nat_nat(suc,M)),hAPP_nat_nat(suc,N_5)) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,M),N_5)) ).
fof(fact_525_list_Osize_I4_J,axiom,
! [A_18,List_1] : size_s2106320494le_alt(cons_A77766063le_alt(A_18,List_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,size_s2106320494le_alt(List_1)),hAPP_nat_nat(suc,zero_zero_nat)) ).
fof(fact_526_list_Osize_I2_J,axiom,
! [Fa,Aa,List] : list_s99318913le_alt(Fa,cons_A77766063le_alt(Aa,List)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_A533009232lt_nat(Fa,Aa)),list_s99318913le_alt(Fa,List))),hAPP_nat_nat(suc,zero_zero_nat)) ).
fof(fact_527_list__ex__simps_I1_J,axiom,
! [P_1,X_9,Xs_22] :
( hBOOL(hAPP_l300482276t_bool(list_e1101825597le_alt(P_1),cons_A77766063le_alt(X_9,Xs_22)))
<=> ( hBOOL(hAPP_A1120018583t_bool(P_1,X_9))
| hBOOL(hAPP_l300482276t_bool(list_e1101825597le_alt(P_1),Xs_22)) ) ) ).
fof(fact_528_list__ex__simps_I2_J,axiom,
! [P_1] : ~ hBOOL(hAPP_list_nat_bool(list_ex_nat(P_1),nil_nat)) ).
fof(fact_529_list__ex__simps_I2_J,axiom,
! [P_1] : ~ hBOOL(hAPP_l300482276t_bool(list_e1101825597le_alt(P_1),nil_Ar1135217151le_alt)) ).
fof(fact_530_list__ex__append,axiom,
! [P_1,Xs_22,Ys_4] :
( hBOOL(hAPP_l300482276t_bool(list_e1101825597le_alt(P_1),append28105492le_alt(Xs_22,Ys_4)))
<=> ( hBOOL(hAPP_l300482276t_bool(list_e1101825597le_alt(P_1),Xs_22))
| hBOOL(hAPP_l300482276t_bool(list_e1101825597le_alt(P_1),Ys_4)) ) ) ).
fof(fact_531_zero__less__double__add__iff__zero__less__single__add,axiom,
! [Aa] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Aa),Aa)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),Aa)) ) ).
fof(fact_532_double__add__less__zero__iff__single__add__less__zero,axiom,
! [Aa] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Aa),Aa)),zero_zero_int))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Aa),zero_zero_int)) ) ).
fof(fact_533_add__pos__pos,axiom,
! [B_8,A_17] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),A_17))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),B_8))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_17),B_8))) ) ) ).
fof(fact_534_add__pos__pos,axiom,
! [B_8,A_17] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_17))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_8))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_17),B_8))) ) ) ).
fof(fact_535_add__neg__neg,axiom,
! [B_7,A_16] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_16),zero_zero_nat))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_7),zero_zero_nat))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_16),B_7)),zero_zero_nat)) ) ) ).
fof(fact_536_add__neg__neg,axiom,
! [B_7,A_16] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_16),zero_zero_int))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_7),zero_zero_int))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_16),B_7)),zero_zero_int)) ) ) ).
fof(fact_537_list__ex__rev,axiom,
! [P_1,Xs_22] :
( hBOOL(hAPP_list_nat_bool(list_ex_nat(P_1),rev_nat(Xs_22)))
<=> hBOOL(hAPP_list_nat_bool(list_ex_nat(P_1),Xs_22)) ) ).
fof(fact_538_list__ex__rev,axiom,
! [P_1,Xs_22] :
( hBOOL(hAPP_l300482276t_bool(list_e1101825597le_alt(P_1),rev_Ar955429983le_alt(Xs_22)))
<=> hBOOL(hAPP_l300482276t_bool(list_e1101825597le_alt(P_1),Xs_22)) ) ).
fof(fact_539_gr0__conv__Suc,axiom,
! [N_12] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_12))
<=> ? [M_2] : N_12 = hAPP_nat_nat(suc,M_2) ) ).
fof(fact_540_less__Suc0,axiom,
! [N_12] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_12),hAPP_nat_nat(suc,zero_zero_nat)))
<=> N_12 = zero_zero_nat ) ).
fof(fact_541_less__Suc__eq__0__disj,axiom,
! [M_1,N_12] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),hAPP_nat_nat(suc,N_12)))
<=> ( M_1 = zero_zero_nat
| ? [J_3] :
( M_1 = hAPP_nat_nat(suc,J_3)
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,J_3),N_12)) ) ) ) ).
fof(fact_542_add__gr__0,axiom,
! [M_1,N_12] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),N_12)))
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),M_1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_12)) ) ) ).
fof(fact_543_nth__Cons__Suc,axiom,
! [X_20,Xs_41,N_27] : hAPP_nat_nat(nth_nat(cons_nat(X_20,Xs_41)),hAPP_nat_nat(suc,N_27)) = hAPP_nat_nat(nth_nat(Xs_41),N_27) ).
fof(fact_544_nth__Cons__Suc,axiom,
! [X_20,Xs_41,N_27] : hAPP_n1410269210le_alt(nth_Ar2122385664le_alt(cons_A77766063le_alt(X_20,Xs_41)),hAPP_nat_nat(suc,N_27)) = hAPP_n1410269210le_alt(nth_Ar2122385664le_alt(Xs_41),N_27) ).
fof(fact_545_length__append,axiom,
! [Xs_40,Ys_8] : size_s2106320494le_alt(append28105492le_alt(Xs_40,Ys_8)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,size_s2106320494le_alt(Xs_40)),size_s2106320494le_alt(Ys_8)) ).
fof(fact_546_drop__Suc__Cons,axiom,
! [N_26,X_19,Xs_39] : drop_A1195732799le_alt(hAPP_nat_nat(suc,N_26),cons_A77766063le_alt(X_19,Xs_39)) = drop_A1195732799le_alt(N_26,Xs_39) ).
fof(fact_547_list__update__code_I3_J,axiom,
! [X_18,Xs_38,I_11,Y_4] : hAPP_A1849759038le_alt(list_u2058984551le_alt(cons_A77766063le_alt(X_18,Xs_38),hAPP_nat_nat(suc,I_11)),Y_4) = cons_A77766063le_alt(X_18,hAPP_A1849759038le_alt(list_u2058984551le_alt(Xs_38,I_11),Y_4)) ).
fof(fact_548_replicate__Suc,axiom,
! [N_25,X_17] : hAPP_A1849759038le_alt(replic1360561849le_alt(hAPP_nat_nat(suc,N_25)),X_17) = cons_A77766063le_alt(X_17,hAPP_A1849759038le_alt(replic1360561849le_alt(N_25),X_17)) ).
fof(fact_549_replicate__add,axiom,
! [N_24,M_3,X_16] : hAPP_A1849759038le_alt(replic1360561849le_alt(hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_24),M_3)),X_16) = append28105492le_alt(hAPP_A1849759038le_alt(replic1360561849le_alt(N_24),X_16),hAPP_A1849759038le_alt(replic1360561849le_alt(M_3),X_16)) ).
fof(fact_550_drop__Suc,axiom,
! [N_23,Xs_37] : drop_A1195732799le_alt(hAPP_nat_nat(suc,N_23),Xs_37) = drop_A1195732799le_alt(N_23,tl_Arr314474198le_alt(Xs_37)) ).
fof(fact_551_length__splice,axiom,
! [Xs_36,Ys_7] : size_s2106320494le_alt(splice1369921490le_alt(Xs_36,Ys_7)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,size_s2106320494le_alt(Xs_36)),size_s2106320494le_alt(Ys_7)) ).
fof(fact_552_nth__append__length__plus,axiom,
! [Xs_35,Ys_6,N_22] : hAPP_nat_nat(nth_nat(append_nat(Xs_35,Ys_6)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,size_size_list_nat(Xs_35)),N_22)) = hAPP_nat_nat(nth_nat(Ys_6),N_22) ).
fof(fact_553_nth__append__length__plus,axiom,
! [Xs_35,Ys_6,N_22] : hAPP_n1410269210le_alt(nth_Ar2122385664le_alt(append28105492le_alt(Xs_35,Ys_6)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,size_s2106320494le_alt(Xs_35)),N_22)) = hAPP_n1410269210le_alt(nth_Ar2122385664le_alt(Ys_6),N_22) ).
fof(fact_554_less__imp__Suc__add,axiom,
! [M,N_5] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N_5))
=> ? [K_6] : N_5 = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),K_6)) ) ).
fof(fact_555_length__Suc__conv,axiom,
! [Xs_22,N_12] :
( size_s2106320494le_alt(Xs_22) = hAPP_nat_nat(suc,N_12)
<=> ? [Y_3,Ys_5] :
( is_Arr723427730le_alt(Y_3)
& Xs_22 = cons_A77766063le_alt(Y_3,Ys_5)
& size_s2106320494le_alt(Ys_5) = N_12 ) ) ).
fof(fact_556_Suc__length__conv,axiom,
! [N_12,Xs_22] :
( hAPP_nat_nat(suc,N_12) = size_s2106320494le_alt(Xs_22)
<=> ? [Y_3,Ys_5] :
( is_Arr723427730le_alt(Y_3)
& Xs_22 = cons_A77766063le_alt(Y_3,Ys_5)
& size_s2106320494le_alt(Ys_5) = N_12 ) ) ).
fof(fact_557_less__imp__add__positive,axiom,
! [I_3,J] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_3),J))
=> ? [K_6] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K_6))
& hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_3),K_6) = J ) ) ).
fof(fact_558_psubsetD,axiom,
! [C_1,A,B] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le1912455174t_bool,A),B))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,C_1),A))
=> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,C_1),B)) ) ) ).
fof(fact_559_psubsetD,axiom,
! [C_1,A,B] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,A),B))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_1),A))
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_1),B)) ) ) ).
fof(fact_560_gr0__implies__Suc,axiom,
! [N_5] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_5))
=> ? [M_2] : N_5 = hAPP_nat_nat(suc,M_2) ) ).
fof(fact_561_lift__Suc__mono__less,axiom,
! [N_12,N_21,F] :
( ! [N_7] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(F,N_7)),hAPP_nat_nat(F,hAPP_nat_nat(suc,N_7))))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_12),N_21))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(F,N_12)),hAPP_nat_nat(F,N_21))) ) ) ).
fof(fact_562_lift__Suc__mono__less__iff,axiom,
! [N_12,M_1,F] :
( ! [N_7] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(F,N_7)),hAPP_nat_nat(F,hAPP_nat_nat(suc,N_7))))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(F,N_12)),hAPP_nat_nat(F,M_1)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_12),M_1)) ) ) ).
fof(fact_563_even__less__0__iff,axiom,
! [Aa] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Aa),Aa)),zero_zero_int))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Aa),zero_zero_int)) ) ).
fof(fact_564_pos__add__strict,axiom,
! [B_6,C_9,A_15] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_15))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_6),C_9))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_6),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_15),C_9))) ) ) ).
fof(fact_565_pos__add__strict,axiom,
! [B_6,C_9,A_15] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),A_15))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_6),C_9))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_6),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_15),C_9))) ) ) ).
fof(fact_566_double__eq__0__iff,axiom,
! [Aa] :
( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Aa),Aa) = zero_zero_int
<=> Aa = zero_zero_int ) ).
fof(fact_567_lessE,axiom,
! [I_3,K_4] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_3),K_4))
=> ( K_4 != hAPP_nat_nat(suc,I_3)
=> ~ ! [J_3] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_3),J_3))
=> K_4 != hAPP_nat_nat(suc,J_3) ) ) ) ).
fof(fact_568_Suc__lessE,axiom,
! [I_3,K_4] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,I_3)),K_4))
=> ~ ! [J_3] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_3),J_3))
=> K_4 != hAPP_nat_nat(suc,J_3) ) ) ).
fof(fact_569_nat_Oexhaust,axiom,
! [Y] :
( Y != zero_zero_nat
=> ~ ! [Nat] : Y != hAPP_nat_nat(suc,Nat) ) ).
fof(fact_570_not0__implies__Suc,axiom,
! [N_5] :
( N_5 != zero_zero_nat
=> ? [M_2] : N_5 = hAPP_nat_nat(suc,M_2) ) ).
fof(fact_571_nat__induct,axiom,
! [N_12,P_1] :
( hBOOL(hAPP_nat_bool(P_1,zero_zero_nat))
=> ( ! [N_7] :
( hBOOL(hAPP_nat_bool(P_1,N_7))
=> hBOOL(hAPP_nat_bool(P_1,hAPP_nat_nat(suc,N_7))) )
=> hBOOL(hAPP_nat_bool(P_1,N_12)) ) ) ).
fof(fact_572_zero__induct,axiom,
! [P_1,K_3] :
( hBOOL(hAPP_nat_bool(P_1,K_3))
=> ( ! [N_7] :
( hBOOL(hAPP_nat_bool(P_1,hAPP_nat_nat(suc,N_7)))
=> hBOOL(hAPP_nat_bool(P_1,N_7)) )
=> hBOOL(hAPP_nat_bool(P_1,zero_zero_nat)) ) ) ).
fof(fact_573_take__hd__drop,axiom,
! [N_20,Xs_34] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_20),size_s2106320494le_alt(Xs_34)))
=> append28105492le_alt(take_A463070695le_alt(N_20,Xs_34),cons_A77766063le_alt(hd_Arr1814706386le_alt(drop_A1195732799le_alt(N_20,Xs_34)),nil_Ar1135217151le_alt)) = take_A463070695le_alt(hAPP_nat_nat(suc,N_20),Xs_34) ) ).
fof(fact_574_take__tl,axiom,
! [N_19,Xs_33] : take_A463070695le_alt(N_19,tl_Arr314474198le_alt(Xs_33)) = tl_Arr314474198le_alt(take_A463070695le_alt(hAPP_nat_nat(suc,N_19),Xs_33)) ).
fof(fact_575_take__Nil,axiom,
! [N_18] : take_A463070695le_alt(N_18,nil_Ar1135217151le_alt) = nil_Ar1135217151le_alt ).
fof(fact_576_distinct__take,axiom,
! [I_10,Xs_32] :
( hBOOL(hAPP_l300482276t_bool(distin85347314le_alt,Xs_32))
=> hBOOL(hAPP_l300482276t_bool(distin85347314le_alt,take_A463070695le_alt(I_10,Xs_32))) ) ).
fof(fact_577_takeWhile__eq__take,axiom,
! [P_1,Xs_22] : takeWh1545314552le_alt(P_1,Xs_22) = take_A463070695le_alt(size_s2106320494le_alt(takeWh1545314552le_alt(P_1,Xs_22)),Xs_22) ).
fof(fact_578_append__take__drop__id,axiom,
! [N_17,Xs_31] : append28105492le_alt(take_A463070695le_alt(N_17,Xs_31),drop_A1195732799le_alt(N_17,Xs_31)) = Xs_31 ).
fof(fact_579_take__Suc__Cons,axiom,
! [N_16,X_15,Xs_30] : take_A463070695le_alt(hAPP_nat_nat(suc,N_16),cons_A77766063le_alt(X_15,Xs_30)) = cons_A77766063le_alt(X_15,take_A463070695le_alt(N_16,Xs_30)) ).
fof(fact_580_take__eq__Nil,axiom,
! [N_12,Xs_22] :
( take_A463070695le_alt(N_12,Xs_22) = nil_Ar1135217151le_alt
<=> ( N_12 = zero_zero_nat
| Xs_22 = nil_Ar1135217151le_alt ) ) ).
fof(fact_581_take__0,axiom,
! [Xs_29] : take_A463070695le_alt(zero_zero_nat,Xs_29) = nil_Ar1135217151le_alt ).
fof(fact_582_append__eq__conv__conj,axiom,
! [Xs_22,Ys_4,Zs] :
( append28105492le_alt(Xs_22,Ys_4) = Zs
<=> ( Xs_22 = take_A463070695le_alt(size_s2106320494le_alt(Xs_22),Zs)
& Ys_4 = drop_A1195732799le_alt(size_s2106320494le_alt(Xs_22),Zs) ) ) ).
fof(fact_583_take__add,axiom,
! [I_9,J_2,Xs_28] : take_A463070695le_alt(hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_9),J_2),Xs_28) = append28105492le_alt(take_A463070695le_alt(I_9,Xs_28),take_A463070695le_alt(J_2,drop_A1195732799le_alt(I_9,Xs_28))) ).
fof(fact_584_take__butlast,axiom,
! [N_15,Xs_27] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_15),size_s2106320494le_alt(Xs_27)))
=> take_A463070695le_alt(N_15,butlas123970891le_alt(Xs_27)) = take_A463070695le_alt(N_15,Xs_27) ) ).
fof(fact_585_take__Suc,axiom,
! [N_14,Xs_26] :
( Xs_26 != nil_Ar1135217151le_alt
=> take_A463070695le_alt(hAPP_nat_nat(suc,N_14),Xs_26) = cons_A77766063le_alt(hd_Arr1814706386le_alt(Xs_26),take_A463070695le_alt(N_14,tl_Arr314474198le_alt(Xs_26))) ) ).
fof(fact_586_take__Suc__conv__app__nth,axiom,
! [I_8,Xs_25] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_8),size_s2106320494le_alt(Xs_25)))
=> take_A463070695le_alt(hAPP_nat_nat(suc,I_8),Xs_25) = append28105492le_alt(take_A463070695le_alt(I_8,Xs_25),cons_A77766063le_alt(hAPP_n1410269210le_alt(nth_Ar2122385664le_alt(Xs_25),I_8),nil_Ar1135217151le_alt)) ) ).
fof(fact_587_id__take__nth__drop,axiom,
! [I_7,Xs_24] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_7),size_s2106320494le_alt(Xs_24)))
=> Xs_24 = append28105492le_alt(take_A463070695le_alt(I_7,Xs_24),cons_A77766063le_alt(hAPP_n1410269210le_alt(nth_Ar2122385664le_alt(Xs_24),I_7),drop_A1195732799le_alt(hAPP_nat_nat(suc,I_7),Xs_24))) ) ).
fof(fact_588_upd__conv__take__nth__drop,axiom,
! [A_14,I_6,Xs_23] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_6),size_s2106320494le_alt(Xs_23)))
=> hAPP_A1849759038le_alt(list_u2058984551le_alt(Xs_23,I_6),A_14) = append28105492le_alt(take_A463070695le_alt(I_6,Xs_23),cons_A77766063le_alt(A_14,drop_A1195732799le_alt(hAPP_nat_nat(suc,I_6),Xs_23))) ) ).
fof(fact_589_takeWhile__eq__take__P__nth,axiom,
! [P_1,Xs_22,N_12] :
( ! [I_5] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_5),N_12))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_5),size_s2106320494le_alt(Xs_22)))
=> hBOOL(hAPP_A1120018583t_bool(P_1,hAPP_n1410269210le_alt(nth_Ar2122385664le_alt(Xs_22),I_5))) ) )
=> ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_12),size_s2106320494le_alt(Xs_22)))
=> ~ hBOOL(hAPP_A1120018583t_bool(P_1,hAPP_n1410269210le_alt(nth_Ar2122385664le_alt(Xs_22),N_12))) )
=> takeWh1545314552le_alt(P_1,Xs_22) = take_A463070695le_alt(N_12,Xs_22) ) ) ).
fof(fact_590_termination__basic__simps_I1_J,axiom,
! [Z_1,X,Y] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X),Y))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Y),Z_1))) ) ).
fof(fact_591_termination__basic__simps_I2_J,axiom,
! [Y,X,Z_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X),Z_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Y),Z_1))) ) ).
fof(fact_592_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom,
! [A_13] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,zero_zero_int),A_13) = A_13 ).
fof(fact_593_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom,
! [A_13] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,zero_zero_nat),A_13) = A_13 ).
fof(fact_594_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom,
! [A_12] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_12),zero_zero_int) = A_12 ).
fof(fact_595_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom,
! [A_12] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_12),zero_zero_nat) = A_12 ).
fof(fact_596_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom,
! [A_11,B_5,C_8,D_4] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_11),B_5)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,C_8),D_4)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_11),C_8)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,B_5),D_4)) ).
fof(fact_597_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom,
! [A_11,B_5,C_8,D_4] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_11),B_5)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_8),D_4)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_11),C_8)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_5),D_4)) ).
fof(fact_598_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
! [A_10,B_4,C_7] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_10),B_4)),C_7) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_10),C_7)),B_4) ).
fof(fact_599_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
! [A_10,B_4,C_7] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_10),B_4)),C_7) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_10),C_7)),B_4) ).
fof(fact_600_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom,
! [A_9,B_3,C_6] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_9),B_3)),C_6) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_9),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,B_3),C_6)) ).
fof(fact_601_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom,
! [A_9,B_3,C_6] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_9),B_3)),C_6) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_9),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_3),C_6)) ).
fof(fact_602_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom,
! [A_8,C_5,D_3] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_8),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,C_5),D_3)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_8),C_5)),D_3) ).
fof(fact_603_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom,
! [A_8,C_5,D_3] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_8),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_5),D_3)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_8),C_5)),D_3) ).
fof(fact_604_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom,
! [A_7,C_4,D_2] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_7),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,C_4),D_2)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,C_4),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_7),D_2)) ).
fof(fact_605_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom,
! [A_7,C_4,D_2] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_7),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_4),D_2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_4),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_7),D_2)) ).
fof(fact_606_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
! [A_6,C_3] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_6),C_3) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,C_3),A_6) ).
fof(fact_607_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
! [A_6,C_3] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_6),C_3) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_3),A_6) ).
fof(fact_608_add__0__iff,axiom,
! [Ba,Aa] :
( Ba = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Ba),Aa)
<=> Aa = zero_zero_int ) ).
fof(fact_609_add__0__iff,axiom,
! [Ba,Aa] :
( Ba = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Ba),Aa)
<=> Aa = zero_zero_nat ) ).
fof(fact_610_rev__nth,axiom,
! [N_13,Xs_21] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_13),size_s2106320494le_alt(Xs_21)))
=> hAPP_n1410269210le_alt(nth_Ar2122385664le_alt(rev_Ar955429983le_alt(Xs_21)),N_13) = hAPP_n1410269210le_alt(nth_Ar2122385664le_alt(Xs_21),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,size_s2106320494le_alt(Xs_21)),hAPP_nat_nat(suc,N_13))) ) ).
fof(fact_611_drop__replicate,axiom,
! [I_4,K_5,X_14] : drop_A1195732799le_alt(I_4,hAPP_A1849759038le_alt(replic1360561849le_alt(K_5),X_14)) = hAPP_A1849759038le_alt(replic1360561849le_alt(hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,K_5),I_4)),X_14) ).
fof(fact_612_diff__cancel2,axiom,
! [M,K_4,N_5] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),K_4)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_5),K_4)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M),N_5) ).
fof(fact_613_diff__cancel,axiom,
! [K_4,M,N_5] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K_4),M)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K_4),N_5)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M),N_5) ).
fof(fact_614_diff__diff__left,axiom,
! [I_3,J,K_4] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,I_3),J)),K_4) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,I_3),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J),K_4)) ).
fof(fact_615_diff__add__inverse,axiom,
! [N_5,M] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_5),M)),N_5) = M ).
fof(fact_616_diff__add__inverse2,axiom,
! [M,N_5] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),N_5)),N_5) = M ).
fof(fact_617_diff__eq__diff__less,axiom,
! [Aa,Ba,C_1,D_1] :
( hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,Aa),Ba) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,C_1),D_1)
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Aa),Ba))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,C_1),D_1)) ) ) ).
fof(fact_618_add__diff__cancel,axiom,
! [A_5,B_2] : hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_5),B_2)),B_2) = A_5 ).
fof(fact_619_diff__add__cancel,axiom,
! [A_4,B_1] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,A_4),B_1)),B_1) = A_4 ).
fof(fact_620_less__imp__diff__less,axiom,
! [N_5,J,K_4] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,J),K_4))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J),N_5)),K_4)) ) ).
fof(fact_621_diff__less__mono2,axiom,
! [L,M,N_5] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N_5))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),L))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,L),N_5)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,L),M))) ) ) ).
fof(fact_622_less__iff__diff__less__0,axiom,
! [Aa,Ba] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Aa),Ba))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,Aa),Ba)),zero_zero_int)) ) ).
fof(fact_623_diff__less,axiom,
! [M,N_5] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_5))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),M))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M),N_5)),M)) ) ) ).
fof(fact_624_zero__less__diff,axiom,
! [N_12,M_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N_12),M_1)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_12)) ) ).
fof(fact_625_diff__less__Suc,axiom,
! [M,N_5] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M),N_5)),hAPP_nat_nat(suc,M))) ).
fof(fact_626_diff__add__0,axiom,
! [N_5,M] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N_5),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_5),M)) = zero_zero_nat ).
fof(fact_627_less__diff__conv,axiom,
! [I,J_1,K_3] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J_1),K_3)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),K_3)),J_1)) ) ).
fof(fact_628_add__diff__inverse,axiom,
! [M,N_5] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N_5))
=> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_5),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M),N_5)) = M ) ).
fof(fact_629_diff__commute,axiom,
! [I_3,J,K_4] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,I_3),J)),K_4) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,I_3),K_4)),J) ).
fof(fact_630_max__diff__distrib__left,axiom,
! [X_13,Y_2,Z] : hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_int_int(hAPP_int_fun_int_int(ord_max_int,X_13),Y_2)),Z) = hAPP_int_int(hAPP_int_fun_int_int(ord_max_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X_13),Z)),hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,Y_2),Z)) ).
fof(fact_631_diff__eq__diff__eq,axiom,
! [Aa,Ba,C_1,D_1] :
( hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,Aa),Ba) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,C_1),D_1)
=> ( Aa = Ba
<=> C_1 = D_1 ) ) ).
fof(fact_632_diff__0__right,axiom,
! [A_3] : hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,A_3),zero_zero_int) = A_3 ).
fof(fact_633_diff__self,axiom,
! [A_2] : hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,A_2),A_2) = zero_zero_int ).
fof(fact_634_eq__iff__diff__eq__0,axiom,
! [Aa,Ba] :
( Aa = Ba
<=> hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,Aa),Ba) = zero_zero_int ) ).
fof(fact_635_right__minus__eq,axiom,
! [Aa,Ba] :
( hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,Aa),Ba) = zero_zero_int
<=> Aa = Ba ) ).
fof(fact_636_diffs0__imp__equal,axiom,
! [M,N_5] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M),N_5) = zero_zero_nat
=> ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N_5),M) = zero_zero_nat
=> M = N_5 ) ) ).
fof(fact_637_diff__self__eq__0,axiom,
! [M] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M),M) = zero_zero_nat ).
fof(fact_638_minus__nat_Odiff__0,axiom,
! [M] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M),zero_zero_nat) = M ).
fof(fact_639_diff__0__eq__0,axiom,
! [N_5] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,zero_zero_nat),N_5) = zero_zero_nat ).
fof(fact_640_diff__Suc__Suc,axiom,
! [M,N_5] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,M)),hAPP_nat_nat(suc,N_5)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M),N_5) ).
fof(fact_641_Suc__diff__diff,axiom,
! [M,N_5,K_4] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,M)),N_5)),hAPP_nat_nat(suc,K_4)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M),N_5)),K_4) ).
fof(fact_642_nat__minus__add__max,axiom,
! [N_5,M] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N_5),M)),M) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,N_5),M) ).
fof(fact_643_diff__Suc__less,axiom,
! [I_3,N_5] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N_5),hAPP_nat_nat(suc,I_3))),N_5)) ) ).
fof(fact_644_Suc__pred,axiom,
! [N_5] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_5))
=> hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N_5),hAPP_nat_nat(suc,zero_zero_nat))) = N_5 ) ).
fof(fact_645_nat__diff__split,axiom,
! [P_1,Aa,Ba] :
( hBOOL(hAPP_nat_bool(P_1,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,Aa),Ba)))
<=> ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),Ba))
=> hBOOL(hAPP_nat_bool(P_1,zero_zero_nat)) )
& ! [D] :
( Aa = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Ba),D)
=> hBOOL(hAPP_nat_bool(P_1,D)) ) ) ) ).
fof(fact_646_nat__diff__split__asm,axiom,
! [P_1,Aa,Ba] :
( hBOOL(hAPP_nat_bool(P_1,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,Aa),Ba)))
<=> ~ ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),Ba))
& ~ hBOOL(hAPP_nat_bool(P_1,zero_zero_nat)) )
| ? [D] :
( Aa = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Ba),D)
& ~ hBOOL(hAPP_nat_bool(P_1,D)) ) ) ) ).
fof(fact_647_take__append,axiom,
! [N_11,Xs_20,Ys_3] : take_A463070695le_alt(N_11,append28105492le_alt(Xs_20,Ys_3)) = append28105492le_alt(take_A463070695le_alt(N_11,Xs_20),take_A463070695le_alt(hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N_11),size_s2106320494le_alt(Xs_20)),Ys_3)) ).
fof(fact_648_drop__append,axiom,
! [N_10,Xs_19,Ys_2] : drop_A1195732799le_alt(N_10,append28105492le_alt(Xs_19,Ys_2)) = append28105492le_alt(drop_A1195732799le_alt(N_10,Xs_19),drop_A1195732799le_alt(hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N_10),size_s2106320494le_alt(Xs_19)),Ys_2)) ).
fof(fact_649_nth__append,axiom,
! [Ys_1,N_9,Xs_18] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_9),size_s2106320494le_alt(Xs_18)))
=> hAPP_n1410269210le_alt(nth_Ar2122385664le_alt(append28105492le_alt(Xs_18,Ys_1)),N_9) = hAPP_n1410269210le_alt(nth_Ar2122385664le_alt(Xs_18),N_9) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_9),size_s2106320494le_alt(Xs_18)))
=> hAPP_n1410269210le_alt(nth_Ar2122385664le_alt(append28105492le_alt(Xs_18,Ys_1)),N_9) = hAPP_n1410269210le_alt(nth_Ar2122385664le_alt(Ys_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N_9),size_s2106320494le_alt(Xs_18))) ) ) ).
fof(fact_650_list__update__append,axiom,
! [Ys,X_12,N_8,Xs_17] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_8),size_s2106320494le_alt(Xs_17)))
=> hAPP_A1849759038le_alt(list_u2058984551le_alt(append28105492le_alt(Xs_17,Ys),N_8),X_12) = append28105492le_alt(hAPP_A1849759038le_alt(list_u2058984551le_alt(Xs_17,N_8),X_12),Ys) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_8),size_s2106320494le_alt(Xs_17)))
=> hAPP_A1849759038le_alt(list_u2058984551le_alt(append28105492le_alt(Xs_17,Ys),N_8),X_12) = append28105492le_alt(Xs_17,hAPP_A1849759038le_alt(list_u2058984551le_alt(Ys,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N_8),size_s2106320494le_alt(Xs_17))),X_12)) ) ) ).
fof(fact_651_rev__drop,axiom,
! [I_2,Xs_16] : rev_Ar955429983le_alt(drop_A1195732799le_alt(I_2,Xs_16)) = take_A463070695le_alt(hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,size_s2106320494le_alt(Xs_16)),I_2),rev_Ar955429983le_alt(Xs_16)) ).
fof(fact_652_rev__take,axiom,
! [I_1,Xs_15] : rev_Ar955429983le_alt(take_A463070695le_alt(I_1,Xs_15)) = drop_A1195732799le_alt(hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,size_s2106320494le_alt(Xs_15)),I_1),rev_Ar955429983le_alt(Xs_15)) ).
fof(fact_653_zero__induct__lemma,axiom,
! [I,P_1,K_3] :
( hBOOL(hAPP_nat_bool(P_1,K_3))
=> ( ! [N_7] :
( hBOOL(hAPP_nat_bool(P_1,hAPP_nat_nat(suc,N_7)))
=> hBOOL(hAPP_nat_bool(P_1,N_7)) )
=> hBOOL(hAPP_nat_bool(P_1,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,K_3),I))) ) ) ).
fof(fact_654_last__list__update,axiom,
! [X_11,K_2,Xs_14] :
( is_Arr723427730le_alt(X_11)
=> ( Xs_14 != nil_Ar1135217151le_alt
=> ( ( K_2 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,size_s2106320494le_alt(Xs_14)),one_one_nat)
=> last_A1066338328le_alt(hAPP_A1849759038le_alt(list_u2058984551le_alt(Xs_14,K_2),X_11)) = X_11 )
& ( K_2 != hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,size_s2106320494le_alt(Xs_14)),one_one_nat)
=> last_A1066338328le_alt(hAPP_A1849759038le_alt(list_u2058984551le_alt(Xs_14,K_2),X_11)) = last_A1066338328le_alt(Xs_14) ) ) ) ) ).
fof(fact_655_empty__Diff,axiom,
! [A] : hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,bot_bot_fun_nat_bool),A) = bot_bot_fun_nat_bool ).
fof(fact_656_Diff__empty,axiom,
! [A] : hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),bot_bot_fun_nat_bool) = A ).
fof(fact_657_Diff__cancel,axiom,
! [A] : hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),A) = bot_bot_fun_nat_bool ).
fof(fact_658_diff__Suc__1,axiom,
! [N_5] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,N_5)),one_one_nat) = N_5 ).
fof(fact_659_diff__Suc__eq__diff__pred,axiom,
! [M,N_5] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M),hAPP_nat_nat(suc,N_5)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M),one_one_nat)),N_5) ).
fof(fact_660_Suc__eq__plus1__left,axiom,
! [N_5] : hAPP_nat_nat(suc,N_5) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),N_5) ).
fof(fact_661_Suc__eq__plus1,axiom,
! [N_5] : hAPP_nat_nat(suc,N_5) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_5),one_one_nat) ).
fof(fact_662_drop__1__Cons,axiom,
! [X_10,Xs_13] : drop_A1195732799le_alt(one_one_nat,cons_A77766063le_alt(X_10,Xs_13)) = Xs_13 ).
fof(fact_663_one__reorient,axiom,
! [X_9] :
( one_one_nat = X_9
<=> X_9 = one_one_nat ) ).
fof(fact_664_One__nat__def,axiom,
one_one_nat = hAPP_nat_nat(suc,zero_zero_nat) ).
fof(fact_665_less__add__one,axiom,
! [A_1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_1),one_one_nat))) ).
fof(fact_666_less__add__one,axiom,
! [A_1] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_1),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_1),one_one_int))) ).
fof(fact_667_not__one__less__zero,axiom,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,one_one_nat),zero_zero_nat)) ).
fof(fact_668_zero__less__one,axiom,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),one_one_nat)) ).
fof(fact_669_one__neq__zero,axiom,
one_one_nat != zero_zero_nat ).
fof(fact_670_zero__neq__one,axiom,
zero_zero_nat != one_one_nat ).
fof(fact_671_zero__less__two,axiom,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),one_one_nat))) ).
fof(fact_672_zero__less__two,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),one_one_int))) ).
fof(fact_673_take__1__Cons,axiom,
! [X_8,Xs_12] : take_A463070695le_alt(one_one_nat,cons_A77766063le_alt(X_8,Xs_12)) = cons_A77766063le_alt(X_8,nil_Ar1135217151le_alt) ).
fof(fact_674_length__butlast,axiom,
! [Xs_11] : size_s2106320494le_alt(butlas123970891le_alt(Xs_11)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,size_s2106320494le_alt(Xs_11)),one_one_nat) ).
fof(fact_675_length__tl,axiom,
! [Xs_10] : size_s2106320494le_alt(tl_Arr314474198le_alt(Xs_10)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,size_s2106320494le_alt(Xs_10)),one_one_nat) ).
fof(fact_676_tl__take,axiom,
! [N_6,Xs_9] : tl_Arr314474198le_alt(take_A463070695le_alt(N_6,Xs_9)) = take_A463070695le_alt(hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N_6),one_one_nat),tl_Arr314474198le_alt(Xs_9)) ).
fof(fact_677_Suc__pred_H,axiom,
! [N_5] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_5))
=> N_5 = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N_5),one_one_nat)) ) ).
fof(fact_678_Suc__diff__1,axiom,
! [N_5] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_5))
=> hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N_5),one_one_nat)) = N_5 ) ).
fof(fact_679_add__eq__if,axiom,
! [N_5,M] :
( ( M = zero_zero_nat
=> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),N_5) = N_5 )
& ( M != zero_zero_nat
=> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),N_5) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M),one_one_nat)),N_5)) ) ) ).
fof(fact_680_nth__Cons_H,axiom,
! [X_7,Xs_8,N_4] :
( is_Arr723427730le_alt(X_7)
=> ( ( N_4 = zero_zero_nat
=> hAPP_n1410269210le_alt(nth_Ar2122385664le_alt(cons_A77766063le_alt(X_7,Xs_8)),N_4) = X_7 )
& ( N_4 != zero_zero_nat
=> hAPP_n1410269210le_alt(nth_Ar2122385664le_alt(cons_A77766063le_alt(X_7,Xs_8)),N_4) = hAPP_n1410269210le_alt(nth_Ar2122385664le_alt(Xs_8),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N_4),one_one_nat)) ) ) ) ).
fof(fact_681_drop__Cons_H,axiom,
! [X_6,Xs_7,N_3] :
( ( N_3 = zero_zero_nat
=> drop_A1195732799le_alt(N_3,cons_A77766063le_alt(X_6,Xs_7)) = cons_A77766063le_alt(X_6,Xs_7) )
& ( N_3 != zero_zero_nat
=> drop_A1195732799le_alt(N_3,cons_A77766063le_alt(X_6,Xs_7)) = drop_A1195732799le_alt(hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N_3),one_one_nat),Xs_7) ) ) ).
fof(fact_682_butlast__conv__take,axiom,
! [Xs_6] : butlas123970891le_alt(Xs_6) = take_A463070695le_alt(hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,size_s2106320494le_alt(Xs_6)),one_one_nat),Xs_6) ).
fof(fact_683_butlast__list__update,axiom,
! [X_5,K_1,Xs_5] :
( ( K_1 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,size_s2106320494le_alt(Xs_5)),one_one_nat)
=> butlas123970891le_alt(hAPP_A1849759038le_alt(list_u2058984551le_alt(Xs_5,K_1),X_5)) = butlas123970891le_alt(Xs_5) )
& ( K_1 != hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,size_s2106320494le_alt(Xs_5)),one_one_nat)
=> butlas123970891le_alt(hAPP_A1849759038le_alt(list_u2058984551le_alt(Xs_5,K_1),X_5)) = hAPP_A1849759038le_alt(list_u2058984551le_alt(butlas123970891le_alt(Xs_5),K_1),X_5) ) ) ).
fof(fact_684_tl__replicate,axiom,
! [X_4,N_2] :
( N_2 != zero_zero_nat
=> tl_Arr314474198le_alt(hAPP_A1849759038le_alt(replic1360561849le_alt(N_2),X_4)) = hAPP_A1849759038le_alt(replic1360561849le_alt(hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N_2),one_one_nat)),X_4) ) ).
fof(fact_685_nth__Cons__pos,axiom,
! [X_3,Xs_4,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1))
=> hAPP_n1410269210le_alt(nth_Ar2122385664le_alt(cons_A77766063le_alt(X_3,Xs_4)),N_1) = hAPP_n1410269210le_alt(nth_Ar2122385664le_alt(Xs_4),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N_1),one_one_nat)) ) ).
fof(fact_686_take__Cons_H,axiom,
! [X_2,Xs_3,N] :
( ( N = zero_zero_nat
=> take_A463070695le_alt(N,cons_A77766063le_alt(X_2,Xs_3)) = nil_Ar1135217151le_alt )
& ( N != zero_zero_nat
=> take_A463070695le_alt(N,cons_A77766063le_alt(X_2,Xs_3)) = cons_A77766063le_alt(X_2,take_A463070695le_alt(hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N),one_one_nat),Xs_3)) ) ) ).
fof(fact_687_rev__update,axiom,
! [Y_1,K,Xs_2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,K),size_s2106320494le_alt(Xs_2)))
=> rev_Ar955429983le_alt(hAPP_A1849759038le_alt(list_u2058984551le_alt(Xs_2,K),Y_1)) = hAPP_A1849759038le_alt(list_u2058984551le_alt(rev_Ar955429983le_alt(Xs_2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,size_s2106320494le_alt(Xs_2)),K)),one_one_nat)),Y_1) ) ).
fof(fact_688_last__conv__nth,axiom,
! [Xs_1] :
( Xs_1 != nil_Ar1135217151le_alt
=> last_A1066338328le_alt(Xs_1) = hAPP_n1410269210le_alt(nth_Ar2122385664le_alt(Xs_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,size_s2106320494le_alt(Xs_1)),one_one_nat)) ) ).
fof(fact_689_take__Cons__number__of,axiom,
! [X_1,Xs,V_2] :
( ( number_number_of_nat(V_2) = zero_zero_nat
=> take_A463070695le_alt(number_number_of_nat(V_2),cons_A77766063le_alt(X_1,Xs)) = nil_Ar1135217151le_alt )
& ( number_number_of_nat(V_2) != zero_zero_nat
=> take_A463070695le_alt(number_number_of_nat(V_2),cons_A77766063le_alt(X_1,Xs)) = cons_A77766063le_alt(X_1,take_A463070695le_alt(hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,number_number_of_nat(V_2)),one_one_nat),Xs)) ) ) ).
fof(fact_690_Ints__odd__less__0,axiom,
! [Aa] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Aa),ring_1_Ints_int))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),Aa)),Aa)),zero_zero_int))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Aa),zero_zero_int)) ) ) ).
fof(fact_691_DiffE,axiom,
! [C_1,A,B] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_1),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),B)))
=> ~ ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_1),A))
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_1),B)) ) ) ).
fof(fact_692_DiffI,axiom,
! [B,C_1,A] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_1),A))
=> ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_1),B))
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_1),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),B))) ) ) ).
fof(fact_693_Ints__diff,axiom,
! [Ba,Aa] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Aa),ring_1_Ints_int))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Ba),ring_1_Ints_int))
=> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,Aa),Ba)),ring_1_Ints_int)) ) ) ).
fof(fact_694_number__of__diff,axiom,
! [V_1,W_1] : number_number_of_int(hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,V_1),W_1)) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,number_number_of_int(V_1)),number_number_of_int(W_1)) ).
fof(fact_695_add__number__of__diff1,axiom,
! [V,W,C_2] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,number_number_of_int(V)),hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,number_number_of_int(W)),C_2)) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,number_number_of_int(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,V),W))),C_2) ).
fof(fact_696_DiffD2,axiom,
! [C_1,A,B] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_1),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),B)))
=> ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_1),B)) ) ).
fof(fact_697_DiffD1,axiom,
! [C_1,A,B] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_1),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),B)))
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_1),A)) ) ).
fof(fact_698_Diff__iff,axiom,
! [C_1,A,B] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_1),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),B)))
<=> ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_1),A))
& ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_1),B)) ) ) ).
fof(fact_699_set__diff__eq,axiom,
! [A,B] : hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),B) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,cOMBC_226598744l_bool(member_nat,A)),cOMBB_bool_bool_nat(fNot,cOMBC_226598744l_bool(member_nat,B)))) ).
%----Helper facts (14)
fof(help_fNot_1_1_U,axiom,
! [P] :
( ~ hBOOL(hAPP_bool_bool(fNot,P))
| ~ hBOOL(P) ) ).
fof(help_fNot_2_1_U,axiom,
! [P] :
( hBOOL(P)
| hBOOL(hAPP_bool_bool(fNot,P)) ) ).
fof(help_fconj_1_1_U,axiom,
! [Q,P] :
( ~ hBOOL(P)
| ~ hBOOL(Q)
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,P),Q)) ) ).
fof(help_fconj_2_1_U,axiom,
! [P,Q] :
( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,P),Q))
| hBOOL(P) ) ).
fof(help_fconj_3_1_U,axiom,
! [P,Q] :
( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,P),Q))
| hBOOL(Q) ) ).
fof(help_fFalse_1_1_U,axiom,
~ hBOOL(fFalse) ).
fof(help_fFalse_1_1_T,axiom,
! [P] :
( is_bool(P)
=> ( P = fTrue
| P = fFalse ) ) ).
fof(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Nat__Onat_U,axiom,
! [P,Q] :
( is_bool(P)
=> hAPP_nat_bool(cOMBK_bool_nat(P),Q) = P ) ).
fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Nat__Onat_U,axiom,
! [P,Q,R] : hAPP_nat_bool(cOMBB_bool_bool_nat(P,Q),R) = hAPP_bool_bool(P,hAPP_nat_bool(Q,R)) ).
fof(help_COMBS_1_1_COMBS_000tc__Nat__Onat_000tc__HOL__Obool_000tc__HOL__Obool_U,axiom,
! [P,Q,R] : hAPP_nat_bool(cOMBS_nat_bool_bool(P,Q),R) = hAPP_bool_bool(hAPP_n1006566506l_bool(P,R),hAPP_nat_bool(Q,R)) ).
fof(help_fequal_1_1_fequal_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____wy,axiom,
! [X,Y] :
( ~ hBOOL(hAPP_l300482276t_bool(hAPP_l2066632447t_bool(fequal1028827333le_alt,X),Y))
| X = Y ) ).
fof(help_fequal_2_1_fequal_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____wy,axiom,
! [X,Y] :
( X != Y
| hBOOL(hAPP_l300482276t_bool(hAPP_l2066632447t_bool(fequal1028827333le_alt,X),Y)) ) ).
fof(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_,axiom,
! [P,Q,R] : hAPP_nat_bool(cOMBC_226598744l_bool(P,Q),R) = hAPP_f54304608l_bool(hAPP_n215258509l_bool(P,R),Q) ).
fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo,axiom,
! [P,Q,R] : hAPP_n1006566506l_bool(cOMBB_1015721476ol_nat(P,Q),R) = hAPP_b589554111l_bool(P,hAPP_nat_bool(Q,R)) ).
%----Conjectures (2)
fof(conj_0,hypothesis,
a != b ).
fof(conj_1,conjecture,
? [C] : hBOOL(hAPP_l300482276t_bool(distin85347314le_alt,cons_A77766063le_alt(a,cons_A77766063le_alt(b,cons_A77766063le_alt(C,nil_Ar1135217151le_alt))))) ).
%------------------------------------------------------------------------------