TPTP Problem File: SCT169^1.p
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%------------------------------------------------------------------------------
% File : SCT169^1 : TPTP v8.2.0. Released v5.3.0.
% Domain : Social Choice Theory
% Problem : Arrow's Impossibility Theorem line 29, 100 axioms selected
% Version : Especial.
% English :
% Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe
% Source : [Bla11]
% Names : arrow_100_thf_l29 [Bla11]
% Status : Theorem
% Rating : 1.00 v5.3.0
% Syntax : Number of formulae : 121 ( 37 unt; 23 typ; 0 def)
% Number of atoms : 189 ( 158 equ; 0 cnn)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 588 ( 36 ~; 5 |; 19 &; 454 @)
% ( 30 <=>; 44 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 35 ( 35 >; 0 *; 0 +; 0 <<)
% Number of symbols : 21 ( 20 usr; 3 con; 0-2 aty)
% Number of variables : 202 ( 0 ^; 189 !; 13 ?; 202 :)
% SPC : TH0_THM_EQU_NAR
% Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 2011-08-09 18:57:48
%------------------------------------------------------------------------------
%----Should-be-implicit typings (3)
thf(ty_ty_tc__Arrow____Order____Mirabelle____sdiojnqkdh__Oalt,type,
arrow_1346734812le_alt: $tType ).
thf(ty_ty_tc__List__Olist_Itc__Arrow____Order____Mirabelle____sdiojnqkdh__Oalt_J,type,
list_A1528105233le_alt: $tType ).
thf(ty_ty_tc__Nat__Onat,type,
nat: $tType ).
%----Explicit typings (20)
thf(sy_c_HOL_Oequal__class_Oequal_000tc__List__Olist_Itc__Arrow____Order____Mirabell,type,
equal_2044961839le_alt: list_A1528105233le_alt > list_A1528105233le_alt > $o ).
thf(sy_c_List_Oappend_000tc__Arrow____Order____Mirabelle____sdiojnqkdh__Oalt,type,
append1050458273le_alt: list_A1528105233le_alt > list_A1528105233le_alt > list_A1528105233le_alt ).
thf(sy_c_List_Obutlast_000tc__Arrow____Order____Mirabelle____sdiojnqkdh__Oalt,type,
butlas1146323672le_alt: list_A1528105233le_alt > list_A1528105233le_alt ).
thf(sy_c_List_Odistinct_000tc__Arrow____Order____Mirabelle____sdiojnqkdh__Oalt,type,
distin1107700095le_alt: list_A1528105233le_alt > $o ).
thf(sy_c_List_OdropWhile_000tc__Arrow____Order____Mirabelle____sdiojnqkdh__Oalt,type,
dropWh40674093le_alt: ( arrow_1346734812le_alt > $o ) > list_A1528105233le_alt > list_A1528105233le_alt ).
thf(sy_c_List_Ohd_000tc__Arrow____Order____Mirabelle____sdiojnqkdh__Oalt,type,
hd_Arr689575519le_alt: list_A1528105233le_alt > arrow_1346734812le_alt ).
thf(sy_c_List_Oinsert_000tc__Arrow____Order____Mirabelle____sdiojnqkdh__Oalt,type,
insert844458914le_alt: arrow_1346734812le_alt > list_A1528105233le_alt > list_A1528105233le_alt ).
thf(sy_c_List_Olast_000tc__Arrow____Order____Mirabelle____sdiojnqkdh__Oalt,type,
last_A2088691109le_alt: list_A1528105233le_alt > arrow_1346734812le_alt ).
thf(sy_c_List_Olist_OCons_000tc__Arrow____Order____Mirabelle____sdiojnqkdh__Oalt,type,
cons_A1100118844le_alt: arrow_1346734812le_alt > list_A1528105233le_alt > list_A1528105233le_alt ).
thf(sy_c_List_Olist_ONil_000tc__Arrow____Order____Mirabelle____sdiojnqkdh__Oalt,type,
nil_Ar10086284le_alt: list_A1528105233le_alt ).
thf(sy_c_List_Omaps_000tc__Arrow____Order____Mirabelle____sdiojnqkdh__Oalt_000tc__Ar,type,
maps_A51637569le_alt: ( arrow_1346734812le_alt > list_A1528105233le_alt ) > list_A1528105233le_alt > list_A1528105233le_alt ).
thf(sy_c_List_Onull_000tc__Arrow____Order____Mirabelle____sdiojnqkdh__Oalt,type,
null_A244857236le_alt: list_A1528105233le_alt > $o ).
thf(sy_c_List_Oreplicate_000tc__Arrow____Order____Mirabelle____sdiojnqkdh__Oalt,type,
replic235430982le_alt: nat > arrow_1346734812le_alt > list_A1528105233le_alt ).
thf(sy_c_List_Orev_000tc__Arrow____Order____Mirabelle____sdiojnqkdh__Oalt,type,
rev_Ar1977782764le_alt: list_A1528105233le_alt > list_A1528105233le_alt ).
thf(sy_c_List_Orotate1_000tc__Arrow____Order____Mirabelle____sdiojnqkdh__Oalt,type,
rotate1206725081le_alt: list_A1528105233le_alt > list_A1528105233le_alt ).
thf(sy_c_List_Osplice_000tc__Arrow____Order____Mirabelle____sdiojnqkdh__Oalt,type,
splice244790623le_alt: list_A1528105233le_alt > list_A1528105233le_alt > list_A1528105233le_alt ).
thf(sy_c_List_Otl_000tc__Arrow____Order____Mirabelle____sdiojnqkdh__Oalt,type,
tl_Arr1336826979le_alt: list_A1528105233le_alt > list_A1528105233le_alt ).
thf(sy_c_fequal_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____sdiojnqkdh__O,type,
fequal194154450le_alt: list_A1528105233le_alt > list_A1528105233le_alt > $o ).
thf(sy_v_a,type,
a: arrow_1346734812le_alt ).
thf(sy_v_b,type,
b: arrow_1346734812le_alt ).
%----Relevant facts (94)
thf(fact_0_alt3,axiom,
? [A_2: arrow_1346734812le_alt,B: arrow_1346734812le_alt,C: arrow_1346734812le_alt] : ( distin1107700095le_alt @ ( cons_A1100118844le_alt @ A_2 @ ( cons_A1100118844le_alt @ B @ ( cons_A1100118844le_alt @ C @ nil_Ar10086284le_alt ) ) ) ) ).
thf(fact_1_distinct_Osimps_I1_J,axiom,
distin1107700095le_alt @ nil_Ar10086284le_alt ).
thf(fact_2_list_Osimps_I2_J,axiom,
! [A_4: arrow_1346734812le_alt,List_4: list_A1528105233le_alt] :
( nil_Ar10086284le_alt
!= ( cons_A1100118844le_alt @ A_4 @ List_4 ) ) ).
thf(fact_3_list_Osimps_I3_J,axiom,
! [A_3: arrow_1346734812le_alt,List_3: list_A1528105233le_alt] :
( ( cons_A1100118844le_alt @ A_3 @ List_3 )
!= nil_Ar10086284le_alt ) ).
thf(fact_4_neq__Nil__conv,axiom,
! [Xs_71: list_A1528105233le_alt] :
( ( Xs_71 != nil_Ar10086284le_alt )
<=> ? [Y_3: arrow_1346734812le_alt,Ys_7: list_A1528105233le_alt] :
( Xs_71
= ( cons_A1100118844le_alt @ Y_3 @ Ys_7 ) ) ) ).
thf(fact_5_list_Oexhaust,axiom,
! [Y_7: list_A1528105233le_alt] :
( ( Y_7 != nil_Ar10086284le_alt )
=> ~ ! [A_2: arrow_1346734812le_alt,List_2: list_A1528105233le_alt] :
( Y_7
!= ( cons_A1100118844le_alt @ A_2 @ List_2 ) ) ) ).
thf(fact_6_not__Cons__self,axiom,
! [Xs_70: list_A1528105233le_alt,X_33: arrow_1346734812le_alt] :
( Xs_70
!= ( cons_A1100118844le_alt @ X_33 @ Xs_70 ) ) ).
thf(fact_7_not__Cons__self2,axiom,
! [X_32: arrow_1346734812le_alt,Xs_69: list_A1528105233le_alt] :
( ( cons_A1100118844le_alt @ X_32 @ Xs_69 )
!= Xs_69 ) ).
thf(fact_8_list_Oinject,axiom,
! [A_1: arrow_1346734812le_alt,List_1: list_A1528105233le_alt,A: arrow_1346734812le_alt,List: list_A1528105233le_alt] :
( ( ( cons_A1100118844le_alt @ A_1 @ List_1 )
= ( cons_A1100118844le_alt @ A @ List ) )
<=> ( ( A_1 = A )
& ( List_1 = List ) ) ) ).
thf(fact_9_splice_Osimps_I2_J,axiom,
! [V: arrow_1346734812le_alt,Va: list_A1528105233le_alt] :
( ( splice244790623le_alt @ ( cons_A1100118844le_alt @ V @ Va ) @ nil_Ar10086284le_alt )
= ( cons_A1100118844le_alt @ V @ Va ) ) ).
thf(fact_10_insert__Nil,axiom,
! [X_31: arrow_1346734812le_alt] :
( ( insert844458914le_alt @ X_31 @ nil_Ar10086284le_alt )
= ( cons_A1100118844le_alt @ X_31 @ nil_Ar10086284le_alt ) ) ).
thf(fact_11_list__nonempty__induct,axiom,
! [P_5: list_A1528105233le_alt > $o,Xs_68: list_A1528105233le_alt] :
( ( Xs_68 != nil_Ar10086284le_alt )
=> ( ! [X_20: arrow_1346734812le_alt] : ( P_5 @ ( cons_A1100118844le_alt @ X_20 @ nil_Ar10086284le_alt ) )
=> ( ! [X_20: arrow_1346734812le_alt,Xs_23: list_A1528105233le_alt] :
( ( Xs_23 != nil_Ar10086284le_alt )
=> ( ( P_5 @ Xs_23 )
=> ( P_5 @ ( cons_A1100118844le_alt @ X_20 @ Xs_23 ) ) ) )
=> ( P_5 @ Xs_68 ) ) ) ) ).
thf(fact_12_distinct__butlast,axiom,
! [Xs_67: list_A1528105233le_alt] :
( ( Xs_67 != nil_Ar10086284le_alt )
=> ( ( distin1107700095le_alt @ Xs_67 )
=> ( distin1107700095le_alt @ ( butlas1146323672le_alt @ Xs_67 ) ) ) ) ).
thf(fact_13_butlast_Osimps_I1_J,axiom,
( ( butlas1146323672le_alt @ nil_Ar10086284le_alt )
= nil_Ar10086284le_alt ) ).
thf(fact_14_distinct__insert,axiom,
! [X_30: arrow_1346734812le_alt,Xs_66: list_A1528105233le_alt] :
( ( distin1107700095le_alt @ Xs_66 )
=> ( distin1107700095le_alt @ ( insert844458914le_alt @ X_30 @ Xs_66 ) ) ) ).
thf(fact_15_splice_Osimps_I3_J,axiom,
! [X_29: arrow_1346734812le_alt,Xs_65: list_A1528105233le_alt,Y_6: arrow_1346734812le_alt,Ys_33: list_A1528105233le_alt] :
( ( splice244790623le_alt @ ( cons_A1100118844le_alt @ X_29 @ Xs_65 ) @ ( cons_A1100118844le_alt @ Y_6 @ Ys_33 ) )
= ( cons_A1100118844le_alt @ X_29 @ ( cons_A1100118844le_alt @ Y_6 @ ( splice244790623le_alt @ Xs_65 @ Ys_33 ) ) ) ) ).
thf(fact_16_splice__Nil2,axiom,
! [Xs_64: list_A1528105233le_alt] :
( ( splice244790623le_alt @ Xs_64 @ nil_Ar10086284le_alt )
= Xs_64 ) ).
thf(fact_17_splice_Osimps_I1_J,axiom,
! [Ys_32: list_A1528105233le_alt] :
( ( splice244790623le_alt @ nil_Ar10086284le_alt @ Ys_32 )
= Ys_32 ) ).
thf(fact_18_butlast_Osimps_I2_J,axiom,
! [X_28: arrow_1346734812le_alt,Xs_63: list_A1528105233le_alt] :
( ( ( Xs_63 = nil_Ar10086284le_alt )
=> ( ( butlas1146323672le_alt @ ( cons_A1100118844le_alt @ X_28 @ Xs_63 ) )
= nil_Ar10086284le_alt ) )
& ( ( Xs_63 != nil_Ar10086284le_alt )
=> ( ( butlas1146323672le_alt @ ( cons_A1100118844le_alt @ X_28 @ Xs_63 ) )
= ( cons_A1100118844le_alt @ X_28 @ ( butlas1146323672le_alt @ Xs_63 ) ) ) ) ) ).
thf(fact_19_eq__Nil__null,axiom,
! [Xs_62: list_A1528105233le_alt] :
( ( Xs_62 = nil_Ar10086284le_alt )
<=> ( null_A244857236le_alt @ Xs_62 ) ) ).
thf(fact_20_List_Onull__def,axiom,
! [Xs_61: list_A1528105233le_alt] :
( ( null_A244857236le_alt @ Xs_61 )
<=> ( Xs_61 = nil_Ar10086284le_alt ) ) ).
thf(fact_21_null__rec_I2_J,axiom,
null_A244857236le_alt @ nil_Ar10086284le_alt ).
thf(fact_22_null__rec_I1_J,axiom,
! [X_27: arrow_1346734812le_alt,Xs_60: list_A1528105233le_alt] :
~ ( null_A244857236le_alt @ ( cons_A1100118844le_alt @ X_27 @ Xs_60 ) ) ).
thf(fact_23_butlast__snoc,axiom,
! [Xs_59: list_A1528105233le_alt,X_26: arrow_1346734812le_alt] :
( ( butlas1146323672le_alt @ ( append1050458273le_alt @ Xs_59 @ ( cons_A1100118844le_alt @ X_26 @ nil_Ar10086284le_alt ) ) )
= Xs_59 ) ).
thf(fact_24_append__assoc,axiom,
! [Xs_58: list_A1528105233le_alt,Ys_31: list_A1528105233le_alt,Zs_8: list_A1528105233le_alt] :
( ( append1050458273le_alt @ ( append1050458273le_alt @ Xs_58 @ Ys_31 ) @ Zs_8 )
= ( append1050458273le_alt @ Xs_58 @ ( append1050458273le_alt @ Ys_31 @ Zs_8 ) ) ) ).
thf(fact_25_append__eq__append__conv2,axiom,
! [Xs_57: list_A1528105233le_alt,Ys_30: list_A1528105233le_alt,Zs_7: list_A1528105233le_alt,Ts: list_A1528105233le_alt] :
( ( ( append1050458273le_alt @ Xs_57 @ Ys_30 )
= ( append1050458273le_alt @ Zs_7 @ Ts ) )
<=> ? [Us_1: list_A1528105233le_alt] :
( ( ( Xs_57
= ( append1050458273le_alt @ Zs_7 @ Us_1 ) )
& ( ( append1050458273le_alt @ Us_1 @ Ys_30 )
= Ts ) )
| ( ( ( append1050458273le_alt @ Xs_57 @ Us_1 )
= Zs_7 )
& ( Ys_30
= ( append1050458273le_alt @ Us_1 @ Ts ) ) ) ) ) ).
thf(fact_26_same__append__eq,axiom,
! [Xs_56: list_A1528105233le_alt,Ys_29: list_A1528105233le_alt,Zs_6: list_A1528105233le_alt] :
( ( ( append1050458273le_alt @ Xs_56 @ Ys_29 )
= ( append1050458273le_alt @ Xs_56 @ Zs_6 ) )
<=> ( Ys_29 = Zs_6 ) ) ).
thf(fact_27_append__same__eq,axiom,
! [Ys_28: list_A1528105233le_alt,Xs_55: list_A1528105233le_alt,Zs_5: list_A1528105233le_alt] :
( ( ( append1050458273le_alt @ Ys_28 @ Xs_55 )
= ( append1050458273le_alt @ Zs_5 @ Xs_55 ) )
<=> ( Ys_28 = Zs_5 ) ) ).
thf(fact_28_append__eq__appendI,axiom,
! [Ys_27: list_A1528105233le_alt,Us: list_A1528105233le_alt,Xs_54: list_A1528105233le_alt,Xs1_1: list_A1528105233le_alt,Zs_4: list_A1528105233le_alt] :
( ( ( append1050458273le_alt @ Xs_54 @ Xs1_1 )
= Zs_4 )
=> ( ( Ys_27
= ( append1050458273le_alt @ Xs1_1 @ Us ) )
=> ( ( append1050458273le_alt @ Xs_54 @ Ys_27 )
= ( append1050458273le_alt @ Zs_4 @ Us ) ) ) ) ).
thf(fact_29_append__Cons,axiom,
! [X_25: arrow_1346734812le_alt,Xs_53: list_A1528105233le_alt,Ys_26: list_A1528105233le_alt] :
( ( append1050458273le_alt @ ( cons_A1100118844le_alt @ X_25 @ Xs_53 ) @ Ys_26 )
= ( cons_A1100118844le_alt @ X_25 @ ( append1050458273le_alt @ Xs_53 @ Ys_26 ) ) ) ).
thf(fact_30_Cons__eq__appendI,axiom,
! [Xs_52: list_A1528105233le_alt,Zs_3: list_A1528105233le_alt,X_24: arrow_1346734812le_alt,Xs1: list_A1528105233le_alt,Ys_25: list_A1528105233le_alt] :
( ( ( cons_A1100118844le_alt @ X_24 @ Xs1 )
= Ys_25 )
=> ( ( Xs_52
= ( append1050458273le_alt @ Xs1 @ Zs_3 ) )
=> ( ( cons_A1100118844le_alt @ X_24 @ Xs_52 )
= ( append1050458273le_alt @ Ys_25 @ Zs_3 ) ) ) ) ).
thf(fact_31_append__Nil,axiom,
! [Ys_24: list_A1528105233le_alt] :
( ( append1050458273le_alt @ nil_Ar10086284le_alt @ Ys_24 )
= Ys_24 ) ).
thf(fact_32_Nil__is__append__conv,axiom,
! [Xs_51: list_A1528105233le_alt,Ys_23: list_A1528105233le_alt] :
( ( nil_Ar10086284le_alt
= ( append1050458273le_alt @ Xs_51 @ Ys_23 ) )
<=> ( ( Xs_51 = nil_Ar10086284le_alt )
& ( Ys_23 = nil_Ar10086284le_alt ) ) ) ).
thf(fact_33_append__Nil2,axiom,
! [Xs_50: list_A1528105233le_alt] :
( ( append1050458273le_alt @ Xs_50 @ nil_Ar10086284le_alt )
= Xs_50 ) ).
thf(fact_34_self__append__conv,axiom,
! [Xs_49: list_A1528105233le_alt,Ys_22: list_A1528105233le_alt] :
( ( Xs_49
= ( append1050458273le_alt @ Xs_49 @ Ys_22 ) )
<=> ( Ys_22 = nil_Ar10086284le_alt ) ) ).
thf(fact_35_self__append__conv2,axiom,
! [Ys_21: list_A1528105233le_alt,Xs_48: list_A1528105233le_alt] :
( ( Ys_21
= ( append1050458273le_alt @ Xs_48 @ Ys_21 ) )
<=> ( Xs_48 = nil_Ar10086284le_alt ) ) ).
thf(fact_36_append__is__Nil__conv,axiom,
! [Xs_47: list_A1528105233le_alt,Ys_20: list_A1528105233le_alt] :
( ( ( append1050458273le_alt @ Xs_47 @ Ys_20 )
= nil_Ar10086284le_alt )
<=> ( ( Xs_47 = nil_Ar10086284le_alt )
& ( Ys_20 = nil_Ar10086284le_alt ) ) ) ).
thf(fact_37_append__self__conv,axiom,
! [Xs_46: list_A1528105233le_alt,Ys_19: list_A1528105233le_alt] :
( ( ( append1050458273le_alt @ Xs_46 @ Ys_19 )
= Xs_46 )
<=> ( Ys_19 = nil_Ar10086284le_alt ) ) ).
thf(fact_38_append__self__conv2,axiom,
! [Xs_45: list_A1528105233le_alt,Ys_18: list_A1528105233le_alt] :
( ( ( append1050458273le_alt @ Xs_45 @ Ys_18 )
= Ys_18 )
<=> ( Xs_45 = nil_Ar10086284le_alt ) ) ).
thf(fact_39_eq__Nil__appendI,axiom,
! [Xs_44: list_A1528105233le_alt,Ys_17: list_A1528105233le_alt] :
( ( Xs_44 = Ys_17 )
=> ( Xs_44
= ( append1050458273le_alt @ nil_Ar10086284le_alt @ Ys_17 ) ) ) ).
thf(fact_40_append__eq__Cons__conv,axiom,
! [Ys_16: list_A1528105233le_alt,Zs_2: list_A1528105233le_alt,X_23: arrow_1346734812le_alt,Xs_43: list_A1528105233le_alt] :
( ( ( append1050458273le_alt @ Ys_16 @ Zs_2 )
= ( cons_A1100118844le_alt @ X_23 @ Xs_43 ) )
<=> ( ( ( Ys_16 = nil_Ar10086284le_alt )
& ( Zs_2
= ( cons_A1100118844le_alt @ X_23 @ Xs_43 ) ) )
| ? [Ys_15: list_A1528105233le_alt] :
( ( Ys_16
= ( cons_A1100118844le_alt @ X_23 @ Ys_15 ) )
& ( ( append1050458273le_alt @ Ys_15 @ Zs_2 )
= Xs_43 ) ) ) ) ).
thf(fact_41_Cons__eq__append__conv,axiom,
! [X_22: arrow_1346734812le_alt,Xs_42: list_A1528105233le_alt,Ys_14: list_A1528105233le_alt,Zs_1: list_A1528105233le_alt] :
( ( ( cons_A1100118844le_alt @ X_22 @ Xs_42 )
= ( append1050458273le_alt @ Ys_14 @ Zs_1 ) )
<=> ( ( ( Ys_14 = nil_Ar10086284le_alt )
& ( ( cons_A1100118844le_alt @ X_22 @ Xs_42 )
= Zs_1 ) )
| ? [Ys_15: list_A1528105233le_alt] :
( ( ( cons_A1100118844le_alt @ X_22 @ Ys_15 )
= Ys_14 )
& ( Xs_42
= ( append1050458273le_alt @ Ys_15 @ Zs_1 ) ) ) ) ) ).
thf(fact_42_append1__eq__conv,axiom,
! [Xs_41: list_A1528105233le_alt,X_21: arrow_1346734812le_alt,Ys_13: list_A1528105233le_alt,Y_5: arrow_1346734812le_alt] :
( ( ( append1050458273le_alt @ Xs_41 @ ( cons_A1100118844le_alt @ X_21 @ nil_Ar10086284le_alt ) )
= ( append1050458273le_alt @ Ys_13 @ ( cons_A1100118844le_alt @ Y_5 @ nil_Ar10086284le_alt ) ) )
<=> ( ( Xs_41 = Ys_13 )
& ( X_21 = Y_5 ) ) ) ).
thf(fact_43_butlast__append,axiom,
! [Xs_40: list_A1528105233le_alt,Ys_12: list_A1528105233le_alt] :
( ( ( Ys_12 = nil_Ar10086284le_alt )
=> ( ( butlas1146323672le_alt @ ( append1050458273le_alt @ Xs_40 @ Ys_12 ) )
= ( butlas1146323672le_alt @ Xs_40 ) ) )
& ( ( Ys_12 != nil_Ar10086284le_alt )
=> ( ( butlas1146323672le_alt @ ( append1050458273le_alt @ Xs_40 @ Ys_12 ) )
= ( append1050458273le_alt @ Xs_40 @ ( butlas1146323672le_alt @ Ys_12 ) ) ) ) ) ).
thf(fact_44_rev__induct,axiom,
! [Xs_39: list_A1528105233le_alt,P_4: list_A1528105233le_alt > $o] :
( ( P_4 @ nil_Ar10086284le_alt )
=> ( ! [X_20: arrow_1346734812le_alt,Xs_23: list_A1528105233le_alt] :
( ( P_4 @ Xs_23 )
=> ( P_4 @ ( append1050458273le_alt @ Xs_23 @ ( cons_A1100118844le_alt @ X_20 @ nil_Ar10086284le_alt ) ) ) )
=> ( P_4 @ Xs_39 ) ) ) ).
thf(fact_45_rev__cases,axiom,
! [Xs_38: list_A1528105233le_alt] :
( ( Xs_38 != nil_Ar10086284le_alt )
=> ~ ! [Ys_7: list_A1528105233le_alt,Y_3: arrow_1346734812le_alt] :
( Xs_38
!= ( append1050458273le_alt @ Ys_7 @ ( cons_A1100118844le_alt @ Y_3 @ nil_Ar10086284le_alt ) ) ) ) ).
thf(fact_46_equal__Nil__null,axiom,
! [Xs_37: list_A1528105233le_alt] :
( ( equal_2044961839le_alt @ Xs_37 @ nil_Ar10086284le_alt )
<=> ( null_A244857236le_alt @ Xs_37 ) ) ).
thf(fact_47_snoc__eq__iff__butlast,axiom,
! [Xs_36: list_A1528105233le_alt,X_19: arrow_1346734812le_alt,Ys_11: list_A1528105233le_alt] :
( ( ( append1050458273le_alt @ Xs_36 @ ( cons_A1100118844le_alt @ X_19 @ nil_Ar10086284le_alt ) )
= Ys_11 )
<=> ( ( Ys_11 != nil_Ar10086284le_alt )
& ( ( butlas1146323672le_alt @ Ys_11 )
= Xs_36 )
& ( ( last_A2088691109le_alt @ Ys_11 )
= X_19 ) ) ) ).
thf(fact_48_append__butlast__last__id,axiom,
! [Xs_35: list_A1528105233le_alt] :
( ( Xs_35 != nil_Ar10086284le_alt )
=> ( ( append1050458273le_alt @ ( butlas1146323672le_alt @ Xs_35 ) @ ( cons_A1100118844le_alt @ ( last_A2088691109le_alt @ Xs_35 ) @ nil_Ar10086284le_alt ) )
= Xs_35 ) ) ).
thf(fact_49_rotate__simps,axiom,
! [X_18: arrow_1346734812le_alt,Xs_34: list_A1528105233le_alt] :
( ( ( rotate1206725081le_alt @ nil_Ar10086284le_alt )
= nil_Ar10086284le_alt )
& ( ( rotate1206725081le_alt @ ( cons_A1100118844le_alt @ X_18 @ Xs_34 ) )
= ( append1050458273le_alt @ Xs_34 @ ( cons_A1100118844le_alt @ X_18 @ nil_Ar10086284le_alt ) ) ) ) ).
thf(fact_50_equal__list__def,axiom,
! [X_17: list_A1528105233le_alt,Y_4: list_A1528105233le_alt] :
( ( equal_2044961839le_alt @ X_17 @ Y_4 )
<=> ( X_17 = Y_4 ) ) ).
thf(fact_51_rotate1__is__Nil__conv,axiom,
! [Xs_33: list_A1528105233le_alt] :
( ( ( rotate1206725081le_alt @ Xs_33 )
= nil_Ar10086284le_alt )
<=> ( Xs_33 = nil_Ar10086284le_alt ) ) ).
thf(fact_52_distinct1__rotate,axiom,
! [Xs_32: list_A1528105233le_alt] :
( ( distin1107700095le_alt @ ( rotate1206725081le_alt @ Xs_32 ) )
<=> ( distin1107700095le_alt @ Xs_32 ) ) ).
thf(fact_53_last__ConsL,axiom,
! [X_16: arrow_1346734812le_alt,Xs_31: list_A1528105233le_alt] :
( ( Xs_31 = nil_Ar10086284le_alt )
=> ( ( last_A2088691109le_alt @ ( cons_A1100118844le_alt @ X_16 @ Xs_31 ) )
= X_16 ) ) ).
thf(fact_54_last__ConsR,axiom,
! [X_15: arrow_1346734812le_alt,Xs_30: list_A1528105233le_alt] :
( ( Xs_30 != nil_Ar10086284le_alt )
=> ( ( last_A2088691109le_alt @ ( cons_A1100118844le_alt @ X_15 @ Xs_30 ) )
= ( last_A2088691109le_alt @ Xs_30 ) ) ) ).
thf(fact_55_last_Osimps,axiom,
! [X_14: arrow_1346734812le_alt,Xs_29: list_A1528105233le_alt] :
( ( ( Xs_29 = nil_Ar10086284le_alt )
=> ( ( last_A2088691109le_alt @ ( cons_A1100118844le_alt @ X_14 @ Xs_29 ) )
= X_14 ) )
& ( ( Xs_29 != nil_Ar10086284le_alt )
=> ( ( last_A2088691109le_alt @ ( cons_A1100118844le_alt @ X_14 @ Xs_29 ) )
= ( last_A2088691109le_alt @ Xs_29 ) ) ) ) ).
thf(fact_56_last__appendL,axiom,
! [Xs_28: list_A1528105233le_alt,Ys_10: list_A1528105233le_alt] :
( ( Ys_10 = nil_Ar10086284le_alt )
=> ( ( last_A2088691109le_alt @ ( append1050458273le_alt @ Xs_28 @ Ys_10 ) )
= ( last_A2088691109le_alt @ Xs_28 ) ) ) ).
thf(fact_57_last__appendR,axiom,
! [Xs_27: list_A1528105233le_alt,Ys_9: list_A1528105233le_alt] :
( ( Ys_9 != nil_Ar10086284le_alt )
=> ( ( last_A2088691109le_alt @ ( append1050458273le_alt @ Xs_27 @ Ys_9 ) )
= ( last_A2088691109le_alt @ Ys_9 ) ) ) ).
thf(fact_58_last__append,axiom,
! [Xs_26: list_A1528105233le_alt,Ys_8: list_A1528105233le_alt] :
( ( ( Ys_8 = nil_Ar10086284le_alt )
=> ( ( last_A2088691109le_alt @ ( append1050458273le_alt @ Xs_26 @ Ys_8 ) )
= ( last_A2088691109le_alt @ Xs_26 ) ) )
& ( ( Ys_8 != nil_Ar10086284le_alt )
=> ( ( last_A2088691109le_alt @ ( append1050458273le_alt @ Xs_26 @ Ys_8 ) )
= ( last_A2088691109le_alt @ Ys_8 ) ) ) ) ).
thf(fact_59_last__snoc,axiom,
! [Xs_25: list_A1528105233le_alt,X_13: arrow_1346734812le_alt] :
( ( last_A2088691109le_alt @ ( append1050458273le_alt @ Xs_25 @ ( cons_A1100118844le_alt @ X_13 @ nil_Ar10086284le_alt ) ) )
= X_13 ) ).
thf(fact_60_maps__simps_I1_J,axiom,
! [F: arrow_1346734812le_alt > list_A1528105233le_alt,X_12: arrow_1346734812le_alt,Xs_24: list_A1528105233le_alt] :
( ( maps_A51637569le_alt @ F @ ( cons_A1100118844le_alt @ X_12 @ Xs_24 ) )
= ( append1050458273le_alt @ ( F @ X_12 ) @ ( maps_A51637569le_alt @ F @ Xs_24 ) ) ) ).
thf(fact_61_not__distinct__decomp,axiom,
! [Ws: list_A1528105233le_alt] :
( ~ ( distin1107700095le_alt @ Ws )
=> ? [Xs_23: list_A1528105233le_alt,Ys_7: list_A1528105233le_alt,Zs: list_A1528105233le_alt,Y_3: arrow_1346734812le_alt] :
( Ws
= ( append1050458273le_alt @ Xs_23 @ ( append1050458273le_alt @ ( cons_A1100118844le_alt @ Y_3 @ nil_Ar10086284le_alt ) @ ( append1050458273le_alt @ Ys_7 @ ( append1050458273le_alt @ ( cons_A1100118844le_alt @ Y_3 @ nil_Ar10086284le_alt ) @ Zs ) ) ) ) ) ) ).
thf(fact_62_equal,axiom,
equal_2044961839le_alt = fequal194154450le_alt ).
thf(fact_63_equal__refl,axiom,
! [X_11: list_A1528105233le_alt] : ( equal_2044961839le_alt @ X_11 @ X_11 ) ).
thf(fact_64_eq__equal,axiom,
fequal194154450le_alt = equal_2044961839le_alt ).
thf(fact_65_equal__eq,axiom,
! [X_10: list_A1528105233le_alt,Y_2: list_A1528105233le_alt] :
( ( equal_2044961839le_alt @ X_10 @ Y_2 )
<=> ( X_10 = Y_2 ) ) ).
thf(fact_66_replicate__append__same,axiom,
! [I: nat,X_9: arrow_1346734812le_alt] :
( ( append1050458273le_alt @ ( replic235430982le_alt @ I @ X_9 ) @ ( cons_A1100118844le_alt @ X_9 @ nil_Ar10086284le_alt ) )
= ( cons_A1100118844le_alt @ X_9 @ ( replic235430982le_alt @ I @ X_9 ) ) ) ).
thf(fact_67_rev_Osimps_I2_J,axiom,
! [X_8: arrow_1346734812le_alt,Xs_22: list_A1528105233le_alt] :
( ( rev_Ar1977782764le_alt @ ( cons_A1100118844le_alt @ X_8 @ Xs_22 ) )
= ( append1050458273le_alt @ ( rev_Ar1977782764le_alt @ Xs_22 ) @ ( cons_A1100118844le_alt @ X_8 @ nil_Ar10086284le_alt ) ) ) ).
thf(fact_68_rev__eq__Cons__iff,axiom,
! [Xs_21: list_A1528105233le_alt,Y_1: arrow_1346734812le_alt,Ys_6: list_A1528105233le_alt] :
( ( ( rev_Ar1977782764le_alt @ Xs_21 )
= ( cons_A1100118844le_alt @ Y_1 @ Ys_6 ) )
<=> ( Xs_21
= ( append1050458273le_alt @ ( rev_Ar1977782764le_alt @ Ys_6 ) @ ( cons_A1100118844le_alt @ Y_1 @ nil_Ar10086284le_alt ) ) ) ) ).
thf(fact_69_rev__is__rev__conv,axiom,
! [Xs_20: list_A1528105233le_alt,Ys_5: list_A1528105233le_alt] :
( ( ( rev_Ar1977782764le_alt @ Xs_20 )
= ( rev_Ar1977782764le_alt @ Ys_5 ) )
<=> ( Xs_20 = Ys_5 ) ) ).
thf(fact_70_rev__swap,axiom,
! [Xs_19: list_A1528105233le_alt,Ys_4: list_A1528105233le_alt] :
( ( ( rev_Ar1977782764le_alt @ Xs_19 )
= Ys_4 )
<=> ( Xs_19
= ( rev_Ar1977782764le_alt @ Ys_4 ) ) ) ).
thf(fact_71_rev__replicate,axiom,
! [N_2: nat,X_7: arrow_1346734812le_alt] :
( ( rev_Ar1977782764le_alt @ ( replic235430982le_alt @ N_2 @ X_7 ) )
= ( replic235430982le_alt @ N_2 @ X_7 ) ) ).
thf(fact_72_rev__rev__ident,axiom,
! [Xs_18: list_A1528105233le_alt] :
( ( rev_Ar1977782764le_alt @ ( rev_Ar1977782764le_alt @ Xs_18 ) )
= Xs_18 ) ).
thf(fact_73_append__replicate__commute,axiom,
! [N_1: nat,X_6: arrow_1346734812le_alt,K: nat] :
( ( append1050458273le_alt @ ( replic235430982le_alt @ N_1 @ X_6 ) @ ( replic235430982le_alt @ K @ X_6 ) )
= ( append1050458273le_alt @ ( replic235430982le_alt @ K @ X_6 ) @ ( replic235430982le_alt @ N_1 @ X_6 ) ) ) ).
thf(fact_74_distinct__rev,axiom,
! [Xs_17: list_A1528105233le_alt] :
( ( distin1107700095le_alt @ ( rev_Ar1977782764le_alt @ Xs_17 ) )
<=> ( distin1107700095le_alt @ Xs_17 ) ) ).
thf(fact_75_rev__append,axiom,
! [Xs_16: list_A1528105233le_alt,Ys_3: list_A1528105233le_alt] :
( ( rev_Ar1977782764le_alt @ ( append1050458273le_alt @ Xs_16 @ Ys_3 ) )
= ( append1050458273le_alt @ ( rev_Ar1977782764le_alt @ Ys_3 ) @ ( rev_Ar1977782764le_alt @ Xs_16 ) ) ) ).
thf(fact_76_rev_Osimps_I1_J,axiom,
( ( rev_Ar1977782764le_alt @ nil_Ar10086284le_alt )
= nil_Ar10086284le_alt ) ).
thf(fact_77_Nil__is__rev__conv,axiom,
! [Xs_15: list_A1528105233le_alt] :
( ( nil_Ar10086284le_alt
= ( rev_Ar1977782764le_alt @ Xs_15 ) )
<=> ( Xs_15 = nil_Ar10086284le_alt ) ) ).
thf(fact_78_rev__is__Nil__conv,axiom,
! [Xs_14: list_A1528105233le_alt] :
( ( ( rev_Ar1977782764le_alt @ Xs_14 )
= nil_Ar10086284le_alt )
<=> ( Xs_14 = nil_Ar10086284le_alt ) ) ).
thf(fact_79_singleton__rev__conv,axiom,
! [X_5: arrow_1346734812le_alt,Xs_13: list_A1528105233le_alt] :
( ( ( cons_A1100118844le_alt @ X_5 @ nil_Ar10086284le_alt )
= ( rev_Ar1977782764le_alt @ Xs_13 ) )
<=> ( Xs_13
= ( cons_A1100118844le_alt @ X_5 @ nil_Ar10086284le_alt ) ) ) ).
thf(fact_80_rev__singleton__conv,axiom,
! [Xs_12: list_A1528105233le_alt,X_4: arrow_1346734812le_alt] :
( ( ( rev_Ar1977782764le_alt @ Xs_12 )
= ( cons_A1100118844le_alt @ X_4 @ nil_Ar10086284le_alt ) )
<=> ( Xs_12
= ( cons_A1100118844le_alt @ X_4 @ nil_Ar10086284le_alt ) ) ) ).
thf(fact_81_replicate__app__Cons__same,axiom,
! [N: nat,X_3: arrow_1346734812le_alt,Xs_11: list_A1528105233le_alt] :
( ( append1050458273le_alt @ ( replic235430982le_alt @ N @ X_3 ) @ ( cons_A1100118844le_alt @ X_3 @ Xs_11 ) )
= ( cons_A1100118844le_alt @ X_3 @ ( append1050458273le_alt @ ( replic235430982le_alt @ N @ X_3 ) @ Xs_11 ) ) ) ).
thf(fact_82_hd__rev,axiom,
! [Xs_10: list_A1528105233le_alt] :
( ( Xs_10 != nil_Ar10086284le_alt )
=> ( ( hd_Arr689575519le_alt @ ( rev_Ar1977782764le_alt @ Xs_10 ) )
= ( last_A2088691109le_alt @ Xs_10 ) ) ) ).
thf(fact_83_last__rev,axiom,
! [Xs_9: list_A1528105233le_alt] :
( ( Xs_9 != nil_Ar10086284le_alt )
=> ( ( last_A2088691109le_alt @ ( rev_Ar1977782764le_alt @ Xs_9 ) )
= ( hd_Arr689575519le_alt @ Xs_9 ) ) ) ).
thf(fact_84_hd_Osimps,axiom,
! [X_2: arrow_1346734812le_alt,Xs_8: list_A1528105233le_alt] :
( ( hd_Arr689575519le_alt @ ( cons_A1100118844le_alt @ X_2 @ Xs_8 ) )
= X_2 ) ).
thf(fact_85_hd__append,axiom,
! [Ys_2: list_A1528105233le_alt,Xs_7: list_A1528105233le_alt] :
( ( ( Xs_7 = nil_Ar10086284le_alt )
=> ( ( hd_Arr689575519le_alt @ ( append1050458273le_alt @ Xs_7 @ Ys_2 ) )
= ( hd_Arr689575519le_alt @ Ys_2 ) ) )
& ( ( Xs_7 != nil_Ar10086284le_alt )
=> ( ( hd_Arr689575519le_alt @ ( append1050458273le_alt @ Xs_7 @ Ys_2 ) )
= ( hd_Arr689575519le_alt @ Xs_7 ) ) ) ) ).
thf(fact_86_hd__append2,axiom,
! [Ys_1: list_A1528105233le_alt,Xs_6: list_A1528105233le_alt] :
( ( Xs_6 != nil_Ar10086284le_alt )
=> ( ( hd_Arr689575519le_alt @ ( append1050458273le_alt @ Xs_6 @ Ys_1 ) )
= ( hd_Arr689575519le_alt @ Xs_6 ) ) ) ).
thf(fact_87_rotate1__hd__tl,axiom,
! [Xs_5: list_A1528105233le_alt] :
( ( Xs_5 != nil_Ar10086284le_alt )
=> ( ( rotate1206725081le_alt @ Xs_5 )
= ( append1050458273le_alt @ ( tl_Arr1336826979le_alt @ Xs_5 ) @ ( cons_A1100118844le_alt @ ( hd_Arr689575519le_alt @ Xs_5 ) @ nil_Ar10086284le_alt ) ) ) ) ).
thf(fact_88_hd__dropWhile,axiom,
! [P_3: arrow_1346734812le_alt > $o,Xs_4: list_A1528105233le_alt] :
( ( ( dropWh40674093le_alt @ P_3 @ Xs_4 )
!= nil_Ar10086284le_alt )
=> ~ ( P_3 @ ( hd_Arr689575519le_alt @ ( dropWh40674093le_alt @ P_3 @ Xs_4 ) ) ) ) ).
thf(fact_89_tl__append2,axiom,
! [Ys: list_A1528105233le_alt,Xs_3: list_A1528105233le_alt] :
( ( Xs_3 != nil_Ar10086284le_alt )
=> ( ( tl_Arr1336826979le_alt @ ( append1050458273le_alt @ Xs_3 @ Ys ) )
= ( append1050458273le_alt @ ( tl_Arr1336826979le_alt @ Xs_3 ) @ Ys ) ) ) ).
thf(fact_90_distinct__tl,axiom,
! [Xs_2: list_A1528105233le_alt] :
( ( distin1107700095le_alt @ Xs_2 )
=> ( distin1107700095le_alt @ ( tl_Arr1336826979le_alt @ Xs_2 ) ) ) ).
thf(fact_91_distinct__dropWhile,axiom,
! [P_2: arrow_1346734812le_alt > $o,Xs_1: list_A1528105233le_alt] :
( ( distin1107700095le_alt @ Xs_1 )
=> ( distin1107700095le_alt @ ( dropWh40674093le_alt @ P_2 @ Xs_1 ) ) ) ).
thf(fact_92_dropWhile_Osimps_I1_J,axiom,
! [P_1: arrow_1346734812le_alt > $o] :
( ( dropWh40674093le_alt @ P_1 @ nil_Ar10086284le_alt )
= nil_Ar10086284le_alt ) ).
thf(fact_93_dropWhile_Osimps_I2_J,axiom,
! [Xs: list_A1528105233le_alt,P: arrow_1346734812le_alt > $o,X_1: arrow_1346734812le_alt] :
( ( ( P @ X_1 )
=> ( ( dropWh40674093le_alt @ P @ ( cons_A1100118844le_alt @ X_1 @ Xs ) )
= ( dropWh40674093le_alt @ P @ Xs ) ) )
& ( ~ ( P @ X_1 )
=> ( ( dropWh40674093le_alt @ P @ ( cons_A1100118844le_alt @ X_1 @ Xs ) )
= ( cons_A1100118844le_alt @ X_1 @ Xs ) ) ) ) ).
%----Helper facts (2)
thf(help_fequal_1_1_fequal_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____sd,axiom,
! [X: list_A1528105233le_alt,Y: list_A1528105233le_alt] :
( ~ ( fequal194154450le_alt @ X @ Y )
| ( X = Y ) ) ).
thf(help_fequal_2_1_fequal_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____sd,axiom,
! [X: list_A1528105233le_alt,Y: list_A1528105233le_alt] :
( ( X != Y )
| ( fequal194154450le_alt @ X @ Y ) ) ).
%----Conjectures (2)
thf(conj_0,hypothesis,
a != b ).
thf(conj_1,conjecture,
? [C: arrow_1346734812le_alt] : ( distin1107700095le_alt @ ( cons_A1100118844le_alt @ a @ ( cons_A1100118844le_alt @ b @ ( cons_A1100118844le_alt @ C @ nil_Ar10086284le_alt ) ) ) ) ).
%------------------------------------------------------------------------------