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_fofmg_l29 [Bla11]
% Status : Theorem
% Rating : 1.00 v5.4.0, 0.96 v5.3.0
% Syntax : Number of formulae : 105 ( 39 unt; 0 def)
% Number of atoms : 223 ( 158 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 154 ( 36 ~; 5 |; 26 &)
% ( 30 <=>; 57 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 0 prp; 1-2 aty)
% Number of functors : 26 ( 26 usr; 8 con; 0-2 aty)
% Number of variables : 208 ( 195 !; 13 ?)
% SPC : FOF_THM_RFO_SEQ
% Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 2011-08-09 15:17:53
% : Encoded with monomorphized guards.
%------------------------------------------------------------------------------
%----Explicit typings (7)
fof(gsy_c_HOL_Oundefined_000tc__Arrow____Order____Mirabelle____fjewxadnqg__Oalt,axiom,
is_Arr553848933le_alt(undefi1301554228le_alt(arrow_1812558424le_alt)) ).
fof(gsy_c_List_Ohd_000tc__Arrow____Order____Mirabelle____fjewxadnqg__Oalt,axiom,
! [B_1] : is_Arr553848933le_alt(hd_Arr1645127589le_alt(B_1)) ).
fof(gsy_c_List_Olast_000tc__Arrow____Order____Mirabelle____fjewxadnqg__Oalt,axiom,
! [B_1] : is_Arr553848933le_alt(last_A896759531le_alt(B_1)) ).
fof(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____fjewxadnqg__Oalt_000tc__HOL__Ob,axiom,
! [B_1,B_2] :
( is_Arr553848933le_alt(B_2)
=> is_bool(hAPP_A1960806890t_bool(B_1,B_2)) ) ).
fof(gsy_c_hAPP_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____fjewxadnqg__Oa,hypothesis,
! [B_1,B_2] : is_bool(hAPP_l1656811191t_bool(B_1,B_2)) ).
fof(gsy_v_a,hypothesis,
is_Arr553848933le_alt(a) ).
fof(gsy_v_b,hypothesis,
is_Arr553848933le_alt(b) ).
%----Relevant facts (94)
fof(fact_0_alt3,axiom,
? [A_1,B,C] :
( is_Arr553848933le_alt(A_1)
& is_Arr553848933le_alt(B)
& is_Arr553848933le_alt(C)
& hBOOL(hAPP_l1656811191t_bool(distin2063252165le_alt,cons_A2055670914le_alt(A_1,cons_A2055670914le_alt(B,cons_A2055670914le_alt(C,nil_Ar965638354le_alt))))) ) ).
fof(fact_1_distinct_Osimps_I1_J,axiom,
hBOOL(hAPP_l1656811191t_bool(distin2063252165le_alt,nil_Ar965638354le_alt)) ).
fof(fact_2_list_Osimps_I2_J,axiom,
! [A_2,List_3] : nil_Ar965638354le_alt != cons_A2055670914le_alt(A_2,List_3) ).
fof(fact_3_list_Osimps_I3_J,axiom,
! [A,List] : cons_A2055670914le_alt(A,List) != nil_Ar965638354le_alt ).
fof(fact_4_neq__Nil__conv,axiom,
! [Xs] :
( Xs != nil_Ar965638354le_alt
<=> ? [Y_2,Ys_5] :
( is_Arr553848933le_alt(Y_2)
& Xs = cons_A2055670914le_alt(Y_2,Ys_5) ) ) ).
fof(fact_5_list_Oexhaust,axiom,
! [Y_4] :
( Y_4 != nil_Ar965638354le_alt
=> ~ ! [A_1,List_2] :
( is_Arr553848933le_alt(A_1)
=> Y_4 != cons_A2055670914le_alt(A_1,List_2) ) ) ).
fof(fact_6_not__Cons__self,axiom,
! [Xs_39,X_24] : Xs_39 != cons_A2055670914le_alt(X_24,Xs_39) ).
fof(fact_7_not__Cons__self2,axiom,
! [X_23,Xs_38] : cons_A2055670914le_alt(X_23,Xs_38) != Xs_38 ).
fof(fact_8_list_Oinject,axiom,
! [Aa,List_1,A,List] :
( ( is_Arr553848933le_alt(Aa)
& is_Arr553848933le_alt(A) )
=> ( cons_A2055670914le_alt(Aa,List_1) = cons_A2055670914le_alt(A,List)
<=> ( Aa = A
& List_1 = List ) ) ) ).
fof(fact_9_splice_Osimps_I2_J,axiom,
! [V,Va] : splice1200342693le_alt(cons_A2055670914le_alt(V,Va),nil_Ar965638354le_alt) = cons_A2055670914le_alt(V,Va) ).
fof(fact_10_insert__Nil,axiom,
! [X_22] : insert1800010984le_alt(X_22,nil_Ar965638354le_alt) = cons_A2055670914le_alt(X_22,nil_Ar965638354le_alt) ).
fof(fact_11_list__nonempty__induct,axiom,
! [P,Xs] :
( Xs != nil_Ar965638354le_alt
=> ( ! [X_14] :
( is_Arr553848933le_alt(X_14)
=> hBOOL(hAPP_l1656811191t_bool(P,cons_A2055670914le_alt(X_14,nil_Ar965638354le_alt))) )
=> ( ! [X_14,Xs_13] :
( is_Arr553848933le_alt(X_14)
=> ( Xs_13 != nil_Ar965638354le_alt
=> ( hBOOL(hAPP_l1656811191t_bool(P,Xs_13))
=> hBOOL(hAPP_l1656811191t_bool(P,cons_A2055670914le_alt(X_14,Xs_13))) ) ) )
=> hBOOL(hAPP_l1656811191t_bool(P,Xs)) ) ) ) ).
fof(fact_12_distinct__butlast,axiom,
! [Xs_37] :
( Xs_37 != nil_Ar965638354le_alt
=> ( hBOOL(hAPP_l1656811191t_bool(distin2063252165le_alt,Xs_37))
=> hBOOL(hAPP_l1656811191t_bool(distin2063252165le_alt,butlas2101875742le_alt(Xs_37))) ) ) ).
fof(fact_13_butlast_Osimps_I1_J,axiom,
butlas2101875742le_alt(nil_Ar965638354le_alt) = nil_Ar965638354le_alt ).
fof(fact_14_distinct__insert,axiom,
! [X_21,Xs_36] :
( hBOOL(hAPP_l1656811191t_bool(distin2063252165le_alt,Xs_36))
=> hBOOL(hAPP_l1656811191t_bool(distin2063252165le_alt,insert1800010984le_alt(X_21,Xs_36))) ) ).
fof(fact_15_splice_Osimps_I3_J,axiom,
! [X_20,Xs_35,Y_3,Ys_18] : splice1200342693le_alt(cons_A2055670914le_alt(X_20,Xs_35),cons_A2055670914le_alt(Y_3,Ys_18)) = cons_A2055670914le_alt(X_20,cons_A2055670914le_alt(Y_3,splice1200342693le_alt(Xs_35,Ys_18))) ).
fof(fact_16_splice__Nil2,axiom,
! [Xs_34] : splice1200342693le_alt(Xs_34,nil_Ar965638354le_alt) = Xs_34 ).
fof(fact_17_splice_Osimps_I1_J,axiom,
! [Ys_17] : splice1200342693le_alt(nil_Ar965638354le_alt,Ys_17) = Ys_17 ).
fof(fact_18_butlast_Osimps_I2_J,axiom,
! [X_19,Xs_33] :
( ( Xs_33 = nil_Ar965638354le_alt
=> butlas2101875742le_alt(cons_A2055670914le_alt(X_19,Xs_33)) = nil_Ar965638354le_alt )
& ( Xs_33 != nil_Ar965638354le_alt
=> butlas2101875742le_alt(cons_A2055670914le_alt(X_19,Xs_33)) = cons_A2055670914le_alt(X_19,butlas2101875742le_alt(Xs_33)) ) ) ).
fof(fact_19_eq__Nil__null,axiom,
! [Xs] :
( Xs = nil_Ar965638354le_alt
<=> hBOOL(hAPP_l1656811191t_bool(null_A1200409306le_alt,Xs)) ) ).
fof(fact_20_List_Onull__def,axiom,
! [Xs] :
( hBOOL(hAPP_l1656811191t_bool(null_A1200409306le_alt,Xs))
<=> Xs = nil_Ar965638354le_alt ) ).
fof(fact_21_null__rec_I2_J,axiom,
hBOOL(hAPP_l1656811191t_bool(null_A1200409306le_alt,nil_Ar965638354le_alt)) ).
fof(fact_22_null__rec_I1_J,axiom,
! [X_18,Xs_32] : ~ hBOOL(hAPP_l1656811191t_bool(null_A1200409306le_alt,cons_A2055670914le_alt(X_18,Xs_32))) ).
fof(fact_23_butlast__snoc,axiom,
! [Xs_31,X_17] : butlas2101875742le_alt(append2006010343le_alt(Xs_31,cons_A2055670914le_alt(X_17,nil_Ar965638354le_alt))) = Xs_31 ).
fof(fact_24_append__assoc,axiom,
! [Xs_30,Ys_16,Zs_4] : append2006010343le_alt(append2006010343le_alt(Xs_30,Ys_16),Zs_4) = append2006010343le_alt(Xs_30,append2006010343le_alt(Ys_16,Zs_4)) ).
fof(fact_25_append__eq__append__conv2,axiom,
! [Xs,Ys_4,Zs_1,Ts] :
( append2006010343le_alt(Xs,Ys_4) = append2006010343le_alt(Zs_1,Ts)
<=> ? [Us_1] :
( ( Xs = append2006010343le_alt(Zs_1,Us_1)
& append2006010343le_alt(Us_1,Ys_4) = Ts )
| ( append2006010343le_alt(Xs,Us_1) = Zs_1
& Ys_4 = append2006010343le_alt(Us_1,Ts) ) ) ) ).
fof(fact_26_same__append__eq,axiom,
! [Xs,Ys_4,Zs_1] :
( append2006010343le_alt(Xs,Ys_4) = append2006010343le_alt(Xs,Zs_1)
<=> Ys_4 = Zs_1 ) ).
fof(fact_27_append__same__eq,axiom,
! [Ys_4,Xs,Zs_1] :
( append2006010343le_alt(Ys_4,Xs) = append2006010343le_alt(Zs_1,Xs)
<=> Ys_4 = Zs_1 ) ).
fof(fact_28_append__eq__appendI,axiom,
! [Ys_15,Us,Xs_29,Xs1_1,Zs_3] :
( append2006010343le_alt(Xs_29,Xs1_1) = Zs_3
=> ( Ys_15 = append2006010343le_alt(Xs1_1,Us)
=> append2006010343le_alt(Xs_29,Ys_15) = append2006010343le_alt(Zs_3,Us) ) ) ).
fof(fact_29_append__Cons,axiom,
! [X_16,Xs_28,Ys_14] : append2006010343le_alt(cons_A2055670914le_alt(X_16,Xs_28),Ys_14) = cons_A2055670914le_alt(X_16,append2006010343le_alt(Xs_28,Ys_14)) ).
fof(fact_30_Cons__eq__appendI,axiom,
! [Xs_27,Zs_2,X_15,Xs1,Ys_13] :
( cons_A2055670914le_alt(X_15,Xs1) = Ys_13
=> ( Xs_27 = append2006010343le_alt(Xs1,Zs_2)
=> cons_A2055670914le_alt(X_15,Xs_27) = append2006010343le_alt(Ys_13,Zs_2) ) ) ).
fof(fact_31_append__Nil,axiom,
! [Ys_12] : append2006010343le_alt(nil_Ar965638354le_alt,Ys_12) = Ys_12 ).
fof(fact_32_Nil__is__append__conv,axiom,
! [Xs,Ys_4] :
( nil_Ar965638354le_alt = append2006010343le_alt(Xs,Ys_4)
<=> ( Xs = nil_Ar965638354le_alt
& Ys_4 = nil_Ar965638354le_alt ) ) ).
fof(fact_33_append__Nil2,axiom,
! [Xs_26] : append2006010343le_alt(Xs_26,nil_Ar965638354le_alt) = Xs_26 ).
fof(fact_34_self__append__conv,axiom,
! [Xs,Ys_4] :
( Xs = append2006010343le_alt(Xs,Ys_4)
<=> Ys_4 = nil_Ar965638354le_alt ) ).
fof(fact_35_self__append__conv2,axiom,
! [Ys_4,Xs] :
( Ys_4 = append2006010343le_alt(Xs,Ys_4)
<=> Xs = nil_Ar965638354le_alt ) ).
fof(fact_36_append__is__Nil__conv,axiom,
! [Xs,Ys_4] :
( append2006010343le_alt(Xs,Ys_4) = nil_Ar965638354le_alt
<=> ( Xs = nil_Ar965638354le_alt
& Ys_4 = nil_Ar965638354le_alt ) ) ).
fof(fact_37_append__self__conv,axiom,
! [Xs,Ys_4] :
( append2006010343le_alt(Xs,Ys_4) = Xs
<=> Ys_4 = nil_Ar965638354le_alt ) ).
fof(fact_38_append__self__conv2,axiom,
! [Xs,Ys_4] :
( append2006010343le_alt(Xs,Ys_4) = Ys_4
<=> Xs = nil_Ar965638354le_alt ) ).
fof(fact_39_eq__Nil__appendI,axiom,
! [Xs_25,Ys_11] :
( Xs_25 = Ys_11
=> Xs_25 = append2006010343le_alt(nil_Ar965638354le_alt,Ys_11) ) ).
fof(fact_40_append__eq__Cons__conv,axiom,
! [Ys_4,Zs_1,X_1,Xs] :
( append2006010343le_alt(Ys_4,Zs_1) = cons_A2055670914le_alt(X_1,Xs)
<=> ( ( Ys_4 = nil_Ar965638354le_alt
& Zs_1 = cons_A2055670914le_alt(X_1,Xs) )
| ? [Ys_10] :
( Ys_4 = cons_A2055670914le_alt(X_1,Ys_10)
& append2006010343le_alt(Ys_10,Zs_1) = Xs ) ) ) ).
fof(fact_41_Cons__eq__append__conv,axiom,
! [X_1,Xs,Ys_4,Zs_1] :
( cons_A2055670914le_alt(X_1,Xs) = append2006010343le_alt(Ys_4,Zs_1)
<=> ( ( Ys_4 = nil_Ar965638354le_alt
& cons_A2055670914le_alt(X_1,Xs) = Zs_1 )
| ? [Ys_10] :
( cons_A2055670914le_alt(X_1,Ys_10) = Ys_4
& Xs = append2006010343le_alt(Ys_10,Zs_1) ) ) ) ).
fof(fact_42_append1__eq__conv,axiom,
! [Xs,X_1,Ys_4,Y_1] :
( ( is_Arr553848933le_alt(X_1)
& is_Arr553848933le_alt(Y_1) )
=> ( append2006010343le_alt(Xs,cons_A2055670914le_alt(X_1,nil_Ar965638354le_alt)) = append2006010343le_alt(Ys_4,cons_A2055670914le_alt(Y_1,nil_Ar965638354le_alt))
<=> ( Xs = Ys_4
& X_1 = Y_1 ) ) ) ).
fof(fact_43_butlast__append,axiom,
! [Xs_24,Ys_9] :
( ( Ys_9 = nil_Ar965638354le_alt
=> butlas2101875742le_alt(append2006010343le_alt(Xs_24,Ys_9)) = butlas2101875742le_alt(Xs_24) )
& ( Ys_9 != nil_Ar965638354le_alt
=> butlas2101875742le_alt(append2006010343le_alt(Xs_24,Ys_9)) = append2006010343le_alt(Xs_24,butlas2101875742le_alt(Ys_9)) ) ) ).
fof(fact_44_rev__induct,axiom,
! [Xs,P] :
( hBOOL(hAPP_l1656811191t_bool(P,nil_Ar965638354le_alt))
=> ( ! [X_14,Xs_13] :
( is_Arr553848933le_alt(X_14)
=> ( hBOOL(hAPP_l1656811191t_bool(P,Xs_13))
=> hBOOL(hAPP_l1656811191t_bool(P,append2006010343le_alt(Xs_13,cons_A2055670914le_alt(X_14,nil_Ar965638354le_alt)))) ) )
=> hBOOL(hAPP_l1656811191t_bool(P,Xs)) ) ) ).
fof(fact_45_rev__cases,axiom,
! [Xs_23] :
( Xs_23 != nil_Ar965638354le_alt
=> ~ ! [Ys_5,Y_2] :
( is_Arr553848933le_alt(Y_2)
=> Xs_23 != append2006010343le_alt(Ys_5,cons_A2055670914le_alt(Y_2,nil_Ar965638354le_alt)) ) ) ).
fof(fact_46_equal__Nil__null,axiom,
! [Xs] :
( hBOOL(hAPP_l1656811191t_bool(hAPP_l1565956415t_bool(equal_35123829le_alt,Xs),nil_Ar965638354le_alt))
<=> hBOOL(hAPP_l1656811191t_bool(null_A1200409306le_alt,Xs)) ) ).
fof(fact_47_snoc__eq__iff__butlast,axiom,
! [Xs,X_1,Ys_4] :
( is_Arr553848933le_alt(X_1)
=> ( append2006010343le_alt(Xs,cons_A2055670914le_alt(X_1,nil_Ar965638354le_alt)) = Ys_4
<=> ( Ys_4 != nil_Ar965638354le_alt
& butlas2101875742le_alt(Ys_4) = Xs
& last_A896759531le_alt(Ys_4) = X_1 ) ) ) ).
fof(fact_48_append__butlast__last__id,axiom,
! [Xs_22] :
( Xs_22 != nil_Ar965638354le_alt
=> append2006010343le_alt(butlas2101875742le_alt(Xs_22),cons_A2055670914le_alt(last_A896759531le_alt(Xs_22),nil_Ar965638354le_alt)) = Xs_22 ) ).
fof(fact_49_rotate__simps,axiom,
! [X_13,Xs_21] :
( rotate14793503le_alt(nil_Ar965638354le_alt) = nil_Ar965638354le_alt
& rotate14793503le_alt(cons_A2055670914le_alt(X_13,Xs_21)) = append2006010343le_alt(Xs_21,cons_A2055670914le_alt(X_13,nil_Ar965638354le_alt)) ) ).
fof(fact_50_equal__list__def,axiom,
! [X_1,Y_1] :
( hBOOL(hAPP_l1656811191t_bool(hAPP_l1565956415t_bool(equal_35123829le_alt,X_1),Y_1))
<=> X_1 = Y_1 ) ).
fof(fact_51_rotate1__is__Nil__conv,axiom,
! [Xs] :
( rotate14793503le_alt(Xs) = nil_Ar965638354le_alt
<=> Xs = nil_Ar965638354le_alt ) ).
fof(fact_52_distinct1__rotate,axiom,
! [Xs] :
( hBOOL(hAPP_l1656811191t_bool(distin2063252165le_alt,rotate14793503le_alt(Xs)))
<=> hBOOL(hAPP_l1656811191t_bool(distin2063252165le_alt,Xs)) ) ).
fof(fact_53_last__ConsL,axiom,
! [X_12,Xs_20] :
( is_Arr553848933le_alt(X_12)
=> ( Xs_20 = nil_Ar965638354le_alt
=> last_A896759531le_alt(cons_A2055670914le_alt(X_12,Xs_20)) = X_12 ) ) ).
fof(fact_54_last__ConsR,axiom,
! [X_11,Xs_19] :
( Xs_19 != nil_Ar965638354le_alt
=> last_A896759531le_alt(cons_A2055670914le_alt(X_11,Xs_19)) = last_A896759531le_alt(Xs_19) ) ).
fof(fact_55_last_Osimps,axiom,
! [X_10,Xs_18] :
( is_Arr553848933le_alt(X_10)
=> ( ( Xs_18 = nil_Ar965638354le_alt
=> last_A896759531le_alt(cons_A2055670914le_alt(X_10,Xs_18)) = X_10 )
& ( Xs_18 != nil_Ar965638354le_alt
=> last_A896759531le_alt(cons_A2055670914le_alt(X_10,Xs_18)) = last_A896759531le_alt(Xs_18) ) ) ) ).
fof(fact_56_last__appendL,axiom,
! [Xs_17,Ys_8] :
( Ys_8 = nil_Ar965638354le_alt
=> last_A896759531le_alt(append2006010343le_alt(Xs_17,Ys_8)) = last_A896759531le_alt(Xs_17) ) ).
fof(fact_57_last__appendR,axiom,
! [Xs_16,Ys_7] :
( Ys_7 != nil_Ar965638354le_alt
=> last_A896759531le_alt(append2006010343le_alt(Xs_16,Ys_7)) = last_A896759531le_alt(Ys_7) ) ).
fof(fact_58_last__append,axiom,
! [Xs_15,Ys_6] :
( ( Ys_6 = nil_Ar965638354le_alt
=> last_A896759531le_alt(append2006010343le_alt(Xs_15,Ys_6)) = last_A896759531le_alt(Xs_15) )
& ( Ys_6 != nil_Ar965638354le_alt
=> last_A896759531le_alt(append2006010343le_alt(Xs_15,Ys_6)) = last_A896759531le_alt(Ys_6) ) ) ).
fof(fact_59_last__snoc,axiom,
! [Xs_14,X_9] :
( is_Arr553848933le_alt(X_9)
=> last_A896759531le_alt(append2006010343le_alt(Xs_14,cons_A2055670914le_alt(X_9,nil_Ar965638354le_alt))) = X_9 ) ).
fof(fact_60_maps__simps_I1_J,axiom,
! [F,X_1,Xs] : maps_A1380093889le_alt(F,cons_A2055670914le_alt(X_1,Xs)) = append2006010343le_alt(hAPP_A285010404le_alt(F,X_1),maps_A1380093889le_alt(F,Xs)) ).
fof(fact_61_not__distinct__decomp,axiom,
! [Ws] :
( ~ hBOOL(hAPP_l1656811191t_bool(distin2063252165le_alt,Ws))
=> ? [Xs_13,Ys_5,Zs,Y_2] :
( is_Arr553848933le_alt(Y_2)
& Ws = append2006010343le_alt(Xs_13,append2006010343le_alt(cons_A2055670914le_alt(Y_2,nil_Ar965638354le_alt),append2006010343le_alt(Ys_5,append2006010343le_alt(cons_A2055670914le_alt(Y_2,nil_Ar965638354le_alt),Zs)))) ) ) ).
fof(fact_62_equal,axiom,
equal_35123829le_alt = fequal331800088le_alt ).
fof(fact_63_equal__refl,axiom,
! [X_8] : hBOOL(hAPP_l1656811191t_bool(hAPP_l1565956415t_bool(equal_35123829le_alt,X_8),X_8)) ).
fof(fact_64_eq__equal,axiom,
fequal331800088le_alt = equal_35123829le_alt ).
fof(fact_65_equal__eq,axiom,
! [X_1,Y_1] :
( hBOOL(hAPP_l1656811191t_bool(hAPP_l1565956415t_bool(equal_35123829le_alt,X_1),Y_1))
<=> X_1 = Y_1 ) ).
fof(fact_66_replicate__append__same,axiom,
! [I,X_7] : append2006010343le_alt(hAPP_A285010404le_alt(replic1190983052le_alt(I),X_7),cons_A2055670914le_alt(X_7,nil_Ar965638354le_alt)) = cons_A2055670914le_alt(X_7,hAPP_A285010404le_alt(replic1190983052le_alt(I),X_7)) ).
fof(fact_67_rev_Osimps_I2_J,axiom,
! [X_6,Xs_12] : rev_Ar785851186le_alt(cons_A2055670914le_alt(X_6,Xs_12)) = append2006010343le_alt(rev_Ar785851186le_alt(Xs_12),cons_A2055670914le_alt(X_6,nil_Ar965638354le_alt)) ).
fof(fact_68_rev__eq__Cons__iff,axiom,
! [Xs,Y_1,Ys_4] :
( rev_Ar785851186le_alt(Xs) = cons_A2055670914le_alt(Y_1,Ys_4)
<=> Xs = append2006010343le_alt(rev_Ar785851186le_alt(Ys_4),cons_A2055670914le_alt(Y_1,nil_Ar965638354le_alt)) ) ).
fof(fact_69_rev__is__rev__conv,axiom,
! [Xs,Ys_4] :
( rev_Ar785851186le_alt(Xs) = rev_Ar785851186le_alt(Ys_4)
<=> Xs = Ys_4 ) ).
fof(fact_70_rev__swap,axiom,
! [Xs,Ys_4] :
( rev_Ar785851186le_alt(Xs) = Ys_4
<=> Xs = rev_Ar785851186le_alt(Ys_4) ) ).
fof(fact_71_rev__replicate,axiom,
! [N_2,X_5] : rev_Ar785851186le_alt(hAPP_A285010404le_alt(replic1190983052le_alt(N_2),X_5)) = hAPP_A285010404le_alt(replic1190983052le_alt(N_2),X_5) ).
fof(fact_72_rev__rev__ident,axiom,
! [Xs_11] : rev_Ar785851186le_alt(rev_Ar785851186le_alt(Xs_11)) = Xs_11 ).
fof(fact_73_append__replicate__commute,axiom,
! [N_1,X_4,K] : append2006010343le_alt(hAPP_A285010404le_alt(replic1190983052le_alt(N_1),X_4),hAPP_A285010404le_alt(replic1190983052le_alt(K),X_4)) = append2006010343le_alt(hAPP_A285010404le_alt(replic1190983052le_alt(K),X_4),hAPP_A285010404le_alt(replic1190983052le_alt(N_1),X_4)) ).
fof(fact_74_distinct__rev,axiom,
! [Xs] :
( hBOOL(hAPP_l1656811191t_bool(distin2063252165le_alt,rev_Ar785851186le_alt(Xs)))
<=> hBOOL(hAPP_l1656811191t_bool(distin2063252165le_alt,Xs)) ) ).
fof(fact_75_rev__append,axiom,
! [Xs_10,Ys_3] : rev_Ar785851186le_alt(append2006010343le_alt(Xs_10,Ys_3)) = append2006010343le_alt(rev_Ar785851186le_alt(Ys_3),rev_Ar785851186le_alt(Xs_10)) ).
fof(fact_76_rev_Osimps_I1_J,axiom,
rev_Ar785851186le_alt(nil_Ar965638354le_alt) = nil_Ar965638354le_alt ).
fof(fact_77_Nil__is__rev__conv,axiom,
! [Xs] :
( nil_Ar965638354le_alt = rev_Ar785851186le_alt(Xs)
<=> Xs = nil_Ar965638354le_alt ) ).
fof(fact_78_rev__is__Nil__conv,axiom,
! [Xs] :
( rev_Ar785851186le_alt(Xs) = nil_Ar965638354le_alt
<=> Xs = nil_Ar965638354le_alt ) ).
fof(fact_79_singleton__rev__conv,axiom,
! [X_1,Xs] :
( cons_A2055670914le_alt(X_1,nil_Ar965638354le_alt) = rev_Ar785851186le_alt(Xs)
<=> Xs = cons_A2055670914le_alt(X_1,nil_Ar965638354le_alt) ) ).
fof(fact_80_rev__singleton__conv,axiom,
! [Xs,X_1] :
( rev_Ar785851186le_alt(Xs) = cons_A2055670914le_alt(X_1,nil_Ar965638354le_alt)
<=> Xs = cons_A2055670914le_alt(X_1,nil_Ar965638354le_alt) ) ).
fof(fact_81_replicate__app__Cons__same,axiom,
! [N,X_3,Xs_9] : append2006010343le_alt(hAPP_A285010404le_alt(replic1190983052le_alt(N),X_3),cons_A2055670914le_alt(X_3,Xs_9)) = cons_A2055670914le_alt(X_3,append2006010343le_alt(hAPP_A285010404le_alt(replic1190983052le_alt(N),X_3),Xs_9)) ).
fof(fact_82_hd__rev,axiom,
! [Xs_8] :
( Xs_8 != nil_Ar965638354le_alt
=> hd_Arr1645127589le_alt(rev_Ar785851186le_alt(Xs_8)) = last_A896759531le_alt(Xs_8) ) ).
fof(fact_83_last__rev,axiom,
! [Xs_7] :
( Xs_7 != nil_Ar965638354le_alt
=> last_A896759531le_alt(rev_Ar785851186le_alt(Xs_7)) = hd_Arr1645127589le_alt(Xs_7) ) ).
fof(fact_84_hd_Osimps,axiom,
! [X_2,Xs_6] :
( is_Arr553848933le_alt(X_2)
=> hd_Arr1645127589le_alt(cons_A2055670914le_alt(X_2,Xs_6)) = X_2 ) ).
fof(fact_85_hd__append,axiom,
! [Ys_2,Xs_5] :
( ( Xs_5 = nil_Ar965638354le_alt
=> hd_Arr1645127589le_alt(append2006010343le_alt(Xs_5,Ys_2)) = hd_Arr1645127589le_alt(Ys_2) )
& ( Xs_5 != nil_Ar965638354le_alt
=> hd_Arr1645127589le_alt(append2006010343le_alt(Xs_5,Ys_2)) = hd_Arr1645127589le_alt(Xs_5) ) ) ).
fof(fact_86_hd__append2,axiom,
! [Ys_1,Xs_4] :
( Xs_4 != nil_Ar965638354le_alt
=> hd_Arr1645127589le_alt(append2006010343le_alt(Xs_4,Ys_1)) = hd_Arr1645127589le_alt(Xs_4) ) ).
fof(fact_87_rotate1__hd__tl,axiom,
! [Xs_3] :
( Xs_3 != nil_Ar965638354le_alt
=> rotate14793503le_alt(Xs_3) = append2006010343le_alt(tl_Arr144895401le_alt(Xs_3),cons_A2055670914le_alt(hd_Arr1645127589le_alt(Xs_3),nil_Ar965638354le_alt)) ) ).
fof(fact_88_hd__dropWhile,axiom,
! [P,Xs] :
( dropWh996226163le_alt(P,Xs) != nil_Ar965638354le_alt
=> ~ hBOOL(hAPP_A1960806890t_bool(P,hd_Arr1645127589le_alt(dropWh996226163le_alt(P,Xs)))) ) ).
fof(fact_89_tl__append2,axiom,
! [Ys,Xs_2] :
( Xs_2 != nil_Ar965638354le_alt
=> tl_Arr144895401le_alt(append2006010343le_alt(Xs_2,Ys)) = append2006010343le_alt(tl_Arr144895401le_alt(Xs_2),Ys) ) ).
fof(fact_90_distinct__tl,axiom,
! [Xs_1] :
( hBOOL(hAPP_l1656811191t_bool(distin2063252165le_alt,Xs_1))
=> hBOOL(hAPP_l1656811191t_bool(distin2063252165le_alt,tl_Arr144895401le_alt(Xs_1))) ) ).
fof(fact_91_distinct__dropWhile,axiom,
! [P,Xs] :
( hBOOL(hAPP_l1656811191t_bool(distin2063252165le_alt,Xs))
=> hBOOL(hAPP_l1656811191t_bool(distin2063252165le_alt,dropWh996226163le_alt(P,Xs))) ) ).
fof(fact_92_dropWhile_Osimps_I1_J,axiom,
! [P] : dropWh996226163le_alt(P,nil_Ar965638354le_alt) = nil_Ar965638354le_alt ).
fof(fact_93_dropWhile_Osimps_I2_J,axiom,
! [Xs,P,X_1] :
( ( hBOOL(hAPP_A1960806890t_bool(P,X_1))
=> dropWh996226163le_alt(P,cons_A2055670914le_alt(X_1,Xs)) = dropWh996226163le_alt(P,Xs) )
& ( ~ hBOOL(hAPP_A1960806890t_bool(P,X_1))
=> dropWh996226163le_alt(P,cons_A2055670914le_alt(X_1,Xs)) = cons_A2055670914le_alt(X_1,Xs) ) ) ).
%----Helper facts (2)
fof(help_fequal_1_1_fequal_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____fj,axiom,
! [X,Y] :
( ~ hBOOL(hAPP_l1656811191t_bool(hAPP_l1565956415t_bool(fequal331800088le_alt,X),Y))
| X = Y ) ).
fof(help_fequal_2_1_fequal_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____fj,axiom,
! [X,Y] :
( X != Y
| hBOOL(hAPP_l1656811191t_bool(hAPP_l1565956415t_bool(fequal331800088le_alt,X),Y)) ) ).
%----Conjectures (2)
fof(conj_0,hypothesis,
a != b ).
fof(conj_1,conjecture,
? [C] : hBOOL(hAPP_l1656811191t_bool(distin2063252165le_alt,cons_A2055670914le_alt(a,cons_A2055670914le_alt(b,cons_A2055670914le_alt(C,nil_Ar965638354le_alt))))) ).
%------------------------------------------------------------------------------