TPTP Problem File: LCL811-1.p

%------------------------------------------------------------------------------
% File     : LCL811-1 : TPTP v8.2.0. Released v4.1.0.
% Domain   : Logic Calculi
% Problem  : Strong normalization of typed lambda calculus 172_26
% Version  : Especial.
% English  :

% Refs     : [vON99] von Oheimb & Nipkow (1999), Machine-Checking the Java
%          : [Nip10] Nipkow (2010), Email to Geoff Sutcliffe
%          : [BN10]  Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% Source   : [Nip10]
% Names    : StrongNorm-172_26 [Nip10]

% Status   : Unsatisfiable
% Rating   : 0.30 v8.2.0, 0.38 v8.1.0, 0.26 v7.5.0, 0.37 v7.4.0, 0.24 v7.3.0, 0.25 v7.1.0, 0.17 v7.0.0, 0.40 v6.4.0, 0.33 v6.3.0, 0.27 v6.2.0, 0.50 v6.1.0, 0.64 v6.0.0, 0.70 v5.5.0, 0.90 v5.3.0, 0.89 v5.2.0, 0.81 v5.1.0, 0.82 v5.0.0, 0.86 v4.1.0
% Syntax   : Number of clauses     :  432 ( 180 unt;  20 nHn; 201 RR)
%            Number of literals    :  758 ( 405 equ; 326 neg)
%            Maximal clause size   :    6 (   1 avg)
%            Maximal term depth    :    7 (   2 avg)
%            Number of predicates  :   36 (  35 usr;   0 prp; 1-5 aty)
%            Number of functors    :   67 (  67 usr;  17 con; 0-6 aty)
%            Number of variables   : 1449 ( 237 sgn)
% SPC      : CNF_UNS_RFO_SEQ_NHN

% Comments :
%------------------------------------------------------------------------------
cnf(cls_append__eq__conv__conj_1,axiom,
    V_ys = c_List_Odrop(c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)),c_List_Oappend(V_xs,V_ys,T_a),T_a) ).

cnf(cls_distinct__filter_0,axiom,
    ( c_List_Odistinct(c_List_Ofilter(V_P,V_xs,T_a),T_a)
    | ~ c_List_Odistinct(V_xs,T_a) ) ).

cnf(cls_filter_Osimps_I1_J_0,axiom,
    c_List_Ofilter(V_P,c_List_Olist_ONil(T_a),T_a) = c_List_Olist_ONil(T_a) ).

cnf(cls_take__eq__Nil_0,axiom,
    ( c_List_Otake(V_n,V_xs,T_a) != c_List_Olist_ONil(T_a)
    | V_xs = c_List_Olist_ONil(T_a)
    | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ).

cnf(cls_list__all2__append1_5,axiom,
    ( c_Nat_Osize__class_Osize(V_xa,tc_List_Olist(T_b)) != c_Nat_Osize__class_Osize(V_ys,tc_List_Olist(T_a))
    | c_Nat_Osize__class_Osize(V_x,tc_List_Olist(T_b)) != c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a))
    | c_List_Olist__all2(V_P,c_List_Oappend(V_xs,V_ys,T_a),c_List_Oappend(V_x,V_xa,T_b),T_a,T_b)
    | ~ c_List_Olist__all2(V_P,V_ys,V_xa,T_a,T_b)
    | ~ c_List_Olist__all2(V_P,V_xs,V_x,T_a,T_b) ) ).

cnf(cls_list__all2__append2_5,axiom,
    ( c_Nat_Osize__class_Osize(V_xa,tc_List_Olist(T_a)) != c_Nat_Osize__class_Osize(V_zs,tc_List_Olist(T_b))
    | c_Nat_Osize__class_Osize(V_x,tc_List_Olist(T_a)) != c_Nat_Osize__class_Osize(V_ys,tc_List_Olist(T_b))
    | c_List_Olist__all2(V_P,c_List_Oappend(V_x,V_xa,T_a),c_List_Oappend(V_ys,V_zs,T_b),T_a,T_b)
    | ~ c_List_Olist__all2(V_P,V_xa,V_zs,T_a,T_b)
    | ~ c_List_Olist__all2(V_P,V_x,V_ys,T_a,T_b) ) ).

cnf(cls_list__all2__appendI_0,axiom,
    ( c_List_Olist__all2(V_P,c_List_Oappend(V_a,V_c,T_a),c_List_Oappend(V_b,V_d,T_b),T_a,T_b)
    | ~ c_List_Olist__all2(V_P,V_c,V_d,T_a,T_b)
    | ~ c_List_Olist__all2(V_P,V_a,V_b,T_a,T_b) ) ).

cnf(cls_Abs__eq__apps__conv_0,axiom,
    ( c_Lambda_OdB_OAbs(V_r) != c_List_Ofoldl(c_Lambda_OdB_OApp,V_s,V_ss,tc_Lambda_OdB,tc_Lambda_OdB)
    | c_Lambda_OdB_OAbs(V_r) = V_s ) ).

cnf(cls_typing_OVar_0,axiom,
    c_Type_Otyping(V_env,c_Lambda_OdB_OVar(V_x),hAPP(V_env,V_x)) ).

cnf(cls_listsum_Osimps_I1_J_0,axiom,
    ( ~ class_OrderedGroup_Omonoid__add(T_a)
    | c_List_Olistsum(c_List_Olist_ONil(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_inf__sup__aci_I1_J_0,axiom,
    ( ~ class_Lattices_Olattice(T_a)
    | c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_y,V_x,T_a) ) ).

cnf(cls_inf__commute_0,axiom,
    ( ~ class_Lattices_Olower__semilattice(T_a)
    | c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_y,V_x,T_a) ) ).

cnf(cls_Int__commute_0,axiom,
    c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(V_B,V_A,tc_fun(T_a,tc_bool)) ).

cnf(cls_rev__eq__Cons__iff_0,axiom,
    ( c_List_Orev(V_xs,T_a) != c_List_Olist_OCons(V_y,V_ys,T_a)
    | V_xs = c_List_Oappend(c_List_Orev(V_ys,T_a),c_List_Olist_OCons(V_y,c_List_Olist_ONil(T_a),T_a),T_a) ) ).

cnf(cls_rev__singleton__conv_1,axiom,
    c_List_Orev(c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a) = c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a) ).

cnf(cls_Snoc__step1__SnocD_1,axiom,
    ( hBOOL(hAPP(hAPP(V_r,V_y),V_x))
    | c_ListOrder_Ostep1(V_r,V_ys,V_xs,T_a)
    | ~ c_ListOrder_Ostep1(V_r,c_List_Oappend(V_ys,c_List_Olist_OCons(V_y,c_List_Olist_ONil(T_a),T_a),T_a),c_List_Oappend(V_xs,c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a),T_a) ) ).

cnf(cls_sorted_Osimps_I1_J_0,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_List_Olinorder__class_Osorted(c_List_Olist_ONil(T_a),T_a) ) ).

cnf(cls_list__all2__eq_1,axiom,
    ( V_xs = V_ys
    | ~ c_List_Olist__all2(c_fequal(T_a),V_xs,V_ys,T_a,T_a) ) ).

cnf(cls_rev_Osimps_I2_J_0,axiom,
    c_List_Orev(c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = c_List_Oappend(c_List_Orev(V_xs,T_a),c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a) ).

cnf(cls_of__nat__1_0,axiom,
    ( ~ class_Ring__and__Field_Osemiring__1(T_a)
    | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),T_a) = c_HOL_Oone__class_Oone(T_a) ) ).

cnf(cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I1_J_0,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_Lattices_Olower__semilattice__class_Oinf(V_a,V_b,T_a)),V_c) = c_Lattices_Olower__semilattice__class_Oinf(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c),T_a) ) ).

cnf(cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I2_J_0,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),c_Lattices_Olower__semilattice__class_Oinf(V_b,V_c,T_a)) = c_Lattices_Olower__semilattice__class_Oinf(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),T_a) ) ).

cnf(cls_add__inf__distrib__right_0,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__add__meet(T_a)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_Lattices_Olower__semilattice__class_Oinf(V_a,V_b,T_a)),V_c) = c_Lattices_Olower__semilattice__class_Oinf(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c),T_a) ) ).

cnf(cls_add__inf__distrib__left_0,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__add__meet(T_a)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),c_Lattices_Olower__semilattice__class_Oinf(V_b,V_c,T_a)) = c_Lattices_Olower__semilattice__class_Oinf(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),T_a) ) ).

cnf(cls_COMBK__def_0,axiom,
    hAPP(c_COMBK(V_P,T_a,T_b),V_Q) = V_P ).

cnf(cls_list__all2__takeI_0,axiom,
    ( c_List_Olist__all2(V_P,c_List_Otake(V_n,V_xs,T_a),c_List_Otake(V_n,V_ys,T_b),T_a,T_b)
    | ~ c_List_Olist__all2(V_P,V_xs,V_ys,T_a,T_b) ) ).

cnf(cls_power__one_0,axiom,
    ( ~ class_OrderedGroup_Omonoid__mult(T_a)
    | c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(T_a),V_n,T_a) = c_HOL_Oone__class_Oone(T_a) ) ).

cnf(cls_nth__list__update__neq_0,axiom,
    ( c_List_Onth(c_List_Olist__update(V_xs,V_i,V_x,T_a),V_j,T_a) = c_List_Onth(V_xs,V_j,T_a)
    | V_i = V_j ) ).

cnf(cls_add__cancel__21_0,axiom,
    ( ~ class_OrderedGroup_Oab__group__add(T_a)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_y),V_z)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_y),V_u)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_z) = V_u ) ).

cnf(cls_take__drop_0,axiom,
    c_List_Otake(V_n,c_List_Odrop(V_m,V_xs,T_a),T_a) = c_List_Odrop(V_m,c_List_Otake(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_m),V_xs,T_a),T_a) ).

cnf(cls_class__semiring_Osemiring__rules_I21_J_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c)) ) ).

cnf(cls_class__semiring_Osemiring__rules_I22_J_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_d)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_d)) ) ).

cnf(cls_class__semiring_Osemiring__rules_I23_J_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c)),V_b) ) ).

cnf(cls_class__semiring_Osemiring__rules_I25_J_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_d)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c)),V_d) ) ).

cnf(cls_ab__semigroup__add__class_Oadd__ac_I1_J_0,axiom,
    ( ~ class_OrderedGroup_Oab__semigroup__add(T_a)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c)) ) ).

cnf(cls_comm__monoid__add_Omult__left__commute_0,axiom,
    ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c)) ) ).

cnf(cls_comm__monoid__add_Omult__assoc_0,axiom,
    ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c)) ) ).

cnf(cls_nat__add__assoc_0,axiom,
    hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)),V_k) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_k)) ).

cnf(cls_nat__add__left__commute_0,axiom,
    hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_x),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_y),V_z)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_y),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_x),V_z)) ).

cnf(cls_add__cancel__21_1,axiom,
    ( ~ class_OrderedGroup_Oab__group__add(T_a)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_y),V_z)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_y),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_z)) ) ).

cnf(cls_class__semiring_Oadd__a_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_y),V_z)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_y)),V_z) ) ).

cnf(cls_sorted__drop_0,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_List_Olinorder__class_Osorted(c_List_Odrop(V_n,V_xs,T_a),T_a)
    | ~ c_List_Olinorder__class_Osorted(V_xs,T_a) ) ).

cnf(cls_listsum_0,axiom,
    ( ~ class_OrderedGroup_Omonoid__add(T_a)
    | c_List_Olistsum(V_xs,T_a) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Ozero__class_Ozero(T_a),V_xs,T_a,T_a) ) ).

cnf(cls_list_Osplit_0,axiom,
    ( ~ hBOOL(hAPP(V_P,c_List_Olist_Olist__case(V_f1,V_f2,c_List_Olist_ONil(t_b),t_a,t_b)))
    | hBOOL(hAPP(V_P,V_f1)) ) ).

cnf(cls_singleton__rev__conv_0,axiom,
    ( c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a) != c_List_Orev(V_xs,T_a)
    | V_xs = c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a) ) ).

cnf(cls_append__step1I_0,axiom,
    ( ~ c_ListOrder_Ostep1(V_r,V_ys,V_xs,T_a)
    | c_ListOrder_Ostep1(V_r,c_List_Oappend(V_ys,V_x,T_a),c_List_Oappend(V_xs,V_x,T_a),T_a) ) ).

cnf(cls_append__step1I_1,axiom,
    ( c_ListOrder_Ostep1(V_r,c_List_Oappend(V_x,V_vs,T_a),c_List_Oappend(V_x,V_us,T_a),T_a)
    | ~ c_ListOrder_Ostep1(V_r,V_vs,V_us,T_a) ) ).

cnf(cls_take__1__Cons_0,axiom,
    c_List_Otake(c_HOL_Oone__class_Oone(tc_nat),c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a) ).

cnf(cls_takeWhile_Osimps_I2_J_1,axiom,
    ( c_List_OtakeWhile(V_P,c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = c_List_Olist_ONil(T_a)
    | hBOOL(hAPP(V_P,V_x)) ) ).

cnf(cls_list__all_Osimps_I1_J_0,axiom,
    c_List_Olist__all(V_P,c_List_Olist_ONil(T_a),T_a) ).

cnf(cls_replicate__eq__replicate_0,axiom,
    ( c_List_Oreplicate(V_m,V_x,T_a) != c_List_Oreplicate(V_n,V_y,T_a)
    | V_m = V_n ) ).

cnf(cls_append__same__eq_0,axiom,
    ( c_List_Oappend(V_ys,V_xs,T_a) != c_List_Oappend(V_zs,V_xs,T_a)
    | V_ys = V_zs ) ).

cnf(cls_same__append__eq_0,axiom,
    ( c_List_Oappend(V_xs,V_ys,T_a) != c_List_Oappend(V_xs,V_zs,T_a)
    | V_ys = V_zs ) ).

cnf(cls_sorted__take_0,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_List_Olinorder__class_Osorted(c_List_Otake(V_n,V_xs,T_a),T_a)
    | ~ c_List_Olinorder__class_Osorted(V_xs,T_a) ) ).

cnf(cls_nth__append__length_0,axiom,
    c_List_Onth(c_List_Oappend(V_xs,c_List_Olist_OCons(V_x,V_ys,T_a),T_a),c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)),T_a) = V_x ).

cnf(cls_take__eq__Nil_2,axiom,
    c_List_Otake(V_n,c_List_Olist_ONil(T_a),T_a) = c_List_Olist_ONil(T_a) ).

cnf(cls_takeWhile__eq__take_0,axiom,
    c_List_OtakeWhile(V_P,V_xs,T_a) = c_List_Otake(c_Nat_Osize__class_Osize(c_List_OtakeWhile(V_P,V_xs,T_a),tc_List_Olist(T_a)),V_xs,T_a) ).

cnf(cls_append__Nil2_0,axiom,
    c_List_Oappend(V_xs,c_List_Olist_ONil(T_a),T_a) = V_xs ).

cnf(cls_eq__Nil__appendI_0,axiom,
    V_x = c_List_Oappend(c_List_Olist_ONil(T_a),V_x,T_a) ).

cnf(cls_self__append__conv_1,axiom,
    V_xs = c_List_Oappend(V_xs,c_List_Olist_ONil(T_a),T_a) ).

cnf(cls_append__Nil_0,axiom,
    c_List_Oappend(c_List_Olist_ONil(T_a),V_ys,T_a) = V_ys ).

cnf(cls_self__append__conv2_1,axiom,
    V_ys = c_List_Oappend(c_List_Olist_ONil(T_a),V_ys,T_a) ).

cnf(cls_distinct__append_0,axiom,
    ( c_List_Odistinct(V_xs,T_a)
    | ~ c_List_Odistinct(c_List_Oappend(V_xs,V_ys,T_a),T_a) ) ).

cnf(cls_distinct__append_1,axiom,
    ( c_List_Odistinct(V_ys,T_a)
    | ~ c_List_Odistinct(c_List_Oappend(V_xs,V_ys,T_a),T_a) ) ).

cnf(cls_rev__swap_0,axiom,
    V_xs = c_List_Orev(c_List_Orev(V_xs,T_a),T_a) ).

cnf(cls_rev__swap_1,axiom,
    c_List_Orev(c_List_Orev(V_ys,T_a),T_a) = V_ys ).

cnf(cls_rev__rev__ident_0,axiom,
    c_List_Orev(c_List_Orev(V_xs,T_a),T_a) = V_xs ).

cnf(cls_append__eq__conv__conj_0,axiom,
    V_xs = c_List_Otake(c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)),c_List_Oappend(V_xs,V_ys,T_a),T_a) ).

cnf(cls_list__all2__rev_0,axiom,
    ( c_List_Olist__all2(V_P,V_xs,V_ys,T_a,T_b)
    | ~ c_List_Olist__all2(V_P,c_List_Orev(V_xs,T_a),c_List_Orev(V_ys,T_b),T_a,T_b) ) ).

cnf(cls_list__all2__rev_1,axiom,
    ( c_List_Olist__all2(V_P,c_List_Orev(V_xs,T_a),c_List_Orev(V_ys,T_b),T_a,T_b)
    | ~ c_List_Olist__all2(V_P,V_xs,V_ys,T_a,T_b) ) ).

cnf(cls_substn_Osimps_I3_J_0,axiom,
    c_Lambda_Osubstn(c_Lambda_OdB_OAbs(V_t),V_s,V_k) = c_Lambda_OdB_OAbs(c_Lambda_Osubstn(V_t,V_s,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),c_HOL_Oone__class_Oone(tc_nat)))) ).

cnf(cls_class__semiring_Osemiring__rules_I24_J_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_a) ) ).

cnf(cls_comm__monoid__add_Omult__commute_0,axiom,
    ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_a) ) ).

cnf(cls_nat__add__commute_0,axiom,
    hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_m) ).

cnf(cls_class__semiring_Oadd__c_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_y) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_y),V_x) ) ).

cnf(cls_foldl__assoc_0,axiom,
    ( ~ class_OrderedGroup_Osemigroup__add(T_a)
    | c_List_Ofoldl(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_y),V_zs,T_a,T_a) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(T_a),V_y,V_zs,T_a,T_a)) ) ).

cnf(cls_rev__replicate_0,axiom,
    c_List_Orev(c_List_Oreplicate(V_n,V_x,T_a),T_a) = c_List_Oreplicate(V_n,V_x,T_a) ).

cnf(cls_Snoc__step1__SnocD_3,axiom,
    ( hBOOL(hAPP(hAPP(V_r,V_y),V_x))
    | V_y = V_x
    | ~ c_ListOrder_Ostep1(V_r,c_List_Oappend(V_ys,c_List_Olist_OCons(V_y,c_List_Olist_ONil(T_a),T_a),T_a),c_List_Oappend(V_xs,c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a),T_a) ) ).

cnf(cls_of__nat__eq__iff_0,axiom,
    ( ~ class_Nat_Osemiring__char__0(T_a)
    | c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a) != c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a)
    | V_m = V_n ) ).

cnf(cls_rev__singleton__conv_0,axiom,
    ( c_List_Orev(V_xs,T_a) != c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a)
    | V_xs = c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a) ) ).

cnf(cls_typing__elims_I1_J_0,axiom,
    ( hAPP(V_e,V_i) = V_T
    | ~ c_Type_Otyping(V_e,c_Lambda_OdB_OVar(V_i),V_T) ) ).

cnf(cls_drop__Nil_0,axiom,
    c_List_Odrop(V_n,c_List_Olist_ONil(T_a),T_a) = c_List_Olist_ONil(T_a) ).

cnf(cls_o__apply_0,axiom,
    hAPP(c_Fun_Ocomp(V_f,V_g,T_b,T_a,T_c),V_x) = hAPP(V_f,hAPP(V_g,V_x)) ).

cnf(cls_o__eq__dest__lhs_0,axiom,
    hAPP(V_a,hAPP(V_b,V_v)) = hAPP(c_Fun_Ocomp(V_a,V_b,T_c,T_b,T_a),V_v) ).

cnf(cls_dB_Osimps_I6_J_0,axiom,
    c_Lambda_OdB_OVar(V_nat) != c_Lambda_OdB_OAbs(V_dB_H) ).

cnf(cls_list__all2__def_0,axiom,
    ( c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)) = c_Nat_Osize__class_Osize(V_ys,tc_List_Olist(T_b))
    | ~ c_List_Olist__all2(V_P,V_xs,V_ys,T_a,T_b) ) ).

cnf(cls_class__semiring_Osemiring__rules_I33_J_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
    | c_Power_Opower__class_Opower(V_x,c_HOL_Oone__class_Oone(tc_nat),T_a) = V_x ) ).

cnf(cls_power__one__right_0,axiom,
    ( ~ class_OrderedGroup_Omonoid__mult(T_a)
    | c_Power_Opower__class_Opower(V_a,c_HOL_Oone__class_Oone(tc_nat),T_a) = V_a ) ).

cnf(cls_not__Nil__step1_0,axiom,
    ~ c_ListOrder_Ostep1(V_r,c_List_Olist_ONil(T_a),V_xs,T_a) ).

cnf(cls_not__step1__Nil_0,axiom,
    ~ c_ListOrder_Ostep1(V_r,V_xs,c_List_Olist_ONil(T_a),T_a) ).

cnf(cls_foldl__absorb0_0,axiom,
    ( ~ class_OrderedGroup_Omonoid__add(T_a)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Ozero__class_Ozero(T_a),V_zs,T_a,T_a)) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(T_a),V_x,V_zs,T_a,T_a) ) ).

cnf(cls_filter__replicate_0,axiom,
    ( c_List_Ofilter(V_P,c_List_Oreplicate(V_n,V_x,T_a),T_a) = c_List_Oreplicate(V_n,V_x,T_a)
    | ~ hBOOL(hAPP(V_P,V_x)) ) ).

cnf(cls_foldl__Nil_0,axiom,
    c_List_Ofoldl(V_f,V_a,c_List_Olist_ONil(T_b),T_a,T_b) = V_a ).

cnf(cls_shift__eq_0,axiom,
    hAPP(c_Type_Oshift(V_e,V_x,V_T,T_a),V_x) = V_T ).

cnf(cls_Var__apps__neq__Abs__apps_0,axiom,
    c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),V_ts,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_r),V_ss,tc_Lambda_OdB,tc_Lambda_OdB) ).

cnf(cls_inf__sup__aci_I2_J_0,axiom,
    ( ~ class_Lattices_Olattice(T_a)
    | c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),V_z,T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a) ) ).

cnf(cls_inf__sup__aci_I3_J_0,axiom,
    ( ~ class_Lattices_Olattice(T_a)
    | c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_y,c_Lattices_Olower__semilattice__class_Oinf(V_x,V_z,T_a),T_a) ) ).

cnf(cls_inf__left__commute_0,axiom,
    ( ~ class_Lattices_Olower__semilattice(T_a)
    | c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_y,c_Lattices_Olower__semilattice__class_Oinf(V_x,V_z,T_a),T_a) ) ).

cnf(cls_inf__assoc_0,axiom,
    ( ~ class_Lattices_Olower__semilattice(T_a)
    | c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),V_z,T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a) ) ).

cnf(cls_Int__assoc_0,axiom,
    c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),V_C,tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(V_A,c_Lattices_Olower__semilattice__class_Oinf(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ).

cnf(cls_Int__left__commute_0,axiom,
    c_Lattices_Olower__semilattice__class_Oinf(V_A,c_Lattices_Olower__semilattice__class_Oinf(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(V_B,c_Lattices_Olower__semilattice__class_Oinf(V_A,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ).

cnf(cls_Nil__is__append__conv_0,axiom,
    ( c_List_Olist_ONil(T_a) != c_List_Oappend(V_xs,V_ys,T_a)
    | V_xs = c_List_Olist_ONil(T_a) ) ).

cnf(cls_Nil__is__append__conv_1,axiom,
    ( c_List_Olist_ONil(T_a) != c_List_Oappend(V_xs,V_ys,T_a)
    | V_ys = c_List_Olist_ONil(T_a) ) ).

cnf(cls_dB_Osimps_I3_J_0,axiom,
    ( c_Lambda_OdB_OAbs(V_dB) != c_Lambda_OdB_OAbs(V_dB_H)
    | V_dB = V_dB_H ) ).

cnf(cls_map__replicate__const_0,axiom,
    c_List_Omap(c_COMBK(V_k,T_a,T_b),V_lst,T_b,T_a) = c_List_Oreplicate(c_Nat_Osize__class_Osize(V_lst,tc_List_Olist(T_b)),V_k,T_a) ).

cnf(cls_list__update__nonempty_1,axiom,
    c_List_Olist__update(c_List_Olist_ONil(T_a),V_k,V_x,T_a) = c_List_Olist_ONil(T_a) ).

cnf(cls_list__update__code_I1_J_0,axiom,
    c_List_Olist__update(c_List_Olist_ONil(T_a),V_i,V_y,T_a) = c_List_Olist_ONil(T_a) ).

cnf(cls_list__update_Osimps_I1_J_0,axiom,
    c_List_Olist__update(c_List_Olist_ONil(T_a),V_i,V_v,T_a) = c_List_Olist_ONil(T_a) ).

cnf(cls_natgb_Oadd__cancel_0,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_x),V_y) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_x),V_z)
    | V_y = V_z ) ).

cnf(cls_nat__add__right__cancel_0,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_k) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_k)
    | V_m = V_n ) ).

cnf(cls_nat__add__left__cancel_0,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),V_m) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),V_n)
    | V_m = V_n ) ).

cnf(cls_class__ringb_Oadd__cancel_0,axiom,
    ( ~ class_Ring__and__Field_Oidom(T_a)
    | ~ class_Int_Onumber__ring(T_a)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_y) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_z)
    | V_y = V_z ) ).

cnf(cls_add__imp__eq_0,axiom,
    ( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(T_a)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c)
    | V_b = V_c ) ).

cnf(cls_add__left__cancel_0,axiom,
    ( ~ class_OrderedGroup_Ocancel__semigroup__add(T_a)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c)
    | V_b = V_c ) ).

cnf(cls_add__right__cancel_0,axiom,
    ( ~ class_OrderedGroup_Ocancel__semigroup__add(T_a)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_a) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_a)
    | V_b = V_c ) ).

cnf(cls_drop__1__Cons_0,axiom,
    c_List_Odrop(c_HOL_Oone__class_Oone(tc_nat),c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = V_xs ).

cnf(cls_sorted__takeWhile_0,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_List_Olinorder__class_Osorted(c_List_OtakeWhile(V_P,V_xs,T_a),T_a)
    | ~ c_List_Olinorder__class_Osorted(V_xs,T_a) ) ).

cnf(cls_apps__eq__tail__conv_0,axiom,
    ( c_List_Ofoldl(c_Lambda_OdB_OApp,V_r,V_ts,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,V_s,V_ts,tc_Lambda_OdB,tc_Lambda_OdB)
    | V_r = V_s ) ).

cnf(cls_append__take__drop__id_0,axiom,
    c_List_Oappend(c_List_Otake(V_n,V_xs,T_a),c_List_Odrop(V_n,V_xs,T_a),T_a) = V_xs ).

cnf(cls_remove1_Osimps_I1_J_0,axiom,
    c_List_Oremove1(V_x,c_List_Olist_ONil(T_a),T_a) = c_List_Olist_ONil(T_a) ).

cnf(cls_class__semiring_Osemiring__rules_I20_J_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_d)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_d)) ) ).

cnf(cls_appR_0,axiom,
    ( c_Lambda_Obeta(hAPP(hAPP(c_Lambda_OdB_OApp,V_u),V_s),hAPP(hAPP(c_Lambda_OdB_OApp,V_u),V_t))
    | ~ c_Lambda_Obeta(V_s,V_t) ) ).

cnf(cls_appL_0,axiom,
    ( c_Lambda_Obeta(hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_u),hAPP(hAPP(c_Lambda_OdB_OApp,V_t),V_u))
    | ~ c_Lambda_Obeta(V_s,V_t) ) ).

cnf(cls_rev__eq__Cons__iff_1,axiom,
    c_List_Orev(c_List_Oappend(c_List_Orev(V_ys,T_a),c_List_Olist_OCons(V_y,c_List_Olist_ONil(T_a),T_a),T_a),T_a) = c_List_Olist_OCons(V_y,V_ys,T_a) ).

cnf(cls_distinct__drop_0,axiom,
    ( c_List_Odistinct(c_List_Odrop(V_i,V_xs,T_a),T_a)
    | ~ c_List_Odistinct(V_xs,T_a) ) ).

cnf(cls_distinct__rev_1,axiom,
    ( c_List_Odistinct(c_List_Orev(V_xs,T_a),T_a)
    | ~ c_List_Odistinct(V_xs,T_a) ) ).

cnf(cls_distinct__rev_0,axiom,
    ( c_List_Odistinct(V_xs,T_a)
    | ~ c_List_Odistinct(c_List_Orev(V_xs,T_a),T_a) ) ).

cnf(cls_liftn_Osimps_I2_J_0,axiom,
    c_Lambda_Oliftn(V_n,hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_t),V_k) = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Oliftn(V_n,V_s,V_k)),c_Lambda_Oliftn(V_n,V_t,V_k)) ).

cnf(cls_replicate__empty_1,axiom,
    c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),V_x,T_a) = c_List_Olist_ONil(T_a) ).

cnf(cls_list_Osimps_I4_J_0,axiom,
    c_List_Olist_Olist__case(V_f1,V_f2,c_List_Olist_ONil(T_b),T_a,T_b) = V_f1 ).

cnf(cls_rev__is__Nil__conv_0,axiom,
    ( c_List_Orev(V_xs,T_a) != c_List_Olist_ONil(T_a)
    | V_xs = c_List_Olist_ONil(T_a) ) ).

cnf(cls_list__all2__append_2,axiom,
    ( c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)) != c_Nat_Osize__class_Osize(V_ys,tc_List_Olist(T_b))
    | c_List_Olist__all2(V_P,c_List_Oappend(V_xs,V_us,T_a),c_List_Oappend(V_ys,V_vs,T_b),T_a,T_b)
    | ~ c_List_Olist__all2(V_P,V_us,V_vs,T_a,T_b)
    | ~ c_List_Olist__all2(V_P,V_xs,V_ys,T_a,T_b) ) ).

cnf(cls_rotate__is__Nil__conv_1,axiom,
    c_List_Orotate(V_n,c_List_Olist_ONil(T_a),T_a) = c_List_Olist_ONil(T_a) ).

cnf(cls_length__list__update_0,axiom,
    c_Nat_Osize__class_Osize(c_List_Olist__update(V_xs,V_i,V_x,T_a),tc_List_Olist(T_a)) = c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)) ).

cnf(cls_Cons__eq__append__conv_4,axiom,
    c_List_Olist_OCons(V_x,V_xs,T_a) = c_List_Oappend(c_List_Olist_ONil(T_a),c_List_Olist_OCons(V_x,V_xs,T_a),T_a) ).

cnf(cls_singleton__rev__conv_1,axiom,
    c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a) = c_List_Orev(c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a) ).

cnf(cls_app__Var__IT_0,axiom,
    ( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,V_t),c_Lambda_OdB_OVar(V_i))))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,V_t)) ) ).

cnf(cls_subst__lemma_0,axiom,
    ( ~ c_Type_Otyping(V_e_H,V_u,V_U)
    | ~ c_Type_Otyping(c_Type_Oshift(V_e_H,V_i,V_U,tc_Type_Otype),V_t,V_T)
    | c_Type_Otyping(V_e_H,hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_u),V_i),V_T) ) ).

cnf(cls_Snoc__step1__SnocD_0,axiom,
    ( V_ys = V_xs
    | c_ListOrder_Ostep1(V_r,V_ys,V_xs,T_a)
    | ~ c_ListOrder_Ostep1(V_r,c_List_Oappend(V_ys,c_List_Olist_OCons(V_y,c_List_Olist_ONil(T_a),T_a),T_a),c_List_Oappend(V_xs,c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a),T_a) ) ).

cnf(cls_Nil__is__append__conv_2,axiom,
    c_List_Olist_ONil(T_a) = c_List_Oappend(c_List_Olist_ONil(T_a),c_List_Olist_ONil(T_a),T_a) ).

cnf(cls_inf1E_1,axiom,
    ( hBOOL(hAPP(V_B,V_x))
    | ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),V_x)) ) ).

cnf(cls_inf1E_0,axiom,
    ( hBOOL(hAPP(V_A,V_x))
    | ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),V_x)) ) ).

cnf(cls_list__all__append_2,axiom,
    ( c_List_Olist__all(V_P,c_List_Oappend(V_xs,V_ys,T_a),T_a)
    | ~ c_List_Olist__all(V_P,V_ys,T_a)
    | ~ c_List_Olist__all(V_P,V_xs,T_a) ) ).

cnf(cls_sorted_Osimps_I2_J_0,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_List_Olinorder__class_Osorted(c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a) ) ).

cnf(cls_Abs__App__neq__Var__apps_0,axiom,
    hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_s)),V_t) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),V_ss,tc_Lambda_OdB,tc_Lambda_OdB) ).

cnf(cls_distinct__take_0,axiom,
    ( c_List_Odistinct(c_List_Otake(V_i,V_xs,T_a),T_a)
    | ~ c_List_Odistinct(V_xs,T_a) ) ).

cnf(cls_abs_0,axiom,
    ( c_Lambda_Obeta(c_Lambda_OdB_OAbs(V_s),c_Lambda_OdB_OAbs(V_t))
    | ~ c_Lambda_Obeta(V_s,V_t) ) ).

cnf(cls_replicate__append__same_0,axiom,
    c_List_Oappend(c_List_Oreplicate(V_i,V_x,T_a),c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a) = c_List_Olist_OCons(V_x,c_List_Oreplicate(V_i,V_x,T_a),T_a) ).

cnf(cls_rev__is__Nil__conv_1,axiom,
    c_List_Orev(c_List_Olist_ONil(T_a),T_a) = c_List_Olist_ONil(T_a) ).

cnf(cls_distinct__takeWhile_0,axiom,
    ( c_List_Odistinct(c_List_OtakeWhile(V_P,V_xs,T_a),T_a)
    | ~ c_List_Odistinct(V_xs,T_a) ) ).

cnf(cls_substn_Osimps_I2_J_0,axiom,
    c_Lambda_Osubstn(hAPP(hAPP(c_Lambda_OdB_OApp,V_t),V_u),V_s,V_k) = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Osubstn(V_t,V_s,V_k)),c_Lambda_Osubstn(V_u,V_s,V_k)) ).

cnf(cls_rev__append_0,axiom,
    c_List_Orev(c_List_Oappend(V_xs,V_ys,T_a),T_a) = c_List_Oappend(c_List_Orev(V_ys,T_a),c_List_Orev(V_xs,T_a),T_a) ).

cnf(cls_foldl__append_0,axiom,
    c_List_Ofoldl(V_f,V_a,c_List_Oappend(V_xs,V_ys,T_b),T_a,T_b) = c_List_Ofoldl(V_f,c_List_Ofoldl(V_f,V_a,V_xs,T_a,T_b),V_ys,T_a,T_b) ).

cnf(cls_rotate__rotate_0,axiom,
    c_List_Orotate(V_m,c_List_Orotate(V_n,V_xs,T_a),T_a) = c_List_Orotate(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n),V_xs,T_a) ).

cnf(cls_dB_Osimps_I5_J_0,axiom,
    hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1_H),V_dB2_H) != c_Lambda_OdB_OVar(V_nat) ).

cnf(cls_filter__append_0,axiom,
    c_List_Ofilter(V_P,c_List_Oappend(V_xs,V_ys,T_a),T_a) = c_List_Oappend(c_List_Ofilter(V_P,V_xs,T_a),c_List_Ofilter(V_P,V_ys,T_a),T_a) ).

cnf(cls_list__update__nonempty_0,axiom,
    ( c_List_Olist__update(V_xs,V_k,V_x,T_a) != c_List_Olist_ONil(T_a)
    | V_xs = c_List_Olist_ONil(T_a) ) ).

cnf(cls_list__all2__rev1_1,axiom,
    ( c_List_Olist__all2(V_P,c_List_Orev(V_xs,T_a),V_ys,T_a,T_b)
    | ~ c_List_Olist__all2(V_P,V_xs,c_List_Orev(V_ys,T_b),T_a,T_b) ) ).

cnf(cls_list__all2__rev1_0,axiom,
    ( c_List_Olist__all2(V_P,V_xs,c_List_Orev(V_ys,T_b),T_a,T_b)
    | ~ c_List_Olist__all2(V_P,c_List_Orev(V_xs,T_a),V_ys,T_a,T_b) ) ).

cnf(cls_IT_OVar_0,axiom,
    ( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),V_rs,tc_Lambda_OdB,tc_Lambda_OdB)))
    | ~ c_List_Olistsp(c_InductTermi_OIT,V_rs,tc_Lambda_OdB) ) ).

cnf(cls_power__eq__0__iff_0,axiom,
    ( ~ class_Ring__and__Field_Ozero__neq__one(T_a)
    | ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
    | ~ class_Ring__and__Field_Omult__zero(T_a)
    | ~ class_Power_Opower(T_a)
    | c_Power_Opower__class_Opower(V_a,V_n,T_a) != c_HOL_Ozero__class_Ozero(T_a)
    | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_field__power__not__zero_0,axiom,
    ( ~ class_Ring__and__Field_Oring__1__no__zero__divisors(T_a)
    | c_Power_Opower__class_Opower(V_a,V_n,T_a) != c_HOL_Ozero__class_Ozero(T_a)
    | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_one__neq__zero_0,axiom,
    ( ~ class_Ring__and__Field_Ozero__neq__one(T_a)
    | c_HOL_Oone__class_Oone(T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_double__eq__0__iff_0,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a) != c_HOL_Ozero__class_Ozero(T_a)
    | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_class__ringb_Oadd__r0__iff_0,axiom,
    ( ~ class_Ring__and__Field_Oidom(T_a)
    | ~ class_Int_Onumber__ring(T_a)
    | V_x != hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_a)
    | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_double__eq__0__iff_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Ozero__class_Ozero(T_a)),c_HOL_Ozero__class_Ozero(T_a)) = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_zero__neq__one_0,axiom,
    ( ~ class_Ring__and__Field_Ozero__neq__one(T_a)
    | c_HOL_Ozero__class_Ozero(T_a) != c_HOL_Oone__class_Oone(T_a) ) ).

cnf(cls_class__semiring_Oadd__0_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_x) = V_x ) ).

cnf(cls_comm__monoid__add_Omult__1_0,axiom,
    ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_a) = V_a ) ).

cnf(cls_class__ringb_Oadd__r0__iff_1,axiom,
    ( ~ class_Ring__and__Field_Oidom(T_a)
    | ~ class_Int_Onumber__ring(T_a)
    | V_x = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),c_HOL_Ozero__class_Ozero(T_a)) ) ).

cnf(cls_comm__monoid__add_Omult__1__right_0,axiom,
    ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),c_HOL_Ozero__class_Ozero(T_a)) = V_a ) ).

cnf(cls_add__0__left_0,axiom,
    ( ~ class_OrderedGroup_Omonoid__add(T_a)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_a) = V_a ) ).

cnf(cls_monoid__add__class_Oadd__0__right_0,axiom,
    ( ~ class_OrderedGroup_Omonoid__add(T_a)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),c_HOL_Ozero__class_Ozero(T_a)) = V_a ) ).

cnf(cls_class__semiring_Osemiring__rules_I6_J_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),c_HOL_Ozero__class_Ozero(T_a)) = V_a ) ).

cnf(cls_class__semiring_Osemiring__rules_I5_J_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_a) = V_a ) ).

cnf(cls_power__0__left_0,axiom,
    ( ~ class_Ring__and__Field_Osemiring__0(T_a)
    | ~ class_Power_Opower(T_a)
    | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(tc_nat),T_a) = c_HOL_Oone__class_Oone(T_a) ) ).

cnf(cls_liftn__0_0,axiom,
    c_Lambda_Oliftn(c_HOL_Ozero__class_Ozero(tc_nat),V_t,V_k) = V_t ).

cnf(cls_add__is__0_1,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n) != c_HOL_Ozero__class_Ozero(tc_nat)
    | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ).

cnf(cls_add__is__0_0,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n) != c_HOL_Ozero__class_Ozero(tc_nat)
    | V_m = c_HOL_Ozero__class_Ozero(tc_nat) ) ).

cnf(cls_natgb_Oadd__r0__iff_0,axiom,
    ( V_x != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_x),V_a)
    | V_a = c_HOL_Ozero__class_Ozero(tc_nat) ) ).

cnf(cls_add__eq__self__zero_0,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n) != V_m
    | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ).

cnf(cls_add__is__0_2,axiom,
    hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Ozero__class_Ozero(tc_nat) ).

cnf(cls_drop__0_0,axiom,
    c_List_Odrop(c_HOL_Ozero__class_Ozero(tc_nat),V_xs,T_a) = V_xs ).

cnf(cls_replicate__eq__replicate_2,axiom,
    c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),V_x,T_a) = c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),V_y,T_a) ).

cnf(cls_replicate__eq__replicate_1,axiom,
    ( c_List_Oreplicate(V_m,V_x,T_a) != c_List_Oreplicate(V_n,V_y,T_a)
    | V_x = V_y
    | V_m = c_HOL_Ozero__class_Ozero(tc_nat) ) ).

cnf(cls_natgb_Oadd__r0__iff_1,axiom,
    V_x = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_x),c_HOL_Ozero__class_Ozero(tc_nat)) ).

cnf(cls_plus__nat_Oadd__0_0,axiom,
    hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),V_n) = V_n ).

cnf(cls_Nat_Oadd__0__right_0,axiom,
    hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),c_HOL_Ozero__class_Ozero(tc_nat)) = V_m ).

cnf(cls_take__Cons_H_0,axiom,
    c_List_Otake(c_HOL_Ozero__class_Ozero(tc_nat),c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = c_List_Olist_ONil(T_a) ).

cnf(cls_list_Osplit__asm_1,axiom,
    ( ~ hBOOL(hAPP(V_P,c_List_Olist_Olist__case(V_f1,V_f2,c_List_Olist_OCons(V_xa,V_xb,t_b),t_a,t_b)))
    | hBOOL(hAPP(V_P,hAPP(hAPP(V_f2,V_xa),V_xb))) ) ).

cnf(cls_list_Osplit_1,axiom,
    ( ~ hBOOL(hAPP(V_P,c_List_Olist_Olist__case(V_f1,V_f2,c_List_Olist_OCons(V_a,V_list,t_b),t_a,t_b)))
    | hBOOL(hAPP(V_P,hAPP(hAPP(V_f2,V_a),V_list))) ) ).

cnf(cls_filter_Osimps_I2_J_1,axiom,
    ( c_List_Ofilter(V_P,c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = c_List_Ofilter(V_P,V_xs,T_a)
    | hBOOL(hAPP(V_P,V_x)) ) ).

cnf(cls_list__all_Osimps_I2_J_2,axiom,
    ( c_List_Olist__all(V_P,c_List_Olist_OCons(V_x,V_xs,T_a),T_a)
    | ~ c_List_Olist__all(V_P,V_xs,T_a)
    | ~ hBOOL(hAPP(V_P,V_x)) ) ).

cnf(cls_Cons__step1__Cons_5,axiom,
    ( c_ListOrder_Ostep1(V_r,c_List_Olist_OCons(V_x,V_ys,T_a),c_List_Olist_OCons(V_x,V_xs,T_a),T_a)
    | ~ c_ListOrder_Ostep1(V_r,V_ys,V_xs,T_a) ) ).

cnf(cls_Cons__step1__Cons_1,axiom,
    ( c_ListOrder_Ostep1(V_r,V_ys,V_xs,T_a)
    | hBOOL(hAPP(hAPP(V_r,V_y),V_x))
    | ~ c_ListOrder_Ostep1(V_r,c_List_Olist_OCons(V_y,V_ys,T_a),c_List_Olist_OCons(V_x,V_xs,T_a),T_a) ) ).

cnf(cls_list_Osimps_I2_J_0,axiom,
    c_List_Olist_ONil(T_a) != c_List_Olist_OCons(V_a_H,V_list_H,T_a) ).

cnf(cls_Cons__step1__Cons_3,axiom,
    ( c_ListOrder_Ostep1(V_r,V_ys,V_xs,T_a)
    | V_xs = V_ys
    | ~ c_ListOrder_Ostep1(V_r,c_List_Olist_OCons(V_y,V_ys,T_a),c_List_Olist_OCons(V_x,V_xs,T_a),T_a) ) ).

cnf(cls_remove1_Osimps_I2_J_1,axiom,
    ( c_List_Oremove1(V_x,c_List_Olist_OCons(V_y,V_xs,T_a),T_a) = c_List_Olist_OCons(V_y,c_List_Oremove1(V_x,V_xs,T_a),T_a)
    | V_x = V_y ) ).

cnf(cls_list__all2__Cons2_3,axiom,
    ( c_List_Olist__all2(V_P,c_List_Olist_OCons(V_x,V_xa,T_a),c_List_Olist_OCons(V_y,V_ys,T_b),T_a,T_b)
    | ~ c_List_Olist__all2(V_P,V_xa,V_ys,T_a,T_b)
    | ~ hBOOL(hAPP(hAPP(V_P,V_x),V_y)) ) ).

cnf(cls_list__all2__Cons1_3,axiom,
    ( c_List_Olist__all2(V_P,c_List_Olist_OCons(V_x,V_xs,T_a),c_List_Olist_OCons(V_xa,V_xb,T_b),T_a,T_b)
    | ~ c_List_Olist__all2(V_P,V_xs,V_xb,T_a,T_b)
    | ~ hBOOL(hAPP(hAPP(V_P,V_x),V_xa)) ) ).

cnf(cls_list__all2__Cons_2,axiom,
    ( c_List_Olist__all2(V_P,c_List_Olist_OCons(V_x,V_xs,T_a),c_List_Olist_OCons(V_y,V_ys,T_b),T_a,T_b)
    | ~ c_List_Olist__all2(V_P,V_xs,V_ys,T_a,T_b)
    | ~ hBOOL(hAPP(hAPP(V_P,V_x),V_y)) ) ).

cnf(cls_elem_0,axiom,
    c_List_OListMem(V_x,c_List_Olist_OCons(V_x,V_xs,T_a),T_a) ).

cnf(cls_list__all2__Cons_1,axiom,
    ( c_List_Olist__all2(V_P,V_xs,V_ys,T_a,T_b)
    | ~ c_List_Olist__all2(V_P,c_List_Olist_OCons(V_x,V_xs,T_a),c_List_Olist_OCons(V_y,V_ys,T_b),T_a,T_b) ) ).

cnf(cls_filter__eq__ConsD_2,axiom,
    ( c_List_Ofilter(V_P,V_ys,T_a) != c_List_Olist_OCons(V_x,V_xs,T_a)
    | hBOOL(hAPP(V_P,V_x)) ) ).

cnf(cls_append__is__Nil__conv_0,axiom,
    ( c_List_Oappend(V_xs,V_ys,T_a) != c_List_Olist_ONil(T_a)
    | V_xs = c_List_Olist_ONil(T_a) ) ).

cnf(cls_append__is__Nil__conv_1,axiom,
    ( c_List_Oappend(V_xs,V_ys,T_a) != c_List_Olist_ONil(T_a)
    | V_ys = c_List_Olist_ONil(T_a) ) ).

cnf(cls_length__0__conv_1,axiom,
    c_Nat_Osize__class_Osize(c_List_Olist_ONil(T_a),tc_List_Olist(T_a)) = c_HOL_Ozero__class_Ozero(tc_nat) ).

cnf(cls_append__eq__conv__conj_2,axiom,
    ( V_xs != c_List_Otake(c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)),V_zs,T_a)
    | c_List_Oappend(V_xs,c_List_Odrop(c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)),V_zs,T_a),T_a) = V_zs ) ).

cnf(cls_dB_Osimps_I4_J_0,axiom,
    c_Lambda_OdB_OVar(V_nat) != hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1_H),V_dB2_H) ).

cnf(cls_distinct__remove1_0,axiom,
    ( c_List_Odistinct(c_List_Oremove1(V_x,V_xs,T_a),T_a)
    | ~ c_List_Odistinct(V_xs,T_a) ) ).

cnf(cls_Var__eq__apps__conv_0,axiom,
    ( c_Lambda_OdB_OVar(V_m) != c_List_Ofoldl(c_Lambda_OdB_OApp,V_s,V_ss,tc_Lambda_OdB,tc_Lambda_OdB)
    | c_Lambda_OdB_OVar(V_m) = V_s ) ).

cnf(cls_list__all2__append_0,axiom,
    ( c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)) != c_Nat_Osize__class_Osize(V_ys,tc_List_Olist(T_b))
    | c_List_Olist__all2(V_P,V_xs,V_ys,T_a,T_b)
    | ~ c_List_Olist__all2(V_P,c_List_Oappend(V_xs,V_us,T_a),c_List_Oappend(V_ys,V_vs,T_b),T_a,T_b) ) ).

cnf(cls_list__all2__append_1,axiom,
    ( c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)) != c_Nat_Osize__class_Osize(V_ys,tc_List_Olist(T_b))
    | c_List_Olist__all2(V_P,V_us,V_vs,T_a,T_b)
    | ~ c_List_Olist__all2(V_P,c_List_Oappend(V_xs,V_us,T_a),c_List_Oappend(V_ys,V_vs,T_b),T_a,T_b) ) ).

cnf(cls_apps__preserves__beta_0,axiom,
    ( c_Lambda_Obeta(c_List_Ofoldl(c_Lambda_OdB_OApp,V_r,V_ss,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,V_s,V_ss,tc_Lambda_OdB,tc_Lambda_OdB))
    | ~ c_Lambda_Obeta(V_r,V_s) ) ).

cnf(cls_length__rotate_0,axiom,
    c_Nat_Osize__class_Osize(c_List_Orotate(V_n,V_xs,T_a),tc_List_Olist(T_a)) = c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)) ).

cnf(cls_takeWhile__tail_0,axiom,
    ( c_List_OtakeWhile(V_P,c_List_Oappend(V_xs,c_List_Olist_OCons(V_x,V_l,T_a),T_a),T_a) = c_List_OtakeWhile(V_P,V_xs,T_a)
    | hBOOL(hAPP(V_P,V_x)) ) ).

cnf(cls_empty__replicate_1,axiom,
    c_List_Olist_ONil(T_a) = c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),V_x,T_a) ).

cnf(cls_beta_0,axiom,
    c_Lambda_Obeta(hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_s)),V_t),hAPP(hAPP(hAPP(c_Lambda_Osubst,V_s),V_t),c_HOL_Ozero__class_Ozero(tc_nat))) ).

cnf(cls_length__append_0,axiom,
    c_Nat_Osize__class_Osize(c_List_Oappend(V_xs,V_ys,T_a),tc_List_Olist(T_a)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a))),c_Nat_Osize__class_Osize(V_ys,tc_List_Olist(T_a))) ).

cnf(cls_listsum_Osimps_I2_J_0,axiom,
    ( ~ class_OrderedGroup_Omonoid__add(T_a)
    | c_List_Olistsum(c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),c_List_Olistsum(V_xs,T_a)) ) ).

cnf(cls_liftn_Osimps_I3_J_0,axiom,
    c_Lambda_Oliftn(V_n,c_Lambda_OdB_OAbs(V_s),V_k) = c_Lambda_OdB_OAbs(c_Lambda_Oliftn(V_n,V_s,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),c_HOL_Oone__class_Oone(tc_nat)))) ).

cnf(cls_var__app__type__eq_0,axiom,
    ( V_T = V_U
    | ~ c_Type_Otyping(V_e,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_i),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),V_U)
    | ~ c_Type_Otyping(V_e,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_i),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),V_T) ) ).

cnf(cls_append__replicate__commute_0,axiom,
    c_List_Oappend(c_List_Oreplicate(V_n,V_x,T_a),c_List_Oreplicate(V_k,V_x,T_a),T_a) = c_List_Oappend(c_List_Oreplicate(V_k,V_x,T_a),c_List_Oreplicate(V_n,V_x,T_a),T_a) ).

cnf(cls_dB_Osimps_I2_J_1,axiom,
    ( hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2) != hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1_H),V_dB2_H)
    | V_dB2 = V_dB2_H ) ).

cnf(cls_dB_Osimps_I2_J_0,axiom,
    ( hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2) != hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1_H),V_dB2_H)
    | V_dB1 = V_dB1_H ) ).

cnf(cls_list__all2__dropI_0,axiom,
    ( c_List_Olist__all2(V_P,c_List_Odrop(V_n,V_as,T_a),c_List_Odrop(V_n,V_bs,T_b),T_a,T_b)
    | ~ c_List_Olist__all2(V_P,V_as,V_bs,T_a,T_b) ) ).

cnf(cls_Abs__apps__eq__Abs__apps__conv_1,axiom,
    ( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_r),V_rs,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_s),V_ss,tc_Lambda_OdB,tc_Lambda_OdB)
    | V_rs = V_ss ) ).

cnf(cls_Abs__apps__eq__Abs__apps__conv_0,axiom,
    ( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_r),V_rs,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_s),V_ss,tc_Lambda_OdB,tc_Lambda_OdB)
    | V_r = V_s ) ).

cnf(cls_apps__eq__Abs__conv_0,axiom,
    ( c_List_Ofoldl(c_Lambda_OdB_OApp,V_s,V_ss,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(V_r)
    | V_s = c_Lambda_OdB_OAbs(V_r) ) ).

cnf(cls_distinct_Osimps_I1_J_0,axiom,
    c_List_Odistinct(c_List_Olist_ONil(T_a),T_a) ).

cnf(cls_beta__cases_I1_J_0,axiom,
    ~ c_Lambda_Obeta(c_Lambda_OdB_OVar(V_i),V_t) ).

cnf(cls_remove1__filter__not_0,axiom,
    ( c_List_Oremove1(V_x,c_List_Ofilter(V_P,V_xs,T_a),T_a) = c_List_Ofilter(V_P,V_xs,T_a)
    | hBOOL(hAPP(V_P,V_x)) ) ).

cnf(cls_filter__replicate_1,axiom,
    ( c_List_Ofilter(V_P,c_List_Oreplicate(V_n,V_x,T_a),T_a) = c_List_Olist_ONil(T_a)
    | hBOOL(hAPP(V_P,V_x)) ) ).

cnf(cls_drop__drop_0,axiom,
    c_List_Odrop(V_n,c_List_Odrop(V_m,V_xs,T_a),T_a) = c_List_Odrop(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_m),V_xs,T_a) ).

cnf(cls_replicate__add_0,axiom,
    c_List_Oreplicate(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_m),V_x,T_a) = c_List_Oappend(c_List_Oreplicate(V_n,V_x,T_a),c_List_Oreplicate(V_m,V_x,T_a),T_a) ).

cnf(cls_list__all2__Nil_0,axiom,
    ( V_ys = c_List_Olist_ONil(T_b)
    | ~ c_List_Olist__all2(V_P,c_List_Olist_ONil(T_a),V_ys,T_a,T_b) ) ).

cnf(cls_list__all2__Nil2_0,axiom,
    ( V_xs = c_List_Olist_ONil(T_a)
    | ~ c_List_Olist__all2(V_P,V_xs,c_List_Olist_ONil(T_b),T_a,T_b) ) ).

cnf(cls_take__0_0,axiom,
    c_List_Otake(c_HOL_Ozero__class_Ozero(tc_nat),V_xs,T_a) = c_List_Olist_ONil(T_a) ).

cnf(cls_rev__is__rev__conv_0,axiom,
    ( c_List_Orev(V_xs,T_a) != c_List_Orev(V_ys,T_a)
    | V_xs = V_ys ) ).

cnf(cls_Snoc__step1__SnocD_2,axiom,
    ( V_ys = V_xs
    | V_y = V_x
    | ~ c_ListOrder_Ostep1(V_r,c_List_Oappend(V_ys,c_List_Olist_OCons(V_y,c_List_Olist_ONil(T_a),T_a),T_a),c_List_Oappend(V_xs,c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a),T_a) ) ).

cnf(cls_power__0_0,axiom,
    ( ~ class_Power_Opower(T_a)
    | c_Power_Opower__class_Opower(V_a,c_HOL_Ozero__class_Ozero(tc_nat),T_a) = c_HOL_Oone__class_Oone(T_a) ) ).

cnf(cls_class__semiring_Opwr__0_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
    | c_Power_Opower__class_Opower(V_x,c_HOL_Ozero__class_Ozero(tc_nat),T_a) = c_HOL_Oone__class_Oone(T_a) ) ).

cnf(cls_distinct__rotate_0,axiom,
    ( c_List_Odistinct(V_xs,T_a)
    | ~ c_List_Odistinct(c_List_Orotate(V_n,V_xs,T_a),T_a) ) ).

cnf(cls_distinct__rotate_1,axiom,
    ( c_List_Odistinct(c_List_Orotate(V_n,V_xs,T_a),T_a)
    | ~ c_List_Odistinct(V_xs,T_a) ) ).

cnf(cls_replicate__empty_0,axiom,
    ( c_List_Oreplicate(V_n,V_x,T_a) != c_List_Olist_ONil(T_a)
    | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ).

cnf(cls_listsum__rev_0,axiom,
    ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
    | c_List_Olistsum(c_List_Orev(V_xs,T_a),T_a) = c_List_Olistsum(V_xs,T_a) ) ).

cnf(cls_o__assoc_0,axiom,
    c_Fun_Ocomp(V_f,c_Fun_Ocomp(V_g,V_h,T_d,T_c,T_a),T_c,T_b,T_a) = c_Fun_Ocomp(c_Fun_Ocomp(V_f,V_g,T_c,T_b,T_d),V_h,T_d,T_b,T_a) ).

cnf(cls_length__replicate_0,axiom,
    c_Nat_Osize__class_Osize(c_List_Oreplicate(V_n,V_x,T_a),tc_List_Olist(T_a)) = V_n ).

cnf(cls_empty__replicate_0,axiom,
    ( c_List_Olist_ONil(T_a) != c_List_Oreplicate(V_n,V_x,T_a)
    | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ).

cnf(cls_length__0__conv_0,axiom,
    ( c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)) != c_HOL_Ozero__class_Ozero(tc_nat)
    | V_xs = c_List_Olist_ONil(T_a) ) ).

cnf(cls_Nil__is__rev__conv_0,axiom,
    ( c_List_Olist_ONil(T_a) != c_List_Orev(V_xs,T_a)
    | V_xs = c_List_Olist_ONil(T_a) ) ).

cnf(cls_list__update__id_0,axiom,
    c_List_Olist__update(V_xs,V_i,c_List_Onth(V_xs,V_i,T_a),T_a) = V_xs ).

cnf(cls_inf__sup__aci_I4_J_0,axiom,
    ( ~ class_Lattices_Olattice(T_a)
    | c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) ) ).

cnf(cls_inf__left__idem_0,axiom,
    ( ~ class_Lattices_Olower__semilattice(T_a)
    | c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) ) ).

cnf(cls_Int__left__absorb_0,axiom,
    c_Lattices_Olower__semilattice__class_Oinf(V_A,c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)) ).

cnf(cls_rotate__is__Nil__conv_0,axiom,
    ( c_List_Orotate(V_n,V_xs,T_a) != c_List_Olist_ONil(T_a)
    | V_xs = c_List_Olist_ONil(T_a) ) ).

cnf(cls_list__update__length_0,axiom,
    c_List_Olist__update(c_List_Oappend(V_xs,c_List_Olist_OCons(V_x,V_ys,T_a),T_a),c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)),V_y,T_a) = c_List_Oappend(V_xs,c_List_Olist_OCons(V_y,V_ys,T_a),T_a) ).

cnf(cls_append__self__conv_0,axiom,
    ( c_List_Oappend(V_xs,V_ys,T_a) != V_xs
    | V_ys = c_List_Olist_ONil(T_a) ) ).

cnf(cls_self__append__conv_0,axiom,
    ( V_xs != c_List_Oappend(V_xs,V_ys,T_a)
    | V_ys = c_List_Olist_ONil(T_a) ) ).

cnf(cls_append__self__conv2_0,axiom,
    ( c_List_Oappend(V_xs,V_ys,T_a) != V_ys
    | V_xs = c_List_Olist_ONil(T_a) ) ).

cnf(cls_self__append__conv2_0,axiom,
    ( V_ys != c_List_Oappend(V_xs,V_ys,T_a)
    | V_xs = c_List_Olist_ONil(T_a) ) ).

cnf(cls_append__eq__Cons__conv_4,axiom,
    c_List_Oappend(c_List_Olist_ONil(T_a),c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = c_List_Olist_OCons(V_x,V_xs,T_a) ).

cnf(cls_takeWhile_Osimps_I1_J_0,axiom,
    c_List_OtakeWhile(V_P,c_List_Olist_ONil(T_a),T_a) = c_List_Olist_ONil(T_a) ).

cnf(cls_inf__idem_0,axiom,
    ( ~ class_Lattices_Olower__semilattice(T_a)
    | c_Lattices_Olower__semilattice__class_Oinf(V_x,V_x,T_a) = V_x ) ).

cnf(cls_Int__absorb_0,axiom,
    c_Lattices_Olower__semilattice__class_Oinf(V_A,V_A,tc_fun(T_a,tc_bool)) = V_A ).

cnf(cls_nth__via__drop_0,axiom,
    ( c_List_Odrop(V_n,V_xs,T_a) != c_List_Olist_OCons(V_y,V_ys,T_a)
    | c_List_Onth(V_xs,V_n,T_a) = V_y ) ).

cnf(cls_append__eq__append__conv__if_6,axiom,
    ( c_List_Oappend(c_List_Odrop(c_Nat_Osize__class_Osize(V_ys_092_060_094isub_0621,tc_List_Olist(T_a)),V_xs_092_060_094isub_0621,T_a),c_List_Oappend(c_List_Odrop(c_Nat_Osize__class_Osize(V_xs_092_060_094isub_0621,tc_List_Olist(T_a)),V_ys_092_060_094isub_0621,T_a),V_ys_092_060_094isub_0622,T_a),T_a) != V_ys_092_060_094isub_0622
    | c_List_Otake(c_Nat_Osize__class_Osize(V_ys_092_060_094isub_0621,tc_List_Olist(T_a)),V_xs_092_060_094isub_0621,T_a) != V_ys_092_060_094isub_0621
    | V_xs_092_060_094isub_0621 != c_List_Otake(c_Nat_Osize__class_Osize(V_xs_092_060_094isub_0621,tc_List_Olist(T_a)),V_ys_092_060_094isub_0621,T_a)
    | c_List_Oappend(V_xs_092_060_094isub_0621,c_List_Oappend(c_List_Odrop(c_Nat_Osize__class_Osize(V_xs_092_060_094isub_0621,tc_List_Olist(T_a)),V_ys_092_060_094isub_0621,T_a),V_ys_092_060_094isub_0622,T_a),T_a) = c_List_Oappend(V_ys_092_060_094isub_0621,V_ys_092_060_094isub_0622,T_a) ) ).

cnf(cls_Var__apps__eq__Var__apps__conv_1,axiom,
    ( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_m),V_rs,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),V_ss,tc_Lambda_OdB,tc_Lambda_OdB)
    | V_rs = V_ss ) ).

cnf(cls_Var__apps__eq__Var__apps__conv_0,axiom,
    ( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_m),V_rs,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),V_ss,tc_Lambda_OdB,tc_Lambda_OdB)
    | V_m = V_n ) ).

cnf(cls_subject__reduction_0,axiom,
    ( c_Type_Otyping(V_e,V_t_H,V_T)
    | ~ c_Lambda_Obeta(V_t,V_t_H)
    | ~ c_Type_Otyping(V_e,V_t,V_T) ) ).

cnf(cls_sorted__append_0,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_List_Olinorder__class_Osorted(V_xs,T_a)
    | ~ c_List_Olinorder__class_Osorted(c_List_Oappend(V_xs,V_ys,T_a),T_a) ) ).

cnf(cls_sorted__append_1,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_List_Olinorder__class_Osorted(V_ys,T_a)
    | ~ c_List_Olinorder__class_Osorted(c_List_Oappend(V_xs,V_ys,T_a),T_a) ) ).

cnf(cls_dB_Osimps_I9_J_0,axiom,
    c_Lambda_OdB_OAbs(V_dB_H) != hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2) ).

cnf(cls_list__update__swap_0,axiom,
    ( c_List_Olist__update(c_List_Olist__update(V_xs,V_i,V_x,T_a),V_i_H,V_x_H,T_a) = c_List_Olist__update(c_List_Olist__update(V_xs,V_i_H,V_x_H,T_a),V_i,V_x,T_a)
    | V_i = V_i_H ) ).

cnf(cls_dB_Osimps_I1_J_0,axiom,
    ( c_Lambda_OdB_OVar(V_nat) != c_Lambda_OdB_OVar(V_nat_H)
    | V_nat = V_nat_H ) ).

cnf(cls_list__all__rev_0,axiom,
    ( c_List_Olist__all(V_P,V_xs,T_a)
    | ~ c_List_Olist__all(V_P,c_List_Orev(V_xs,T_a),T_a) ) ).

cnf(cls_list__all__rev_1,axiom,
    ( c_List_Olist__all(V_P,c_List_Orev(V_xs,T_a),T_a)
    | ~ c_List_Olist__all(V_P,V_xs,T_a) ) ).

cnf(cls_dB_Osimps_I8_J_0,axiom,
    hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2) != c_Lambda_OdB_OAbs(V_dB_H) ).

cnf(cls_dB_Osimps_I7_J_0,axiom,
    c_Lambda_OdB_OAbs(V_dB_H) != c_Lambda_OdB_OVar(V_nat) ).

cnf(cls_replicate__app__Cons__same_0,axiom,
    c_List_Oappend(c_List_Oreplicate(V_n,V_x,T_a),c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = c_List_Olist_OCons(V_x,c_List_Oappend(c_List_Oreplicate(V_n,V_x,T_a),V_xs,T_a),T_a) ).

cnf(cls_o__eq__dest_0,axiom,
    ( c_Fun_Ocomp(V_a,V_b,T_c,T_b,T_a) != c_Fun_Ocomp(V_c,V_d,T_d,T_b,T_a)
    | hAPP(V_a,hAPP(V_b,V_v)) = hAPP(V_c,hAPP(V_d,V_v)) ) ).

cnf(cls_comp__cong_0,axiom,
    ( hAPP(V_f,hAPP(V_g,V_x)) != hAPP(V_f_H,hAPP(V_g_H,V_x_H))
    | hAPP(c_Fun_Ocomp(V_f,V_g,T_b,T_a,T_c),V_x) = hAPP(c_Fun_Ocomp(V_f_H,V_g_H,T_d,T_a,T_e),V_x_H) ) ).

cnf(cls_Nil__is__rev__conv_1,axiom,
    c_List_Olist_ONil(T_a) = c_List_Orev(c_List_Olist_ONil(T_a),T_a) ).

cnf(cls_length__rev_0,axiom,
    c_Nat_Osize__class_Osize(c_List_Orev(V_xs,T_a),tc_List_Olist(T_a)) = c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)) ).

cnf(cls_nth__append__length__plus_0,axiom,
    c_List_Onth(c_List_Oappend(V_xs,V_ys,T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a))),V_n),T_a) = c_List_Onth(V_ys,V_n,T_a) ).

cnf(cls_of__nat__add_0,axiom,
    ( ~ class_Ring__and__Field_Osemiring__1(T_a)
    | c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n),T_a) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a)),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a)) ) ).

cnf(cls_list__all2__Nil_1,axiom,
    c_List_Olist__all2(V_P,c_List_Olist_ONil(T_a),c_List_Olist_ONil(T_b),T_a,T_b) ).

cnf(cls_inf1I_0,axiom,
    ( hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),V_x))
    | ~ hBOOL(hAPP(V_B,V_x))
    | ~ hBOOL(hAPP(V_A,V_x)) ) ).

cnf(cls_rev__filter_0,axiom,
    c_List_Orev(c_List_Ofilter(V_P,V_xs,T_a),T_a) = c_List_Ofilter(V_P,c_List_Orev(V_xs,T_a),T_a) ).

cnf(cls_listsum__append_0,axiom,
    ( ~ class_OrderedGroup_Omonoid__add(T_a)
    | c_List_Olistsum(c_List_Oappend(V_xs,V_ys,T_a),T_a) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_List_Olistsum(V_xs,T_a)),c_List_Olistsum(V_ys,T_a)) ) ).

cnf(cls_list__all2__eq_0,axiom,
    c_List_Olist__all2(c_fequal(T_a),V_x,V_x,T_a,T_a) ).

cnf(cls_append1__eq__conv_0,axiom,
    ( c_List_Oappend(V_xs,c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a) != c_List_Oappend(V_ys,c_List_Olist_OCons(V_y,c_List_Olist_ONil(T_a),T_a),T_a)
    | V_xs = V_ys ) ).

cnf(cls_append1__eq__conv_1,axiom,
    ( c_List_Oappend(V_xs,c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a) != c_List_Oappend(V_ys,c_List_Olist_OCons(V_y,c_List_Olist_ONil(T_a),T_a),T_a)
    | V_x = V_y ) ).

cnf(cls_list__all__append_0,axiom,
    ( c_List_Olist__all(V_P,V_xs,T_a)
    | ~ c_List_Olist__all(V_P,c_List_Oappend(V_xs,V_ys,T_a),T_a) ) ).

cnf(cls_list__all__append_1,axiom,
    ( c_List_Olist__all(V_P,V_ys,T_a)
    | ~ c_List_Olist__all(V_P,c_List_Oappend(V_xs,V_ys,T_a),T_a) ) ).

cnf(cls_append__is__Nil__conv_2,axiom,
    c_List_Oappend(c_List_Olist_ONil(T_a),c_List_Olist_ONil(T_a),T_a) = c_List_Olist_ONil(T_a) ).

cnf(cls_lift_Osimps_I3_J_0,axiom,
    hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OAbs(V_s)),V_k) = c_Lambda_OdB_OAbs(hAPP(hAPP(c_Lambda_Olift,V_s),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),c_HOL_Oone__class_Oone(tc_nat)))) ).

cnf(cls_list__update__overwrite_0,axiom,
    c_List_Olist__update(c_List_Olist__update(V_xs,V_i,V_x,T_a),V_i,V_y,T_a) = c_List_Olist__update(V_xs,V_i,V_y,T_a) ).

cnf(cls_append__assoc_0,axiom,
    c_List_Oappend(c_List_Oappend(V_xs,V_ys,T_a),V_zs,T_a) = c_List_Oappend(V_xs,c_List_Oappend(V_ys,V_zs,T_a),T_a) ).

cnf(cls_append__eq__appendI_0,axiom,
    c_List_Oappend(V_xs,c_List_Oappend(V_xs1,V_us,T_a),T_a) = c_List_Oappend(c_List_Oappend(V_xs,V_xs1,T_a),V_us,T_a) ).

cnf(cls_append__eq__append__conv2_4,axiom,
    c_List_Oappend(c_List_Oappend(V_zs,V_x,T_a),V_ys,T_a) = c_List_Oappend(V_zs,c_List_Oappend(V_x,V_ys,T_a),T_a) ).

cnf(cls_append__eq__append__conv2_5,axiom,
    c_List_Oappend(V_xs,c_List_Oappend(V_x,V_ts,T_a),T_a) = c_List_Oappend(c_List_Oappend(V_xs,V_x,T_a),V_ts,T_a) ).

cnf(cls_sorted__remove1_0,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_List_Olinorder__class_Osorted(c_List_Oremove1(V_a,V_xs,T_a),T_a)
    | ~ c_List_Olinorder__class_Osorted(V_xs,T_a) ) ).

cnf(cls_lift__type_0,axiom,
    ( c_Type_Otyping(c_Type_Oshift(V_e,V_i,V_U,tc_Type_Otype),hAPP(hAPP(c_Lambda_Olift,V_t),V_i),V_T)
    | ~ c_Type_Otyping(V_e,V_t,V_T) ) ).

cnf(cls_Cons__step1__Cons_4,axiom,
    ( ~ hBOOL(hAPP(hAPP(V_r,V_y),V_xa))
    | c_ListOrder_Ostep1(V_r,c_List_Olist_OCons(V_y,V_x,T_a),c_List_Olist_OCons(V_xa,V_x,T_a),T_a) ) ).

cnf(cls_Cons__step1__Cons_2,axiom,
    ( V_x = V_y
    | V_xs = V_ys
    | ~ c_ListOrder_Ostep1(V_r,c_List_Olist_OCons(V_y,V_ys,T_a),c_List_Olist_OCons(V_x,V_xs,T_a),T_a) ) ).

cnf(cls_filter_Osimps_I2_J_0,axiom,
    ( c_List_Ofilter(V_P,c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = c_List_Olist_OCons(V_x,c_List_Ofilter(V_P,V_xs,T_a),T_a)
    | ~ hBOOL(hAPP(V_P,V_x)) ) ).

cnf(cls_Cons__eq__filterD_2,axiom,
    ( c_List_Olist_OCons(V_x,V_xs,T_a) != c_List_Ofilter(V_P,V_ys,T_a)
    | hBOOL(hAPP(V_P,V_x)) ) ).

cnf(cls_foldl__Cons_0,axiom,
    c_List_Ofoldl(V_f,V_a,c_List_Olist_OCons(V_x,V_xs,T_b),T_a,T_b) = c_List_Ofoldl(V_f,hAPP(hAPP(V_f,V_a),V_x),V_xs,T_a,T_b) ).

cnf(cls_sorted_Osimps_I3_J_1,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_List_Olinorder__class_Osorted(c_List_Olist_OCons(V_y,V_zs,T_a),T_a)
    | ~ c_List_Olinorder__class_Osorted(c_List_Olist_OCons(V_x,c_List_Olist_OCons(V_y,V_zs,T_a),T_a),T_a) ) ).

cnf(cls_append__eq__Cons__conv_5,axiom,
    c_List_Oappend(c_List_Olist_OCons(V_x,V_xa,T_a),V_zs,T_a) = c_List_Olist_OCons(V_x,c_List_Oappend(V_xa,V_zs,T_a),T_a) ).

cnf(cls_append__Cons_0,axiom,
    c_List_Oappend(c_List_Olist_OCons(V_x,V_xs,T_a),V_ys,T_a) = c_List_Olist_OCons(V_x,c_List_Oappend(V_xs,V_ys,T_a),T_a) ).

cnf(cls_list_Osimps_I5_J_0,axiom,
    c_List_Olist_Olist__case(V_f1,V_f2,c_List_Olist_OCons(V_a,V_list,T_b),T_a,T_b) = hAPP(hAPP(V_f2,V_a),V_list) ).

cnf(cls_remove1_Osimps_I2_J_0,axiom,
    c_List_Oremove1(V_x,c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = V_xs ).

cnf(cls_list__all2__Cons_0,axiom,
    ( hBOOL(hAPP(hAPP(V_P,V_x),V_y))
    | ~ c_List_Olist__all2(V_P,c_List_Olist_OCons(V_x,V_xs,T_a),c_List_Olist_OCons(V_y,V_ys,T_b),T_a,T_b) ) ).

cnf(cls_Cons__eq__append__conv_5,axiom,
    c_List_Olist_OCons(V_x,c_List_Oappend(V_xa,V_zs,T_a),T_a) = c_List_Oappend(c_List_Olist_OCons(V_x,V_xa,T_a),V_zs,T_a) ).

cnf(cls_Cons__eq__appendI_0,axiom,
    c_List_Olist_OCons(V_x,c_List_Oappend(V_xs1,V_zs,T_a),T_a) = c_List_Oappend(c_List_Olist_OCons(V_x,V_xs1,T_a),V_zs,T_a) ).

cnf(cls_neq__Nil__conv_1,axiom,
    c_List_Olist_OCons(V_x,V_xa,T_a) != c_List_Olist_ONil(T_a) ).

cnf(cls_list_Osimps_I3_J_0,axiom,
    c_List_Olist_OCons(V_a_H,V_list_H,T_a) != c_List_Olist_ONil(T_a) ).

cnf(cls_Cons__step1__Cons_0,axiom,
    ( V_x = V_y
    | hBOOL(hAPP(hAPP(V_r,V_y),V_x))
    | ~ c_ListOrder_Ostep1(V_r,c_List_Olist_OCons(V_y,V_ys,T_a),c_List_Olist_OCons(V_x,V_xs,T_a),T_a) ) ).

cnf(cls_sorted__Cons_0,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_List_Olinorder__class_Osorted(V_xs,T_a)
    | ~ c_List_Olinorder__class_Osorted(c_List_Olist_OCons(V_x,V_xs,T_a),T_a) ) ).

cnf(cls_takeWhile_Osimps_I2_J_0,axiom,
    ( c_List_OtakeWhile(V_P,c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = c_List_Olist_OCons(V_x,c_List_OtakeWhile(V_P,V_xs,T_a),T_a)
    | ~ hBOOL(hAPP(V_P,V_x)) ) ).

cnf(cls_list__all_Osimps_I2_J_1,axiom,
    ( c_List_Olist__all(V_P,V_xs,T_a)
    | ~ c_List_Olist__all(V_P,c_List_Olist_OCons(V_x,V_xs,T_a),T_a) ) ).

cnf(cls_list__all_Osimps_I2_J_0,axiom,
    ( hBOOL(hAPP(V_P,V_x))
    | ~ c_List_Olist__all(V_P,c_List_Olist_OCons(V_x,V_xs,T_a),T_a) ) ).

cnf(cls_insert_0,axiom,
    ( c_List_OListMem(V_x,c_List_Olist_OCons(V_y,V_xs,T_a),T_a)
    | ~ c_List_OListMem(V_x,V_xs,T_a) ) ).

cnf(cls_distinct_Osimps_I2_J_1,axiom,
    ( c_List_Odistinct(V_xs,T_a)
    | ~ c_List_Odistinct(c_List_Olist_OCons(V_x,V_xs,T_a),T_a) ) ).

cnf(cls_listsum__0_0,axiom,
    ( ~ class_OrderedGroup_Omonoid__add(T_a)
    | c_List_Olistsum(c_List_Omap(c_COMBK(c_HOL_Ozero__class_Ozero(T_a),T_a,T_b),V_xs,T_b,T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_map__eq__Cons__conv_0,axiom,
    ( c_List_Omap(V_f,V_xs,T_b,T_a) != c_List_Olist_OCons(V_y,V_ys,T_a)
    | V_xs = c_List_Olist_OCons(c_List_Osko__List__Xmap__eq__Cons__conv__1__1(V_f,V_xs,V_y,V_ys,T_b,T_a),c_List_Osko__List__Xmap__eq__Cons__conv__1__2(V_f,V_xs,V_y,V_ys,T_b,T_a),T_b) ) ).

cnf(cls_Cons__eq__map__conv_0,axiom,
    ( c_List_Olist_OCons(V_x,V_xs,T_a) != c_List_Omap(V_f,V_ys,T_b,T_a)
    | V_ys = c_List_Olist_OCons(c_List_Osko__List__XCons__eq__map__conv__1__1(V_f,V_x,V_xs,V_ys,T_b,T_a),c_List_Osko__List__XCons__eq__map__conv__1__2(V_f,V_x,V_xs,V_ys,T_b,T_a),T_b) ) ).

cnf(cls_map__eq__Cons__D_0,axiom,
    ( c_List_Omap(V_f,V_xs,T_b,T_a) != c_List_Olist_OCons(V_y,V_ys,T_a)
    | V_xs = c_List_Olist_OCons(c_List_Osko__List__Xmap__eq__Cons__D__1__1(V_f,V_xs,V_y,V_ys,T_b,T_a),c_List_Osko__List__Xmap__eq__Cons__D__1__2(V_f,V_xs,V_y,V_ys,T_b,T_a),T_b) ) ).

cnf(cls_Cons__eq__map__D_0,axiom,
    ( c_List_Olist_OCons(V_x,V_xs,T_a) != c_List_Omap(V_f,V_ys,T_b,T_a)
    | V_ys = c_List_Olist_OCons(c_List_Osko__List__XCons__eq__map__D__1__1(V_f,V_x,V_xs,V_ys,T_b,T_a),c_List_Osko__List__XCons__eq__map__D__1__2(V_f,V_x,V_xs,V_ys,T_b,T_a),T_b) ) ).

cnf(cls_substn__subst__n_0,axiom,
    c_Lambda_Osubstn(V_t,V_s,V_n) = hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),c_Lambda_Oliftn(V_n,V_s,c_HOL_Ozero__class_Ozero(tc_nat))),V_n) ).

cnf(cls_map__is__Nil__conv_0,axiom,
    ( c_List_Omap(V_f,V_xs,T_b,T_a) != c_List_Olist_ONil(T_a)
    | V_xs = c_List_Olist_ONil(T_b) ) ).

cnf(cls_drop__map_0,axiom,
    c_List_Odrop(V_n,c_List_Omap(V_f,V_xs,T_b,T_a),T_a) = c_List_Omap(V_f,c_List_Odrop(V_n,V_xs,T_b),T_b,T_a) ).

cnf(cls_map__idI_1,axiom,
    ( hAPP(V_f,c_List_Osko__List__Xmap__idI__1__1(V_f,V_xs,T_a)) != c_List_Osko__List__Xmap__idI__1__1(V_f,V_xs,T_a)
    | c_List_Omap(V_f,V_xs,T_a,T_a) = V_xs ) ).

cnf(cls_distinct__map_0,axiom,
    ( c_List_Odistinct(V_xs,T_b)
    | ~ c_List_Odistinct(c_List_Omap(V_f,V_xs,T_b,T_a),T_a) ) ).

cnf(cls_map__append_0,axiom,
    c_List_Omap(V_f,c_List_Oappend(V_xs,V_ys,T_b),T_b,T_a) = c_List_Oappend(c_List_Omap(V_f,V_xs,T_b,T_a),c_List_Omap(V_f,V_ys,T_b,T_a),T_a) ).

cnf(cls_map__eq__imp__length__eq_0,axiom,
    ( c_List_Omap(V_f,V_xs,T_b,T_a) != c_List_Omap(V_f,V_ys,T_b,T_a)
    | c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_b)) = c_Nat_Osize__class_Osize(V_ys,tc_List_Olist(T_b)) ) ).

cnf(cls_Nil__is__map__conv_0,axiom,
    ( c_List_Olist_ONil(T_a) != c_List_Omap(V_f,V_xs,T_b,T_a)
    | V_xs = c_List_Olist_ONil(T_b) ) ).

cnf(cls_map__replicate_0,axiom,
    c_List_Omap(V_f,c_List_Oreplicate(V_n,V_x,T_b),T_b,T_a) = c_List_Oreplicate(V_n,hAPP(V_f,V_x),T_a) ).

cnf(cls_length__map_0,axiom,
    c_Nat_Osize__class_Osize(c_List_Omap(V_f,V_xs,T_b,T_a),tc_List_Olist(T_a)) = c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_b)) ).

cnf(cls_rotate__map_0,axiom,
    c_List_Orotate(V_n,c_List_Omap(V_f,V_xs,T_b,T_a),T_a) = c_List_Omap(V_f,c_List_Orotate(V_n,V_xs,T_b),T_b,T_a) ).

cnf(cls_rev__map_0,axiom,
    c_List_Orev(c_List_Omap(V_f,V_xs,T_b,T_a),T_a) = c_List_Omap(V_f,c_List_Orev(V_xs,T_b),T_b,T_a) ).

cnf(cls_map__ext_1,axiom,
    ( hAPP(V_f,c_List_Osko__List__Xmap__ext__1__1(V_f,V_g,V_xs,T_a,T_b)) != hAPP(V_g,c_List_Osko__List__Xmap__ext__1__1(V_f,V_g,V_xs,T_a,T_b))
    | c_List_Omap(V_f,V_xs,T_a,T_b) = c_List_Omap(V_g,V_xs,T_a,T_b) ) ).

cnf(cls_take__map_0,axiom,
    c_List_Otake(V_n,c_List_Omap(V_f,V_xs,T_b,T_a),T_a) = c_List_Omap(V_f,c_List_Otake(V_n,V_xs,T_b),T_b,T_a) ).

cnf(cls_map__is__Nil__conv_1,axiom,
    c_List_Omap(V_f,c_List_Olist_ONil(T_b),T_b,T_a) = c_List_Olist_ONil(T_a) ).

cnf(cls_map__map_0,axiom,
    c_List_Omap(V_f,c_List_Omap(V_g,V_xs,T_c,T_b),T_b,T_a) = c_List_Omap(c_Fun_Ocomp(V_f,V_g,T_b,T_a,T_c),V_xs,T_c,T_a) ).

cnf(cls_map__cong_1,axiom,
    ( hAPP(V_f,c_List_Osko__List__Xmap__cong__1__1(V_f,V_g,V_x,T_a,T_b)) != hAPP(V_g,c_List_Osko__List__Xmap__cong__1__1(V_f,V_g,V_x,T_a,T_b))
    | c_List_Omap(V_f,V_x,T_a,T_b) = c_List_Omap(V_g,V_x,T_a,T_b) ) ).

cnf(cls_map__eq__conv_2,axiom,
    ( hAPP(V_f,c_List_Osko__List__Xmap__eq__conv__1__1(V_f,V_g,V_xs,T_b,T_a)) != hAPP(V_g,c_List_Osko__List__Xmap__eq__conv__1__1(V_f,V_g,V_xs,T_b,T_a))
    | c_List_Omap(V_f,V_xs,T_b,T_a) = c_List_Omap(V_g,V_xs,T_b,T_a) ) ).

cnf(cls_map__update_0,axiom,
    c_List_Omap(V_f,c_List_Olist__update(V_xs,V_k,V_y,T_b),T_b,T_a) = c_List_Olist__update(c_List_Omap(V_f,V_xs,T_b,T_a),V_k,hAPP(V_f,V_y),T_a) ).

cnf(cls_Nil__is__map__conv_1,axiom,
    c_List_Olist_ONil(T_a) = c_List_Omap(V_f,c_List_Olist_ONil(T_b),T_b,T_a) ).

cnf(cls_Beta_0,axiom,
    ( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_r)),V_s),V_ss,tc_Lambda_OdB,tc_Lambda_OdB)))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,V_s))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,V_r),V_s),c_HOL_Ozero__class_Ozero(tc_nat)),V_ss,tc_Lambda_OdB,tc_Lambda_OdB))) ) ).

cnf(cls_subst__App_0,axiom,
    hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_OdB_OApp,V_t),V_u)),V_s),V_k) = hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_s),V_k)),hAPP(hAPP(hAPP(c_Lambda_Osubst,V_u),V_s),V_k)) ).

cnf(cls_subst__eq_0,axiom,
    hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(V_k)),V_u),V_k) = V_u ).

cnf(cls_subst__preserves__beta_0,axiom,
    ( c_Lambda_Obeta(hAPP(hAPP(hAPP(c_Lambda_Osubst,V_r),V_t),V_i),hAPP(hAPP(hAPP(c_Lambda_Osubst,V_s),V_t),V_i))
    | ~ c_Lambda_Obeta(V_r,V_s) ) ).

cnf(cls_subst__Abs_0,axiom,
    hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OAbs(V_t)),V_s),V_k) = c_Lambda_OdB_OAbs(hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),hAPP(hAPP(c_Lambda_Olift,V_s),c_HOL_Ozero__class_Ozero(tc_nat))),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),c_HOL_Oone__class_Oone(tc_nat)))) ).

cnf(cls_Var__IT_0,axiom,
    hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(V_n))) ).

cnf(cls_Var_I3_J_0,axiom,
    hBOOL(hAPP(c_InductTermi_OIT,v_ua______)) ).

cnf(cls_Lambda_0,axiom,
    ( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(V_r)))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,V_r)) ) ).

cnf(cls_append__in__listsp__conv_2,axiom,
    ( c_List_Olistsp(V_A,c_List_Oappend(V_xs,V_ys,T_a),T_a)
    | ~ c_List_Olistsp(V_A,V_ys,T_a)
    | ~ c_List_Olistsp(V_A,V_xs,T_a) ) ).

cnf(cls_in__listsp__conv__set_2,axiom,
    ( c_List_Olistsp(V_A,V_xs,T_a)
    | ~ hBOOL(hAPP(V_A,c_List_Osko__List__Xin__listsp__conv__set__1__1(V_A,V_xs,T_a))) ) ).

cnf(cls_listsp__infI_0,axiom,
    ( c_List_Olistsp(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),V_l,T_a)
    | ~ c_List_Olistsp(V_B,V_l,T_a)
    | ~ c_List_Olistsp(V_A,V_l,T_a) ) ).

cnf(cls_listsp_ONil_0,axiom,
    c_List_Olistsp(V_A,c_List_Olist_ONil(T_a),T_a) ).

cnf(cls_append__in__listsp__conv_1,axiom,
    ( c_List_Olistsp(V_A,V_ys,T_a)
    | ~ c_List_Olistsp(V_A,c_List_Oappend(V_xs,V_ys,T_a),T_a) ) ).

cnf(cls_append__in__listsp__conv_0,axiom,
    ( c_List_Olistsp(V_A,V_xs,T_a)
    | ~ c_List_Olistsp(V_A,c_List_Oappend(V_xs,V_ys,T_a),T_a) ) ).

cnf(cls_lift_Osimps_I2_J_0,axiom,
    hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_t)),V_k) = hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_Olift,V_s),V_k)),hAPP(hAPP(c_Lambda_Olift,V_t),V_k)) ).

cnf(cls_lift__preserves__beta_0,axiom,
    ( c_Lambda_Obeta(hAPP(hAPP(c_Lambda_Olift,V_r),V_i),hAPP(hAPP(c_Lambda_Olift,V_s),V_i))
    | ~ c_Lambda_Obeta(V_r,V_s) ) ).

cnf(cls_I_0,axiom,
    ( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),V_ua),V_ia)))
    | ~ c_Type_Otyping(V_ea,V_ua,v_T____)
    | ~ hBOOL(hAPP(c_InductTermi_OIT,V_ua))
    | ~ c_Type_Otyping(c_Type_Oshift(V_ea,V_ia,v_T____,tc_Type_Otype),v_b____,V_T_H) ) ).

cnf(cls_Cons_I1_J_0,axiom,
    ( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),V_u),V_ia)))
    | ~ c_Type_Otyping(V_ea,V_u,v_T____)
    | ~ hBOOL(hAPP(c_InductTermi_OIT,V_u))
    | ~ c_Type_Otyping(c_Type_Oshift(V_ea,V_ia,v_T____,tc_Type_Otype),v_b____,V_T_H) ) ).

cnf(cls_True_0,axiom,
    v_n____ = v_i____ ).

cnf(cls_power__eq__0__iff_2,axiom,
    ( ~ class_Ring__and__Field_Ozero__neq__one(T_a)
    | ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
    | ~ class_Ring__and__Field_Omult__zero(T_a)
    | ~ class_Power_Opower(T_a)
    | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),V_n,T_a) = c_HOL_Ozero__class_Ozero(T_a)
    | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ).

cnf(cls_power__0__left_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring__0(T_a)
    | ~ class_Power_Opower(T_a)
    | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),V_n,T_a) = c_HOL_Ozero__class_Ozero(T_a)
    | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ).

cnf(cls_power__eq__0__iff_1,axiom,
    ( ~ class_Ring__and__Field_Ozero__neq__one(T_a)
    | ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
    | ~ class_Ring__and__Field_Omult__zero(T_a)
    | ~ class_Power_Opower(T_a)
    | c_Power_Opower__class_Opower(V_a,c_HOL_Ozero__class_Ozero(tc_nat),T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_of__nat__0_0,axiom,
    ( ~ class_Ring__and__Field_Osemiring__1(T_a)
    | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_substs__lemma_0,axiom,
    ( c_Type_Otypings(V_e,c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,V_u,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),V_i,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),V_Ts)
    | ~ c_Type_Otypings(c_Type_Oshift(V_e,V_i,V_T,tc_Type_Otype),V_ts,V_Ts)
    | ~ c_Type_Otyping(V_e,V_u,V_T) ) ).

cnf(cls_nth__Cons_H_0,axiom,
    c_List_Onth(c_List_Olist_OCons(V_x,V_xs,T_a),c_HOL_Ozero__class_Ozero(tc_nat),T_a) = V_x ).

cnf(cls_drop__Cons_H_0,axiom,
    c_List_Odrop(c_HOL_Ozero__class_Ozero(tc_nat),c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = c_List_Olist_OCons(V_x,V_xs,T_a) ).

cnf(cls_list__update__code_I2_J_0,axiom,
    c_List_Olist__update(c_List_Olist_OCons(V_x,V_xs,T_a),c_HOL_Ozero__class_Ozero(tc_nat),V_y,T_a) = c_List_Olist_OCons(V_y,V_xs,T_a) ).

cnf(cls_map__eq__Cons__D_2,axiom,
    ( c_List_Omap(V_f,V_xs,T_b,T_a) != c_List_Olist_OCons(V_y,V_ys,T_a)
    | c_List_Omap(V_f,c_List_Osko__List__Xmap__eq__Cons__D__1__2(V_f,V_xs,V_y,V_ys,T_b,T_a),T_b,T_a) = V_ys ) ).

cnf(cls_Cons__eq__map__conv_2,axiom,
    ( c_List_Olist_OCons(V_x,V_xs,T_a) != c_List_Omap(V_f,V_ys,T_b,T_a)
    | V_xs = c_List_Omap(V_f,c_List_Osko__List__XCons__eq__map__conv__1__2(V_f,V_x,V_xs,V_ys,T_b,T_a),T_b,T_a) ) ).

cnf(cls_map__eq__Cons__D_1,axiom,
    ( c_List_Omap(V_f,V_xs,T_b,T_a) != c_List_Olist_OCons(V_y,V_ys,T_a)
    | hAPP(V_f,c_List_Osko__List__Xmap__eq__Cons__D__1__1(V_f,V_xs,V_y,V_ys,T_b,T_a)) = V_y ) ).

cnf(cls_map__eq__Cons__conv_1,axiom,
    ( c_List_Omap(V_f,V_xs,T_b,T_a) != c_List_Olist_OCons(V_y,V_ys,T_a)
    | hAPP(V_f,c_List_Osko__List__Xmap__eq__Cons__conv__1__1(V_f,V_xs,V_y,V_ys,T_b,T_a)) = V_y ) ).

cnf(cls_map__eq__Cons__conv_2,axiom,
    ( c_List_Omap(V_f,V_xs,T_b,T_a) != c_List_Olist_OCons(V_y,V_ys,T_a)
    | c_List_Omap(V_f,c_List_Osko__List__Xmap__eq__Cons__conv__1__2(V_f,V_xs,V_y,V_ys,T_b,T_a),T_b,T_a) = V_ys ) ).

cnf(cls_Cons__eq__map__conv_1,axiom,
    ( c_List_Olist_OCons(V_x,V_xs,T_a) != c_List_Omap(V_f,V_ys,T_b,T_a)
    | V_x = hAPP(V_f,c_List_Osko__List__XCons__eq__map__conv__1__1(V_f,V_x,V_xs,V_ys,T_b,T_a)) ) ).

cnf(cls_Cons__eq__map__D_1,axiom,
    ( c_List_Olist_OCons(V_x,V_xs,T_a) != c_List_Omap(V_f,V_ys,T_b,T_a)
    | V_x = hAPP(V_f,c_List_Osko__List__XCons__eq__map__D__1__1(V_f,V_x,V_xs,V_ys,T_b,T_a)) ) ).

cnf(cls_Cons__eq__map__D_2,axiom,
    ( c_List_Olist_OCons(V_x,V_xs,T_a) != c_List_Omap(V_f,V_ys,T_b,T_a)
    | V_xs = c_List_Omap(V_f,c_List_Osko__List__XCons__eq__map__D__1__2(V_f,V_x,V_xs,V_ys,T_b,T_a),T_b,T_a) ) ).

cnf(cls_substn__subst__0_0,axiom,
    c_Lambda_Osubstn(V_t,V_s,c_HOL_Ozero__class_Ozero(tc_nat)) = hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_s),c_HOL_Ozero__class_Ozero(tc_nat)) ).

cnf(cls_lift__map_0,axiom,
    hAPP(hAPP(c_Lambda_Olift,c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB)),V_i) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_Olift,V_t),V_i),c_List_Omap(c_COMBC(c_Lambda_Olift,V_i,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) ).

cnf(cls_lift__types_0,axiom,
    ( c_Type_Otypings(c_Type_Oshift(V_e,V_i,V_U,tc_Type_Otype),c_List_Omap(c_COMBC(c_Lambda_Olift,V_i,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),V_Ts)
    | ~ c_Type_Otypings(V_e,V_ts,V_Ts) ) ).

cnf(cls_subst__Var__IT_0,axiom,
    ( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,V_r),c_Lambda_OdB_OVar(V_i)),V_j)))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,V_r)) ) ).

cnf(cls_subst__map_0,axiom,
    hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB)),V_u),V_i) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_u),V_i),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,V_u,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),V_i,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) ).

cnf(cls_lifts__IT_0,axiom,
    ( c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)
    | ~ c_List_Olistsp(c_InductTermi_OIT,V_ts,tc_Lambda_OdB) ) ).

cnf(cls_list_Oinject_1,axiom,
    ( c_List_Olist_OCons(V_a,V_list,T_a) != c_List_Olist_OCons(V_a_H,V_list_H,T_a)
    | V_list = V_list_H ) ).

cnf(cls_list_Oinject_0,axiom,
    ( c_List_Olist_OCons(V_a,V_list,T_a) != c_List_Olist_OCons(V_a_H,V_list_H,T_a)
    | V_a = V_a_H ) ).

cnf(cls_lift__IT_0,axiom,
    ( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_Olift,V_t),V_i)))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,V_t)) ) ).

cnf(cls_COMBC__def_0,axiom,
    hAPP(c_COMBC(V_P,V_Q,T_b,T_c,T_a),V_R) = hAPP(hAPP(V_P,V_R),V_Q) ).

cnf(cls_Cons_I3_J_0,axiom,
    c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_bs____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB) ).

cnf(cls_map__eq__Cons__conv_3,axiom,
    c_List_Omap(V_f,c_List_Olist_OCons(V_x,V_xa,T_b),T_b,T_a) = c_List_Olist_OCons(hAPP(V_f,V_x),c_List_Omap(V_f,V_xa,T_b,T_a),T_a) ).

cnf(cls_Cons__eq__map__conv_3,axiom,
    c_List_Olist_OCons(hAPP(V_f,V_xa),c_List_Omap(V_f,V_xb,T_b,T_a),T_a) = c_List_Omap(V_f,c_List_Olist_OCons(V_xa,V_xb,T_b),T_b,T_a) ).

cnf(cls_map_Osimps_I2_J_0,axiom,
    c_List_Omap(V_f,c_List_Olist_OCons(V_x,V_xs,T_b),T_b,T_a) = c_List_Olist_OCons(hAPP(V_f,V_x),c_List_Omap(V_f,V_xs,T_b,T_a),T_a) ).

cnf(cls_uIT_0,axiom,
    hBOOL(hAPP(c_InductTermi_OIT,v_u____)) ).

cnf(cls_subst__lift_0,axiom,
    hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,V_t),V_k)),V_s),V_k) = V_t ).

cnf(cls_not__Cons__self2_0,axiom,
    c_List_Olist_OCons(V_x,V_t,T_a) != V_t ).

cnf(cls_not__Cons__self_0,axiom,
    V_xs != c_List_Olist_OCons(V_x,V_xs,T_a) ).

cnf(cls_CHAINED_0,axiom,
    c_List_Olistsp(c_InductTermi_OIT,c_List_Olist_OCons(hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),v_u____),v_i____)),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_bs____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB) ).

cnf(cls_conjecture_0,negated_conjecture,
    ~ c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_List_Olist_OCons(v_b____,v_bs____,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB) ).

cnf(clsarity_fun__Lattices_Olower__semilattice,axiom,
    ( class_Lattices_Olower__semilattice(tc_fun(T_2,T_1))
    | ~ class_Lattices_Olattice(T_1) ) ).

cnf(clsarity_fun__Lattices_Olattice,axiom,
    ( class_Lattices_Olattice(tc_fun(T_2,T_1))
    | ~ class_Lattices_Olattice(T_1) ) ).

cnf(clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add,axiom,
    class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) ).

cnf(clsarity_nat__OrderedGroup_Ocancel__semigroup__add,axiom,
    class_OrderedGroup_Ocancel__semigroup__add(tc_nat) ).

cnf(clsarity_nat__Ring__and__Field_Ono__zero__divisors,axiom,
    class_Ring__and__Field_Ono__zero__divisors(tc_nat) ).

cnf(clsarity_nat__Ring__and__Field_Ocomm__semiring__1,axiom,
    class_Ring__and__Field_Ocomm__semiring__1(tc_nat) ).

cnf(clsarity_nat__OrderedGroup_Oab__semigroup__add,axiom,
    class_OrderedGroup_Oab__semigroup__add(tc_nat) ).

cnf(clsarity_nat__OrderedGroup_Ocomm__monoid__add,axiom,
    class_OrderedGroup_Ocomm__monoid__add(tc_nat) ).

cnf(clsarity_nat__Ring__and__Field_Ozero__neq__one,axiom,
    class_Ring__and__Field_Ozero__neq__one(tc_nat) ).

cnf(clsarity_nat__OrderedGroup_Osemigroup__add,axiom,
    class_OrderedGroup_Osemigroup__add(tc_nat) ).

cnf(clsarity_nat__Lattices_Olower__semilattice,axiom,
    class_Lattices_Olower__semilattice(tc_nat) ).

cnf(clsarity_nat__Ring__and__Field_Osemiring__1,axiom,
    class_Ring__and__Field_Osemiring__1(tc_nat) ).

cnf(clsarity_nat__Ring__and__Field_Osemiring__0,axiom,
    class_Ring__and__Field_Osemiring__0(tc_nat) ).

cnf(clsarity_nat__Ring__and__Field_Omult__zero,axiom,
    class_Ring__and__Field_Omult__zero(tc_nat) ).

cnf(clsarity_nat__OrderedGroup_Omonoid__mult,axiom,
    class_OrderedGroup_Omonoid__mult(tc_nat) ).

cnf(clsarity_nat__OrderedGroup_Omonoid__add,axiom,
    class_OrderedGroup_Omonoid__add(tc_nat) ).

cnf(clsarity_nat__Nat_Osemiring__char__0,axiom,
    class_Nat_Osemiring__char__0(tc_nat) ).

cnf(clsarity_nat__Orderings_Olinorder,axiom,
    class_Orderings_Olinorder(tc_nat) ).

cnf(clsarity_nat__Lattices_Olattice,axiom,
    class_Lattices_Olattice(tc_nat) ).

cnf(clsarity_nat__Power_Opower,axiom,
    class_Power_Opower(tc_nat) ).

cnf(clsarity_bool__Lattices_Olower__semilattice,axiom,
    class_Lattices_Olower__semilattice(tc_bool) ).

cnf(clsarity_bool__Lattices_Olattice,axiom,
    class_Lattices_Olattice(tc_bool) ).

cnf(cls_ATP__Linkup_OCOMBC__def_0,axiom,
    hAPP(c_COMBC(V_P,V_Q,T_b,T_c,T_a),V_R) = hAPP(hAPP(V_P,V_R),V_Q) ).

cnf(cls_ATP__Linkup_OCOMBB__def_0,axiom,
    c_COMBB(V_P,V_Q,V_R,T_b,T_a,T_c) = hAPP(V_P,hAPP(V_Q,V_R)) ).

cnf(cls_ATP__Linkup_Oequal__imp__fequal_0,axiom,
    hBOOL(hAPP(hAPP(c_fequal(T_a),V_x),V_x)) ).

cnf(cls_ATP__Linkup_Ofequal__imp__equal_0,axiom,
    ( V_X = V_Y
    | ~ hBOOL(hAPP(hAPP(c_fequal(T_a),V_X),V_Y)) ) ).

%------------------------------------------------------------------------------