%------------------------------------------------------------------------------
% File     : LCL788-1 : TPTP v8.2.0. Released v4.1.0.
% Domain   : Logic Calculi
% Problem  : Strong normalization of typed lambda calculus 131_13
% 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-131_13 [Nip10]

% Status   : Unsatisfiable
% Rating   : 0.20 v8.2.0, 0.19 v8.1.0, 0.16 v7.5.0, 0.21 v7.4.0, 0.18 v7.3.0, 0.17 v7.1.0, 0.08 v7.0.0, 0.33 v6.3.0, 0.18 v6.2.0, 0.30 v6.1.0, 0.29 v6.0.0, 0.30 v5.5.0, 0.50 v5.2.0, 0.44 v5.1.0, 0.47 v5.0.0, 0.36 v4.1.0
% Syntax   : Number of clauses     :  242 ( 115 unt;  39 nHn; 126 RR)
%            Number of literals    :  409 ( 268 equ; 147 neg)
%            Maximal clause size   :    6 (   1 avg)
%            Maximal term depth    :    6 (   1 avg)
%            Number of predicates  :    7 (   6 usr;   0 prp; 1-4 aty)
%            Number of functors    :   60 (  60 usr;  22 con; 0-5 aty)
%            Number of variables   :  796 ( 160 sgn)
% SPC      : CNF_UNS_RFO_SEQ_NHN

% Comments :
%------------------------------------------------------------------------------
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_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_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_hd__replicate_0,axiom,
    ( c_List_Ohd(c_List_Oreplicate(V_n,V_x,T_a),T_a) = V_x
    | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ).

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

cnf(cls_types__snocE_2,axiom,
    ( c_Type_Otyping(V_e,V_t,c_Type_Osko__Type__Xtypes__snocE__1__2(V_Ts,V_e,V_t,V_ts))
    | ~ c_Type_Otypings(V_e,c_List_Oappend(V_ts,c_List_Olist_OCons(V_t,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),V_Ts) ) ).

cnf(cls_last__replicate_0,axiom,
    ( c_List_Olast(c_List_Oreplicate(V_n,V_x,T_a),T_a) = V_x
    | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ).

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__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_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_apps__eq__Abs__conv_2,axiom,
    c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_r),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) = c_Lambda_OdB_OAbs(V_r) ).

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_apps__eq__Abs__conv_1,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_ss = c_List_Olist_ONil(tc_Lambda_OdB) ) ).

cnf(cls_hd__dropWhile_0,axiom,
    ( ~ hBOOL(hAPP(V_P,c_List_Ohd(c_List_OdropWhile(V_P,V_xs,T_a),T_a)))
    | c_List_OdropWhile(V_P,V_xs,T_a) = c_List_Olist_ONil(T_a) ) ).

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_Abs__eq__apps__conv_2,axiom,
    c_Lambda_OdB_OAbs(V_r) = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_r),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) ).

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

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_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_listsp_ONil_0,axiom,
    c_List_Olistsp(V_A,c_List_Olist_ONil(T_a),T_a) ).

cnf(cls_Var_I4_J_0,axiom,
    c_Type_Otyping(v_ea______,v_ua______,v_T____) ).

cnf(cls_dropWhile_Osimps_I1_J_0,axiom,
    c_List_OdropWhile(V_P,c_List_Olist_ONil(T_a),T_a) = c_List_Olist_ONil(T_a) ).

cnf(cls_dropWhile__eq__Cons__conv_1,axiom,
    ( c_List_OdropWhile(V_P,V_xs,T_a) != c_List_Olist_OCons(V_y,V_ys,T_a)
    | ~ hBOOL(hAPP(V_P,V_y)) ) ).

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

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,c_Lambda_Osubst(V_r,V_s,c_HOL_Ozero__class_Ozero(tc_nat)),V_ss,tc_Lambda_OdB,tc_Lambda_OdB))) ) ).

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_splice__Cons__Cons_0,axiom,
    c_List_Osplice(c_List_Olist_OCons(V_x,V_xs,T_a),c_List_Olist_OCons(V_y,V_ys,T_a),T_a) = c_List_Olist_OCons(V_x,c_List_Olist_OCons(V_y,c_List_Osplice(V_xs,V_ys,T_a),T_a),T_a) ).

cnf(cls_App__eq__foldl__conv_5,axiom,
    ( V_r != c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,V_r),V_s),V_xa,tc_Lambda_OdB,tc_Lambda_OdB)
    | hAPP(hAPP(c_Lambda_OdB_OApp,V_r),V_s) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,V_r),V_s),c_List_Oappend(V_xa,c_List_Olist_OCons(V_s,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) ) ).

cnf(cls_Abs__eq__apps__conv_1,axiom,
    ( c_Lambda_OdB_OAbs(V_r) != c_List_Ofoldl(c_Lambda_OdB_OApp,V_s,V_ss,tc_Lambda_OdB,tc_Lambda_OdB)
    | V_ss = c_List_Olist_ONil(tc_Lambda_OdB) ) ).

cnf(cls_dropWhile_Osimps_I2_J_0,axiom,
    ( c_List_OdropWhile(V_P,c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = c_List_OdropWhile(V_P,V_xs,T_a)
    | ~ hBOOL(hAPP(V_P,V_x)) ) ).

cnf(cls_dropWhile_Osimps_I2_J_1,axiom,
    ( c_List_OdropWhile(V_P,c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = c_List_Olist_OCons(V_x,V_xs,T_a)
    | hBOOL(hAPP(V_P,V_x)) ) ).

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_App__eq__foldl__conv_0,axiom,
    ( hAPP(hAPP(c_Lambda_OdB_OApp,V_r),V_s) != c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)
    | hAPP(hAPP(c_Lambda_OdB_OApp,V_r),V_s) = V_t ) ).

cnf(cls_takeWhile__dropWhile__id_0,axiom,
    c_List_Oappend(c_List_OtakeWhile(V_P,V_xs,T_a),c_List_OdropWhile(V_P,V_xs,T_a),T_a) = V_xs ).

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_splice_Osimps_I1_J_0,axiom,
    c_List_Osplice(c_List_Olist_ONil(T_a),V_ys,T_a) = V_ys ).

cnf(cls_splice__Nil2_0,axiom,
    c_List_Osplice(V_xs,c_List_Olist_ONil(T_a),T_a) = V_xs ).

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_app__last_0,axiom,
    hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB)),V_u) = c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,c_List_Oappend(V_ts,c_List_Olist_OCons(V_u,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) ).

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_App__eq__foldl__conv_4,axiom,
    hAPP(hAPP(c_Lambda_OdB_OApp,V_r),V_s) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,V_r),V_s),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) ).

cnf(cls_App__eq__foldl__conv_3,axiom,
    ( c_List_Oappend(V_x,c_List_Olist_OCons(V_s,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB) = c_List_Olist_ONil(tc_Lambda_OdB)
    | hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_x,tc_Lambda_OdB,tc_Lambda_OdB)),V_s) = c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,c_List_Oappend(V_x,c_List_Olist_OCons(V_s,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) ) ).

cnf(cls_Abs_0,axiom,
    ( c_Type_Otyping(V_env,c_Lambda_OdB_OAbs(V_t),hAPP(hAPP(c_Type_Otype_OFun,V_T),V_U))
    | ~ c_Type_Otyping(c_Type_Oshift(V_env,c_HOL_Ozero__class_Ozero(tc_nat),V_T,tc_Type_Otype),V_t,V_U) ) ).

cnf(cls_splice_Osimps_I2_J_0,axiom,
    c_List_Osplice(c_List_Olist_OCons(V_x,V_xs,T_a),c_List_Olist_ONil(T_a),T_a) = c_List_Olist_OCons(V_x,V_xs,T_a) ).

cnf(cls_Cons__eq__append__conv_2,axiom,
    ( c_List_Olist_OCons(V_x,V_xs,T_a) != c_List_Oappend(V_ys,V_zs,T_a)
    | c_List_Olist_OCons(V_x,c_List_Osko__List__XCons__eq__append__conv__1__1(V_x,V_xs,V_ys,V_zs,T_a),T_a) = V_ys
    | c_List_Olist_OCons(V_x,V_xs,T_a) = V_zs ) ).

cnf(cls_append__eq__Cons__conv_3,axiom,
    ( c_List_Oappend(V_ys,V_zs,T_a) != c_List_Olist_OCons(V_x,V_xs,T_a)
    | c_List_Oappend(c_List_Osko__List__Xappend__eq__Cons__conv__1__1(V_x,V_xs,V_ys,V_zs,T_a),V_zs,T_a) = V_xs
    | V_zs = c_List_Olist_OCons(V_x,V_xs,T_a) ) ).

cnf(cls_butlast_Osimps_I2_J_1,axiom,
    ( c_List_Obutlast(c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = c_List_Olist_OCons(V_x,c_List_Obutlast(V_xs,T_a),T_a)
    | V_xs = c_List_Olist_ONil(T_a) ) ).

cnf(cls_last_Osimps_0,axiom,
    c_List_Olast(c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a) = V_x ).

cnf(cls_butlast_Osimps_I2_J_0,axiom,
    c_List_Obutlast(c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a) = c_List_Olist_ONil(T_a) ).

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_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_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_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_last_Osimps_1,axiom,
    ( c_List_Olast(c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = c_List_Olast(V_xs,T_a)
    | V_xs = c_List_Olist_ONil(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_var__app__types_0,axiom,
    ( V_U = c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__types__1__1(V_T,V_U,V_e,V_us),V_T,tc_Type_Otype,tc_Type_Otype)
    | ~ 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_Otypings(V_e,V_ts,V_Ts)
    | ~ c_Type_Otyping(V_e,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_i),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),V_us,tc_Lambda_OdB,tc_Lambda_OdB),V_T) ) ).

cnf(cls_append__butlast__last__id_0,axiom,
    ( c_List_Oappend(c_List_Obutlast(V_xs,T_a),c_List_Olist_OCons(c_List_Olast(V_xs,T_a),c_List_Olist_ONil(T_a),T_a),T_a) = V_xs
    | V_xs = c_List_Olist_ONil(T_a) ) ).

cnf(cls_Var_I2_J_0,axiom,
    c_Type_Otyping(c_Type_Oshift(v_ea______,v_ia______,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_Ha______) ).

cnf(cls_hd_Osimps_0,axiom,
    c_List_Ohd(c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = V_x ).

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

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_var__app__typesE_1,axiom,
    ( c_Type_Otypings(V_e,V_ts,c_Type_Osko__Type__Xvar__app__typesE__1__1(V_T,V_e,V_i,V_ts))
    | ~ 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_butlast_Osimps_I1_J_0,axiom,
    c_List_Obutlast(c_List_Olist_ONil(T_a),T_a) = c_List_Olist_ONil(T_a) ).

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_subst__eq_0,axiom,
    c_Lambda_Osubst(c_Lambda_OdB_OVar(V_k),V_u,V_k) = V_u ).

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_tl_Osimps_I1_J_0,axiom,
    c_List_Otl(c_List_Olist_ONil(T_a),T_a) = c_List_Olist_ONil(T_a) ).

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

cnf(cls_list__app__typeD_1,axiom,
    ( c_Type_Otypings(V_e,V_ts,c_Type_Osko__Type__Xlist__app__typeD__1__1(V_T,V_e,V_t,V_ts))
    | ~ c_Type_Otyping(V_e,c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB),V_T) ) ).

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_foldr__foldl_0,axiom,
    c_List_Ofoldr(V_f,V_xs,V_a,T_b,T_a) = c_List_Ofoldl(c_COMBC(V_f,T_b,T_a,T_a),V_a,c_List_Orev(V_xs,T_b),T_a,T_b) ).

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_concat__map_Osimps_I1_J_0,axiom,
    c_List_Oconcat__map(V_f,c_List_Olist_ONil(T_b),T_b,T_a) = c_List_Olist_ONil(T_a) ).

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_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_tl_Osimps_I2_J_0,axiom,
    c_List_Otl(c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = V_xs ).

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_splice_Osimps_I2_J_1,axiom,
    ( c_List_Osplice(c_List_Olist_OCons(V_x,V_xs,T_a),V_ys,T_a) = c_List_Olist_OCons(V_x,c_List_Olist_OCons(c_List_Ohd(V_ys,T_a),c_List_Osplice(V_xs,c_List_Otl(V_ys,T_a),T_a),T_a),T_a)
    | V_ys = c_List_Olist_ONil(T_a) ) ).

cnf(cls_dropWhile__eq__Cons__conv_2,axiom,
    ( V_xs != c_List_Oappend(c_List_OtakeWhile(V_P,V_xs,T_a),c_List_Olist_OCons(V_y,V_ys,T_a),T_a)
    | c_List_OdropWhile(V_P,V_xs,T_a) = c_List_Olist_OCons(V_y,V_ys,T_a)
    | hBOOL(hAPP(V_P,V_y)) ) ).

cnf(cls_dropWhile__eq__Cons__conv_0,axiom,
    ( c_List_OdropWhile(V_P,V_xs,T_a) != c_List_Olist_OCons(V_y,V_ys,T_a)
    | V_xs = c_List_Oappend(c_List_OtakeWhile(V_P,V_xs,T_a),c_List_Olist_OCons(V_y,V_ys,T_a),T_a) ) ).

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_lift__IT_0,axiom,
    ( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Olift(V_t,V_i)))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,V_t)) ) ).

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_not__step1__Nil_0,axiom,
    ~ c_ListOrder_Ostep1(V_r,V_xs,c_List_Olist_ONil(T_a),T_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_hd__rev_0,axiom,
    ( c_List_Ohd(c_List_Orev(V_xs,T_a),T_a) = c_List_Olast(V_xs,T_a)
    | V_xs = c_List_Olist_ONil(T_a) ) ).

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

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_lift_Osimps_I2_J_0,axiom,
    c_Lambda_Olift(hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_t),V_k) = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Olift(V_s,V_k)),c_Lambda_Olift(V_t,V_k)) ).

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

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

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

cnf(cls_rotate1__is__Nil__conv_0,axiom,
    ( c_List_Orotate1(V_xs,T_a) != c_List_Olist_ONil(T_a)
    | V_xs = c_List_Olist_ONil(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_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_rotate__simps_0,axiom,
    c_List_Orotate1(c_List_Olist_ONil(T_a),T_a) = c_List_Olist_ONil(T_a) ).

cnf(cls_last__rev_0,axiom,
    ( c_List_Olast(c_List_Orev(V_xs,T_a),T_a) = c_List_Ohd(V_xs,T_a)
    | V_xs = c_List_Olist_ONil(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_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_Var__eq__apps__conv_2,axiom,
    c_Lambda_OdB_OVar(V_m) = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_m),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) ).

cnf(cls_list__app__typeE_1,axiom,
    ( c_Type_Otypings(V_e,V_ts,c_Type_Osko__Type__Xlist__app__typeE__1__1(V_T,V_e,V_t,V_ts))
    | ~ c_Type_Otyping(V_e,c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB),V_T) ) ).

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_rotate1__hd__tl_0,axiom,
    ( c_List_Orotate1(V_xs,T_a) = c_List_Oappend(c_List_Otl(V_xs,T_a),c_List_Olist_OCons(c_List_Ohd(V_xs,T_a),c_List_Olist_ONil(T_a),T_a),T_a)
    | V_xs = 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_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_var__app__types_1,axiom,
    ( c_Type_Otypings(V_e,V_us,c_Type_Osko__Type__Xvar__app__types__1__1(V_T,V_U,V_e,V_us))
    | ~ 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_Otypings(V_e,V_ts,V_Ts)
    | ~ c_Type_Otyping(V_e,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_i),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),V_us,tc_Lambda_OdB,tc_Lambda_OdB),V_T) ) ).

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

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_subst__lift_0,axiom,
    c_Lambda_Osubst(c_Lambda_Olift(V_t,V_k),V_s,V_k) = V_t ).

cnf(cls_Cons_0,axiom,
    v_rs____ = c_List_Olist_OCons(v_a____,v_as____,tc_Lambda_OdB) ).

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_Var__eq__apps__conv_1,axiom,
    ( c_Lambda_OdB_OVar(V_m) != c_List_Ofoldl(c_Lambda_OdB_OApp,V_s,V_ss,tc_Lambda_OdB,tc_Lambda_OdB)
    | V_ss = c_List_Olist_ONil(tc_Lambda_OdB) ) ).

cnf(cls_foldl__foldr_0,axiom,
    c_List_Ofoldl(V_f,V_a,V_xs,T_a,T_b) = c_List_Ofoldr(c_COMBC(V_f,T_a,T_b,T_a),c_List_Orev(V_xs,T_b),V_a,T_b,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_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_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_split__list__last__prop__iff_6,axiom,
    ( hBOOL(hAPP(V_P,c_List_Osko__List__Xsplit__list__last__prop__iff__1__5(V_P,c_List_Oappend(V_x,c_List_Olist_OCons(V_xa,V_xb,T_a),T_a),T_a)))
    | hBOOL(hAPP(V_P,c_List_Osko__List__Xsplit__list__last__prop__iff__1__5(V_P,V_xb,T_a)))
    | ~ hBOOL(hAPP(V_P,V_xa)) ) ).

cnf(cls_concat__map_Osimps_I2_J_0,axiom,
    c_List_Oconcat__map(V_f,c_List_Olist_OCons(V_x,V_xs,T_b),T_b,T_a) = c_List_Oappend(hAPP(V_f,V_x),c_List_Oconcat__map(V_f,V_xs,T_b,T_a),T_a) ).

cnf(cls_split__list__first__prop__iff_6,axiom,
    ( hBOOL(hAPP(V_P,c_List_Osko__List__Xsplit__list__first__prop__iff__1__5(V_P,c_List_Oappend(V_x,c_List_Olist_OCons(V_xa,V_xb,T_a),T_a),T_a)))
    | hBOOL(hAPP(V_P,c_List_Osko__List__Xsplit__list__first__prop__iff__1__5(V_P,V_x,T_a)))
    | ~ hBOOL(hAPP(V_P,V_xa)) ) ).

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_append__eq__Cons__conv_2,axiom,
    ( c_List_Oappend(V_ys,V_zs,T_a) != c_List_Olist_OCons(V_x,V_xs,T_a)
    | V_ys = c_List_Olist_OCons(V_x,c_List_Osko__List__Xappend__eq__Cons__conv__1__1(V_x,V_xs,V_ys,V_zs,T_a),T_a)
    | V_zs = c_List_Olist_OCons(V_x,V_xs,T_a) ) ).

cnf(cls_Cons__eq__append__conv_3,axiom,
    ( c_List_Olist_OCons(V_x,V_xs,T_a) != c_List_Oappend(V_ys,V_zs,T_a)
    | V_xs = c_List_Oappend(c_List_Osko__List__XCons__eq__append__conv__1__1(V_x,V_xs,V_ys,V_zs,T_a),V_zs,T_a)
    | c_List_Olist_OCons(V_x,V_xs,T_a) = V_zs ) ).

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_hd__append_1,axiom,
    ( c_List_Ohd(c_List_Oappend(V_xs,V_ys,T_a),T_a) = c_List_Ohd(V_xs,T_a)
    | V_xs = c_List_Olist_ONil(T_a) ) ).

cnf(cls_butlast__append_0,axiom,
    c_List_Obutlast(c_List_Oappend(V_xs,c_List_Olist_ONil(T_a),T_a),T_a) = c_List_Obutlast(V_xs,T_a) ).

cnf(cls_tl__append2_0,axiom,
    ( c_List_Otl(c_List_Oappend(V_xs,V_ys,T_a),T_a) = c_List_Oappend(c_List_Otl(V_xs,T_a),V_ys,T_a)
    | V_xs = c_List_Olist_ONil(T_a) ) ).

cnf(cls_last__append_1,axiom,
    ( c_List_Olast(c_List_Oappend(V_xs,V_ys,T_a),T_a) = c_List_Olast(V_ys,T_a)
    | V_ys = c_List_Olist_ONil(T_a) ) ).

cnf(cls_last__append_0,axiom,
    c_List_Olast(c_List_Oappend(V_xs,c_List_Olist_ONil(T_a),T_a),T_a) = c_List_Olast(V_xs,T_a) ).

cnf(cls_hd__append_0,axiom,
    c_List_Ohd(c_List_Oappend(c_List_Olist_ONil(T_a),V_ys,T_a),T_a) = c_List_Ohd(V_ys,T_a) ).

cnf(cls_butlast__append_1,axiom,
    ( c_List_Obutlast(c_List_Oappend(V_xs,V_ys,T_a),T_a) = c_List_Oappend(V_xs,c_List_Obutlast(V_ys,T_a),T_a)
    | V_ys = c_List_Olist_ONil(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_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_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_typing__elims_I2_J_1,axiom,
    ( c_Type_Otyping(V_e,V_u,c_Type_Osko__Type__Xtyping__elims__2__1(V_T,V_e,V_t,V_u))
    | ~ c_Type_Otyping(V_e,hAPP(hAPP(c_Lambda_OdB_OApp,V_t),V_u),V_T) ) ).

cnf(cls_list__app__typeD_0,axiom,
    ( c_Type_Otyping(V_e,V_t,c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeD__1__1(V_T,V_e,V_t,V_ts),V_T,tc_Type_Otype,tc_Type_Otype))
    | ~ c_Type_Otyping(V_e,c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB),V_T) ) ).

cnf(cls_list__app__typeI_0,axiom,
    ( c_Type_Otyping(V_e,c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB),V_T)
    | ~ c_Type_Otypings(V_e,V_ts,V_Ts)
    | ~ c_Type_Otyping(V_e,V_t,c_List_Ofoldr(c_Type_Otype_OFun,V_Ts,V_T,tc_Type_Otype,tc_Type_Otype)) ) ).

cnf(cls_list__app__typeE_0,axiom,
    ( c_Type_Otyping(V_e,V_t,c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeE__1__1(V_T,V_e,V_t,V_ts),V_T,tc_Type_Otype,tc_Type_Otype))
    | ~ c_Type_Otyping(V_e,c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB),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,c_Lambda_Osubst(V_t,V_u,V_i),V_T) ) ).

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

cnf(cls_MI1_0,axiom,
    ( v_T____ != hAPP(hAPP(c_Type_Otype_OFun,V_T1),V_T2)
    | hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(V_t,V_u,V_i)))
    | ~ c_Type_Otyping(V_e,V_u,V_T1)
    | ~ hBOOL(hAPP(c_InductTermi_OIT,V_u))
    | ~ c_Type_Otyping(c_Type_Oshift(V_e,V_i,V_T1,tc_Type_Otype),V_t,V_Ta)
    | ~ hBOOL(hAPP(c_InductTermi_OIT,V_t)) ) ).

cnf(cls_MI2_0,axiom,
    ( v_T____ != hAPP(hAPP(c_Type_Otype_OFun,V_T1),V_T2)
    | hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(V_t,V_u,V_i)))
    | ~ c_Type_Otyping(V_e,V_u,V_T2)
    | ~ hBOOL(hAPP(c_InductTermi_OIT,V_u))
    | ~ c_Type_Otyping(c_Type_Oshift(V_e,V_i,V_T2,tc_Type_Otype),V_t,V_Ta)
    | ~ hBOOL(hAPP(c_InductTermi_OIT,V_t)) ) ).

cnf(cls_var__app__typesE_0,axiom,
    ( c_Type_Otyping(V_e,c_Lambda_OdB_OVar(V_i),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__typesE__1__1(V_T,V_e,V_i,V_ts),V_T,tc_Type_Otype,tc_Type_Otype))
    | ~ 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_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_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_rotate__simps_1,axiom,
    c_List_Orotate1(c_List_Olist_OCons(V_x,V_xs,T_b),T_b) = c_List_Oappend(V_xs,c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_b),T_b),T_b) ).

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_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_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_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_Cons__eq__append__conv_0,axiom,
    ( c_List_Olist_OCons(V_x,V_xs,T_a) != c_List_Oappend(V_ys,V_zs,T_a)
    | c_List_Olist_OCons(V_x,c_List_Osko__List__XCons__eq__append__conv__1__1(V_x,V_xs,V_ys,V_zs,T_a),T_a) = V_ys
    | V_ys = c_List_Olist_ONil(T_a) ) ).

cnf(cls_append__eq__Cons__conv_1,axiom,
    ( c_List_Oappend(V_ys,V_zs,T_a) != c_List_Olist_OCons(V_x,V_xs,T_a)
    | c_List_Oappend(c_List_Osko__List__Xappend__eq__Cons__conv__1__1(V_x,V_xs,V_ys,V_zs,T_a),V_zs,T_a) = V_xs
    | V_ys = c_List_Olist_ONil(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_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_butlast__snoc_0,axiom,
    c_List_Obutlast(c_List_Oappend(V_xs,c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a),T_a) = V_xs ).

cnf(cls_last__snoc_0,axiom,
    c_List_Olast(c_List_Oappend(V_xs,c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a),T_a) = V_x ).

cnf(cls_append__eq__Cons__conv_0,axiom,
    ( c_List_Oappend(V_ys,V_zs,T_a) != c_List_Olist_OCons(V_x,V_xs,T_a)
    | V_ys = c_List_Olist_OCons(V_x,c_List_Osko__List__Xappend__eq__Cons__conv__1__1(V_x,V_xs,V_ys,V_zs,T_a),T_a)
    | V_ys = c_List_Olist_ONil(T_a) ) ).

cnf(cls_Cons__eq__append__conv_1,axiom,
    ( c_List_Olist_OCons(V_x,V_xs,T_a) != c_List_Oappend(V_ys,V_zs,T_a)
    | V_xs = c_List_Oappend(c_List_Osko__List__XCons__eq__append__conv__1__1(V_x,V_xs,V_ys,V_zs,T_a),V_zs,T_a)
    | V_ys = c_List_Olist_ONil(T_a) ) ).

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_typing__elims_I2_J_0,axiom,
    ( c_Type_Otyping(V_e,V_t,hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__2__1(V_T,V_e,V_t,V_u)),V_T))
    | ~ c_Type_Otyping(V_e,hAPP(hAPP(c_Lambda_OdB_OApp,V_t),V_u),V_T) ) ).

cnf(cls_argsT_0,axiom,
    c_Type_Otypings(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_as____,v_Ts____) ).

cnf(cls_uT_0,axiom,
    c_Type_Otyping(v_e____,v_u____,v_T____) ).

cnf(cls_nT_0,axiom,
    c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____) ).

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_type_Osimps_I5_J_0,axiom,
    c_Type_Otype_Otype__case(V_f1,V_f2,c_Type_Otype_OAtom(V_nat),T_a) = hAPP(V_f1,V_nat) ).

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_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_not__Cons__self_0,axiom,
    V_xs != c_List_Olist_OCons(V_x,V_xs,T_a) ).

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

cnf(cls_type_Osplit_0,axiom,
    ( ~ hBOOL(hAPP(V_P,c_Type_Otype_Otype__case(V_f1,V_f2,c_Type_Otype_OAtom(V_nat),t_a)))
    | hBOOL(hAPP(V_P,hAPP(V_f1,V_nat))) ) ).

cnf(cls_type_Osplit__asm_0,axiom,
    ( ~ hBOOL(hAPP(V_P,c_Type_Otype_Otype__case(V_f1,V_f2,c_Type_Otype_OAtom(V_xc),t_a)))
    | hBOOL(hAPP(V_P,hAPP(V_f1,V_xc))) ) ).

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_neq__Nil__conv_1,axiom,
    c_List_Olist_OCons(V_x,V_xa,T_a) != c_List_Olist_ONil(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_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_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_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_typing_OVar_0,axiom,
    c_Type_Otyping(V_env,c_Lambda_OdB_OVar(V_x),hAPP(V_env,V_x)) ).

cnf(cls_type__induct_2,axiom,
    ( hBOOL(hAPP(V_P,V_T))
    | ~ hBOOL(hAPP(V_P,c_Type_Osko__Type__Xtype__induct__1__1(V_P))) ) ).

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_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_type_Osimps_I1_J_0,axiom,
    ( c_Type_Otype_OAtom(V_nat) != c_Type_Otype_OAtom(V_nat_H)
    | V_nat = V_nat_H ) ).

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_True_0,axiom,
    v_n____ = v_i____ ).

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

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_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_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_argT_0,axiom,
    c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,v_T_H_H____) ).

cnf(cls_type_Orecs_I1_J_0,axiom,
    c_Type_Otype_Otype__rec(V_f1,V_f2,c_Type_Otype_OAtom(V_nat),T_a) = hAPP(V_f1,V_nat) ).

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_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_App_0,axiom,
    ( c_Type_Otyping(V_env,hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_t),V_U)
    | ~ c_Type_Otyping(V_env,V_t,V_T)
    | ~ c_Type_Otyping(V_env,V_s,hAPP(hAPP(c_Type_Otype_OFun,V_T),V_U)) ) ).

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_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_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_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_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_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_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_type_Osimps_I4_J_0,axiom,
    hAPP(hAPP(c_Type_Otype_OFun,V_type1_H),V_type2_H) != c_Type_Otype_OAtom(V_nat) ).

cnf(cls_type_Osimps_I2_J_0,axiom,
    ( hAPP(hAPP(c_Type_Otype_OFun,V_type1),V_type2) != hAPP(hAPP(c_Type_Otype_OFun,V_type1_H),V_type2_H)
    | V_type1 = V_type1_H ) ).

cnf(cls_type_Osimps_I2_J_1,axiom,
    ( hAPP(hAPP(c_Type_Otype_OFun,V_type1),V_type2) != hAPP(hAPP(c_Type_Otype_OFun,V_type1_H),V_type2_H)
    | V_type2 = V_type2_H ) ).

cnf(cls_foldr_Osimps_I2_J_0,axiom,
    c_List_Ofoldr(V_f,c_List_Olist_OCons(V_x,V_xs,T_b),V_a,T_b,T_a) = hAPP(hAPP(V_f,V_x),c_List_Ofoldr(V_f,V_xs,V_a,T_b,T_a)) ).

cnf(cls_type__induct_1,axiom,
    ( c_Type_Osko__Type__Xtype__induct__1__1(V_P) != hAPP(hAPP(c_Type_Otype_OFun,V_T1),V_T2)
    | hBOOL(hAPP(V_P,V_T))
    | hBOOL(hAPP(V_P,V_T2)) ) ).

cnf(cls_type__induct_0,axiom,
    ( c_Type_Osko__Type__Xtype__induct__1__1(V_P) != hAPP(hAPP(c_Type_Otype_OFun,V_T1a),V_x)
    | hBOOL(hAPP(V_P,V_T))
    | hBOOL(hAPP(V_P,V_T1a)) ) ).

cnf(cls_foldr__append_0,axiom,
    c_List_Ofoldr(V_f,c_List_Oappend(V_xs,V_ys,T_b),V_a,T_b,T_a) = c_List_Ofoldr(V_f,V_xs,c_List_Ofoldr(V_f,V_ys,V_a,T_b,T_a),T_b,T_a) ).

cnf(cls_varT_0,axiom,
    c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_Lambda_OdB_OVar(v_n____),hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype))) ).

cnf(cls_headT_0,axiom,
    c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)) ).

cnf(cls_foldr_Osimps_I1_J_0,axiom,
    c_List_Ofoldr(V_f,c_List_Olist_ONil(T_b),V_a,T_b,T_a) = V_a ).

cnf(cls_type_Orecs_I2_J_0,axiom,
    c_Type_Otype_Otype__rec(V_f1,V_f2,hAPP(hAPP(c_Type_Otype_OFun,V_type1),V_type2),T_a) = hAPP(hAPP(hAPP(hAPP(V_f2,V_type1),V_type2),c_Type_Otype_Otype__rec(V_f1,V_f2,V_type1,T_a)),c_Type_Otype_Otype__rec(V_f1,V_f2,V_type2,T_a)) ).

cnf(cls_type_Osimps_I6_J_0,axiom,
    c_Type_Otype_Otype__case(V_f1,V_f2,hAPP(hAPP(c_Type_Otype_OFun,V_type1),V_type2),T_a) = hAPP(hAPP(V_f2,V_type1),V_type2) ).

cnf(cls_type_Osplit__asm_1,axiom,
    ( ~ hBOOL(hAPP(V_P,c_Type_Otype_Otype__case(V_f1,V_f2,hAPP(hAPP(c_Type_Otype_OFun,V_xa),V_xb),t_a)))
    | hBOOL(hAPP(V_P,hAPP(hAPP(V_f2,V_xa),V_xb))) ) ).

cnf(cls_type_Osplit_1,axiom,
    ( ~ hBOOL(hAPP(V_P,c_Type_Otype_Otype__case(V_f1,V_f2,hAPP(hAPP(c_Type_Otype_OFun,V_type1),V_type2),t_a)))
    | hBOOL(hAPP(V_P,hAPP(hAPP(V_f2,V_type1),V_type2))) ) ).

cnf(cls_type_Osimps_I3_J_0,axiom,
    c_Type_Otype_OAtom(V_nat) != hAPP(hAPP(c_Type_Otype_OFun,V_type1_H),V_type2_H) ).

cnf(cls_CHAINED_0,axiom,
    v_n____ = v_i____ ).

cnf(cls_CHAINED_0_01,axiom,
    c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_Lambda_OdB_OVar(v_n____),hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype))) ).

cnf(cls_conjecture_0,negated_conjecture,
    v_T____ != hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)) ).

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

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

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