%------------------------------------------------------------------------------
% File     : SCT099-1 : TPTP v8.2.0. Released v4.1.0.
% Domain   : Social Choice Theory
% Problem  : Arrow Order 31_12
% Version  : Especial.
% English  : Formalization of two proofs of Arrow's impossibility theorem. One
%            formalization is based on utility functions, the other one on 
%            strict partial orders.

% Refs     : [Nip09] Nipkow (2009), Social Choice Theory in HOL: Arrow and
%          : [Nip10] Nipkow (2010), Email to Geoff Sutcliffe
%          : [BN10]  Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% Source   : [Nip10]
% Names    : Arrow_Order-31_12 [Nip10]

% Status   : Unsatisfiable
% Rating   : 1.00 v4.1.0
% Syntax   : Number of clauses     :  665 ( 254 unt;  89 nHn; 334 RR)
%            Number of literals    : 1382 ( 552 equ; 661 neg)
%            Maximal clause size   :    6 (   2 avg)
%            Maximal term depth    :    7 (   1 avg)
%            Number of predicates  :   41 (  40 usr;   0 prp; 1-3 aty)
%            Number of functors    :   49 (  49 usr;  11 con; 0-5 aty)
%            Number of variables   : 1721 ( 169 sgn)
% SPC      : CNF_UNS_RFO_SEQ_NHN

% Comments :
%------------------------------------------------------------------------------
cnf(cls_power__strict__decreasing_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(T_a)
    | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_a,V_N,T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Oone__class_Oone(T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
    | ~ c_HOL_Oord__class_Oless(V_n,V_N,tc_nat) ) ).

cnf(cls_less__iff__Suc__add_1,axiom,
    c_HOL_Oord__class_Oless(V_m,c_Suc(c_HOL_Oplus__class_Oplus(V_m,V_x,tc_nat)),tc_nat) ).

cnf(cls_less__add__Suc2_0,axiom,
    c_HOL_Oord__class_Oless(V_i,c_Suc(c_HOL_Oplus__class_Oplus(V_m,V_i,tc_nat)),tc_nat) ).

cnf(cls_less__add__Suc1_0,axiom,
    c_HOL_Oord__class_Oless(V_i,c_Suc(c_HOL_Oplus__class_Oplus(V_i,V_m,tc_nat)),tc_nat) ).

cnf(cls_min__less__iff__conj_2,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_HOL_Oord__class_Oless(V_z,c_Orderings_Oord__class_Omin(V_x,V_y,T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(V_z,V_y,T_a)
    | ~ c_HOL_Oord__class_Oless(V_z,V_x,T_a) ) ).

cnf(cls_less__Suc0_0,axiom,
    ( V_n = c_HOL_Ozero__class_Ozero(tc_nat)
    | ~ c_HOL_Oord__class_Oless(V_n,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ) ).

cnf(cls_diff__less__Suc_0,axiom,
    c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),c_Suc(V_m),tc_nat) ).

cnf(cls_order__less__trans_0,axiom,
    ( ~ class_Orderings_Opreorder(T_a)
    | c_HOL_Oord__class_Oless(V_x,V_z,T_a)
    | ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a)
    | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ).

cnf(cls_xt1_I10_J_0,axiom,
    ( ~ class_Orderings_Oorder(T_a)
    | c_HOL_Oord__class_Oless(V_z,V_x,T_a)
    | ~ c_HOL_Oord__class_Oless(V_z,V_y,T_a)
    | ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ).

cnf(cls_add__gr__0_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),tc_nat) ) ).

cnf(cls_gr__implies__not0_0,axiom,
    ~ c_HOL_Oord__class_Oless(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ).

cnf(cls_not__less0_0,axiom,
    ~ c_HOL_Oord__class_Oless(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ).

cnf(cls_mod__less__divisor_0,axiom,
    ( c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat),V_n,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ) ).

cnf(cls_not__leE_0,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_HOL_Oord__class_Oless(V_x,V_y,T_a)
    | c_lessequals(V_y,V_x,T_a) ) ).

cnf(cls_linorder__antisym__conv2_1,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | ~ c_lessequals(V_x,V_x,T_a)
    | ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ).

cnf(cls_linorder__antisym__conv1_1,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_HOL_Oord__class_Oless(V_x,V_x,T_a)
    | c_lessequals(V_x,V_x,T_a) ) ).

cnf(cls_linorder__not__less_1,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a)
    | ~ c_lessequals(V_y,V_x,T_a) ) ).

cnf(cls_linorder__not__less_0,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_lessequals(V_y,V_x,T_a)
    | c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ).

cnf(cls_linorder__not__le_1,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | ~ c_lessequals(V_x,V_y,T_a)
    | ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ).

cnf(cls_linorder__not__le_0,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_HOL_Oord__class_Oless(V_y,V_x,T_a)
    | c_lessequals(V_x,V_y,T_a) ) ).

cnf(cls_less__le__not__le_1,axiom,
    ( ~ class_Orderings_Opreorder(T_a)
    | ~ c_lessequals(V_y,V_x,T_a)
    | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ).

cnf(cls_zero__less__Suc_0,axiom,
    c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(V_n),tc_nat) ).

cnf(cls_gr0__conv__Suc_1,axiom,
    c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(V_x),tc_nat) ).

cnf(cls_one__less__power_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) ).

cnf(cls_add__neg__neg_0,axiom,
    ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).

cnf(cls_power__strict__mono_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(T_a)
    | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_b,V_n,T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
    | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ).

cnf(cls_min__max_Oless__infI1_0,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(V_a,V_b,T_a),V_x,T_a)
    | ~ c_HOL_Oord__class_Oless(V_a,V_x,T_a) ) ).

cnf(cls_min__max_Oless__infI2_0,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(V_a,V_b,T_a),V_x,T_a)
    | ~ c_HOL_Oord__class_Oless(V_b,V_x,T_a) ) ).

cnf(cls_min__less__iff__conj_0,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_HOL_Oord__class_Oless(V_z,V_x,T_a)
    | ~ c_HOL_Oord__class_Oless(V_z,c_Orderings_Oord__class_Omin(V_x,V_y,T_a),T_a) ) ).

cnf(cls_min__less__iff__conj_1,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_HOL_Oord__class_Oless(V_z,V_y,T_a)
    | ~ c_HOL_Oord__class_Oless(V_z,c_Orderings_Oord__class_Omin(V_x,V_y,T_a),T_a) ) ).

cnf(cls_min__less__iff__disj_1,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(V_x,V_y,T_a),V_z,T_a)
    | ~ c_HOL_Oord__class_Oless(V_x,V_z,T_a) ) ).

cnf(cls_min__less__iff__disj_2,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(V_x,V_y,T_a),V_z,T_a)
    | ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a) ) ).

cnf(cls_Suc__lessI_0,axiom,
    ( c_HOL_Oord__class_Oless(c_Suc(V_m),V_n,tc_nat)
    | c_Suc(V_m) = V_n
    | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ).

cnf(cls_not__less__less__Suc__eq_1,axiom,
    ( c_HOL_Oord__class_Oless(V_x,V_x,tc_nat)
    | c_HOL_Oord__class_Oless(V_x,c_Suc(V_x),tc_nat) ) ).

cnf(cls_not__less__eq_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
    | ~ c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat) ) ).

cnf(cls_not__less__eq_0,axiom,
    ( c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat)
    | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ).

cnf(cls_add__le__less__mono_0,axiom,
    ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_d,T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(V_c,V_d,T_a)
    | ~ c_lessequals(V_a,V_b,T_a) ) ).

cnf(cls_add__less__le__mono_0,axiom,
    ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_d,T_a),T_a)
    | ~ c_lessequals(V_c,V_d,T_a)
    | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ).

cnf(cls_less__Suc__eq__0__disj_3,axiom,
    ( c_HOL_Oord__class_Oless(c_Suc(V_x),c_Suc(V_n),tc_nat)
    | ~ c_HOL_Oord__class_Oless(V_x,V_n,tc_nat) ) ).

cnf(cls_Suc__less__eq_0,axiom,
    ( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_Suc(V_m),c_Suc(V_n),tc_nat) ) ).

cnf(cls_Suc__mono_0,axiom,
    ( c_HOL_Oord__class_Oless(c_Suc(V_m),c_Suc(V_n),tc_nat)
    | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ).

cnf(cls_add__gr__0_2,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ) ).

cnf(cls_add__gr__0_1,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat) ) ).

cnf(cls_zero__less__double__add__iff__zero__less__single__add_0,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),T_a) ) ).

cnf(cls_zero__less__double__add__iff__zero__less__single__add_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).

cnf(cls_add__neg__nonpos_0,axiom,
    ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).

cnf(cls_add__nonpos__neg_0,axiom,
    ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).

cnf(cls_add__strict__increasing_0,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
    | ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
    | c_HOL_Oord__class_Oless(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a)
    | ~ c_lessequals(V_b,V_c,T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).

cnf(cls_add__strict__increasing2_0,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
    | ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
    | c_HOL_Oord__class_Oless(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(V_b,V_c,T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).

cnf(cls_add__nonneg__pos_0,axiom,
    ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).

cnf(cls_add__pos__nonneg_0,axiom,
    ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).

cnf(cls_zero__less__two_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(T_a),c_HOL_Oone__class_Oone(T_a),T_a),T_a) ) ).

cnf(cls_power__less__imp__less__base_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(T_a)
    | c_HOL_Oord__class_Oless(V_a,V_b,T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
    | ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_b,V_n,T_a),T_a) ) ).

cnf(cls_power__gt1_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),c_Power_Opower__class_Opower(V_a,c_Suc(V_n),T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) ).

cnf(cls_diff__Suc__less_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_n,c_Suc(V_i),tc_nat),V_n,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ) ).

cnf(cls_Suc__pred_0,axiom,
    ( c_Suc(c_HOL_Ominus__class_Ominus(V_n,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) = V_n
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ) ).

cnf(cls_length__greater__0__conv_1,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)),tc_nat)
    | V_xs = c_List_Olist_ONil(T_a) ) ).

cnf(cls_length__greater__0__conv_0,axiom,
    ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Nat_Osize__class_Osize(c_List_Olist_ONil(T_a),tc_List_Olist(T_a)),tc_nat) ).

cnf(cls_list__update__append1_0,axiom,
    ( c_List_Olist__update(c_List_Oappend(V_xs,V_ys,T_a),V_i,V_x,T_a) = c_List_Oappend(c_List_Olist__update(V_xs,V_i,V_x,T_a),V_ys,T_a)
    | ~ c_HOL_Oord__class_Oless(V_i,c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)),tc_nat) ) ).

cnf(cls_list__update__append_0,axiom,
    ( c_List_Olist__update(c_List_Oappend(V_xs,V_ys,T_a),V_n,V_x,T_a) = c_List_Oappend(c_List_Olist__update(V_xs,V_n,V_x,T_a),V_ys,T_a)
    | ~ c_HOL_Oord__class_Oless(V_n,c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)),tc_nat) ) ).

cnf(cls_take__butlast_0,axiom,
    ( c_List_Otake(V_n,c_List_Obutlast(V_xs,T_a),T_a) = c_List_Otake(V_n,V_xs,T_a)
    | ~ c_HOL_Oord__class_Oless(V_n,c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)),tc_nat) ) ).

cnf(cls_last__drop_0,axiom,
    ( c_List_Olast(c_List_Odrop(V_n,V_xs,T_a),T_a) = c_List_Olast(V_xs,T_a)
    | ~ c_HOL_Oord__class_Oless(V_n,c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)),tc_nat) ) ).

cnf(cls_termination__basic__simps_I1_J_0,axiom,
    ( c_HOL_Oord__class_Oless(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(V_x,V_y,tc_nat) ) ).

cnf(cls_termination__basic__simps_I2_J_0,axiom,
    ( c_HOL_Oord__class_Oless(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(V_x,V_z,tc_nat) ) ).

cnf(cls_add__lessD1_0,axiom,
    ( c_HOL_Oord__class_Oless(V_i,V_k,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_i,V_j,tc_nat),V_k,tc_nat) ) ).

cnf(cls_trans__less__add1_0,axiom,
    ( c_HOL_Oord__class_Oless(V_i,c_HOL_Oplus__class_Oplus(V_j,V_m,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(V_i,V_j,tc_nat) ) ).

cnf(cls_trans__less__add2_0,axiom,
    ( c_HOL_Oord__class_Oless(V_i,c_HOL_Oplus__class_Oplus(V_m,V_j,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(V_i,V_j,tc_nat) ) ).

cnf(cls_less__add__eq__less_0,axiom,
    ( c_HOL_Oplus__class_Oplus(V_m,V_l,tc_nat) != c_HOL_Oplus__class_Oplus(V_k,V_n,tc_nat)
    | ~ c_HOL_Oord__class_Oless(V_k,V_l,tc_nat)
    | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ).

cnf(cls_diff__less__mono2_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_l,V_n,tc_nat),c_HOL_Ominus__class_Ominus(V_l,V_m,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(V_m,V_l,tc_nat)
    | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ).

cnf(cls_less__Suc0_1,axiom,
    c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ).

cnf(cls_double__add__less__zero__iff__single__less__zero_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).

cnf(cls_double__add__less__zero__iff__single__less__zero_0,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
    | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).

cnf(cls_even__less__0__iff_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(T_a)
    | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).

cnf(cls_even__less__0__iff_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).

cnf(cls_zero__less__power_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).

cnf(cls_min__less__iff__disj_0,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_HOL_Oord__class_Oless(V_y,V_z,T_a)
    | c_HOL_Oord__class_Oless(V_x,V_z,T_a)
    | ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(V_x,V_y,T_a),V_z,T_a) ) ).

cnf(cls_less__SucE_0,axiom,
    ( V_m = V_n
    | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
    | ~ c_HOL_Oord__class_Oless(V_m,c_Suc(V_n),tc_nat) ) ).

cnf(cls_less__antisym_0,axiom,
    ( V_m = V_n
    | ~ c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat)
    | c_HOL_Oord__class_Oless(V_n,V_m,tc_nat) ) ).

cnf(cls_not__less__less__Suc__eq_0,axiom,
    ( V_n = V_m
    | ~ c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat)
    | c_HOL_Oord__class_Oless(V_n,V_m,tc_nat) ) ).

cnf(cls_less__imp__diff__less_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_j,V_n,tc_nat),V_k,tc_nat)
    | ~ c_HOL_Oord__class_Oless(V_j,V_k,tc_nat) ) ).

cnf(cls_mod__if_0,axiom,
    ( c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat) = V_m
    | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ).

cnf(cls_less__le__not__le_2,axiom,
    ( ~ class_Orderings_Opreorder(T_a)
    | c_HOL_Oord__class_Oless(V_x,V_y,T_a)
    | c_lessequals(V_y,V_x,T_a)
    | ~ c_lessequals(V_x,V_y,T_a) ) ).

cnf(cls_nat__less__le_1,axiom,
    ~ c_HOL_Oord__class_Oless(V_x,V_x,tc_nat) ).

cnf(cls_less__not__refl_0,axiom,
    ~ c_HOL_Oord__class_Oless(V_n,V_n,tc_nat) ).

cnf(cls_order__less__le_1,axiom,
    ( ~ class_Orderings_Oorder(T_a)
    | ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ).

cnf(cls_linorder__neq__iff_1,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ).

cnf(cls_order__less__irrefl_0,axiom,
    ( ~ class_Orderings_Opreorder(T_a)
    | ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ).

cnf(cls_add__pos__pos_0,axiom,
    ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).

cnf(cls_linorder__neqE__ordered__idom_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(T_a)
    | c_HOL_Oord__class_Oless(V_y,V_x,T_a)
    | c_HOL_Oord__class_Oless(V_x,V_y,T_a)
    | V_x = V_y ) ).

cnf(cls_not__less__iff__gr__or__eq_0,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | V_x = V_y
    | c_HOL_Oord__class_Oless(V_y,V_x,T_a)
    | c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ).

cnf(cls_nat__neq__iff_0,axiom,
    ( c_HOL_Oord__class_Oless(V_n,V_m,tc_nat)
    | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
    | V_m = V_n ) ).

cnf(cls_linorder__neqE__nat_0,axiom,
    ( c_HOL_Oord__class_Oless(V_y,V_x,tc_nat)
    | c_HOL_Oord__class_Oless(V_x,V_y,tc_nat)
    | V_x = V_y ) ).

cnf(cls_linorder__neqE_0,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_HOL_Oord__class_Oless(V_y,V_x,T_a)
    | c_HOL_Oord__class_Oless(V_x,V_y,T_a)
    | V_x = V_y ) ).

cnf(cls_linorder__less__linear_0,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_HOL_Oord__class_Oless(V_y,V_x,T_a)
    | V_x = V_y
    | c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ).

cnf(cls_linorder__antisym__conv3_0,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | V_x = V_y
    | c_HOL_Oord__class_Oless(V_x,V_y,T_a)
    | c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ).

cnf(cls_add__strict__mono_0,axiom,
    ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_d,T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(V_c,V_d,T_a)
    | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ).

cnf(cls_add__less__mono_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_i,V_k,tc_nat),c_HOL_Oplus__class_Oplus(V_j,V_l,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(V_k,V_l,tc_nat)
    | ~ c_HOL_Oord__class_Oless(V_i,V_j,tc_nat) ) ).

cnf(cls_order__le__less_1,axiom,
    ( ~ class_Orderings_Oorder(T_a)
    | c_lessequals(V_x,V_y,T_a)
    | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ).

cnf(cls_order__less__imp__le_0,axiom,
    ( ~ class_Orderings_Opreorder(T_a)
    | c_lessequals(V_x,V_y,T_a)
    | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ).

cnf(cls_less__iff__diff__less__0_1,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
    | c_HOL_Oord__class_Oless(V_a,V_b,T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).

cnf(cls_less__iff__diff__less__0_0,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ).

cnf(cls_lessI_0,axiom,
    c_HOL_Oord__class_Oless(V_n,c_Suc(V_n),tc_nat) ).

cnf(cls_less__Suc__eq_2,axiom,
    c_HOL_Oord__class_Oless(V_x,c_Suc(V_x),tc_nat) ).

cnf(cls_less__trans__Suc_0,axiom,
    ( c_HOL_Oord__class_Oless(c_Suc(V_i),V_k,tc_nat)
    | ~ c_HOL_Oord__class_Oless(V_j,V_k,tc_nat)
    | ~ c_HOL_Oord__class_Oless(V_i,V_j,tc_nat) ) ).

cnf(cls_less__add__one_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(T_a)
    | c_HOL_Oord__class_Oless(V_a,c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oone__class_Oone(T_a),T_a),T_a) ) ).

cnf(cls_power__inject__exp_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(T_a)
    | c_Power_Opower__class_Opower(V_a,V_m,T_a) != c_Power_Opower__class_Opower(V_a,V_n,T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_a,T_a)
    | V_m = V_n ) ).

cnf(cls_le__number__of__eq__not__less_0,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | ~ class_Int_Onumber(T_a)
    | ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_Int_Onumber__class_Onumber__of(V_v,T_a),T_a)
    | ~ c_lessequals(c_Int_Onumber__class_Onumber__of(V_v,T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a) ) ).

cnf(cls_le__number__of__eq__not__less_1,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | ~ class_Int_Onumber(T_a)
    | c_lessequals(c_Int_Onumber__class_Onumber__of(V_v,T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a)
    | c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_Int_Onumber__class_Onumber__of(V_v,T_a),T_a) ) ).

cnf(cls_gr0I_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)
    | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ).

cnf(cls_neq0__conv_1,axiom,
    ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ).

cnf(cls_pos__add__strict_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(T_a)
    | c_HOL_Oord__class_Oless(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(V_b,V_c,T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).

cnf(cls_power__strict__increasing__iff_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(T_a)
    | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_b,V_x,T_a),c_Power_Opower__class_Opower(V_b,V_y,T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(V_x,V_y,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_b,T_a) ) ).

cnf(cls_power__strict__increasing__iff_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(T_a)
    | c_HOL_Oord__class_Oless(V_x,V_y,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_b,V_x,T_a),c_Power_Opower__class_Opower(V_b,V_y,T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_b,T_a) ) ).

cnf(cls_power__strict__increasing_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(T_a)
    | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_a,V_N,T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_a,T_a)
    | ~ c_HOL_Oord__class_Oless(V_n,V_N,tc_nat) ) ).

cnf(cls_power__less__imp__less__exp_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(T_a)
    | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_a,V_m,T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) ).

cnf(cls_not__add__less1_0,axiom,
    ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_i,V_j,tc_nat),V_i,tc_nat) ).

cnf(cls_not__add__less2_0,axiom,
    ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_j,V_i,tc_nat),V_i,tc_nat) ).

cnf(cls_mod__if_1,axiom,
    ( c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),V_n,tc_nat)
    | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ).

cnf(cls_less__diff__conv_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_i,V_k,tc_nat),V_j,tc_nat)
    | ~ c_HOL_Oord__class_Oless(V_i,c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat),tc_nat) ) ).

cnf(cls_less__diff__conv_1,axiom,
    ( c_HOL_Oord__class_Oless(V_i,c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_i,V_k,tc_nat),V_j,tc_nat) ) ).

cnf(cls_add__strict__right__mono_0,axiom,
    ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ).

cnf(cls_add__less__cancel__right_1,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ).

cnf(cls_add__less__cancel__right_0,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
    | c_HOL_Oord__class_Oless(V_a,V_b,T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a) ) ).

cnf(cls_add__strict__left__mono_0,axiom,
    ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_c,V_a,T_a),c_HOL_Oplus__class_Oplus(V_c,V_b,T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ).

cnf(cls_add__less__cancel__left_1,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_c,V_a,T_a),c_HOL_Oplus__class_Oplus(V_c,V_b,T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ).

cnf(cls_add__less__cancel__left_0,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
    | c_HOL_Oord__class_Oless(V_a,V_b,T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_c,V_a,T_a),c_HOL_Oplus__class_Oplus(V_c,V_b,T_a),T_a) ) ).

cnf(cls_add__less__mono1_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_i,V_k,tc_nat),c_HOL_Oplus__class_Oplus(V_j,V_k,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(V_i,V_j,tc_nat) ) ).

cnf(cls_nat__add__left__cancel__less_0,axiom,
    ( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_k,V_m,tc_nat),c_HOL_Oplus__class_Oplus(V_k,V_n,tc_nat),tc_nat) ) ).

cnf(cls_nat__add__left__cancel__less_1,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_k,V_m,tc_nat),c_HOL_Oplus__class_Oplus(V_k,V_n,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ).

cnf(cls_xt1_I7_J_0,axiom,
    ( ~ class_Orderings_Oorder(T_a)
    | c_HOL_Oord__class_Oless(V_z,V_x,T_a)
    | ~ c_lessequals(V_z,V_y,T_a)
    | ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ).

cnf(cls_xt1_I8_J_0,axiom,
    ( ~ class_Orderings_Oorder(T_a)
    | c_HOL_Oord__class_Oless(V_z,V_x,T_a)
    | ~ c_HOL_Oord__class_Oless(V_z,V_y,T_a)
    | ~ c_lessequals(V_y,V_x,T_a) ) ).

cnf(cls_order__le__less__trans_0,axiom,
    ( ~ class_Orderings_Opreorder(T_a)
    | c_HOL_Oord__class_Oless(V_x,V_z,T_a)
    | ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a)
    | ~ c_lessequals(V_x,V_y,T_a) ) ).

cnf(cls_order__less__le__trans_0,axiom,
    ( ~ class_Orderings_Opreorder(T_a)
    | c_HOL_Oord__class_Oless(V_x,V_z,T_a)
    | ~ c_lessequals(V_y,V_z,T_a)
    | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ).

cnf(cls_zero__less__diff_0,axiom,
    ( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(V_n,V_m,tc_nat),tc_nat) ) ).

cnf(cls_zero__less__diff_1,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(V_n,V_m,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ).

cnf(cls_Suc__lessD_0,axiom,
    ( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_Suc(V_m),V_n,tc_nat) ) ).

cnf(cls_less__SucI_0,axiom,
    ( c_HOL_Oord__class_Oless(V_m,c_Suc(V_n),tc_nat)
    | ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ).

cnf(cls_diff__less_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),V_m,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ) ).

cnf(cls_less__eqI_0,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
    | c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ominus__class_Ominus(V_x_H,V_y_H,T_a)
    | c_HOL_Oord__class_Oless(V_x_H,V_y_H,T_a)
    | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ).

cnf(cls_less__eqI_1,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
    | c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ominus__class_Ominus(V_x_H,V_y_H,T_a)
    | c_HOL_Oord__class_Oless(V_x,V_y,T_a)
    | ~ c_HOL_Oord__class_Oless(V_x_H,V_y_H,T_a) ) ).

cnf(cls_add__diff__inverse_0,axiom,
    ( c_HOL_Oplus__class_Oplus(V_n,c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),tc_nat) = V_m
    | c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ).

cnf(cls_xt1_I11_J_0,axiom,
    ( ~ class_Orderings_Oorder(T_a)
    | c_HOL_Oord__class_Oless(V_b,V_a,T_a)
    | V_a = V_b
    | ~ c_lessequals(V_b,V_a,T_a) ) ).

cnf(cls_xt1_I12_J_0,axiom,
    ( ~ class_Orderings_Oorder(T_a)
    | c_HOL_Oord__class_Oless(V_b,V_a,T_a)
    | ~ c_lessequals(V_b,V_a,T_a)
    | V_a = V_b ) ).

cnf(cls_order__le__less_0,axiom,
    ( ~ class_Orderings_Oorder(T_a)
    | V_x = V_y
    | c_HOL_Oord__class_Oless(V_x,V_y,T_a)
    | ~ c_lessequals(V_x,V_y,T_a) ) ).

cnf(cls_order__less__le_2,axiom,
    ( ~ class_Orderings_Oorder(T_a)
    | c_HOL_Oord__class_Oless(V_x,V_y,T_a)
    | V_x = V_y
    | ~ c_lessequals(V_x,V_y,T_a) ) ).

cnf(cls_order__le__neq__trans_0,axiom,
    ( ~ class_Orderings_Oorder(T_a)
    | c_HOL_Oord__class_Oless(V_a,V_b,T_a)
    | V_a = V_b
    | ~ c_lessequals(V_a,V_b,T_a) ) ).

cnf(cls_order__neq__le__trans_0,axiom,
    ( ~ class_Orderings_Oorder(T_a)
    | c_HOL_Oord__class_Oless(V_a,V_b,T_a)
    | ~ c_lessequals(V_a,V_b,T_a)
    | V_a = V_b ) ).

cnf(cls_linorder__antisym__conv1_0,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | V_x = V_y
    | ~ c_lessequals(V_x,V_y,T_a)
    | c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ).

cnf(cls_linorder__antisym__conv2_0,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | V_x = V_y
    | c_HOL_Oord__class_Oless(V_x,V_y,T_a)
    | ~ c_lessequals(V_x,V_y,T_a) ) ).

cnf(cls_xt1_I9_J_0,axiom,
    ( ~ class_Orderings_Oorder(T_a)
    | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a)
    | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) ) ).

cnf(cls_not__less__iff__gr__or__eq_1,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a)
    | ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ).

cnf(cls_order__less__asym_0,axiom,
    ( ~ class_Orderings_Opreorder(T_a)
    | ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a)
    | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ).

cnf(cls_order__less__asym_H_0,axiom,
    ( ~ class_Orderings_Opreorder(T_a)
    | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a)
    | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ).

cnf(cls_not__one__less__zero_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).

cnf(cls_zero__less__one_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oone__class_Oone(T_a),T_a) ) ).

cnf(cls_power__eq__imp__eq__base_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(T_a)
    | c_Power_Opower__class_Opower(V_a,V_n,T_a) != c_Power_Opower__class_Opower(V_b,V_n,T_a)
    | V_a = V_b
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).

cnf(cls_power__Suc__less__one_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(T_a)
    | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_a,c_Suc(V_n),T_a),c_HOL_Oone__class_Oone(T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Oone__class_Oone(T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).

cnf(cls_Suc__diff__1_0,axiom,
    ( c_Suc(c_HOL_Ominus__class_Ominus(V_n,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = V_n
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ) ).

cnf(cls_Suc__pred_H_0,axiom,
    ( V_n = c_Suc(c_HOL_Ominus__class_Ominus(V_n,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ) ).

cnf(cls_list__update__append_1,axiom,
    ( c_List_Olist__update(c_List_Oappend(V_xs,V_ys,T_a),V_n,V_x,T_a) = c_List_Oappend(V_xs,c_List_Olist__update(V_ys,c_HOL_Ominus__class_Ominus(V_n,c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)),tc_nat),V_x,T_a),T_a)
    | c_HOL_Oord__class_Oless(V_n,c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)),tc_nat) ) ).

cnf(cls_expand__Suc_0,axiom,
    ( c_Int_Onumber__class_Onumber__of(V_v,tc_nat) = c_Suc(c_HOL_Ominus__class_Ominus(c_Int_Onumber__class_Onumber__of(V_v,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat))
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Int_Onumber__class_Onumber__of(V_v,tc_nat),tc_nat) ) ).

cnf(cls_rev__update_0,axiom,
    ( c_List_Orev(c_List_Olist__update(V_xs,V_k,V_y,T_a),T_a) = c_List_Olist__update(c_List_Orev(V_xs,T_a),c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)),V_k,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),V_y,T_a)
    | ~ c_HOL_Oord__class_Oless(V_k,c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)),tc_nat) ) ).

cnf(cls_min__0L_0,axiom,
    c_Orderings_Oord__class_Omin(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ).

cnf(cls_min__max_Ole__infE_0,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_lessequals(V_x,V_a,T_a)
    | ~ c_lessequals(V_x,c_Orderings_Oord__class_Omin(V_a,V_b,T_a),T_a) ) ).

cnf(cls_min__max_Ole__infE_1,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_lessequals(V_x,V_b,T_a)
    | ~ c_lessequals(V_x,c_Orderings_Oord__class_Omin(V_a,V_b,T_a),T_a) ) ).

cnf(cls_min__max_Ole__infI1_0,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_lessequals(c_Orderings_Oord__class_Omin(V_a,V_b,T_a),V_x,T_a)
    | ~ c_lessequals(V_a,V_x,T_a) ) ).

cnf(cls_min__max_Ole__infI2_0,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_lessequals(c_Orderings_Oord__class_Omin(V_a,V_b,T_a),V_x,T_a)
    | ~ c_lessequals(V_b,V_x,T_a) ) ).

cnf(cls_min__le__iff__disj_1,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_lessequals(c_Orderings_Oord__class_Omin(V_x,V_y,T_a),V_z,T_a)
    | ~ c_lessequals(V_x,V_z,T_a) ) ).

cnf(cls_min__le__iff__disj_2,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_lessequals(c_Orderings_Oord__class_Omin(V_x,V_y,T_a),V_z,T_a)
    | ~ c_lessequals(V_y,V_z,T_a) ) ).

cnf(cls_min__max_Ole__inf__iff_0,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_lessequals(V_x,V_y,T_a)
    | ~ c_lessequals(V_x,c_Orderings_Oord__class_Omin(V_y,V_z,T_a),T_a) ) ).

cnf(cls_min__max_Ole__inf__iff_1,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_lessequals(V_x,V_z,T_a)
    | ~ c_lessequals(V_x,c_Orderings_Oord__class_Omin(V_y,V_z,T_a),T_a) ) ).

cnf(cls_class__ringb_Osubr0__iff_1,axiom,
    ( ~ class_Ring__and__Field_Oidom(T_a)
    | ~ class_Int_Onumber__ring(T_a)
    | c_HOL_Ominus__class_Ominus(V_x,V_x,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_minus__nat_Odiff__0_0,axiom,
    c_HOL_Ominus__class_Ominus(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = V_m ).

cnf(cls_diff__self__eq__0_0,axiom,
    c_HOL_Ominus__class_Ominus(V_m,V_m,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ).

cnf(cls_diff__self_0,axiom,
    ( ~ class_OrderedGroup_Ogroup__add(T_a)
    | c_HOL_Ominus__class_Ominus(V_a,V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_diff__0__right_0,axiom,
    ( ~ class_OrderedGroup_Ogroup__add(T_a)
    | c_HOL_Ominus__class_Ominus(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = V_a ) ).

cnf(cls_right__minus__eq_1,axiom,
    ( ~ class_OrderedGroup_Ogroup__add(T_a)
    | c_HOL_Ominus__class_Ominus(V_x,V_x,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_eq__iff__diff__eq__0_0,axiom,
    ( ~ class_OrderedGroup_Oab__group__add(T_a)
    | c_HOL_Ominus__class_Ominus(V_x,V_x,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).

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

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

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

cnf(cls_rotate__conv__mod_0,axiom,
    c_List_Orotate(V_n,V_xs,T_a) = c_List_Orotate(c_Divides_Odiv__class_Omod(V_n,c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)),tc_nat),V_xs,T_a) ).

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

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

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

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

cnf(cls_mod__self_0,axiom,
    ( ~ class_Divides_Osemiring__div(T_a)
    | c_Divides_Odiv__class_Omod(V_a,V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_mod__by__0_0,axiom,
    ( ~ class_Divides_Osemiring__div(T_a)
    | c_Divides_Odiv__class_Omod(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = V_a ) ).

cnf(cls_diff__Suc__1_0,axiom,
    c_HOL_Ominus__class_Ominus(c_Suc(V_n),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = V_n ).

cnf(cls_add__increasing2_0,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
    | ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
    | c_lessequals(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a)
    | ~ c_lessequals(V_b,V_a,T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ).

cnf(cls_add__increasing_0,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
    | ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
    | c_lessequals(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a)
    | ~ c_lessequals(V_b,V_c,T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).

cnf(cls_length__remdups__eq_1,axiom,
    ( c_List_Oremdups(V_xs,T_a) != V_xs
    | c_Nat_Osize__class_Osize(c_List_Oremdups(V_xs,T_a),tc_List_Olist(T_a)) = c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)) ) ).

cnf(cls_length__remdups__eq_0,axiom,
    ( c_Nat_Osize__class_Osize(c_List_Oremdups(V_xs,T_a),tc_List_Olist(T_a)) != c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a))
    | c_List_Oremdups(V_xs,T_a) = V_xs ) ).

cnf(cls_Zero__neq__Suc_0,axiom,
    c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(V_m) ).

cnf(cls_nat_Osimps_I2_J_0,axiom,
    c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(V_nat_H) ).

cnf(cls_add__Suc_0,axiom,
    c_HOL_Oplus__class_Oplus(c_Suc(V_m),V_n,tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat)) ).

cnf(cls_add__Suc__right_0,axiom,
    c_HOL_Oplus__class_Oplus(V_m,c_Suc(V_n),tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat)) ).

cnf(cls_power__0__Suc_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_Suc(V_n),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_one__le__power_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(T_a)
    | c_lessequals(c_HOL_Oone__class_Oone(T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a)
    | ~ c_lessequals(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) ).

cnf(cls_min__max_Oinf__le1_0,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_lessequals(c_Orderings_Oord__class_Omin(V_x,V_y,T_a),V_x,T_a) ) ).

cnf(cls_min__max_Oinf__le2_0,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_lessequals(c_Orderings_Oord__class_Omin(V_x,V_y,T_a),V_y,T_a) ) ).

cnf(cls_min__max_Ole__infI_0,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_lessequals(V_x,c_Orderings_Oord__class_Omin(V_a,V_b,T_a),T_a)
    | ~ c_lessequals(V_x,V_b,T_a)
    | ~ c_lessequals(V_x,V_a,T_a) ) ).

cnf(cls_min__max_Ole__inf__iff_2,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_lessequals(V_x,c_Orderings_Oord__class_Omin(V_y,V_z,T_a),T_a)
    | ~ c_lessequals(V_x,V_z,T_a)
    | ~ c_lessequals(V_x,V_y,T_a) ) ).

cnf(cls_min__max_Oinf__greatest_0,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_lessequals(V_x,c_Orderings_Oord__class_Omin(V_y,V_z,T_a),T_a)
    | ~ c_lessequals(V_x,V_z,T_a)
    | ~ c_lessequals(V_x,V_y,T_a) ) ).

cnf(cls_take__hd__drop_0,axiom,
    ( c_List_Oappend(c_List_Otake(V_n,V_xs,T_a),c_List_Olist_OCons(c_List_Ohd(c_List_Odrop(V_n,V_xs,T_a),T_a),c_List_Olist_ONil(T_a),T_a),T_a) = c_List_Otake(c_Suc(V_n),V_xs,T_a)
    | ~ c_HOL_Oord__class_Oless(V_n,c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)),tc_nat) ) ).

cnf(cls_upd__conv__take__nth__drop_0,axiom,
    ( c_List_Olist__update(V_xs,V_i,V_a,T_a) = c_List_Oappend(c_List_Otake(V_i,V_xs,T_a),c_List_Olist_OCons(V_a,c_List_Odrop(c_Suc(V_i),V_xs,T_a),T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(V_i,c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)),tc_nat) ) ).

cnf(cls_min__0R_0,axiom,
    c_Orderings_Oord__class_Omin(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ).

cnf(cls_add__nonneg__eq__0__iff_1,axiom,
    ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a)
    | c_HOL_Oplus__class_Oplus(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a)
    | V_y = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_add__nonneg__eq__0__iff_0,axiom,
    ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a)
    | c_HOL_Oplus__class_Oplus(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a)
    | V_x = c_HOL_Ozero__class_Ozero(T_a) ) ).

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

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

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

cnf(cls_Suc__inject_0,axiom,
    ( c_Suc(V_x) != c_Suc(V_y)
    | V_x = V_y ) ).

cnf(cls_nat_Oinject_0,axiom,
    ( c_Suc(V_nat) != c_Suc(V_nat_H)
    | V_nat = V_nat_H ) ).

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_min__le__iff__disj_0,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_lessequals(V_y,V_z,T_a)
    | c_lessequals(V_x,V_z,T_a)
    | ~ c_lessequals(c_Orderings_Oord__class_Omin(V_x,V_y,T_a),V_z,T_a) ) ).

cnf(cls_mod__add__cong_0,axiom,
    ( ~ class_Divides_Osemiring__div(T_a)
    | c_Divides_Odiv__class_Omod(V_b,V_c,T_a) != c_Divides_Odiv__class_Omod(V_b_H,V_c,T_a)
    | c_Divides_Odiv__class_Omod(V_a,V_c,T_a) != c_Divides_Odiv__class_Omod(V_a_H,V_c,T_a)
    | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a_H,V_b_H,T_a),V_c,T_a) ) ).

cnf(cls_one__is__add_1,axiom,
    ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat)
    | V_n = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | V_m = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ) ).

cnf(cls_one__is__add_2,axiom,
    ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat)
    | V_m = c_HOL_Ozero__class_Ozero(tc_nat)
    | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ).

cnf(cls_diff__Suc__Suc_0,axiom,
    c_HOL_Ominus__class_Ominus(c_Suc(V_m),c_Suc(V_n),tc_nat) = c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) ).

cnf(cls_mod__1_0,axiom,
    c_Divides_Odiv__class_Omod(V_m,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ).

cnf(cls_add__eq__if_1,axiom,
    ( c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_m,c_HOL_Oone__class_Oone(tc_nat),tc_nat),V_n,tc_nat))
    | V_m = c_HOL_Ozero__class_Ozero(tc_nat) ) ).

cnf(cls_length__take_0,axiom,
    c_Nat_Osize__class_Osize(c_List_Otake(V_n,V_xs,T_a),tc_List_Olist(T_a)) = c_Orderings_Oord__class_Omin(c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)),V_n,tc_nat) ).

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_one__is__add_4,axiom,
    c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oplus__class_Oplus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ).

cnf(cls_length__rotate1_0,axiom,
    c_Nat_Osize__class_Osize(c_List_Orotate1(V_xs,T_a),tc_List_Olist(T_a)) = c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)) ).

cnf(cls_min__max_Oinf__idem_0,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_Orderings_Oord__class_Omin(V_x,V_x,T_a) = V_x ) ).

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)) = c_HOL_Oplus__class_Oplus(c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)),c_Nat_Osize__class_Osize(V_ys,tc_List_Olist(T_a)),tc_nat) ).

cnf(cls_length__drop_0,axiom,
    c_Nat_Osize__class_Osize(c_List_Odrop(V_n,V_xs,T_a),tc_List_Olist(T_a)) = c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)),V_n,tc_nat) ).

cnf(cls_diffs0__imp__equal_0,axiom,
    ( c_HOL_Ominus__class_Ominus(V_n,V_m,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
    | c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
    | V_m = V_n ) ).

cnf(cls_order__eq__iff_2,axiom,
    ( ~ class_Orderings_Oorder(T_a)
    | V_x = V_y
    | ~ c_lessequals(V_y,V_x,T_a)
    | ~ c_lessequals(V_x,V_y,T_a) ) ).

cnf(cls_order__antisym_0,axiom,
    ( ~ class_Orderings_Oorder(T_a)
    | V_x = V_y
    | ~ c_lessequals(V_y,V_x,T_a)
    | ~ c_lessequals(V_x,V_y,T_a) ) ).

cnf(cls_order__antisym__conv_0,axiom,
    ( ~ class_Orderings_Oorder(T_a)
    | V_x = V_y
    | ~ c_lessequals(V_x,V_y,T_a)
    | ~ c_lessequals(V_y,V_x,T_a) ) ).

cnf(cls_mod__diff__cong_0,axiom,
    ( ~ class_Divides_Oring__div(T_a)
    | c_Divides_Odiv__class_Omod(V_b,V_c,T_a) != c_Divides_Odiv__class_Omod(V_b_H,V_c,T_a)
    | c_Divides_Odiv__class_Omod(V_a,V_c,T_a) != c_Divides_Odiv__class_Omod(V_a_H,V_c,T_a)
    | c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(V_a_H,V_b_H,T_a),V_c,T_a) ) ).

cnf(cls_le__iff__diff__le__0_1,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
    | c_lessequals(V_a,V_b,T_a)
    | ~ c_lessequals(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).

cnf(cls_le__iff__diff__le__0_0,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
    | c_lessequals(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_lessequals(V_a,V_b,T_a) ) ).

cnf(cls_length__splice_0,axiom,
    c_Nat_Osize__class_Osize(c_List_Osplice(V_xs,V_ys,T_a),tc_List_Olist(T_a)) = c_HOL_Oplus__class_Oplus(c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)),c_Nat_Osize__class_Osize(V_ys,tc_List_Olist(T_a)),tc_nat) ).

cnf(cls_nat_Osimps_I3_J_0,axiom,
    c_Suc(V_nat_H) != c_HOL_Ozero__class_Ozero(tc_nat) ).

cnf(cls_Suc__neq__Zero_0,axiom,
    c_Suc(V_m) != c_HOL_Ozero__class_Ozero(tc_nat) ).

cnf(cls_add__le__cancel__right_1,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
    | c_lessequals(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a)
    | ~ c_lessequals(V_a,V_b,T_a) ) ).

cnf(cls_add__le__cancel__right_0,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
    | c_lessequals(V_a,V_b,T_a)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a) ) ).

cnf(cls_add__le__cancel__left_1,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
    | c_lessequals(c_HOL_Oplus__class_Oplus(V_c,V_a,T_a),c_HOL_Oplus__class_Oplus(V_c,V_b,T_a),T_a)
    | ~ c_lessequals(V_a,V_b,T_a) ) ).

cnf(cls_add__le__cancel__left_0,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
    | c_lessequals(V_a,V_b,T_a)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(V_c,V_a,T_a),c_HOL_Oplus__class_Oplus(V_c,V_b,T_a),T_a) ) ).

cnf(cls_add__right__mono_0,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(T_a)
    | c_lessequals(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a)
    | ~ c_lessequals(V_a,V_b,T_a) ) ).

cnf(cls_add__left__mono_0,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(T_a)
    | c_lessequals(c_HOL_Oplus__class_Oplus(V_c,V_a,T_a),c_HOL_Oplus__class_Oplus(V_c,V_b,T_a),T_a)
    | ~ c_lessequals(V_a,V_b,T_a) ) ).

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(c_HOL_Oplus__class_Oplus(V_n,V_m,tc_nat),V_xs,T_a) ).

cnf(cls_power__le__imp__le__base_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(T_a)
    | c_lessequals(V_a,V_b,T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
    | ~ c_lessequals(c_Power_Opower__class_Opower(V_a,c_Suc(V_n),T_a),c_Power_Opower__class_Opower(V_b,c_Suc(V_n),T_a),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_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_take__append_0,axiom,
    c_List_Otake(V_n,c_List_Oappend(V_xs,V_ys,T_a),T_a) = c_List_Oappend(c_List_Otake(V_n,V_xs,T_a),c_List_Otake(c_HOL_Ominus__class_Ominus(V_n,c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)),tc_nat),V_ys,T_a),T_a) ).

cnf(cls_length__butlast_0,axiom,
    c_Nat_Osize__class_Osize(c_List_Obutlast(V_xs,T_a),tc_List_Olist(T_a)) = c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ).

cnf(cls_mod__add__self2_0,axiom,
    ( ~ class_Divides_Osemiring__div(T_a)
    | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_b,T_a) = c_Divides_Odiv__class_Omod(V_a,V_b,T_a) ) ).

cnf(cls_mod__add__self1_0,axiom,
    ( ~ class_Divides_Osemiring__div(T_a)
    | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_b,V_a,T_a),V_b,T_a) = c_Divides_Odiv__class_Omod(V_a,V_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_double__add__le__zero__iff__single__add__le__zero_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
    | c_lessequals(c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).

cnf(cls_double__add__le__zero__iff__single__add__le__zero_0,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
    | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).

cnf(cls_Suc__n__not__n_0,axiom,
    c_Suc(V_n) != V_n ).

cnf(cls_n__not__Suc__n_0,axiom,
    V_n != c_Suc(V_n) ).

cnf(cls_mod__Suc__eq__Suc__mod_0,axiom,
    c_Divides_Odiv__class_Omod(c_Suc(V_m),V_n,tc_nat) = c_Divides_Odiv__class_Omod(c_Suc(c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat)),V_n,tc_nat) ).

cnf(cls_xt1_I6_J_0,axiom,
    ( ~ class_Orderings_Oorder(T_a)
    | c_lessequals(V_z,V_x,T_a)
    | ~ c_lessequals(V_z,V_y,T_a)
    | ~ c_lessequals(V_y,V_x,T_a) ) ).

cnf(cls_add__nonpos__nonpos_0,axiom,
    ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a)
    | c_lessequals(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).

cnf(cls_order__eq__iff_0,axiom,
    ( ~ class_Orderings_Oorder(T_a)
    | c_lessequals(V_x,V_x,T_a) ) ).

cnf(cls_order__eq__refl_0,axiom,
    ( ~ class_Orderings_Opreorder(T_a)
    | c_lessequals(V_x,V_x,T_a) ) ).

cnf(cls_le__add__right__mono_0,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
    | c_lessequals(V_a,c_HOL_Oplus__class_Oplus(V_b,V_d,T_a),T_a)
    | ~ c_lessequals(V_c,V_d,T_a)
    | ~ c_lessequals(V_a,c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a) ) ).

cnf(cls_order__trans_0,axiom,
    ( ~ class_Orderings_Opreorder(T_a)
    | c_lessequals(V_x,V_z,T_a)
    | ~ c_lessequals(V_y,V_z,T_a)
    | ~ c_lessequals(V_x,V_y,T_a) ) ).

cnf(cls_min__diff_0,axiom,
    c_Orderings_Oord__class_Omin(c_HOL_Ominus__class_Ominus(V_m,V_i,tc_nat),c_HOL_Ominus__class_Ominus(V_n,V_i,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omin(V_m,V_n,tc_nat),V_i,tc_nat) ).

cnf(cls_add__is__1_5,axiom,
    c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ).

cnf(cls_min__number__of_1,axiom,
    ( ~ class_Int_Onumber(T_a)
    | ~ class_HOL_Oord(T_a)
    | c_Orderings_Oord__class_Omin(c_Int_Onumber__class_Onumber__of(V_u,T_a),c_Int_Onumber__class_Onumber__of(V_v,T_a),T_a) = c_Int_Onumber__class_Onumber__of(V_v,T_a)
    | c_lessequals(c_Int_Onumber__class_Onumber__of(V_u,T_a),c_Int_Onumber__class_Onumber__of(V_v,T_a),T_a) ) ).

cnf(cls_length__tl_0,axiom,
    c_Nat_Osize__class_Osize(c_List_Otl(V_xs,T_a),tc_List_Olist(T_a)) = c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ).

cnf(cls_Nitpick_Olist__size__simp_I2_J_1,axiom,
    ( c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)) = c_Suc(c_Nat_Osize__class_Osize(c_List_Otl(V_xs,T_a),tc_List_Olist(T_a)))
    | V_xs = c_List_Olist_ONil(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_le__eqI_0,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
    | c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ominus__class_Ominus(V_x_H,V_y_H,T_a)
    | c_lessequals(V_y_H,V_x_H,T_a)
    | ~ c_lessequals(V_y,V_x,T_a) ) ).

cnf(cls_le__eqI_1,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
    | c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ominus__class_Ominus(V_x_H,V_y_H,T_a)
    | c_lessequals(V_y,V_x,T_a)
    | ~ c_lessequals(V_y_H,V_x_H,T_a) ) ).

cnf(cls_zmod__simps_I1_J_0,axiom,
    ( ~ class_Divides_Osemiring__div(T_a)
    | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(V_a,V_c,T_a),V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) ) ).

cnf(cls_zmod__simps_I2_J_0,axiom,
    ( ~ class_Divides_Osemiring__div(T_a)
    | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,c_Divides_Odiv__class_Omod(V_b,V_c,T_a),T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) ) ).

cnf(cls_add__is__1_1,axiom,
    ( c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | V_n = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | V_m = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ) ).

cnf(cls_add__is__1_2,axiom,
    ( c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | V_m = c_HOL_Ozero__class_Ozero(tc_nat)
    | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ).

cnf(cls_linorder__linear_0,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_lessequals(V_y,V_x,T_a)
    | c_lessequals(V_x,V_y,T_a) ) ).

cnf(cls_rev__drop_0,axiom,
    c_List_Orev(c_List_Odrop(V_i,V_xs,T_a),T_a) = c_List_Otake(c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)),V_i,tc_nat),c_List_Orev(V_xs,T_a),T_a) ).

cnf(cls_rev__take_0,axiom,
    c_List_Orev(c_List_Otake(V_i,V_xs,T_a),T_a) = c_List_Odrop(c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)),V_i,tc_nat),c_List_Orev(V_xs,T_a),T_a) ).

cnf(cls_butlast__conv__take_0,axiom,
    c_List_Obutlast(V_xs,T_a) = c_List_Otake(c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)),c_HOL_Oone__class_Oone(tc_nat),tc_nat),V_xs,T_a) ).

cnf(cls_butlast__list__update_0,axiom,
    c_List_Obutlast(c_List_Olist__update(V_xs,c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)),c_HOL_Oone__class_Oone(tc_nat),tc_nat),V_x,T_a),T_a) = c_List_Obutlast(V_xs,T_a) ).

cnf(cls_butlast__list__update_1,axiom,
    ( c_List_Obutlast(c_List_Olist__update(V_xs,V_k,V_x,T_a),T_a) = c_List_Olist__update(c_List_Obutlast(V_xs,T_a),V_k,V_x,T_a)
    | V_k = c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)),c_HOL_Oone__class_Oone(tc_nat),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_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_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_zero__le__one_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(T_a)
    | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oone__class_Oone(T_a),T_a) ) ).

cnf(cls_mod__by__1_0,axiom,
    ( ~ class_Divides_Osemiring__div(T_a)
    | c_Divides_Odiv__class_Omod(V_a,c_HOL_Oone__class_Oone(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_not__one__le__zero_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(T_a)
    | ~ c_lessequals(c_HOL_Oone__class_Oone(T_a),c_HOL_Ozero__class_Ozero(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_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_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_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_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_One__nat__def_0,axiom,
    c_HOL_Oone__class_Oone(tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ).

cnf(cls_take__Cons__number__of_1,axiom,
    ( c_List_Otake(c_Int_Onumber__class_Onumber__of(V_v,tc_nat),c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = c_List_Olist_OCons(V_x,c_List_Otake(c_HOL_Ominus__class_Ominus(c_Int_Onumber__class_Onumber__of(V_v,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),V_xs,T_a),T_a)
    | c_Int_Onumber__class_Onumber__of(V_v,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ) ).

cnf(cls_drop__Cons__number__of_1,axiom,
    ( c_List_Odrop(c_Int_Onumber__class_Onumber__of(V_v,tc_nat),c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = c_List_Odrop(c_HOL_Ominus__class_Ominus(c_Int_Onumber__class_Onumber__of(V_v,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),V_xs,T_a)
    | c_Int_Onumber__class_Onumber__of(V_v,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ) ).

cnf(cls_take__Suc__Cons_0,axiom,
    c_List_Otake(c_Suc(V_n),c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = c_List_Olist_OCons(V_x,c_List_Otake(V_n,V_xs,T_a),T_a) ).

cnf(cls_drop__Suc__Cons_0,axiom,
    c_List_Odrop(c_Suc(V_n),c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = c_List_Odrop(V_n,V_xs,T_a) ).

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_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_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_list__update__code_I3_J_0,axiom,
    c_List_Olist__update(c_List_Olist_OCons(V_x,V_xs,T_a),c_Suc(V_i),V_y,T_a) = c_List_Olist_OCons(V_x,c_List_Olist__update(V_xs,V_i,V_y,T_a),T_a) ).

cnf(cls_replicate__Suc_0,axiom,
    c_List_Oreplicate(c_Suc(V_n),V_x,T_a) = c_List_Olist_OCons(V_x,c_List_Oreplicate(V_n,V_x,T_a),T_a) ).

cnf(cls_zero__le__power_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(T_a)
    | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).

cnf(cls_min__diff__distrib__left_0,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
    | c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omin(V_x,V_y,T_a),V_z,T_a) = c_Orderings_Oord__class_Omin(c_HOL_Ominus__class_Ominus(V_x,V_z,T_a),c_HOL_Ominus__class_Ominus(V_y,V_z,T_a),T_a) ) ).

cnf(cls_drop__append_0,axiom,
    c_List_Odrop(V_n,c_List_Oappend(V_xs,V_ys,T_a),T_a) = c_List_Oappend(c_List_Odrop(V_n,V_xs,T_a),c_List_Odrop(c_HOL_Ominus__class_Ominus(V_n,c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)),tc_nat),V_ys,T_a),T_a) ).

cnf(cls_list_Osize_I4_J_0,axiom,
    c_Nat_Osize__class_Osize(c_List_Olist_OCons(V_a,V_list,T_a),tc_List_Olist(T_a)) = c_HOL_Oplus__class_Oplus(c_Nat_Osize__class_Osize(V_list,tc_List_Olist(T_a)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ).

cnf(cls_add__is__1_4,axiom,
    c_HOL_Oplus__class_Oplus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ).

cnf(cls_mod__mod__trivial_0,axiom,
    ( ~ class_Divides_Osemiring__div(T_a)
    | c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(V_a,V_b,T_a),V_b,T_a) = c_Divides_Odiv__class_Omod(V_a,V_b,T_a) ) ).

cnf(cls_Suc__eq__plus1__left_0,axiom,
    c_Suc(V_n) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),V_n,tc_nat) ).

cnf(cls_Suc__eq__plus1_0,axiom,
    c_Suc(V_n) = c_HOL_Oplus__class_Oplus(V_n,c_HOL_Oone__class_Oone(tc_nat),tc_nat) ).

cnf(cls_mod__0_0,axiom,
    ( ~ class_Divides_Osemiring__div(T_a)
    | c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_zero__le__double__add__iff__zero__le__single__add_0,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
    | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),T_a) ) ).

cnf(cls_zero__le__double__add__iff__zero__le__single__add_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
    | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).

cnf(cls_min__max_Oinf__left__idem_0,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_Orderings_Oord__class_Omin(V_x,c_Orderings_Oord__class_Omin(V_x,V_y,T_a),T_a) = c_Orderings_Oord__class_Omin(V_x,V_y,T_a) ) ).

cnf(cls_diff__add__cancel_0,axiom,
    ( ~ class_OrderedGroup_Ogroup__add(T_a)
    | c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_b,T_a) = V_a ) ).

cnf(cls_Suc__length__conv_2,axiom,
    c_Suc(c_Nat_Osize__class_Osize(V_xa,tc_List_Olist(T_a))) = c_Nat_Osize__class_Osize(c_List_Olist_OCons(V_x,V_xa,T_a),tc_List_Olist(T_a)) ).

cnf(cls_take__take_0,axiom,
    c_List_Otake(V_n,c_List_Otake(V_m,V_xs,T_a),T_a) = c_List_Otake(c_Orderings_Oord__class_Omin(V_n,V_m,tc_nat),V_xs,T_a) ).

cnf(cls_mod__Suc_1,axiom,
    ( c_Divides_Odiv__class_Omod(c_Suc(V_m),V_n,tc_nat) = c_Suc(c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat))
    | c_Suc(c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat)) = V_n ) ).

cnf(cls_rotate__rev_0,axiom,
    c_List_Orotate(V_n,c_List_Orev(V_xs,T_a),T_a) = c_List_Orev(c_List_Orotate(c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)),c_Divides_Odiv__class_Omod(V_n,c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)),tc_nat),tc_nat),V_xs,T_a),T_a) ).

cnf(cls_add__mono_0,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(T_a)
    | c_lessequals(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_d,T_a),T_a)
    | ~ c_lessequals(V_c,V_d,T_a)
    | ~ c_lessequals(V_a,V_b,T_a) ) ).

cnf(cls_length__Suc__conv_2,axiom,
    c_Nat_Osize__class_Osize(c_List_Olist_OCons(V_x,V_xa,T_a),tc_List_Olist(T_a)) = c_Suc(c_Nat_Osize__class_Osize(V_xa,tc_List_Olist(T_a))) ).

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

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

cnf(cls_add__nonneg__eq__0__iff_2,axiom,
    ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_mod__add__eq_0,axiom,
    ( ~ class_Divides_Osemiring__div(T_a)
    | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(V_a,V_c,T_a),c_Divides_Odiv__class_Omod(V_b,V_c,T_a),T_a),V_c,T_a) ) ).

cnf(cls_add__nonneg__nonneg_0,axiom,
    ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a)
    | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).

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

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

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

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

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

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

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

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

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

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

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

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

cnf(cls_mod__diff__left__eq_0,axiom,
    ( ~ class_Divides_Oring__div(T_a)
    | c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(V_a,V_c,T_a),V_b,T_a),V_c,T_a) ) ).

cnf(cls_mod__diff__right__eq_0,axiom,
    ( ~ class_Divides_Oring__div(T_a)
    | c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(V_a,c_Divides_Odiv__class_Omod(V_b,V_c,T_a),T_a),V_c,T_a) ) ).

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_min__max_Ole__iff__inf_0,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_Orderings_Oord__class_Omin(V_x,V_y,T_a) = V_x
    | ~ c_lessequals(V_x,V_y,T_a) ) ).

cnf(cls_min__max_Ole__iff__inf_1,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_Orderings_Oord__class_Omin(V_x,V_y,T_a) != V_x
    | c_lessequals(V_x,V_y,T_a) ) ).

cnf(cls_min__max_Oinf__absorb2_0,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_Orderings_Oord__class_Omin(V_x,V_y,T_a) = V_y
    | ~ c_lessequals(V_y,V_x,T_a) ) ).

cnf(cls_mod__add__left__eq_0,axiom,
    ( ~ class_Divides_Osemiring__div(T_a)
    | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(V_a,V_c,T_a),V_b,T_a),V_c,T_a) ) ).

cnf(cls_mod__add__right__eq_0,axiom,
    ( ~ class_Divides_Osemiring__div(T_a)
    | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,c_Divides_Odiv__class_Omod(V_b,V_c,T_a),T_a),V_c,T_a) ) ).

cnf(cls_min__max_Oinf__assoc_0,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omin(V_x,V_y,T_a),V_z,T_a) = c_Orderings_Oord__class_Omin(V_x,c_Orderings_Oord__class_Omin(V_y,V_z,T_a),T_a) ) ).

cnf(cls_min__max_Oinf__left__commute_0,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_Orderings_Oord__class_Omin(V_x,c_Orderings_Oord__class_Omin(V_y,V_z,T_a),T_a) = c_Orderings_Oord__class_Omin(V_y,c_Orderings_Oord__class_Omin(V_x,V_z,T_a),T_a) ) ).

cnf(cls_one__is__add_5,axiom,
    c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ).

cnf(cls_diff__add__0_0,axiom,
    c_HOL_Ominus__class_Ominus(V_n,c_HOL_Oplus__class_Oplus(V_n,V_m,tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ).

cnf(cls_diff__diff__left_0,axiom,
    c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_i,V_j,tc_nat),V_k,tc_nat) = c_HOL_Ominus__class_Ominus(V_i,c_HOL_Oplus__class_Oplus(V_j,V_k,tc_nat),tc_nat) ).

cnf(cls_power__mono_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(T_a)
    | c_lessequals(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_b,V_n,T_a),T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
    | ~ c_lessequals(V_a,V_b,T_a) ) ).

cnf(cls_eq__eqI_1,axiom,
    ( ~ class_OrderedGroup_Oab__group__add(T_a)
    | c_HOL_Ominus__class_Ominus(V_xa,V_y,T_a) != c_HOL_Ominus__class_Ominus(V_x,V_x,T_a)
    | V_xa = V_y ) ).

cnf(cls_eq__eqI_0,axiom,
    ( ~ class_OrderedGroup_Oab__group__add(T_a)
    | c_HOL_Ominus__class_Ominus(V_x,V_x,T_a) != c_HOL_Ominus__class_Ominus(V_x_H,V_y_H,T_a)
    | V_x_H = V_y_H ) ).

cnf(cls_one__is__add_3,axiom,
    ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat)
    | V_n = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ).

cnf(cls_one__is__add_0,axiom,
    ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat)
    | V_m = c_HOL_Ozero__class_Ozero(tc_nat)
    | V_m = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ) ).

cnf(cls_add__Suc__shift_0,axiom,
    c_HOL_Oplus__class_Oplus(c_Suc(V_m),V_n,tc_nat) = c_HOL_Oplus__class_Oplus(V_m,c_Suc(V_n),tc_nat) ).

cnf(cls_eq__number__of_0,axiom,
    ( ~ class_Int_Oring__char__0(T_a)
    | ~ class_Int_Onumber__ring(T_a)
    | c_Int_Onumber__class_Onumber__of(V_x,T_a) != c_Int_Onumber__class_Onumber__of(V_y,T_a)
    | V_x = V_y ) ).

cnf(cls_diff__0__eq__0_0,axiom,
    c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ).

cnf(cls_diff__cancel2_0,axiom,
    c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_m,V_k,tc_nat),c_HOL_Oplus__class_Oplus(V_n,V_k,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) ).

cnf(cls_diff__cancel_0,axiom,
    c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_k,V_m,tc_nat),c_HOL_Oplus__class_Oplus(V_k,V_n,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) ).

cnf(cls_min__max_Oinf__commute_0,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_Orderings_Oord__class_Omin(V_x,V_y,T_a) = c_Orderings_Oord__class_Omin(V_y,V_x,T_a) ) ).

cnf(cls_class__ringb_Osubr0__iff_0,axiom,
    ( ~ class_Ring__and__Field_Oidom(T_a)
    | ~ class_Int_Onumber__ring(T_a)
    | c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(T_a)
    | V_x = V_y ) ).

cnf(cls_right__minus__eq_0,axiom,
    ( ~ class_OrderedGroup_Ogroup__add(T_a)
    | c_HOL_Ominus__class_Ominus(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a)
    | V_a = V_b ) ).

cnf(cls_eq__iff__diff__eq__0_1,axiom,
    ( ~ class_OrderedGroup_Oab__group__add(T_a)
    | c_HOL_Ominus__class_Ominus(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a)
    | V_a = V_b ) ).

cnf(cls_diff__commute_0,axiom,
    c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_i,V_j,tc_nat),V_k,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_i,V_k,tc_nat),V_j,tc_nat) ).

cnf(cls_rotate__id_0,axiom,
    ( c_Divides_Odiv__class_Omod(V_n,c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)),tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
    | c_List_Orotate(V_n,V_xs,T_a) = V_xs ) ).

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

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

cnf(cls_nat__add__left__cancel_0,axiom,
    ( c_HOL_Oplus__class_Oplus(V_k,V_m,tc_nat) != c_HOL_Oplus__class_Oplus(V_k,V_n,tc_nat)
    | 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)
    | c_HOL_Oplus__class_Oplus(V_x,V_y,T_a) != c_HOL_Oplus__class_Oplus(V_x,V_z,T_a)
    | V_y = V_z ) ).

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

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

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

cnf(cls_min__add__distrib__left_0,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
    | c_HOL_Oplus__class_Oplus(c_Orderings_Oord__class_Omin(V_x,V_y,T_a),V_z,T_a) = c_Orderings_Oord__class_Omin(c_HOL_Oplus__class_Oplus(V_x,V_z,T_a),c_HOL_Oplus__class_Oplus(V_y,V_z,T_a),T_a) ) ).

cnf(cls_mod__diff__eq_0,axiom,
    ( ~ class_Divides_Oring__div(T_a)
    | c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(V_a,V_c,T_a),c_Divides_Odiv__class_Omod(V_b,V_c,T_a),T_a),V_c,T_a) ) ).

cnf(cls_mod__Suc_0,axiom,
    ( c_Suc(c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat)) != V_n
    | c_Divides_Odiv__class_Omod(c_Suc(V_m),V_n,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ) ).

cnf(cls_add__is__1_3,axiom,
    ( c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | V_n = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ).

cnf(cls_add__is__1_0,axiom,
    ( c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | V_m = c_HOL_Ozero__class_Ozero(tc_nat)
    | V_m = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ) ).

cnf(cls_Suc__diff__diff_0,axiom,
    c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_Suc(V_m),V_n,tc_nat),c_Suc(V_k),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),V_k,tc_nat) ).

cnf(cls_diff__Suc__eq__diff__pred_0,axiom,
    c_HOL_Ominus__class_Ominus(V_m,c_Suc(V_n),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_m,c_HOL_Oone__class_Oone(tc_nat),tc_nat),V_n,tc_nat) ).

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

cnf(cls_min__number__of_0,axiom,
    ( ~ class_Int_Onumber(T_a)
    | ~ class_HOL_Oord(T_a)
    | c_Orderings_Oord__class_Omin(c_Int_Onumber__class_Onumber__of(V_u,T_a),c_Int_Onumber__class_Onumber__of(V_v,T_a),T_a) = c_Int_Onumber__class_Onumber__of(V_u,T_a)
    | ~ c_lessequals(c_Int_Onumber__class_Onumber__of(V_u,T_a),c_Int_Onumber__class_Onumber__of(V_v,T_a),T_a) ) ).

cnf(cls_min__Suc__Suc_0,axiom,
    c_Orderings_Oord__class_Omin(c_Suc(V_m),c_Suc(V_n),tc_nat) = c_Suc(c_Orderings_Oord__class_Omin(V_m,V_n,tc_nat)) ).

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_power__inject__base_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(T_a)
    | c_Power_Opower__class_Opower(V_a,c_Suc(V_n),T_a) != c_Power_Opower__class_Opower(V_b,c_Suc(V_n),T_a)
    | V_a = V_b
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).

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

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

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

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

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

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

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

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

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

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

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

cnf(cls_diff__add__inverse2_0,axiom,
    c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),V_n,tc_nat) = V_m ).

cnf(cls_diff__add__inverse_0,axiom,
    c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_n,V_m,tc_nat),V_n,tc_nat) = V_m ).

cnf(cls_add__diff__cancel_0,axiom,
    ( ~ class_OrderedGroup_Ogroup__add(T_a)
    | c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_b,T_a) = V_a ) ).

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(c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),V_xs,T_a) ).

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_sorted_Osimps_I3_J_0,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_lessequals(V_x,V_y,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_sorted_Osimps_I3_J_2,axiom,
    ( ~ class_Orderings_Olinorder(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)
    | ~ c_List_Olinorder__class_Osorted(c_List_Olist_OCons(V_y,V_zs,T_a),T_a)
    | ~ c_lessequals(V_x,V_y,T_a) ) ).

cnf(cls_replicate__add_0,axiom,
    c_List_Oreplicate(c_HOL_Oplus__class_Oplus(V_n,V_m,tc_nat),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_take__Suc_0,axiom,
    ( c_List_Otake(c_Suc(V_n),V_xs,T_a) = c_List_Olist_OCons(c_List_Ohd(V_xs,T_a),c_List_Otake(V_n,c_List_Otl(V_xs,T_a),T_a),T_a)
    | V_xs = c_List_Olist_ONil(T_a) ) ).

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(c_HOL_Oplus__class_Oplus(V_n,V_m,tc_nat),V_xs,T_a),T_a) ).

cnf(cls_drop__take_0,axiom,
    c_List_Odrop(V_n,c_List_Otake(V_m,V_xs,T_a),T_a) = c_List_Otake(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),c_List_Odrop(V_n,V_xs,T_a),T_a) ).

cnf(cls_rotate__drop__take_0,axiom,
    c_List_Orotate(V_n,V_xs,T_a) = c_List_Oappend(c_List_Odrop(c_Divides_Odiv__class_Omod(V_n,c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)),tc_nat),V_xs,T_a),c_List_Otake(c_Divides_Odiv__class_Omod(V_n,c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)),tc_nat),V_xs,T_a),T_a) ).

cnf(cls_last__list__update_1,axiom,
    ( c_List_Olast(c_List_Olist__update(V_xs,V_k,V_x,T_a),T_a) = c_List_Olast(V_xs,T_a)
    | V_k = c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
    | V_xs = c_List_Olist_ONil(T_a) ) ).

cnf(cls_last__list__update_0,axiom,
    ( V_xs = c_List_Olist_ONil(T_a)
    | c_List_Olast(c_List_Olist__update(V_xs,c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)),c_HOL_Oone__class_Oone(tc_nat),tc_nat),V_x,T_a),T_a) = V_x ) ).

cnf(cls_take__replicate_0,axiom,
    c_List_Otake(V_i,c_List_Oreplicate(V_k,V_x,T_a),T_a) = c_List_Oreplicate(c_Orderings_Oord__class_Omin(V_i,V_k,tc_nat),V_x,T_a) ).

cnf(cls_drop__replicate_0,axiom,
    c_List_Odrop(V_i,c_List_Oreplicate(V_k,V_x,T_a),T_a) = c_List_Oreplicate(c_HOL_Ominus__class_Ominus(V_k,V_i,tc_nat),V_x,T_a) ).

cnf(cls_take__tl_0,axiom,
    c_List_Otake(V_n,c_List_Otl(V_xs,T_a),T_a) = c_List_Otl(c_List_Otake(c_Suc(V_n),V_xs,T_a),T_a) ).

cnf(cls_drop__Suc_0,axiom,
    c_List_Odrop(c_Suc(V_n),V_xs,T_a) = c_List_Odrop(V_n,c_List_Otl(V_xs,T_a),T_a) ).

cnf(cls_rotate__Suc_0,axiom,
    c_List_Orotate(c_Suc(V_n),V_xs,T_a) = c_List_Orotate1(c_List_Orotate(V_n,V_xs,T_a),T_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_drop__Cons__number__of_0,axiom,
    ( c_Int_Onumber__class_Onumber__of(V_v,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
    | c_List_Odrop(c_Int_Onumber__class_Onumber__of(V_v,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__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__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_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_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_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_tl__take_0,axiom,
    c_List_Otl(c_List_Otake(V_n,V_xs,T_a),T_a) = c_List_Otake(c_HOL_Ominus__class_Ominus(V_n,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_List_Otl(V_xs,T_a),T_a) ).

cnf(cls_take__Cons__number__of_0,axiom,
    ( c_Int_Onumber__class_Onumber__of(V_v,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
    | c_List_Otake(c_Int_Onumber__class_Onumber__of(V_v,tc_nat),c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = c_List_Olist_ONil(T_a) ) ).

cnf(cls_take__Cons_H_1,axiom,
    ( c_List_Otake(V_n,c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = c_List_Olist_OCons(V_x,c_List_Otake(c_HOL_Ominus__class_Ominus(V_n,c_HOL_Oone__class_Oone(tc_nat),tc_nat),V_xs,T_a),T_a)
    | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ).

cnf(cls_drop__Cons_H_1,axiom,
    ( c_List_Odrop(V_n,c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = c_List_Odrop(c_HOL_Ominus__class_Ominus(V_n,c_HOL_Oone__class_Oone(tc_nat),tc_nat),V_xs,T_a)
    | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ).

cnf(cls_tl__replicate_0,axiom,
    ( c_List_Otl(c_List_Oreplicate(V_n,V_x,T_a),T_a) = c_List_Oreplicate(c_HOL_Ominus__class_Ominus(V_n,c_HOL_Oone__class_Oone(tc_nat),tc_nat),V_x,T_a)
    | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ).

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_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__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_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_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_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_elem_0,axiom,
    c_List_OListMem(V_x,c_List_Olist_OCons(V_x,V_xs,T_a),T_a) ).

cnf(cls_removeAll_Osimps_I2_J_1,axiom,
    ( c_List_OremoveAll(V_x,c_List_Olist_OCons(V_y,V_xs,T_a),T_a) = c_List_Olist_OCons(V_y,c_List_OremoveAll(V_x,V_xs,T_a),T_a)
    | V_x = V_y ) ).

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_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_List_Omember_Osimps_I2_J_2,axiom,
    ( c_List_Omember(V_x,c_List_Olist_OCons(V_y,V_ys,T_a),T_a)
    | ~ c_List_Omember(V_x,V_ys,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_List_Omember_Osimps_I2_J_1,axiom,
    c_List_Omember(V_x,c_List_Olist_OCons(V_x,V_ys,T_a),T_a) ).

cnf(cls_removeAll_Osimps_I2_J_0,axiom,
    c_List_OremoveAll(V_x,c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = c_List_OremoveAll(V_x,V_xs,T_a) ).

cnf(cls_List_Onull_Osimps_I2_J_0,axiom,
    ~ c_List_Onull(c_List_Olist_OCons(V_x,V_xs,T_a),T_a) ).

cnf(cls_List_Omember_Osimps_I2_J_0,axiom,
    ( c_List_Omember(V_x,V_ys,T_a)
    | V_x = V_y
    | ~ c_List_Omember(V_x,c_List_Olist_OCons(V_y,V_ys,T_a),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_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_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_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_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_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_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_butlast__drop_0,axiom,
    c_List_Obutlast(c_List_Odrop(V_n,V_xs,T_a),T_a) = c_List_Odrop(V_n,c_List_Obutlast(V_xs,T_a),T_a) ).

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_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_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_tl__drop_0,axiom,
    c_List_Otl(c_List_Odrop(V_n,V_xs,T_a),T_a) = c_List_Odrop(V_n,c_List_Otl(V_xs,T_a),T_a) ).

cnf(cls_drop__butlast_0,axiom,
    c_List_Odrop(V_n,c_List_Obutlast(V_xs,T_a),T_a) = c_List_Obutlast(c_List_Odrop(V_n,V_xs,T_a),T_a) ).

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

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_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_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_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_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_drop__tl_0,axiom,
    c_List_Odrop(V_n,c_List_Otl(V_xs,T_a),T_a) = c_List_Otl(c_List_Odrop(V_n,V_xs,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_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__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_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_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_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_removeAll__append_0,axiom,
    c_List_OremoveAll(V_x,c_List_Oappend(V_xs,V_ys,T_a),T_a) = c_List_Oappend(c_List_OremoveAll(V_x,V_xs,T_a),c_List_OremoveAll(V_x,V_ys,T_a),T_a) ).

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_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_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_distinct__remove1__removeAll_0,axiom,
    ( c_List_Oremove1(V_x,V_xs,T_a) = c_List_OremoveAll(V_x,V_xs,T_a)
    | ~ c_List_Odistinct(V_xs,T_a) ) ).

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_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_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_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_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_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_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_sorted__remdups_0,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_List_Olinorder__class_Osorted(c_List_Oremdups(V_l,T_a),T_a)
    | ~ c_List_Olinorder__class_Osorted(V_l,T_a) ) ).

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_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_rotate1__rotate__swap_0,axiom,
    c_List_Orotate1(c_List_Orotate(V_n,V_xs,T_a),T_a) = c_List_Orotate(V_n,c_List_Orotate1(V_xs,T_a),T_a) ).

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_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_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_list_Onchotomy_0,axiom,
    ( V_v = c_List_Olist_OCons(c_List_Osko__List__Xlist__Xnchotomy__1__1(V_v,T_a),c_List_Osko__List__Xlist__Xnchotomy__1__2(V_v,T_a),T_a)
    | V_v = 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_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_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_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_list_Oexhaust_0,axiom,
    ( V_y = c_List_Olist_OCons(c_List_Osko__List__Xlist__Xexhaust__1__1(V_y,T_a),c_List_Osko__List__Xlist__Xexhaust__1__2(V_y,T_a),T_a)
    | V_y = c_List_Olist_ONil(T_a) ) ).

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_neq__Nil__conv_0,axiom,
    ( V_xs = c_List_Olist_OCons(c_List_Osko__List__Xneq__Nil__conv__1__1(V_xs,T_a),c_List_Osko__List__Xneq__Nil__conv__1__2(V_xs,T_a),T_a)
    | V_xs = c_List_Olist_ONil(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_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_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_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_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__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_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_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_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_empty__null_1,axiom,
    ( V_xs = c_List_Olist_ONil(T_a)
    | ~ c_List_Onull(V_xs,T_a) ) ).

cnf(cls_removeAll_Osimps_I1_J_0,axiom,
    c_List_OremoveAll(V_x,c_List_Olist_ONil(T_a),T_a) = c_List_Olist_ONil(T_a) ).

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_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_remdups__eq__nil__right__iff_1,axiom,
    c_List_Olist_ONil(T_a) = c_List_Oremdups(c_List_Olist_ONil(T_a),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__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__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__conv_0,axiom,
    ( c_List_Oappend(V_xs,V_ys,T_a) != V_xs
    | V_ys = c_List_Olist_ONil(T_a) ) ).

cnf(cls_remdups__eq__nil__iff_0,axiom,
    ( c_List_Oremdups(V_x,T_a) != c_List_Olist_ONil(T_a)
    | V_x = c_List_Olist_ONil(T_a) ) ).

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

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_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_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_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_Omember_Osimps_I1_J_0,axiom,
    ~ c_List_Omember(V_x,c_List_Olist_ONil(T_a),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_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_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_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_remdups__eq__nil__iff_1,axiom,
    c_List_Oremdups(c_List_Olist_ONil(T_a),T_a) = c_List_Olist_ONil(T_a) ).

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_list__inter_Osimps_I1_J_0,axiom,
    c_List_Olist__inter(c_List_Olist_ONil(T_a),V_bs,T_a) = c_List_Olist_ONil(T_a) ).

cnf(cls_self__append__conv2_1,axiom,
    V_ys = c_List_Oappend(c_List_Olist_ONil(T_a),V_ys,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__conv_1,axiom,
    V_xs = c_List_Oappend(V_xs,c_List_Olist_ONil(T_a),T_a) ).

cnf(cls_eq__Nil__appendI_0,axiom,
    V_x = c_List_Oappend(c_List_Olist_ONil(T_a),V_x,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_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_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_rotate__simps_0,axiom,
    c_List_Orotate1(c_List_Olist_ONil(T_a),T_a) = c_List_Olist_ONil(T_a) ).

cnf(cls_empty__null_0,axiom,
    c_List_Onull(c_List_Olist_ONil(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_remdups__eq__nil__right__iff_0,axiom,
    ( c_List_Olist_ONil(T_a) != c_List_Oremdups(V_x,T_a)
    | V_x = c_List_Olist_ONil(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_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_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_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_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_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_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_distinct__remdups_0,axiom,
    c_List_Odistinct(c_List_Oremdups(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_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__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_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_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_distinct1__rotate_1,axiom,
    ( c_List_Odistinct(c_List_Orotate1(V_xs,T_a),T_a)
    | ~ c_List_Odistinct(V_xs,T_a) ) ).

cnf(cls_distinct1__rotate_0,axiom,
    ( c_List_Odistinct(V_xs,T_a)
    | ~ c_List_Odistinct(c_List_Orotate1(V_xs,T_a),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_remdups__id__iff__distinct_0,axiom,
    ( c_List_Oremdups(V_xs,T_a) != V_xs
    | c_List_Odistinct(V_xs,T_a) ) ).

cnf(cls_distinct__remdups__id_0,axiom,
    ( c_List_Oremdups(V_xs,T_a) = V_xs
    | ~ c_List_Odistinct(V_xs,T_a) ) ).

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_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_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_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_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_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_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_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_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_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_alt3_0,axiom,
    c_List_Odistinct(c_List_Olist_OCons(v_sko__Arrow__Order__Mirabelle__Xalt3__1,c_List_Olist_OCons(v_sko__Arrow__Order__Mirabelle__Xalt3__2,c_List_Olist_OCons(v_sko__Arrow__Order__Mirabelle__Xalt3__3,c_List_Olist_ONil(tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ).

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_distinct_Osimps_I1_J_0,axiom,
    c_List_Odistinct(c_List_Olist_ONil(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_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_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_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_CHAINED_0,axiom,
    c_List_Odistinct(c_List_Olist_OCons(v_sko__CHAINED__1,c_List_Olist_OCons(v_sko__CHAINED__2,c_List_Olist_OCons(v_sko__CHAINED__3,c_List_Olist_ONil(tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ).

cnf(cls_conjecture_0,negated_conjecture,
    v_a != v_b ).

cnf(cls_conjecture_1,negated_conjecture,
    ~ c_List_Odistinct(c_List_Olist_OCons(v_a,c_List_Olist_OCons(v_b,c_List_Olist_OCons(V_x,c_List_Olist_ONil(tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ).

cnf(clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add,axiom,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) ).

cnf(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) ).

cnf(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) ).

cnf(clsarity_nat__OrderedGroup_Opordered__comm__monoid__add,axiom,
    class_OrderedGroup_Opordered__comm__monoid__add(tc_nat) ).

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_Oordered__semidom,axiom,
    class_Ring__and__Field_Oordered__semidom(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__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__Divides_Osemiring__div,axiom,
    class_Divides_Osemiring__div(tc_nat) ).

cnf(clsarity_nat__Orderings_Opreorder,axiom,
    class_Orderings_Opreorder(tc_nat) ).

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

cnf(clsarity_nat__Orderings_Oorder,axiom,
    class_Orderings_Oorder(tc_nat) ).

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

cnf(clsarity_nat__Int_Onumber,axiom,
    class_Int_Onumber(tc_nat) ).

cnf(clsarity_nat__HOL_Oord,axiom,
    class_HOL_Oord(tc_nat) ).

cnf(clsarity_Int__Oint__OrderedGroup_Opordered__cancel__ab__semigroup__add,axiom,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_Int_Oint) ).

cnf(clsarity_Int__Oint__OrderedGroup_Opordered__ab__semigroup__add__imp__le,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Int_Oint) ).

cnf(clsarity_Int__Oint__Ring__and__Field_Oring__1__no__zero__divisors,axiom,
    class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Int_Oint) ).

cnf(clsarity_Int__Oint__OrderedGroup_Opordered__ab__semigroup__add,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add(tc_Int_Oint) ).

cnf(clsarity_Int__Oint__OrderedGroup_Opordered__comm__monoid__add,axiom,
    class_OrderedGroup_Opordered__comm__monoid__add(tc_Int_Oint) ).

cnf(clsarity_Int__Oint__OrderedGroup_Ocancel__ab__semigroup__add,axiom,
    class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Int_Oint) ).

cnf(clsarity_Int__Oint__OrderedGroup_Opordered__ab__group__add,axiom,
    class_OrderedGroup_Opordered__ab__group__add(tc_Int_Oint) ).

cnf(clsarity_Int__Oint__OrderedGroup_Olordered__ab__group__add,axiom,
    class_OrderedGroup_Olordered__ab__group__add(tc_Int_Oint) ).

cnf(clsarity_Int__Oint__OrderedGroup_Ocancel__semigroup__add,axiom,
    class_OrderedGroup_Ocancel__semigroup__add(tc_Int_Oint) ).

cnf(clsarity_Int__Oint__Ring__and__Field_Ono__zero__divisors,axiom,
    class_Ring__and__Field_Ono__zero__divisors(tc_Int_Oint) ).

cnf(clsarity_Int__Oint__Ring__and__Field_Oordered__semidom,axiom,
    class_Ring__and__Field_Oordered__semidom(tc_Int_Oint) ).

cnf(clsarity_Int__Oint__Ring__and__Field_Ocomm__semiring__1,axiom,
    class_Ring__and__Field_Ocomm__semiring__1(tc_Int_Oint) ).

cnf(clsarity_Int__Oint__OrderedGroup_Oab__semigroup__add,axiom,
    class_OrderedGroup_Oab__semigroup__add(tc_Int_Oint) ).

cnf(clsarity_Int__Oint__OrderedGroup_Ocomm__monoid__add,axiom,
    class_OrderedGroup_Ocomm__monoid__add(tc_Int_Oint) ).

cnf(clsarity_Int__Oint__Ring__and__Field_Ozero__neq__one,axiom,
    class_Ring__and__Field_Ozero__neq__one(tc_Int_Oint) ).

cnf(clsarity_Int__Oint__Ring__and__Field_Oordered__idom,axiom,
    class_Ring__and__Field_Oordered__idom(tc_Int_Oint) ).

cnf(clsarity_Int__Oint__Ring__and__Field_Osemiring__0,axiom,
    class_Ring__and__Field_Osemiring__0(tc_Int_Oint) ).

cnf(clsarity_Int__Oint__OrderedGroup_Oab__group__add,axiom,
    class_OrderedGroup_Oab__group__add(tc_Int_Oint) ).

cnf(clsarity_Int__Oint__Ring__and__Field_Omult__zero,axiom,
    class_Ring__and__Field_Omult__zero(tc_Int_Oint) ).

cnf(clsarity_Int__Oint__OrderedGroup_Omonoid__mult,axiom,
    class_OrderedGroup_Omonoid__mult(tc_Int_Oint) ).

cnf(clsarity_Int__Oint__OrderedGroup_Omonoid__add,axiom,
    class_OrderedGroup_Omonoid__add(tc_Int_Oint) ).

cnf(clsarity_Int__Oint__OrderedGroup_Ogroup__add,axiom,
    class_OrderedGroup_Ogroup__add(tc_Int_Oint) ).

cnf(clsarity_Int__Oint__Divides_Osemiring__div,axiom,
    class_Divides_Osemiring__div(tc_Int_Oint) ).

cnf(clsarity_Int__Oint__Ring__and__Field_Oidom,axiom,
    class_Ring__and__Field_Oidom(tc_Int_Oint) ).

cnf(clsarity_Int__Oint__Orderings_Opreorder,axiom,
    class_Orderings_Opreorder(tc_Int_Oint) ).

cnf(clsarity_Int__Oint__Orderings_Olinorder,axiom,
    class_Orderings_Olinorder(tc_Int_Oint) ).

cnf(clsarity_Int__Oint__Divides_Oring__div,axiom,
    class_Divides_Oring__div(tc_Int_Oint) ).

cnf(clsarity_Int__Oint__Orderings_Oorder,axiom,
    class_Orderings_Oorder(tc_Int_Oint) ).

cnf(clsarity_Int__Oint__Int_Oring__char__0,axiom,
    class_Int_Oring__char__0(tc_Int_Oint) ).

cnf(clsarity_Int__Oint__Int_Onumber__ring,axiom,
    class_Int_Onumber__ring(tc_Int_Oint) ).

cnf(clsarity_Int__Oint__Power_Opower,axiom,
    class_Power_Opower(tc_Int_Oint) ).

cnf(clsarity_Int__Oint__Int_Onumber,axiom,
    class_Int_Onumber(tc_Int_Oint) ).

cnf(clsarity_Int__Oint__HOL_Oord,axiom,
    class_HOL_Oord(tc_Int_Oint) ).

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