TPTP Problem File: SWV972-1.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : SWV972-1 : TPTP v8.2.0. Released v4.1.0.
% Domain : Software Verification
% Problem : Java type soundness 459_30
% Version : Especial.
% English :
% Refs : [vON99] von Oheimb & Nipkow (1999), Machine-Checking the Java
% : [Nip10] Nipkow (2010), Email to Geoff Sutcliffe
% : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% Source : [Nip10]
% Names : TypeSafe-459_30 [Nip10]
% Status : Unsatisfiable
% Rating : 0.05 v7.4.0, 0.06 v7.3.0, 0.00 v7.0.0, 0.07 v6.3.0, 0.00 v6.2.0, 0.10 v6.1.0, 0.00 v5.5.0, 0.25 v5.3.0, 0.22 v5.2.0, 0.19 v5.1.0, 0.24 v5.0.0, 0.21 v4.1.0
% Syntax : Number of clauses : 508 ( 199 unt; 31 nHn; 289 RR)
% Number of literals : 995 ( 430 equ; 471 neg)
% Maximal clause size : 6 ( 1 avg)
% Maximal term depth : 8 ( 1 avg)
% Number of predicates : 44 ( 43 usr; 1 prp; 0-8 aty)
% Number of functors : 72 ( 72 usr; 20 con; 0-6 aty)
% Number of variables : 1573 ( 201 sgn)
% SPC : CNF_UNS_RFO_SEQ_NHN
% Comments :
%------------------------------------------------------------------------------
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_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_nth__Cons__number__of_0,axiom,
( c_Int_Onumber__class_Onumber__of(V_v,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(c_List_Onth(c_List_Olist_OCons(V_x,V_xs,T_a),T_a),c_Int_Onumber__class_Onumber__of(V_v,tc_nat)) = V_x ) ).
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_WTrt_H__WTrts_H_Ointros_I12_J_0,axiom,
( c_Progress_OWTrt_H(V_P,V_h,V_E,c_Expr_Oexp_OCall(V_e,V_M,V_es,tc_List_Olist(tc_String_Ochar)),V_T)
| ~ c_List_Olist__all2(c_TypeRel_Owiden(V_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),V_Ts_H,V_Ts,tc_Type_Oty,tc_Type_Oty)
| ~ c_Progress_OWTrts_H(V_P,V_h,V_E,V_es,V_Ts_H)
| ~ c_TypeRel_OMethod(V_P,V_C,V_M,V_Ts,V_T,c_Pair(V_pns,V_body,tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))),V_D,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))))
| ~ c_Progress_OWTrt_H(V_P,V_h,V_E,V_e,c_Type_Oty_OClass(V_C)) ) ).
cnf(cls_of__nat__le__iff_0,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(T_a)
| c_lessequals(V_m,V_n,tc_nat)
| ~ c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a) ) ).
cnf(cls_of__nat__le__iff_1,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(T_a)
| c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a)
| ~ c_lessequals(V_m,V_n,tc_nat) ) ).
cnf(cls_wt__wt_H_0,axiom,
( c_Progress_OWTrt_H(V_P,V_h,V_E,V_e,V_T)
| ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e,V_T) ) ).
cnf(cls_wt_H__wt_0,axiom,
( c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e,V_T)
| ~ c_Progress_OWTrt_H(V_P,V_h,V_E,V_e,V_T) ) ).
cnf(cls_nat_Osplit_0,axiom,
( ~ hBOOL(hAPP(V_P,c_Nat_Onat_Onat__case(V_f1,V_f2,c_HOL_Ozero__class_Ozero(tc_nat),t_a)))
| hBOOL(hAPP(V_P,V_f1)) ) ).
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_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_rotate__simps_0,axiom,
c_List_Orotate1(c_List_Olist_ONil(T_a),T_a) = c_List_Olist_ONil(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_nat__diff__split__asm_1,axiom,
( ~ hBOOL(hAPP(V_P,c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_b,V_x,tc_nat),V_b,tc_nat)))
| hBOOL(hAPP(V_P,V_x)) ) ).
cnf(cls_nat__diff__split_1,axiom,
( ~ hBOOL(hAPP(V_P,c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_b,V_d,tc_nat),V_b,tc_nat)))
| hBOOL(hAPP(V_P,V_d)) ) ).
cnf(cls_add__le__mono_0,axiom,
( c_lessequals(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_lessequals(V_k,V_l,tc_nat)
| ~ c_lessequals(V_i,V_j,tc_nat) ) ).
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_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_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_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_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_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_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_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_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_trans__le__add2_0,axiom,
( c_lessequals(V_i,c_HOL_Oplus__class_Oplus(V_m,V_j,tc_nat),tc_nat)
| ~ c_lessequals(V_i,V_j,tc_nat) ) ).
cnf(cls_trans__le__add1_0,axiom,
( c_lessequals(V_i,c_HOL_Oplus__class_Oplus(V_j,V_m,tc_nat),tc_nat)
| ~ c_lessequals(V_i,V_j,tc_nat) ) ).
cnf(cls_add__leE_1,axiom,
( c_lessequals(V_k,V_n,tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(V_m,V_k,tc_nat),V_n,tc_nat) ) ).
cnf(cls_add__leE_0,axiom,
( c_lessequals(V_m,V_n,tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(V_m,V_k,tc_nat),V_n,tc_nat) ) ).
cnf(cls_termination__basic__simps_I4_J_0,axiom,
( c_lessequals(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,tc_nat),tc_nat)
| ~ c_lessequals(V_x,V_z,tc_nat) ) ).
cnf(cls_termination__basic__simps_I3_J_0,axiom,
( c_lessequals(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,tc_nat),tc_nat)
| ~ c_lessequals(V_x,V_y,tc_nat) ) ).
cnf(cls_nth__list__update__neq_0,axiom,
( hAPP(c_List_Onth(c_List_Olist__update(V_xs,V_i,V_x,T_a),T_a),V_j) = hAPP(c_List_Onth(V_xs,T_a),V_j)
| V_i = V_j ) ).
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_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_of__nat__1_0,axiom,
( ~ class_Ring__and__Field_Osemiring__1(T_a)
| c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),T_a) = c_HOL_Oone__class_Oone(T_a) ) ).
cnf(cls_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_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_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_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_ty_Osimps_I21_J_0,axiom,
c_Type_Oty_OClass(V_list_H) != c_Type_Oty_ONT ).
cnf(cls_of__nat__0_0,axiom,
( ~ class_Ring__and__Field_Osemiring__1(T_a)
| c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_WT__implies__WTrt_0,axiom,
( c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e,V_T)
| ~ c_WellType_OWT(V_P,V_E,V_e,V_T) ) ).
cnf(cls_list__update__nonempty_1,axiom,
c_List_Olist__update(c_List_Olist_ONil(T_a),V_k,V_x,T_a) = c_List_Olist_ONil(T_a) ).
cnf(cls_list__update__code_I1_J_0,axiom,
c_List_Olist__update(c_List_Olist_ONil(T_a),V_i,V_y,T_a) = c_List_Olist_ONil(T_a) ).
cnf(cls_list__update_Osimps_I1_J_0,axiom,
c_List_Olist__update(c_List_Olist_ONil(T_a),V_i,V_v,T_a) = c_List_Olist_ONil(T_a) ).
cnf(cls_natgb_Oadd__cancel_0,axiom,
( 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_le__add__diff_0,axiom,
( c_lessequals(V_m,c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_n,V_m,tc_nat),V_k,tc_nat),tc_nat)
| ~ c_lessequals(V_k,V_n,tc_nat) ) ).
cnf(cls_nth__Cons__number__of_1,axiom,
( hAPP(c_List_Onth(c_List_Olist_OCons(V_x,V_xs,T_a),T_a),c_Int_Onumber__class_Onumber__of(V_v,tc_nat)) = hAPP(c_List_Onth(V_xs,T_a),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_Int_Onumber__class_Onumber__of(V_v,tc_nat) = 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_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_nth_Osimps_0,axiom,
hAPP(c_List_Onth(c_List_Olist_OCons(V_x,V_xs,T_a),T_a),V_n) = c_Nat_Onat_Onat__case(V_x,c_List_Onth(V_xs,T_a),V_n,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_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_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_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_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_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_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_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_of__nat__0__le__iff_0,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a) ) ).
cnf(cls_zero__le__imp__of__nat_0,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a),T_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_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_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_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_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_sees__method__idemp_0,axiom,
( c_TypeRel_OMethod(V_P,V_D,V_M,V_Ts,V_T,V_m,V_D,T_a)
| ~ c_TypeRel_OMethod(V_P,V_C,V_M,V_Ts,V_T,V_m,V_D,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_power__increasing_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_a,V_N,T_a),T_a)
| ~ c_lessequals(c_HOL_Oone__class_Oone(T_a),V_a,T_a)
| ~ c_lessequals(V_n,V_N,tc_nat) ) ).
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_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_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_le__diff__conv2_0,axiom,
( c_lessequals(c_HOL_Oplus__class_Oplus(V_i,V_k,tc_nat),V_j,tc_nat)
| ~ c_lessequals(V_i,c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat),tc_nat)
| ~ c_lessequals(V_k,V_j,tc_nat) ) ).
cnf(cls_le__diff__conv2_1,axiom,
( c_lessequals(V_i,c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat),tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(V_i,V_k,tc_nat),V_j,tc_nat)
| ~ c_lessequals(V_k,V_j,tc_nat) ) ).
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_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_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_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_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_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_of__nat__eq__iff_0,axiom,
( ~ class_Nat_Osemiring__char__0(T_a)
| c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a) != c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a)
| V_m = V_n ) ).
cnf(cls_nth__Cons_H_0,axiom,
hAPP(c_List_Onth(c_List_Olist_OCons(V_x,V_xs,T_a),T_a),c_HOL_Ozero__class_Ozero(tc_nat)) = V_x ).
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_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_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_nat__case__0_0,axiom,
c_Nat_Onat_Onat__case(V_f1,V_f2,c_HOL_Ozero__class_Ozero(tc_nat),T_a) = V_f1 ).
cnf(cls_Nitpick_Onat__case__def_0,axiom,
c_Nat_Onat_Onat__case(V_x,V_f,c_HOL_Ozero__class_Ozero(tc_nat),T_a) = V_x ).
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_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_le__diff__conv_0,axiom,
( c_lessequals(V_j,c_HOL_Oplus__class_Oplus(V_i,V_k,tc_nat),tc_nat)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat),V_i,tc_nat) ) ).
cnf(cls_le__diff__conv_1,axiom,
( c_lessequals(c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat),V_i,tc_nat)
| ~ c_lessequals(V_j,c_HOL_Oplus__class_Oplus(V_i,V_k,tc_nat),tc_nat) ) ).
cnf(cls_WTrt_H__WTrts_H_Ointros_I13_J_0,axiom,
( c_Progress_OWTrt_H(V_P,V_h,V_E,c_Expr_Oexp_OCall(V_e,V_M,V_es,tc_List_Olist(tc_String_Ochar)),V_T)
| ~ c_Progress_OWTrts_H(V_P,V_h,V_E,V_es,V_Ts)
| ~ c_Progress_OWTrt_H(V_P,V_h,V_E,V_e,c_Type_Oty_ONT) ) ).
cnf(cls_diff__add__assoc_0,axiom,
( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_i,V_j,tc_nat),V_k,tc_nat) = c_HOL_Oplus__class_Oplus(V_i,c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat),tc_nat)
| ~ c_lessequals(V_k,V_j,tc_nat) ) ).
cnf(cls_diff__add__assoc2_0,axiom,
( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_j,V_i,tc_nat),V_k,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat),V_i,tc_nat)
| ~ c_lessequals(V_k,V_j,tc_nat) ) ).
cnf(cls_diff__diff__right_0,axiom,
( c_HOL_Ominus__class_Ominus(V_i,c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_i,V_k,tc_nat),V_j,tc_nat)
| ~ c_lessequals(V_k,V_j,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_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_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_le__imp__diff__is__add_1,axiom,
( ~ c_lessequals(V_i,c_HOL_Oplus__class_Oplus(V_k,V_i,tc_nat),tc_nat)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_k,V_i,tc_nat),V_i,tc_nat) = V_k ) ).
cnf(cls_le__add1_0,axiom,
c_lessequals(V_n,c_HOL_Oplus__class_Oplus(V_n,V_m,tc_nat),tc_nat) ).
cnf(cls_le__add2_0,axiom,
c_lessequals(V_n,c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),tc_nat) ).
cnf(cls_le__iff__add_1,axiom,
c_lessequals(V_m,c_HOL_Oplus__class_Oplus(V_m,V_x,tc_nat),tc_nat) ).
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_nth__drop_0,axiom,
( hAPP(c_List_Onth(c_List_Odrop(V_n,V_xs,T_a),T_a),V_i) = hAPP(c_List_Onth(V_xs,T_a),c_HOL_Oplus__class_Oplus(V_n,V_i,tc_nat))
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(V_n,V_i,tc_nat),c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)),tc_nat) ) ).
cnf(cls_sees__method__fun_0,axiom,
( V_TS_H = V_TS
| ~ c_TypeRel_OMethod(V_P,V_C,V_M,V_TS_H,V_T_H,V_m_H,V_D_H,T_a)
| ~ c_TypeRel_OMethod(V_P,V_C,V_M,V_TS,V_T,V_m,V_D,T_a) ) ).
cnf(cls_sees__method__fun_1,axiom,
( V_T_H = V_T
| ~ c_TypeRel_OMethod(V_P,V_C,V_M,V_TS_H,V_T_H,V_m_H,V_D_H,T_a)
| ~ c_TypeRel_OMethod(V_P,V_C,V_M,V_TS,V_T,V_m,V_D,T_a) ) ).
cnf(cls_sees__method__fun_2,axiom,
( V_m_H = V_m
| ~ c_TypeRel_OMethod(V_P,V_C,V_M,V_TS_H,V_T_H,V_m_H,V_D_H,T_a)
| ~ c_TypeRel_OMethod(V_P,V_C,V_M,V_TS,V_T,V_m,V_D,T_a) ) ).
cnf(cls_sees__method__fun_3,axiom,
( V_D_H = V_D
| ~ c_TypeRel_OMethod(V_P,V_C,V_M,V_TS_H,V_T_H,V_m_H,V_D_H,T_a)
| ~ c_TypeRel_OMethod(V_P,V_C,V_M,V_TS,V_T,V_m,V_D,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_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_add__le__mono1_0,axiom,
( c_lessequals(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_lessequals(V_i,V_j,tc_nat) ) ).
cnf(cls_nat__add__left__cancel__le_0,axiom,
( c_lessequals(V_m,V_n,tc_nat)
| ~ c_lessequals(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__le_1,axiom,
( c_lessequals(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_lessequals(V_m,V_n,tc_nat) ) ).
cnf(cls_list__update__beyond_0,axiom,
( c_List_Olist__update(V_xs,V_i,V_x,T_a) = V_xs
| ~ c_lessequals(c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)),V_i,tc_nat) ) ).
cnf(cls_le__imp__diff__is__add_0,axiom,
( ~ c_lessequals(V_i,V_j,tc_nat)
| V_j = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_j,V_i,tc_nat),V_i,tc_nat) ) ).
cnf(cls_le__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_lessequals(V_n,V_m,tc_nat) ) ).
cnf(cls_le__add__diff__inverse2_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),V_n,tc_nat) = V_m
| ~ c_lessequals(V_n,V_m,tc_nat) ) ).
cnf(cls_add__diff__assoc_0,axiom,
( c_HOL_Oplus__class_Oplus(V_i,c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_i,V_j,tc_nat),V_k,tc_nat)
| ~ c_lessequals(V_k,V_j,tc_nat) ) ).
cnf(cls_add__diff__assoc2_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat),V_i,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_j,V_i,tc_nat),V_k,tc_nat)
| ~ c_lessequals(V_k,V_j,tc_nat) ) ).
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_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_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_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_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_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_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_length__replicate_0,axiom,
c_Nat_Osize__class_Osize(c_List_Oreplicate(V_n,V_x,T_a),tc_List_Olist(T_a)) = V_n ).
cnf(cls_empty__replicate_0,axiom,
( c_List_Olist_ONil(T_a) != c_List_Oreplicate(V_n,V_x,T_a)
| V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ).
cnf(cls_list__update__id_0,axiom,
c_List_Olist__update(V_xs,V_i,hAPP(c_List_Onth(V_xs,T_a),V_i),T_a) = V_xs ).
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_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_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_ty_Osimps_I20_J_0,axiom,
c_Type_Oty_ONT != c_Type_Oty_OClass(V_list_H) ).
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_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_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_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_WTCall_0,axiom,
( c_WellType_OWT(V_P,V_E,c_Expr_Oexp_OCall(V_e,V_M,V_es,tc_List_Olist(tc_String_Ochar)),V_T)
| ~ c_List_Olist__all2(c_TypeRel_Owiden(V_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),V_Ts_H,V_Ts,tc_Type_Oty,tc_Type_Oty)
| ~ c_WellType_OWTs(V_P,V_E,V_es,V_Ts_H)
| ~ c_TypeRel_OMethod(V_P,V_C,V_M,V_Ts,V_T,c_Pair(V_pns,V_body,tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))),V_D,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))))
| ~ c_WellType_OWT(V_P,V_E,V_e,c_Type_Oty_OClass(V_C)) ) ).
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_nth__append__length__plus_0,axiom,
hAPP(c_List_Onth(c_List_Oappend(V_xs,V_ys,T_a),T_a),c_HOL_Oplus__class_Oplus(c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)),V_n,tc_nat)) = hAPP(c_List_Onth(V_ys,T_a),V_n) ).
cnf(cls_of__nat__add_0,axiom,
( ~ class_Ring__and__Field_Osemiring__1(T_a)
| c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),T_a) = c_HOL_Oplus__class_Oplus(c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),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_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_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_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_append__eq__Cons__conv_2,axiom,
( c_List_Oappend(V_ys,V_zs,T_a) != c_List_Olist_OCons(V_x,V_xs,T_a)
| V_ys = c_List_Olist_OCons(V_x,c_List_Osko__List__Xappend__eq__Cons__conv__1__1(V_x,V_xs,V_ys,V_zs,T_a),T_a)
| V_zs = c_List_Olist_OCons(V_x,V_xs,T_a) ) ).
cnf(cls_Cons__eq__append__conv_3,axiom,
( c_List_Olist_OCons(V_x,V_xs,T_a) != c_List_Oappend(V_ys,V_zs,T_a)
| V_xs = c_List_Oappend(c_List_Osko__List__XCons__eq__append__conv__1__1(V_x,V_xs,V_ys,V_zs,T_a),V_zs,T_a)
| c_List_Olist_OCons(V_x,V_xs,T_a) = V_zs ) ).
cnf(cls_replicate__app__Cons__same_0,axiom,
c_List_Oappend(c_List_Oreplicate(V_n,V_x,T_a),c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = c_List_Olist_OCons(V_x,c_List_Oappend(c_List_Oreplicate(V_n,V_x,T_a),V_xs,T_a),T_a) ).
cnf(cls_butlast__append_0,axiom,
c_List_Obutlast(c_List_Oappend(V_xs,c_List_Olist_ONil(T_a),T_a),T_a) = c_List_Obutlast(V_xs,T_a) ).
cnf(cls_tl__append2_0,axiom,
( c_List_Otl(c_List_Oappend(V_xs,V_ys,T_a),T_a) = c_List_Oappend(c_List_Otl(V_xs,T_a),V_ys,T_a)
| V_xs = c_List_Olist_ONil(T_a) ) ).
cnf(cls_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_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_nth__via__drop_0,axiom,
( c_List_Odrop(V_n,V_xs,T_a) != c_List_Olist_OCons(V_y,V_ys,T_a)
| hAPP(c_List_Onth(V_xs,T_a),V_n) = V_y ) ).
cnf(cls_widen__Class_2,axiom,
hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,T_a),c_Type_Oty_ONT),c_Type_Oty_OClass(V_C))) ).
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_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_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_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_nth__append__length_0,axiom,
hAPP(c_List_Onth(c_List_Oappend(V_xs,c_List_Olist_OCons(V_x,V_ys,T_a),T_a),T_a),c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a))) = V_x ).
cnf(cls_of__nat__diff_0,axiom,
( ~ class_Ring__and__Field_Oring__1(T_a)
| c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),T_a) = c_HOL_Ominus__class_Ominus(c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a)
| ~ c_lessequals(V_n,V_m,tc_nat) ) ).
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_rotate1__length01_0,axiom,
( c_List_Orotate1(V_xs,T_a) = V_xs
| ~ c_lessequals(c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ) ).
cnf(cls_rotate__length01_0,axiom,
( c_List_Orotate(V_n,V_xs,T_a) = V_xs
| ~ c_lessequals(c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ) ).
cnf(cls_Nitpick_Onat__case__def_1,axiom,
( c_Nat_Onat_Onat__case(V_x,V_f,V_n,T_a) = hAPP(V_f,c_HOL_Ominus__class_Ominus(V_n,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
| V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ).
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_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_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_WTrtCallNT_0,axiom,
( c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OCall(V_e,V_M,V_es,tc_List_Olist(tc_String_Ochar)),V_T)
| ~ c_WellTypeRT_OWTrts(V_P,V_h,V_E,V_es,V_Ts)
| ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e,c_Type_Oty_ONT) ) ).
cnf(cls_WTrtCall_0,axiom,
( c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OCall(V_e,V_M,V_es,tc_List_Olist(tc_String_Ochar)),V_T)
| ~ c_List_Olist__all2(c_TypeRel_Owiden(V_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),V_Ts_H,V_Ts,tc_Type_Oty,tc_Type_Oty)
| ~ c_WellTypeRT_OWTrts(V_P,V_h,V_E,V_es,V_Ts_H)
| ~ c_TypeRel_OMethod(V_P,V_C,V_M,V_Ts,V_T,c_Pair(V_pns,V_body,tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))),V_D,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))))
| ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e,c_Type_Oty_OClass(V_C)) ) ).
cnf(cls_WTrt_H__WTrts_H_Ointros_I15_J_0,axiom,
( c_Progress_OWTrts_H(V_P,V_h,V_E,c_List_Olist_OCons(V_e,V_es,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))),c_List_Olist_OCons(V_T,V_Ts,tc_Type_Oty))
| ~ c_Progress_OWTrts_H(V_P,V_h,V_E,V_es,V_Ts)
| ~ c_Progress_OWTrt_H(V_P,V_h,V_E,V_e,V_T) ) ).
cnf(cls_WTCons_0,axiom,
( c_WellType_OWTs(V_P,V_E,c_List_Olist_OCons(V_e,V_es,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))),c_List_Olist_OCons(V_T,V_Ts,tc_Type_Oty))
| ~ c_WellType_OWTs(V_P,V_E,V_es,V_Ts)
| ~ c_WellType_OWT(V_P,V_E,V_e,V_T) ) ).
cnf(cls_power__decreasing_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_a,V_n,T_a),T_a)
| ~ c_lessequals(V_a,c_HOL_Oone__class_Oone(T_a),T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ~ c_lessequals(V_n,V_N,tc_nat) ) ).
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_nth__Cons_H_1,axiom,
( hAPP(c_List_Onth(c_List_Olist_OCons(V_x,V_xs,T_a),T_a),V_n) = hAPP(c_List_Onth(V_xs,T_a),c_HOL_Ominus__class_Ominus(V_n,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
| V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ).
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_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_butlast__take_0,axiom,
( c_List_Obutlast(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),V_xs,T_a)
| ~ c_lessequals(V_n,c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)),tc_nat) ) ).
cnf(cls_take__add_0,axiom,
( c_List_Otake(c_HOL_Oplus__class_Oplus(V_i,V_j,tc_nat),V_xs,T_a) = c_List_Oappend(c_List_Otake(V_i,V_xs,T_a),c_List_Otake(V_j,c_List_Odrop(V_i,V_xs,T_a),T_a),T_a)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(V_i,V_j,tc_nat),c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)),tc_nat) ) ).
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_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_take__all_0,axiom,
( c_List_Otake(V_n,V_xs,T_a) = V_xs
| ~ c_lessequals(c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)),V_n,tc_nat) ) ).
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_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__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_take__eq__Nil_0,axiom,
( c_List_Otake(V_n,V_xs,T_a) != c_List_Olist_ONil(T_a)
| V_xs = c_List_Olist_ONil(T_a)
| V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ).
cnf(cls_list__all2__append1_4,axiom,
( c_List_Olist__all2(V_P,V_ys,c_List_Osko__List__Xlist__all2__append1__1__2(V_P,V_xs,V_ys,V_zs,T_a,T_b),T_a,T_b)
| ~ c_List_Olist__all2(V_P,c_List_Oappend(V_xs,V_ys,T_a),V_zs,T_a,T_b) ) ).
cnf(cls_list__all2__append1_3,axiom,
( c_List_Olist__all2(V_P,V_xs,c_List_Osko__List__Xlist__all2__append1__1__1(V_P,V_xs,V_ys,V_zs,T_a,T_b),T_a,T_b)
| ~ c_List_Olist__all2(V_P,c_List_Oappend(V_xs,V_ys,T_a),V_zs,T_a,T_b) ) ).
cnf(cls_list__all2__append2_4,axiom,
( c_List_Olist__all2(V_P,c_List_Osko__List__Xlist__all2__append2__1__2(V_P,V_xs,V_ys,V_zs,T_a,T_b),V_zs,T_a,T_b)
| ~ c_List_Olist__all2(V_P,V_xs,c_List_Oappend(V_ys,V_zs,T_b),T_a,T_b) ) ).
cnf(cls_list__all2__append2_3,axiom,
( c_List_Olist__all2(V_P,c_List_Osko__List__Xlist__all2__append2__1__1(V_P,V_xs,V_ys,V_zs,T_a,T_b),V_ys,T_a,T_b)
| ~ c_List_Olist__all2(V_P,V_xs,c_List_Oappend(V_ys,V_zs,T_b),T_a,T_b) ) ).
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_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_impossible__Cons_0,axiom,
~ c_lessequals(c_Nat_Osize__class_Osize(c_List_Olist_OCons(V_x,V_ys,T_a),tc_List_Olist(T_a)),c_Nat_Osize__class_Osize(V_ys,tc_List_Olist(T_a)),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_nat__le__linear_0,axiom,
( c_lessequals(V_n,V_m,tc_nat)
| c_lessequals(V_m,V_n,tc_nat) ) ).
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_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_list__all2__append2_0,axiom,
( V_xs = c_List_Oappend(c_List_Osko__List__Xlist__all2__append2__1__1(V_P,V_xs,V_ys,V_zs,T_a,T_b),c_List_Osko__List__Xlist__all2__append2__1__2(V_P,V_xs,V_ys,V_zs,T_a,T_b),T_a)
| ~ c_List_Olist__all2(V_P,V_xs,c_List_Oappend(V_ys,V_zs,T_b),T_a,T_b) ) ).
cnf(cls_exp_Osimps_I80_J_0,axiom,
c_Expr_Oexp_OVal(V_val,T_a) != c_Expr_Oexp_OCall(V_exp_H,V_list1_H,V_list2_H,T_a) ).
cnf(cls_order__eq__refl_0,axiom,
( ~ class_Orderings_Opreorder(T_a)
| c_lessequals(V_x,V_x,T_a) ) ).
cnf(cls_order__eq__iff_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| c_lessequals(V_x,V_x,T_a) ) ).
cnf(cls_eq__imp__le_0,axiom,
c_lessequals(V_x,V_x,tc_nat) ).
cnf(cls_le__trans_0,axiom,
( c_lessequals(V_i,V_k,tc_nat)
| ~ c_lessequals(V_j,V_k,tc_nat)
| ~ c_lessequals(V_i,V_j,tc_nat) ) ).
cnf(cls_le__refl_0,axiom,
c_lessequals(V_n,V_n,tc_nat) ).
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_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_le__0__eq_1,axiom,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ).
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_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_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_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__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_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_le__antisym_0,axiom,
( V_m = V_n
| ~ c_lessequals(V_n,V_m,tc_nat)
| ~ c_lessequals(V_m,V_n,tc_nat) ) ).
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_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_le__0__eq_0,axiom,
( V_n = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_lessequals(V_n,c_HOL_Ozero__class_Ozero(tc_nat),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_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_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_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_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_list__all2__append1_0,axiom,
( V_zs = c_List_Oappend(c_List_Osko__List__Xlist__all2__append1__1__1(V_P,V_xs,V_ys,V_zs,T_a,T_b),c_List_Osko__List__Xlist__all2__append1__1__2(V_P,V_xs,V_ys,V_zs,T_a,T_b),T_b)
| ~ c_List_Olist__all2(V_P,c_List_Oappend(V_xs,V_ys,T_a),V_zs,T_a,T_b) ) ).
cnf(cls_diff__is__0__eq_1,axiom,
( c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_lessequals(V_m,V_n,tc_nat) ) ).
cnf(cls_diff__is__0__eq_0,axiom,
( c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_lessequals(V_m,V_n,tc_nat) ) ).
cnf(cls_diff__le__mono2_0,axiom,
( c_lessequals(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_lessequals(V_m,V_n,tc_nat) ) ).
cnf(cls_diff__le__mono_0,axiom,
( c_lessequals(c_HOL_Ominus__class_Ominus(V_m,V_l,tc_nat),c_HOL_Ominus__class_Ominus(V_n,V_l,tc_nat),tc_nat)
| ~ c_lessequals(V_m,V_n,tc_nat) ) ).
cnf(cls_le__diff__iff_1,axiom,
( c_lessequals(c_HOL_Ominus__class_Ominus(V_m,V_k,tc_nat),c_HOL_Ominus__class_Ominus(V_n,V_k,tc_nat),tc_nat)
| ~ c_lessequals(V_m,V_n,tc_nat)
| ~ c_lessequals(V_k,V_n,tc_nat)
| ~ c_lessequals(V_k,V_m,tc_nat) ) ).
cnf(cls_le__diff__iff_0,axiom,
( c_lessequals(V_m,V_n,tc_nat)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(V_m,V_k,tc_nat),c_HOL_Ominus__class_Ominus(V_n,V_k,tc_nat),tc_nat)
| ~ c_lessequals(V_k,V_n,tc_nat)
| ~ c_lessequals(V_k,V_m,tc_nat) ) ).
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_eq__diff__iff_0,axiom,
( c_HOL_Ominus__class_Ominus(V_m,V_k,tc_nat) != c_HOL_Ominus__class_Ominus(V_n,V_k,tc_nat)
| ~ c_lessequals(V_k,V_n,tc_nat)
| ~ c_lessequals(V_k,V_m,tc_nat)
| V_m = V_n ) ).
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_exp_Osimps_I9_J_0,axiom,
( c_Expr_Oexp_OCall(V_exp,V_list1,V_list2,T_a) != c_Expr_Oexp_OCall(V_exp_H,V_list1_H,V_list2_H,T_a)
| V_exp = V_exp_H ) ).
cnf(cls_exp_Osimps_I9_J_1,axiom,
( c_Expr_Oexp_OCall(V_exp,V_list1,V_list2,T_a) != c_Expr_Oexp_OCall(V_exp_H,V_list1_H,V_list2_H,T_a)
| V_list1 = V_list1_H ) ).
cnf(cls_exp_Osimps_I9_J_2,axiom,
( c_Expr_Oexp_OCall(V_exp,V_list1,V_list2,T_a) != c_Expr_Oexp_OCall(V_exp_H,V_list1_H,V_list2_H,T_a)
| V_list2 = V_list2_H ) ).
cnf(cls_drop__0_0,axiom,
c_List_Odrop(c_HOL_Ozero__class_Ozero(tc_nat),V_xs,T_a) = V_xs ).
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__le__self_0,axiom,
c_lessequals(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),V_m,tc_nat) ).
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_Nat_Odiff__diff__eq_0,axiom,
( c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_m,V_k,tc_nat),c_HOL_Ominus__class_Ominus(V_n,V_k,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat)
| ~ c_lessequals(V_k,V_n,tc_nat)
| ~ c_lessequals(V_k,V_m,tc_nat) ) ).
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_le0_0,axiom,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ).
cnf(cls_exp_Osimps_I81_J_0,axiom,
c_Expr_Oexp_OCall(V_exp_H,V_list1_H,V_list2_H,T_a) != c_Expr_Oexp_OVal(V_val,T_a) ).
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_diff__diff__cancel_0,axiom,
( c_HOL_Ominus__class_Ominus(V_n,c_HOL_Ominus__class_Ominus(V_n,V_i,tc_nat),tc_nat) = V_i
| ~ c_lessequals(V_i,V_n,tc_nat) ) ).
cnf(cls_confs__Cons2_0,axiom,
( V_xs = c_List_Olist_OCons(c_Conform_Osko__Conform__Xconfs__Cons2__1__1(V_P,V_h,V_xs,V_y,V_ys,T_a),c_Conform_Osko__Conform__Xconfs__Cons2__1__2(V_P,V_h,V_xs,V_y,V_ys,T_a),tc_Value_Oval)
| ~ c_List_Olist__all2(c_Conform_Oconf(V_P,V_h,T_a),V_xs,c_List_Olist_OCons(V_y,V_ys,tc_Type_Oty),tc_Value_Oval,tc_Type_Oty) ) ).
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_take__Cons_H_0,axiom,
c_List_Otake(c_HOL_Ozero__class_Ozero(tc_nat),c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = c_List_Olist_ONil(T_a) ).
cnf(cls_list__all2__append2_1,axiom,
( c_Nat_Osize__class_Osize(c_List_Osko__List__Xlist__all2__append2__1__1(V_P,V_xs,V_ys,V_zs,T_a,T_b),tc_List_Olist(T_a)) = c_Nat_Osize__class_Osize(V_ys,tc_List_Olist(T_b))
| ~ c_List_Olist__all2(V_P,V_xs,c_List_Oappend(V_ys,V_zs,T_b),T_a,T_b) ) ).
cnf(cls_list__all2__append1_1,axiom,
( c_Nat_Osize__class_Osize(c_List_Osko__List__Xlist__all2__append1__1__1(V_P,V_xs,V_ys,V_zs,T_a,T_b),tc_List_Olist(T_b)) = c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a))
| ~ c_List_Olist__all2(V_P,c_List_Oappend(V_xs,V_ys,T_a),V_zs,T_a,T_b) ) ).
cnf(cls_list__all2__append2_2,axiom,
( c_Nat_Osize__class_Osize(c_List_Osko__List__Xlist__all2__append2__1__2(V_P,V_xs,V_ys,V_zs,T_a,T_b),tc_List_Olist(T_a)) = c_Nat_Osize__class_Osize(V_zs,tc_List_Olist(T_b))
| ~ c_List_Olist__all2(V_P,V_xs,c_List_Oappend(V_ys,V_zs,T_b),T_a,T_b) ) ).
cnf(cls_list__all2__append1_2,axiom,
( c_Nat_Osize__class_Osize(c_List_Osko__List__Xlist__all2__append1__1__2(V_P,V_xs,V_ys,V_zs,T_a,T_b),tc_List_Olist(T_b)) = c_Nat_Osize__class_Osize(V_ys,tc_List_Olist(T_a))
| ~ c_List_Olist__all2(V_P,c_List_Oappend(V_xs,V_ys,T_a),V_zs,T_a,T_b) ) ).
cnf(cls_wt_0,axiom,
c_WellTypeRT_OWTrt(v_P,v_ha____,v_E____,c_Expr_Oexp_OCall(c_Expr_Oexp_OVal(v_v____,tc_List_Olist(tc_String_Ochar)),v_M____,v_esa____,tc_List_Olist(tc_String_Ochar)),v_T____) ).
cnf(cls_drop__all_0,axiom,
( c_List_Odrop(V_n,V_xs,T_a) = c_List_Olist_ONil(T_a)
| ~ c_lessequals(c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)),V_n,tc_nat) ) ).
cnf(cls_drop__eq__Nil_0,axiom,
( c_List_Odrop(V_n,V_xs,T_a) != c_List_Olist_ONil(T_a)
| c_lessequals(c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)),V_n,tc_nat) ) ).
cnf(cls_append__eq__append__conv__if_0,axiom,
( c_List_Oappend(V_xs_092_060_094isub_0621,V_xs_092_060_094isub_0622,T_a) != c_List_Oappend(V_ys_092_060_094isub_0621,V_ys_092_060_094isub_0622,T_a)
| 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_lessequals(c_Nat_Osize__class_Osize(V_xs_092_060_094isub_0621,tc_List_Olist(T_a)),c_Nat_Osize__class_Osize(V_ys_092_060_094isub_0621,tc_List_Olist(T_a)),tc_nat) ) ).
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_append__eq__append__conv__if_2,axiom,
( c_List_Oappend(V_xs_092_060_094isub_0621,V_xs_092_060_094isub_0622,T_a) != c_List_Oappend(V_ys_092_060_094isub_0621,V_ys_092_060_094isub_0622,T_a)
| 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
| c_lessequals(c_Nat_Osize__class_Osize(V_xs_092_060_094isub_0621,tc_List_Olist(T_a)),c_Nat_Osize__class_Osize(V_ys_092_060_094isub_0621,tc_List_Olist(T_a)),tc_nat) ) ).
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_append__eq__append__conv__if_3,axiom,
( c_List_Oappend(V_xs_092_060_094isub_0621,V_xs_092_060_094isub_0622,T_a) != c_List_Oappend(V_ys_092_060_094isub_0621,V_ys_092_060_094isub_0622,T_a)
| 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),V_xs_092_060_094isub_0622,T_a) = V_ys_092_060_094isub_0622
| c_lessequals(c_Nat_Osize__class_Osize(V_xs_092_060_094isub_0621,tc_List_Olist(T_a)),c_Nat_Osize__class_Osize(V_ys_092_060_094isub_0621,tc_List_Olist(T_a)),tc_nat) ) ).
cnf(cls_append__eq__append__conv__if_1,axiom,
( c_List_Oappend(V_xs_092_060_094isub_0621,V_xs_092_060_094isub_0622,T_a) != c_List_Oappend(V_ys_092_060_094isub_0621,V_ys_092_060_094isub_0622,T_a)
| V_xs_092_060_094isub_0622 = 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)
| ~ c_lessequals(c_Nat_Osize__class_Osize(V_xs_092_060_094isub_0621,tc_List_Olist(T_a)),c_Nat_Osize__class_Osize(V_ys_092_060_094isub_0621,tc_List_Olist(T_a)),tc_nat) ) ).
cnf(cls_WTrtCons_0,axiom,
( c_WellTypeRT_OWTrts(V_P,V_h,V_E,c_List_Olist_OCons(V_e,V_es,tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))),c_List_Olist_OCons(V_T,V_Ts,tc_Type_Oty))
| ~ c_WellTypeRT_OWTrts(V_P,V_h,V_E,V_es,V_Ts)
| ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e,V_T) ) ).
cnf(cls_confs__Cons2_3,axiom,
( c_List_Olist__all2(c_Conform_Oconf(V_P,V_h,T_a),c_List_Olist_OCons(V_x,V_xa,tc_Value_Oval),c_List_Olist_OCons(V_y,V_ys,tc_Type_Oty),tc_Value_Oval,tc_Type_Oty)
| ~ c_List_Olist__all2(c_Conform_Oconf(V_P,V_h,T_a),V_xa,V_ys,tc_Value_Oval,tc_Type_Oty)
| ~ hBOOL(hAPP(hAPP(c_Conform_Oconf(V_P,V_h,T_a),V_x),V_y)) ) ).
cnf(cls_confs__Cons2_2,axiom,
( c_List_Olist__all2(c_Conform_Oconf(V_P,V_h,T_a),c_Conform_Osko__Conform__Xconfs__Cons2__1__2(V_P,V_h,V_xs,V_y,V_ys,T_a),V_ys,tc_Value_Oval,tc_Type_Oty)
| ~ c_List_Olist__all2(c_Conform_Oconf(V_P,V_h,T_a),V_xs,c_List_Olist_OCons(V_y,V_ys,tc_Type_Oty),tc_Value_Oval,tc_Type_Oty) ) ).
cnf(cls_confs__Cons2_1,axiom,
( hBOOL(hAPP(hAPP(c_Conform_Oconf(V_P,V_h,T_a),c_Conform_Osko__Conform__Xconfs__Cons2__1__1(V_P,V_h,V_xs,V_y,V_ys,T_a)),V_y))
| ~ c_List_Olist__all2(c_Conform_Oconf(V_P,V_h,T_a),V_xs,c_List_Olist_OCons(V_y,V_ys,tc_Type_Oty),tc_Value_Oval,tc_Type_Oty) ) ).
cnf(cls_append__eq__append__conv__if_5,axiom,
( 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)
| ~ c_lessequals(c_Nat_Osize__class_Osize(V_xs_092_060_094isub_0621,tc_List_Olist(T_a)),c_Nat_Osize__class_Osize(V_ys_092_060_094isub_0621,tc_List_Olist(T_a)),tc_nat) ) ).
cnf(cls_append__eq__append__conv__if_4,axiom,
( 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
| c_lessequals(c_Nat_Osize__class_Osize(V_xs_092_060_094isub_0621,tc_List_Olist(T_a)),c_Nat_Osize__class_Osize(V_ys_092_060_094isub_0621,tc_List_Olist(T_a)),tc_nat)
| c_List_Oappend(V_xs_092_060_094isub_0621,V_xs_092_060_094isub_0622,T_a) = c_List_Oappend(V_ys_092_060_094isub_0621,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),V_xs_092_060_094isub_0622,T_a),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_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_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_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_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_Cons__eq__append__conv_4,axiom,
c_List_Olist_OCons(V_x,V_xs,T_a) = c_List_Oappend(c_List_Olist_ONil(T_a),c_List_Olist_OCons(V_x,V_xs,T_a),T_a) ).
cnf(cls_not__Cons__self_0,axiom,
V_xs != c_List_Olist_OCons(V_x,V_xs,T_a) ).
cnf(cls_not__Cons__self2_0,axiom,
c_List_Olist_OCons(V_x,V_t,T_a) != V_t ).
cnf(cls_list__all2__append_2,axiom,
( c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)) != c_Nat_Osize__class_Osize(V_ys,tc_List_Olist(T_b))
| c_List_Olist__all2(V_P,c_List_Oappend(V_xs,V_us,T_a),c_List_Oappend(V_ys,V_vs,T_b),T_a,T_b)
| ~ c_List_Olist__all2(V_P,V_us,V_vs,T_a,T_b)
| ~ c_List_Olist__all2(V_P,V_xs,V_ys,T_a,T_b) ) ).
cnf(cls_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_wte_0,axiom,
c_WellTypeRT_OWTrt(v_P,v_ha____,v_E____,c_Expr_Oexp_OVal(v_v____,tc_List_Olist(tc_String_Ochar)),c_Type_Oty_OClass(v_C____)) ).
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_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_list_Osimps_I3_J_0,axiom,
c_List_Olist_OCons(V_a_H,V_list_H,T_a) != c_List_Olist_ONil(T_a) ).
cnf(cls_neq__Nil__conv_1,axiom,
c_List_Olist_OCons(V_x,V_xa,T_a) != c_List_Olist_ONil(T_a) ).
cnf(cls_Cons__eq__appendI_0,axiom,
c_List_Olist_OCons(V_x,c_List_Oappend(V_xs1,V_zs,T_a),T_a) = c_List_Oappend(c_List_Olist_OCons(V_x,V_xs1,T_a),V_zs,T_a) ).
cnf(cls_Cons__eq__append__conv_5,axiom,
c_List_Olist_OCons(V_x,c_List_Oappend(V_xa,V_zs,T_a),T_a) = c_List_Oappend(c_List_Olist_OCons(V_x,V_xa,T_a),V_zs,T_a) ).
cnf(cls_conf__hext_0,axiom,
( hBOOL(hAPP(hAPP(c_Conform_Oconf(V_P,V_h_H,T_a),V_v),V_T))
| ~ hBOOL(hAPP(hAPP(c_Conform_Oconf(V_P,V_h,T_a),V_v),V_T))
| ~ c_Objects_Ohext(V_h,V_h_H) ) ).
cnf(cls_hext__refl_0,axiom,
c_Objects_Ohext(V_h,V_h) ).
cnf(cls_confs__hext_0,axiom,
( c_List_Olist__all2(c_Conform_Oconf(V_P,V_h_H,T_a),V_vs,V_Ts,tc_Value_Oval,tc_Type_Oty)
| ~ c_Objects_Ohext(V_h,V_h_H)
| ~ c_List_Olist__all2(c_Conform_Oconf(V_P,V_h,T_a),V_vs,V_Ts,tc_Value_Oval,tc_Type_Oty) ) ).
cnf(cls_hext__trans_0,axiom,
( c_Objects_Ohext(V_h,V_h_H_H)
| ~ c_Objects_Ohext(V_h_H,V_h_H_H)
| ~ c_Objects_Ohext(V_h,V_h_H) ) ).
cnf(cls_WTrt__hext__mono_0,axiom,
( c_WellTypeRT_OWTrt(V_P,V_h_H,V_E,V_e,V_T)
| ~ c_Objects_Ohext(V_h,V_h_H)
| ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e,V_T) ) ).
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_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_list__all2__append1_5,axiom,
( c_Nat_Osize__class_Osize(V_xa,tc_List_Olist(T_b)) != c_Nat_Osize__class_Osize(V_ys,tc_List_Olist(T_a))
| c_Nat_Osize__class_Osize(V_x,tc_List_Olist(T_b)) != c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a))
| c_List_Olist__all2(V_P,c_List_Oappend(V_xs,V_ys,T_a),c_List_Oappend(V_x,V_xa,T_b),T_a,T_b)
| ~ c_List_Olist__all2(V_P,V_ys,V_xa,T_a,T_b)
| ~ c_List_Olist__all2(V_P,V_xs,V_x,T_a,T_b) ) ).
cnf(cls_list__all2__append2_5,axiom,
( c_Nat_Osize__class_Osize(V_xa,tc_List_Olist(T_a)) != c_Nat_Osize__class_Osize(V_zs,tc_List_Olist(T_b))
| c_Nat_Osize__class_Osize(V_x,tc_List_Olist(T_a)) != c_Nat_Osize__class_Osize(V_ys,tc_List_Olist(T_b))
| c_List_Olist__all2(V_P,c_List_Oappend(V_x,V_xa,T_a),c_List_Oappend(V_ys,V_zs,T_b),T_a,T_b)
| ~ c_List_Olist__all2(V_P,V_xa,V_zs,T_a,T_b)
| ~ c_List_Olist__all2(V_P,V_x,V_ys,T_a,T_b) ) ).
cnf(cls_rev__eq__Cons__iff_0,axiom,
( c_List_Orev(V_xs,T_a) != c_List_Olist_OCons(V_y,V_ys,T_a)
| V_xs = c_List_Oappend(c_List_Orev(V_ys,T_a),c_List_Olist_OCons(V_y,c_List_Olist_ONil(T_a),T_a),T_a) ) ).
cnf(cls_rev__singleton__conv_1,axiom,
c_List_Orev(c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a) = c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a) ).
cnf(cls_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_COMBI__def_0,axiom,
c_COMBI(V_P,T_a) = V_P ).
cnf(cls_singleton__rev__conv_0,axiom,
( c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a) != c_List_Orev(V_xs,T_a)
| V_xs = c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a) ) ).
cnf(cls_append__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_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_append__Nil2_0,axiom,
c_List_Oappend(V_xs,c_List_Olist_ONil(T_a),T_a) = V_xs ).
cnf(cls_eq__Nil__appendI_0,axiom,
V_x = c_List_Oappend(c_List_Olist_ONil(T_a),V_x,T_a) ).
cnf(cls_self__append__conv_1,axiom,
V_xs = c_List_Oappend(V_xs,c_List_Olist_ONil(T_a),T_a) ).
cnf(cls_append__Nil_0,axiom,
c_List_Oappend(c_List_Olist_ONil(T_a),V_ys,T_a) = V_ys ).
cnf(cls_self__append__conv2_1,axiom,
V_ys = c_List_Oappend(c_List_Olist_ONil(T_a),V_ys,T_a) ).
cnf(cls_rev__swap_0,axiom,
V_xs = c_List_Orev(c_List_Orev(V_xs,T_a),T_a) ).
cnf(cls_rev__swap_1,axiom,
c_List_Orev(c_List_Orev(V_ys,T_a),T_a) = V_ys ).
cnf(cls_rev__rev__ident_0,axiom,
c_List_Orev(c_List_Orev(V_xs,T_a),T_a) = V_xs ).
cnf(cls_append__eq__conv__conj_0,axiom,
V_xs = c_List_Otake(c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)),c_List_Oappend(V_xs,V_ys,T_a),T_a) ).
cnf(cls_ty_Oinject_0,axiom,
( c_Type_Oty_OClass(V_list) != c_Type_Oty_OClass(V_list_H)
| V_list = V_list_H ) ).
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_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_Nil__is__append__conv_0,axiom,
( c_List_Olist_ONil(T_a) != c_List_Oappend(V_xs,V_ys,T_a)
| V_xs = c_List_Olist_ONil(T_a) ) ).
cnf(cls_Nil__is__append__conv_1,axiom,
( c_List_Olist_ONil(T_a) != c_List_Oappend(V_xs,V_ys,T_a)
| V_ys = c_List_Olist_ONil(T_a) ) ).
cnf(cls_append__is__Nil__conv_0,axiom,
( c_List_Oappend(V_xs,V_ys,T_a) != c_List_Olist_ONil(T_a)
| V_xs = c_List_Olist_ONil(T_a) ) ).
cnf(cls_append__is__Nil__conv_1,axiom,
( c_List_Oappend(V_xs,V_ys,T_a) != c_List_Olist_ONil(T_a)
| V_ys = c_List_Olist_ONil(T_a) ) ).
cnf(cls_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_list__all2__append_0,axiom,
( c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)) != c_Nat_Osize__class_Osize(V_ys,tc_List_Olist(T_b))
| c_List_Olist__all2(V_P,V_xs,V_ys,T_a,T_b)
| ~ c_List_Olist__all2(V_P,c_List_Oappend(V_xs,V_us,T_a),c_List_Oappend(V_ys,V_vs,T_b),T_a,T_b) ) ).
cnf(cls_list__all2__append_1,axiom,
( c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)) != c_Nat_Osize__class_Osize(V_ys,tc_List_Olist(T_b))
| c_List_Olist__all2(V_P,V_us,V_vs,T_a,T_b)
| ~ c_List_Olist__all2(V_P,c_List_Oappend(V_xs,V_us,T_a),c_List_Oappend(V_ys,V_vs,T_b),T_a,T_b) ) ).
cnf(cls_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_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_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_conf_0,axiom,
c_TypeSafe__Mirabelle_Osconf(v_P,v_E____,c_Pair(v_ha____,v_la____,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))) ).
cnf(cls_append__self__conv_0,axiom,
( c_List_Oappend(V_xs,V_ys,T_a) != V_xs
| V_ys = c_List_Olist_ONil(T_a) ) ).
cnf(cls_self__append__conv_0,axiom,
( V_xs != c_List_Oappend(V_xs,V_ys,T_a)
| V_ys = c_List_Olist_ONil(T_a) ) ).
cnf(cls_append__self__conv2_0,axiom,
( c_List_Oappend(V_xs,V_ys,T_a) != V_ys
| V_xs = c_List_Olist_ONil(T_a) ) ).
cnf(cls_self__append__conv2_0,axiom,
( V_ys != c_List_Oappend(V_xs,V_ys,T_a)
| V_xs = c_List_Olist_ONil(T_a) ) ).
cnf(cls_append__eq__Cons__conv_4,axiom,
c_List_Oappend(c_List_Olist_ONil(T_a),c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = c_List_Olist_OCons(V_x,V_xs,T_a) ).
cnf(cls_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_list_Oinject_0,axiom,
( c_List_Olist_OCons(V_a,V_list,T_a) != c_List_Olist_OCons(V_a_H,V_list_H,T_a)
| V_a = V_a_H ) ).
cnf(cls_list_Oinject_1,axiom,
( c_List_Olist_OCons(V_a,V_list,T_a) != c_List_Olist_OCons(V_a_H,V_list_H,T_a)
| V_list = V_list_H ) ).
cnf(cls_Pair__eq_0,axiom,
( c_Pair(V_a,V_b,T_a,T_b) != c_Pair(V_a_H,V_b_H,T_a,T_b)
| V_a = V_a_H ) ).
cnf(cls_Pair__eq_1,axiom,
( c_Pair(V_a,V_b,T_a,T_b) != c_Pair(V_a_H,V_b_H,T_a,T_b)
| V_b = V_b_H ) ).
cnf(cls_Nil__is__rev__conv_1,axiom,
c_List_Olist_ONil(T_a) = c_List_Orev(c_List_Olist_ONil(T_a),T_a) ).
cnf(cls_length__rev_0,axiom,
c_Nat_Osize__class_Osize(c_List_Orev(V_xs,T_a),tc_List_Olist(T_a)) = c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)) ).
cnf(cls_append1__eq__conv_0,axiom,
( c_List_Oappend(V_xs,c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a) != c_List_Oappend(V_ys,c_List_Olist_OCons(V_y,c_List_Olist_ONil(T_a),T_a),T_a)
| V_xs = V_ys ) ).
cnf(cls_append1__eq__conv_1,axiom,
( c_List_Oappend(V_xs,c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a) != c_List_Oappend(V_ys,c_List_Olist_OCons(V_y,c_List_Olist_ONil(T_a),T_a),T_a)
| V_x = V_y ) ).
cnf(cls_append__is__Nil__conv_2,axiom,
c_List_Oappend(c_List_Olist_ONil(T_a),c_List_Olist_ONil(T_a),T_a) = c_List_Olist_ONil(T_a) ).
cnf(cls_append__assoc_0,axiom,
c_List_Oappend(c_List_Oappend(V_xs,V_ys,T_a),V_zs,T_a) = c_List_Oappend(V_xs,c_List_Oappend(V_ys,V_zs,T_a),T_a) ).
cnf(cls_append__eq__appendI_0,axiom,
c_List_Oappend(V_xs,c_List_Oappend(V_xs1,V_us,T_a),T_a) = c_List_Oappend(c_List_Oappend(V_xs,V_xs1,T_a),V_us,T_a) ).
cnf(cls_append__eq__append__conv2_4,axiom,
c_List_Oappend(c_List_Oappend(V_zs,V_x,T_a),V_ys,T_a) = c_List_Oappend(V_zs,c_List_Oappend(V_x,V_ys,T_a),T_a) ).
cnf(cls_append__eq__append__conv2_5,axiom,
c_List_Oappend(V_xs,c_List_Oappend(V_x,V_ts,T_a),T_a) = c_List_Oappend(c_List_Oappend(V_xs,V_x,T_a),V_ts,T_a) ).
cnf(cls_exp_Osimps_I3_J_0,axiom,
( c_Expr_Oexp_OVal(V_val,T_a) != c_Expr_Oexp_OVal(V_val_H,T_a)
| V_val = V_val_H ) ).
cnf(cls_list__all2__refl_0,axiom,
( c_List_Olist__all2(V_P,V_xs,V_xs,T_a,T_a)
| ~ hBOOL(hAPP(hAPP(V_P,c_List_Osko__List__Xlist__all2__refl__1__1(V_P,T_a)),c_List_Osko__List__Xlist__all2__refl__1__1(V_P,T_a))) ) ).
cnf(cls_list__all2__eq_0,axiom,
c_List_Olist__all2(c_fequal(T_a),V_x,V_x,T_a,T_a) ).
cnf(cls_list__all2__Nil_1,axiom,
c_List_Olist__all2(V_P,c_List_Olist_ONil(T_a),c_List_Olist_ONil(T_b),T_a,T_b) ).
cnf(cls_confs__conv__map_1,axiom,
( c_List_Olist__all2(c_TypeRel_Owiden(V_P,T_a),c_Conform_Osko__Conform__Xconfs__conv__map__1__1(V_P,V_Ts_H,V_h,V_vs,T_a),V_Ts_H,tc_Type_Oty,tc_Type_Oty)
| ~ c_List_Olist__all2(c_Conform_Oconf(V_P,V_h,T_a),V_vs,V_Ts_H,tc_Value_Oval,tc_Type_Oty) ) ).
cnf(cls_that_0,axiom,
( v_thesis____
| ~ c_List_Olist__all2(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),V_Us_H,v_Us____,tc_Type_Oty,tc_Type_Oty)
| ~ c_WellTypeRT_OWTrts(v_P,v_h_Ha____,v_E____,v_es_Ha____,V_Us_H) ) ).
cnf(cls_CallParams_I2_J_0,axiom,
( c_WellTypeRT_OWTrts(v_P,v_h_Ha____,V_E,v_es_Ha____,v_sko__local__XCallParams__2__1(V_E,v_P,V_Ts,v_es_Ha____,v_h_Ha____))
| ~ c_WellTypeRT_OWTrts(v_P,v_ha____,V_E,v_esa____,V_Ts)
| ~ c_TypeSafe__Mirabelle_Osconf(v_P,V_E,c_Pair(v_ha____,v_la____,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))) ) ).
cnf(cls_list__all2__Nil2_0,axiom,
( V_xs = c_List_Olist_ONil(T_a)
| ~ c_List_Olist__all2(V_P,V_xs,c_List_Olist_ONil(T_b),T_a,T_b) ) ).
cnf(cls_list__all2__Nil_0,axiom,
( V_ys = c_List_Olist_ONil(T_b)
| ~ c_List_Olist__all2(V_P,c_List_Olist_ONil(T_a),V_ys,T_a,T_b) ) ).
cnf(cls_list__all2__dropI_0,axiom,
( c_List_Olist__all2(V_P,c_List_Odrop(V_n,V_as,T_a),c_List_Odrop(V_n,V_bs,T_b),T_a,T_b)
| ~ c_List_Olist__all2(V_P,V_as,V_bs,T_a,T_b) ) ).
cnf(cls_widens__Cons_3,axiom,
( c_List_Olist__all2(c_TypeRel_Owiden(V_P,T_a),c_List_Olist_OCons(V_x,V_xs,tc_Type_Oty),c_List_Olist_OCons(V_xa,V_xb,tc_Type_Oty),tc_Type_Oty,tc_Type_Oty)
| ~ c_List_Olist__all2(c_TypeRel_Owiden(V_P,T_a),V_xs,V_xb,tc_Type_Oty,tc_Type_Oty)
| ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,T_a),V_x),V_xa)) ) ).
cnf(cls_IH_1,axiom,
( c_List_Olist__all2(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),v_sko__local__XIH__1(V_Ea,v_P,V_Ts,v_es_Ha____,v_h_Ha____),V_Ts,tc_Type_Oty,tc_Type_Oty)
| ~ c_WellTypeRT_OWTrts(v_P,v_ha____,V_Ea,v_esa____,V_Ts)
| ~ c_TypeSafe__Mirabelle_Osconf(v_P,V_Ea,c_Pair(v_ha____,v_la____,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))) ) ).
cnf(cls_list__all2__def_0,axiom,
( c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)) = c_Nat_Osize__class_Osize(V_ys,tc_List_Olist(T_b))
| ~ c_List_Olist__all2(V_P,V_xs,V_ys,T_a,T_b) ) ).
cnf(cls_calculation_I5_J_0,axiom,
c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,c_Expr_Oexp_OVal(v_v____,tc_List_Olist(tc_String_Ochar)),c_Type_Oty_OClass(v_C____)) ).
cnf(cls_widens__Cons_0,axiom,
( V_ys = c_List_Olist_OCons(c_TypeRel_Osko__TypeRel__Xwidens__Cons__1__1(V_P,V_x,V_xs,V_ys,T_a),c_TypeRel_Osko__TypeRel__Xwidens__Cons__1__2(V_P,V_x,V_xs,V_ys,T_a),tc_Type_Oty)
| ~ c_List_Olist__all2(c_TypeRel_Owiden(V_P,T_a),c_List_Olist_OCons(V_x,V_xs,tc_Type_Oty),V_ys,tc_Type_Oty,tc_Type_Oty) ) ).
cnf(cls_list__all2__Cons2_3,axiom,
( c_List_Olist__all2(V_P,c_List_Olist_OCons(V_x,V_xa,T_a),c_List_Olist_OCons(V_y,V_ys,T_b),T_a,T_b)
| ~ c_List_Olist__all2(V_P,V_xa,V_ys,T_a,T_b)
| ~ hBOOL(hAPP(hAPP(V_P,V_x),V_y)) ) ).
cnf(cls_list__all2__Cons1_3,axiom,
( c_List_Olist__all2(V_P,c_List_Olist_OCons(V_x,V_xs,T_a),c_List_Olist_OCons(V_xa,V_xb,T_b),T_a,T_b)
| ~ c_List_Olist__all2(V_P,V_xs,V_xb,T_a,T_b)
| ~ hBOOL(hAPP(hAPP(V_P,V_x),V_xa)) ) ).
cnf(cls_list__all2__Cons_2,axiom,
( c_List_Olist__all2(V_P,c_List_Olist_OCons(V_x,V_xs,T_a),c_List_Olist_OCons(V_y,V_ys,T_b),T_a,T_b)
| ~ c_List_Olist__all2(V_P,V_xs,V_ys,T_a,T_b)
| ~ hBOOL(hAPP(hAPP(V_P,V_x),V_y)) ) ).
cnf(cls_calculation_I4_J_0,axiom,
c_List_Olist__all2(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),v_Us____,v_Ts____,tc_Type_Oty,tc_Type_Oty) ).
cnf(cls_IH_0,axiom,
( c_WellTypeRT_OWTrts(v_P,v_h_Ha____,V_Ea,v_es_Ha____,v_sko__local__XIH__1(V_Ea,v_P,V_Ts,v_es_Ha____,v_h_Ha____))
| ~ c_WellTypeRT_OWTrts(v_P,v_ha____,V_Ea,v_esa____,V_Ts)
| ~ c_TypeSafe__Mirabelle_Osconf(v_P,V_Ea,c_Pair(v_ha____,v_la____,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))) ) ).
cnf(cls_list__all2__rev_1,axiom,
( c_List_Olist__all2(V_P,c_List_Orev(V_xs,T_a),c_List_Orev(V_ys,T_b),T_a,T_b)
| ~ c_List_Olist__all2(V_P,V_xs,V_ys,T_a,T_b) ) ).
cnf(cls_list__all2__rev_0,axiom,
( c_List_Olist__all2(V_P,V_xs,V_ys,T_a,T_b)
| ~ c_List_Olist__all2(V_P,c_List_Orev(V_xs,T_a),c_List_Orev(V_ys,T_b),T_a,T_b) ) ).
cnf(cls_CallParams_Ohyps_I2_J_0,axiom,
( c_WellTypeRT_OWTrts(v_P,v_h_Ha____,V_E,v_es_Ha____,v_sko__local__XCallParams__Xhyps__2__1(V_E,v_P,V_Ts,v_es_Ha____,v_h_Ha____))
| ~ c_WellTypeRT_OWTrts(v_P,v_ha____,V_E,v_esa____,V_Ts)
| ~ c_TypeSafe__Mirabelle_Osconf(v_P,V_E,c_Pair(v_ha____,v_la____,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))) ) ).
cnf(cls_list__all2__Cons_1,axiom,
( c_List_Olist__all2(V_P,V_xs,V_ys,T_a,T_b)
| ~ c_List_Olist__all2(V_P,c_List_Olist_OCons(V_x,V_xs,T_a),c_List_Olist_OCons(V_y,V_ys,T_b),T_a,T_b) ) ).
cnf(cls_CallParams_Ohyps_I2_J_1,axiom,
( c_List_Olist__all2(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),v_sko__local__XCallParams__Xhyps__2__1(V_E,v_P,V_Ts,v_es_Ha____,v_h_Ha____),V_Ts,tc_Type_Oty,tc_Type_Oty)
| ~ c_WellTypeRT_OWTrts(v_P,v_ha____,V_E,v_esa____,V_Ts)
| ~ c_TypeSafe__Mirabelle_Osconf(v_P,V_E,c_Pair(v_ha____,v_la____,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))) ) ).
cnf(cls_list__all2__takeI_0,axiom,
( c_List_Olist__all2(V_P,c_List_Otake(V_n,V_xs,T_a),c_List_Otake(V_n,V_ys,T_b),T_a,T_b)
| ~ c_List_Olist__all2(V_P,V_xs,V_ys,T_a,T_b) ) ).
cnf(cls_list__all2__eq_1,axiom,
( V_xs = V_ys
| ~ c_List_Olist__all2(c_fequal(T_a),V_xs,V_ys,T_a,T_a) ) ).
cnf(cls_widen__refl_0,axiom,
hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,T_a),V_T),V_T)) ).
cnf(cls_widen__trans_0,axiom,
( hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,T_a),V_S),V_T))
| ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,T_a),V_U),V_T))
| ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,T_a),V_S),V_U)) ) ).
cnf(cls_conf__widen_0,axiom,
( hBOOL(hAPP(hAPP(c_Conform_Oconf(V_P,V_h,T_a),V_v),V_T_H))
| ~ hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,T_a),V_T),V_T_H))
| ~ hBOOL(hAPP(hAPP(c_Conform_Oconf(V_P,V_h,T_a),V_v),V_T)) ) ).
cnf(cls_wts__wts_H_0,axiom,
( c_Progress_OWTrts_H(V_P,V_h,V_E,V_es,V_Ts)
| ~ c_WellTypeRT_OWTrts(V_P,V_h,V_E,V_es,V_Ts) ) ).
cnf(cls_wts_H__wts_0,axiom,
( c_WellTypeRT_OWTrts(V_P,V_h,V_E,V_es,V_Ts)
| ~ c_Progress_OWTrts_H(V_P,V_h,V_E,V_es,V_Ts) ) ).
cnf(cls_WTs__implies__WTrts_0,axiom,
( c_WellTypeRT_OWTrts(V_P,V_h,V_E,V_es,V_Ts)
| ~ c_WellType_OWTs(V_P,V_E,V_es,V_Ts) ) ).
cnf(cls_list__all2__appendI_0,axiom,
( c_List_Olist__all2(V_P,c_List_Oappend(V_a,V_c,T_a),c_List_Oappend(V_b,V_d,T_b),T_a,T_b)
| ~ c_List_Olist__all2(V_P,V_c,V_d,T_a,T_b)
| ~ c_List_Olist__all2(V_P,V_a,V_b,T_a,T_b) ) ).
cnf(cls_WTrts__hext__mono_0,axiom,
( c_WellTypeRT_OWTrts(V_P,V_h_H,V_E,V_es,V_Ts)
| ~ c_Objects_Ohext(V_h,V_h_H)
| ~ c_WellTypeRT_OWTrts(V_P,V_h,V_E,V_es,V_Ts) ) ).
cnf(cls_list__all2__Cons_0,axiom,
( hBOOL(hAPP(hAPP(V_P,V_x),V_y))
| ~ c_List_Olist__all2(V_P,c_List_Olist_OCons(V_x,V_xs,T_a),c_List_Olist_OCons(V_y,V_ys,T_b),T_a,T_b) ) ).
cnf(cls_widens__Cons_1,axiom,
( hBOOL(hAPP(hAPP(c_TypeRel_Owiden(V_P,T_a),V_x),c_TypeRel_Osko__TypeRel__Xwidens__Cons__1__1(V_P,V_x,V_xs,V_ys,T_a)))
| ~ c_List_Olist__all2(c_TypeRel_Owiden(V_P,T_a),c_List_Olist_OCons(V_x,V_xs,tc_Type_Oty),V_ys,tc_Type_Oty,tc_Type_Oty) ) ).
cnf(cls_COMBI__def__raw_0,axiom,
c_COMBI(v_P,t_a) = v_P ).
cnf(cls_widens__Cons_2,axiom,
( c_List_Olist__all2(c_TypeRel_Owiden(V_P,T_a),V_xs,c_TypeRel_Osko__TypeRel__Xwidens__Cons__1__2(V_P,V_x,V_xs,V_ys,T_a),tc_Type_Oty,tc_Type_Oty)
| ~ c_List_Olist__all2(c_TypeRel_Owiden(V_P,T_a),c_List_Olist_OCons(V_x,V_xs,tc_Type_Oty),V_ys,tc_Type_Oty,tc_Type_Oty) ) ).
cnf(cls_widens__trans_0,axiom,
( c_List_Olist__all2(c_TypeRel_Owiden(V_P,T_a),V_Ss,V_Us,tc_Type_Oty,tc_Type_Oty)
| ~ c_List_Olist__all2(c_TypeRel_Owiden(V_P,T_a),V_Ts,V_Us,tc_Type_Oty,tc_Type_Oty)
| ~ c_List_Olist__all2(c_TypeRel_Owiden(V_P,T_a),V_Ss,V_Ts,tc_Type_Oty,tc_Type_Oty) ) ).
cnf(cls_confs__widens_0,axiom,
( c_List_Olist__all2(c_Conform_Oconf(V_P,V_h,T_a),V_vs,V_Ts_H,tc_Value_Oval,tc_Type_Oty)
| ~ c_List_Olist__all2(c_TypeRel_Owiden(V_P,T_a),V_Ts,V_Ts_H,tc_Type_Oty,tc_Type_Oty)
| ~ c_List_Olist__all2(c_Conform_Oconf(V_P,V_h,T_a),V_vs,V_Ts,tc_Value_Oval,tc_Type_Oty) ) ).
cnf(cls_widens__refl_0,axiom,
c_List_Olist__all2(c_TypeRel_Owiden(V_P,T_a),V_xs,V_xs,tc_Type_Oty,tc_Type_Oty) ).
cnf(cls_CallParams_I2_J_1,axiom,
( c_List_Olist__all2(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),v_sko__local__XCallParams__2__1(V_E,v_P,V_Ts,v_es_Ha____,v_h_Ha____),V_Ts,tc_Type_Oty,tc_Type_Oty)
| ~ c_WellTypeRT_OWTrts(v_P,v_ha____,V_E,v_esa____,V_Ts)
| ~ c_TypeSafe__Mirabelle_Osconf(v_P,V_E,c_Pair(v_ha____,v_la____,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))) ) ).
cnf(cls_wtes_0,axiom,
c_WellTypeRT_OWTrts(v_P,v_ha____,v_E____,v_esa____,v_Us____) ).
cnf(cls_list__all2__rev1_1,axiom,
( c_List_Olist__all2(V_P,c_List_Orev(V_xs,T_a),V_ys,T_a,T_b)
| ~ c_List_Olist__all2(V_P,V_xs,c_List_Orev(V_ys,T_b),T_a,T_b) ) ).
cnf(cls_list__all2__rev1_0,axiom,
( c_List_Olist__all2(V_P,V_xs,c_List_Orev(V_ys,T_b),T_a,T_b)
| ~ c_List_Olist__all2(V_P,c_List_Orev(V_xs,T_a),V_ys,T_a,T_b) ) ).
cnf(cls_CHAINED_1,axiom,
c_List_Olist__all2(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),v_sko__CHAINED__1(v_E____,v_P,v_Us____,v_es_Ha____,v_h_Ha____),v_Us____,tc_Type_Oty,tc_Type_Oty) ).
cnf(cls_CHAINED_0,axiom,
c_WellTypeRT_OWTrts(v_P,v_h_Ha____,v_E____,v_es_Ha____,v_sko__CHAINED__1(v_E____,v_P,v_Us____,v_es_Ha____,v_h_Ha____)) ).
cnf(cls_conjecture_0,negated_conjecture,
~ v_thesis____ ).
cnf(cls_conjecture_1,negated_conjecture,
( v_thesis____
| ~ c_List_Olist__all2(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),V_x,v_Us____,tc_Type_Oty,tc_Type_Oty)
| ~ c_WellTypeRT_OWTrts(v_P,v_h_Ha____,v_E____,v_es_Ha____,V_x) ) ).
cnf(clsarity_fun__Orderings_Opreorder,axiom,
( class_Orderings_Opreorder(tc_fun(T_2,T_1))
| ~ class_Orderings_Opreorder(T_1) ) ).
cnf(clsarity_fun__Orderings_Oorder,axiom,
( class_Orderings_Oorder(tc_fun(T_2,T_1))
| ~ class_Orderings_Oorder(T_1) ) ).
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__1,axiom,
class_Ring__and__Field_Osemiring__1(tc_nat) ).
cnf(clsarity_nat__Ring__and__Field_Osemiring__0,axiom,
class_Ring__and__Field_Osemiring__0(tc_nat) ).
cnf(clsarity_nat__Ring__and__Field_Omult__zero,axiom,
class_Ring__and__Field_Omult__zero(tc_nat) ).
cnf(clsarity_nat__OrderedGroup_Omonoid__mult,axiom,
class_OrderedGroup_Omonoid__mult(tc_nat) ).
cnf(clsarity_nat__OrderedGroup_Omonoid__add,axiom,
class_OrderedGroup_Omonoid__add(tc_nat) ).
cnf(clsarity_nat__Nat_Osemiring__char__0,axiom,
class_Nat_Osemiring__char__0(tc_nat) ).
cnf(clsarity_nat__Orderings_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_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_Osemiring__1,axiom,
class_Ring__and__Field_Osemiring__1(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__Ring__and__Field_Oring__1,axiom,
class_Ring__and__Field_Oring__1(tc_Int_Oint) ).
cnf(clsarity_Int__Oint__Ring__and__Field_Oidom,axiom,
class_Ring__and__Field_Oidom(tc_Int_Oint) ).
cnf(clsarity_Int__Oint__Nat_Osemiring__char__0,axiom,
class_Nat_Osemiring__char__0(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__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(cls_ATP__Linkup_Oequal__imp__fequal_0,axiom,
hBOOL(hAPP(hAPP(c_fequal(T_a),V_x),V_x)) ).
cnf(cls_ATP__Linkup_Ofequal__imp__equal_0,axiom,
( V_X = V_Y
| ~ hBOOL(hAPP(hAPP(c_fequal(T_a),V_X),V_Y)) ) ).
%------------------------------------------------------------------------------