%------------------------------------------------------------------------------
% File     : iProverMo---2.5-0.1
% Problem  : LCL778-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : iprover_modulo %s %d

% Computer : n004.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 600s
% DateTime : Sun Jul 17 11:39:32 EDT 2022

% Result   : Unsatisfiable 0.42s 0.60s
% Output   : CNFRefutation 0.46s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named input)

% Comments : 
%------------------------------------------------------------------------------
% Axioms transformation by autotheo
% Orienting (remaining) axiom formulas using strategy Equiv(ClausalAll)
% Orienting axioms whose shape is orientable
cnf(cls_ATP__Linkup_Oequal__imp__fequal_0,axiom,
    hBOOL(hAPP(hAPP(c_fequal(T_a),V_x),V_x)),
    input ).

fof(cls_ATP__Linkup_Oequal__imp__fequal_0_0,plain,
    ! [T_a,V_x] :
      ( hBOOL(hAPP(hAPP(c_fequal(T_a),V_x),V_x))
      | $false ),
    inference(orientation,[status(thm)],[cls_ATP__Linkup_Oequal__imp__fequal_0]) ).

cnf(clsarity_bool__Orderings_Oorder,axiom,
    class_Orderings_Oorder(tc_bool),
    input ).

fof(clsarity_bool__Orderings_Oorder_0,plain,
    ( class_Orderings_Oorder(tc_bool)
    | $false ),
    inference(orientation,[status(thm)],[clsarity_bool__Orderings_Oorder]) ).

cnf(clsarity_bool__Orderings_Opreorder,axiom,
    class_Orderings_Opreorder(tc_bool),
    input ).

fof(clsarity_bool__Orderings_Opreorder_0,plain,
    ( class_Orderings_Opreorder(tc_bool)
    | $false ),
    inference(orientation,[status(thm)],[clsarity_bool__Orderings_Opreorder]) ).

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

fof(clsarity_nat__Power_Opower_0,plain,
    ( class_Power_Opower(tc_nat)
    | $false ),
    inference(orientation,[status(thm)],[clsarity_nat__Power_Opower]) ).

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

fof(clsarity_nat__Orderings_Oorder_0,plain,
    ( class_Orderings_Oorder(tc_nat)
    | $false ),
    inference(orientation,[status(thm)],[clsarity_nat__Orderings_Oorder]) ).

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

fof(clsarity_nat__Orderings_Olinorder_0,plain,
    ( class_Orderings_Olinorder(tc_nat)
    | $false ),
    inference(orientation,[status(thm)],[clsarity_nat__Orderings_Olinorder]) ).

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

fof(clsarity_nat__Orderings_Opreorder_0,plain,
    ( class_Orderings_Opreorder(tc_nat)
    | $false ),
    inference(orientation,[status(thm)],[clsarity_nat__Orderings_Opreorder]) ).

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

fof(clsarity_nat__Nat_Osemiring__char__0_0,plain,
    ( class_Nat_Osemiring__char__0(tc_nat)
    | $false ),
    inference(orientation,[status(thm)],[clsarity_nat__Nat_Osemiring__char__0]) ).

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

fof(clsarity_nat__OrderedGroup_Omonoid__add_0,plain,
    ( class_OrderedGroup_Omonoid__add(tc_nat)
    | $false ),
    inference(orientation,[status(thm)],[clsarity_nat__OrderedGroup_Omonoid__add]) ).

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

fof(clsarity_nat__OrderedGroup_Omonoid__mult_0,plain,
    ( class_OrderedGroup_Omonoid__mult(tc_nat)
    | $false ),
    inference(orientation,[status(thm)],[clsarity_nat__OrderedGroup_Omonoid__mult]) ).

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

fof(clsarity_nat__Ring__and__Field_Omult__zero_0,plain,
    ( class_Ring__and__Field_Omult__zero(tc_nat)
    | $false ),
    inference(orientation,[status(thm)],[clsarity_nat__Ring__and__Field_Omult__zero]) ).

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

fof(clsarity_nat__Ring__and__Field_Osemiring__0_0,plain,
    ( class_Ring__and__Field_Osemiring__0(tc_nat)
    | $false ),
    inference(orientation,[status(thm)],[clsarity_nat__Ring__and__Field_Osemiring__0]) ).

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

fof(clsarity_nat__Ring__and__Field_Osemiring__1_0,plain,
    ( class_Ring__and__Field_Osemiring__1(tc_nat)
    | $false ),
    inference(orientation,[status(thm)],[clsarity_nat__Ring__and__Field_Osemiring__1]) ).

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

fof(clsarity_nat__OrderedGroup_Osemigroup__add_0,plain,
    ( class_OrderedGroup_Osemigroup__add(tc_nat)
    | $false ),
    inference(orientation,[status(thm)],[clsarity_nat__OrderedGroup_Osemigroup__add]) ).

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

fof(clsarity_nat__Ring__and__Field_Ozero__neq__one_0,plain,
    ( class_Ring__and__Field_Ozero__neq__one(tc_nat)
    | $false ),
    inference(orientation,[status(thm)],[clsarity_nat__Ring__and__Field_Ozero__neq__one]) ).

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

fof(clsarity_nat__OrderedGroup_Ocomm__monoid__add_0,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(tc_nat)
    | $false ),
    inference(orientation,[status(thm)],[clsarity_nat__OrderedGroup_Ocomm__monoid__add]) ).

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

fof(clsarity_nat__OrderedGroup_Oab__semigroup__add_0,plain,
    ( class_OrderedGroup_Oab__semigroup__add(tc_nat)
    | $false ),
    inference(orientation,[status(thm)],[clsarity_nat__OrderedGroup_Oab__semigroup__add]) ).

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

fof(clsarity_nat__Ring__and__Field_Ocomm__semiring__1_0,plain,
    ( class_Ring__and__Field_Ocomm__semiring__1(tc_nat)
    | $false ),
    inference(orientation,[status(thm)],[clsarity_nat__Ring__and__Field_Ocomm__semiring__1]) ).

cnf(clsarity_nat__Ring__and__Field_Oordered__semidom,axiom,
    class_Ring__and__Field_Oordered__semidom(tc_nat),
    input ).

fof(clsarity_nat__Ring__and__Field_Oordered__semidom_0,plain,
    ( class_Ring__and__Field_Oordered__semidom(tc_nat)
    | $false ),
    inference(orientation,[status(thm)],[clsarity_nat__Ring__and__Field_Oordered__semidom]) ).

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

fof(clsarity_nat__Ring__and__Field_Ono__zero__divisors_0,plain,
    ( class_Ring__and__Field_Ono__zero__divisors(tc_nat)
    | $false ),
    inference(orientation,[status(thm)],[clsarity_nat__Ring__and__Field_Ono__zero__divisors]) ).

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

fof(clsarity_nat__OrderedGroup_Ocancel__semigroup__add_0,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(tc_nat)
    | $false ),
    inference(orientation,[status(thm)],[clsarity_nat__OrderedGroup_Ocancel__semigroup__add]) ).

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

fof(clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add_0,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat)
    | $false ),
    inference(orientation,[status(thm)],[clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add]) ).

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

fof(clsarity_nat__OrderedGroup_Opordered__comm__monoid__add_0,plain,
    ( class_OrderedGroup_Opordered__comm__monoid__add(tc_nat)
    | $false ),
    inference(orientation,[status(thm)],[clsarity_nat__OrderedGroup_Opordered__comm__monoid__add]) ).

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

fof(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add_0,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat)
    | $false ),
    inference(orientation,[status(thm)],[clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add]) ).

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

fof(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le_0,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat)
    | $false ),
    inference(orientation,[status(thm)],[clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le]) ).

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

fof(clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add_0,plain,
    ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat)
    | $false ),
    inference(orientation,[status(thm)],[clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add]) ).

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

fof(cls_dB_Osimps_I5_J_0_0,plain,
    ! [V_dB1_H,V_dB2_H,V_nat] :
      ( hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1_H),V_dB2_H) != c_Lambda_OdB_OVar(V_nat)
      | $false ),
    inference(orientation,[status(thm)],[cls_dB_Osimps_I5_J_0]) ).

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

fof(cls_Var__IT_0_0,plain,
    ! [V_n] :
      ( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(V_n)))
      | $false ),
    inference(orientation,[status(thm)],[cls_Var__IT_0]) ).

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

fof(cls_dB_Osimps_I4_J_0_0,plain,
    ! [V_dB1_H,V_dB2_H,V_nat] :
      ( c_Lambda_OdB_OVar(V_nat) != hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1_H),V_dB2_H)
      | $false ),
    inference(orientation,[status(thm)],[cls_dB_Osimps_I4_J_0]) ).

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

fof(cls_subst__eq_0_0,plain,
    ! [V_k,V_u] :
      ( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(V_k)),V_u),V_k) = V_u
      | $false ),
    inference(orientation,[status(thm)],[cls_subst__eq_0]) ).

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

fof(cls_subst__App_0_0,plain,
    ! [V_k,V_s,V_t,V_u] :
      ( hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_OdB_OApp,V_t),V_u)),V_s),V_k) = hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_s),V_k)),hAPP(hAPP(hAPP(c_Lambda_Osubst,V_u),V_s),V_k))
      | $false ),
    inference(orientation,[status(thm)],[cls_subst__App_0]) ).

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

fof(cls_Abs__App__neq__Var__apps_0_0,plain,
    ! [V_n,V_s,V_ss,V_t] :
      ( hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_s)),V_t) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),V_ss,tc_Lambda_OdB,tc_Lambda_OdB)
      | $false ),
    inference(orientation,[status(thm)],[cls_Abs__App__neq__Var__apps_0]) ).

cnf(cls_Var__eq__apps__conv_2,axiom,
    c_Lambda_OdB_OVar(V_m) = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_m),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
    input ).

fof(cls_Var__eq__apps__conv_2_0,plain,
    ! [V_m] :
      ( c_Lambda_OdB_OVar(V_m) = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_m),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)
      | $false ),
    inference(orientation,[status(thm)],[cls_Var__eq__apps__conv_2]) ).

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

fof(cls_Var__apps__neq__Abs__apps_0_0,plain,
    ! [V_n,V_r,V_ss,V_ts] :
      ( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),V_ts,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_r),V_ss,tc_Lambda_OdB,tc_Lambda_OdB)
      | $false ),
    inference(orientation,[status(thm)],[cls_Var__apps__neq__Abs__apps_0]) ).

cnf(cls_App__eq__foldl__conv_4,axiom,
    hAPP(hAPP(c_Lambda_OdB_OApp,V_r),V_s) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,V_r),V_s),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
    input ).

fof(cls_App__eq__foldl__conv_4_0,plain,
    ! [V_r,V_s] :
      ( hAPP(hAPP(c_Lambda_OdB_OApp,V_r),V_s) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,V_r),V_s),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)
      | $false ),
    inference(orientation,[status(thm)],[cls_App__eq__foldl__conv_4]) ).

cnf(cls_dB_Osize_I1_J_0,axiom,
    c_Lambda_OdB_OdB__size(c_Lambda_OdB_OVar(V_nat)) = c_HOL_Ozero__class_Ozero(tc_nat),
    input ).

fof(cls_dB_Osize_I1_J_0_0,plain,
    ! [V_nat] :
      ( c_Lambda_OdB_OdB__size(c_Lambda_OdB_OVar(V_nat)) = c_HOL_Ozero__class_Ozero(tc_nat)
      | $false ),
    inference(orientation,[status(thm)],[cls_dB_Osize_I1_J_0]) ).

cnf(cls_dB_Osize_I4_J_0,axiom,
    c_Nat_Osize__class_Osize(c_Lambda_OdB_OVar(V_nat),tc_Lambda_OdB) = c_HOL_Ozero__class_Ozero(tc_nat),
    input ).

fof(cls_dB_Osize_I4_J_0_0,plain,
    ! [V_nat] :
      ( c_Nat_Osize__class_Osize(c_Lambda_OdB_OVar(V_nat),tc_Lambda_OdB) = c_HOL_Ozero__class_Ozero(tc_nat)
      | $false ),
    inference(orientation,[status(thm)],[cls_dB_Osize_I4_J_0]) ).

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

fof(cls_substn__subst__0_0_0,plain,
    ! [V_s,V_t] :
      ( c_Lambda_Osubstn(V_t,V_s,c_HOL_Ozero__class_Ozero(tc_nat)) = hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_s),c_HOL_Ozero__class_Ozero(tc_nat))
      | $false ),
    inference(orientation,[status(thm)],[cls_substn__subst__0_0]) ).

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

fof(cls_beta_0_0,plain,
    ! [V_s,V_t] :
      ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_s)),V_t)),hAPP(hAPP(hAPP(c_Lambda_Osubst,V_s),V_t),c_HOL_Ozero__class_Ozero(tc_nat))))
      | $false ),
    inference(orientation,[status(thm)],[cls_beta_0]) ).

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

fof(cls_typing_OVar_0_0,plain,
    ! [V_env,V_x] :
      ( c_Type_Otyping(V_env,c_Lambda_OdB_OVar(V_x),hAPP(V_env,V_x))
      | $false ),
    inference(orientation,[status(thm)],[cls_typing_OVar_0]) ).

cnf(cls_dB_Osimps_I10_J_0,axiom,
    c_Lambda_OdB_OdB__case(V_f1,V_f2,V_f3,c_Lambda_OdB_OVar(V_nat),T_a) = hAPP(V_f1,V_nat),
    input ).

fof(cls_dB_Osimps_I10_J_0_0,plain,
    ! [T_a,V_f1,V_f2,V_f3,V_nat] :
      ( c_Lambda_OdB_OdB__case(V_f1,V_f2,V_f3,c_Lambda_OdB_OVar(V_nat),T_a) = hAPP(V_f1,V_nat)
      | $false ),
    inference(orientation,[status(thm)],[cls_dB_Osimps_I10_J_0]) ).

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

fof(cls_dB_Osimps_I6_J_0_0,plain,
    ! [V_dB_H,V_nat] :
      ( c_Lambda_OdB_OVar(V_nat) != c_Lambda_OdB_OAbs(V_dB_H)
      | $false ),
    inference(orientation,[status(thm)],[cls_dB_Osimps_I6_J_0]) ).

cnf(cls_dB_Orecs_I1_J_0,axiom,
    c_Lambda_OdB_OdB__rec(V_f1,V_f2,V_f3,c_Lambda_OdB_OVar(V_nat),T_a) = hAPP(V_f1,V_nat),
    input ).

fof(cls_dB_Orecs_I1_J_0_0,plain,
    ! [T_a,V_f1,V_f2,V_f3,V_nat] :
      ( c_Lambda_OdB_OdB__rec(V_f1,V_f2,V_f3,c_Lambda_OdB_OVar(V_nat),T_a) = hAPP(V_f1,V_nat)
      | $false ),
    inference(orientation,[status(thm)],[cls_dB_Orecs_I1_J_0]) ).

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

fof(cls_beta__cases_I1_J_0_0,plain,
    ! [V_i,V_t] :
      ( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OVar(V_i)),V_t))
      | $false ),
    inference(orientation,[status(thm)],[cls_beta__cases_I1_J_0]) ).

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

fof(cls_dB_Osimps_I7_J_0_0,plain,
    ! [V_dB_H,V_nat] :
      ( c_Lambda_OdB_OAbs(V_dB_H) != c_Lambda_OdB_OVar(V_nat)
      | $false ),
    inference(orientation,[status(thm)],[cls_dB_Osimps_I7_J_0]) ).

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

fof(cls_subst__lift_0_0,plain,
    ! [V_k,V_s,V_t] :
      ( hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,V_t),V_k)),V_s),V_k) = V_t
      | $false ),
    inference(orientation,[status(thm)],[cls_subst__lift_0]) ).

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

fof(cls_subst__map_0_0,plain,
    ! [V_i,V_t,V_ts,V_u] :
      ( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB)),V_u),V_i) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_u),V_i),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,V_u,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),V_i,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)
      | $false ),
    inference(orientation,[status(thm)],[cls_subst__map_0]) ).

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

fof(cls_foldl__append_0_0,plain,
    ! [T_a,T_b,V_a,V_f,V_xs,V_ys] :
      ( c_List_Ofoldl(V_f,V_a,c_List_Oappend(V_xs,V_ys,T_b),T_a,T_b) = c_List_Ofoldl(V_f,c_List_Ofoldl(V_f,V_a,V_xs,T_a,T_b),V_ys,T_a,T_b)
      | $false ),
    inference(orientation,[status(thm)],[cls_foldl__append_0]) ).

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

fof(cls_foldl__Cons_0_0,plain,
    ! [T_a,T_b,V_a,V_f,V_x,V_xs] :
      ( c_List_Ofoldl(V_f,V_a,c_List_Olist_OCons(V_x,V_xs,T_b),T_a,T_b) = c_List_Ofoldl(V_f,hAPP(hAPP(V_f,V_a),V_x),V_xs,T_a,T_b)
      | $false ),
    inference(orientation,[status(thm)],[cls_foldl__Cons_0]) ).

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

fof(cls_foldl__Nil_0_0,plain,
    ! [T_a,T_b,V_a,V_f] :
      ( c_List_Ofoldl(V_f,V_a,c_List_Olist_ONil(T_b),T_a,T_b) = V_a
      | $false ),
    inference(orientation,[status(thm)],[cls_foldl__Nil_0]) ).

cnf(cls_apps__eq__Abs__conv_2,axiom,
    c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_r),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) = c_Lambda_OdB_OAbs(V_r),
    input ).

fof(cls_apps__eq__Abs__conv_2_0,plain,
    ! [V_r] :
      ( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_r),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) = c_Lambda_OdB_OAbs(V_r)
      | $false ),
    inference(orientation,[status(thm)],[cls_apps__eq__Abs__conv_2]) ).

cnf(cls_ex__head__tail_0,axiom,
    V_t = c_List_Ofoldl(c_Lambda_OdB_OApp,c_ListApplication_Osko__ListApplication__Xex__head__tail__1__2(V_t),c_ListApplication_Osko__ListApplication__Xex__head__tail__1__1(V_t),tc_Lambda_OdB,tc_Lambda_OdB),
    input ).

fof(cls_ex__head__tail_0_0,plain,
    ! [V_t] :
      ( V_t = c_List_Ofoldl(c_Lambda_OdB_OApp,c_ListApplication_Osko__ListApplication__Xex__head__tail__1__2(V_t),c_ListApplication_Osko__ListApplication__Xex__head__tail__1__1(V_t),tc_Lambda_OdB,tc_Lambda_OdB)
      | $false ),
    inference(orientation,[status(thm)],[cls_ex__head__tail_0]) ).

cnf(cls_Abs__eq__apps__conv_2,axiom,
    c_Lambda_OdB_OAbs(V_r) = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_r),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
    input ).

fof(cls_Abs__eq__apps__conv_2_0,plain,
    ! [V_r] :
      ( c_Lambda_OdB_OAbs(V_r) = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_r),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)
      | $false ),
    inference(orientation,[status(thm)],[cls_Abs__eq__apps__conv_2]) ).

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

fof(cls_substn__subst__n_0_0,plain,
    ! [V_n,V_s,V_t] :
      ( c_Lambda_Osubstn(V_t,V_s,V_n) = hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),c_Lambda_Oliftn(V_n,V_s,c_HOL_Ozero__class_Ozero(tc_nat))),V_n)
      | $false ),
    inference(orientation,[status(thm)],[cls_substn__subst__n_0]) ).

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

fof(cls_substn_Osimps_I2_J_0_0,plain,
    ! [V_k,V_s,V_t,V_u] :
      ( c_Lambda_Osubstn(hAPP(hAPP(c_Lambda_OdB_OApp,V_t),V_u),V_s,V_k) = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Osubstn(V_t,V_s,V_k)),c_Lambda_Osubstn(V_u,V_s,V_k))
      | $false ),
    inference(orientation,[status(thm)],[cls_substn_Osimps_I2_J_0]) ).

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

fof(cls_liftn_Osimps_I2_J_0_0,plain,
    ! [V_k,V_n,V_s,V_t] :
      ( c_Lambda_Oliftn(V_n,hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_t),V_k) = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Oliftn(V_n,V_s,V_k)),c_Lambda_Oliftn(V_n,V_t,V_k))
      | $false ),
    inference(orientation,[status(thm)],[cls_liftn_Osimps_I2_J_0]) ).

cnf(cls_dB_Orecs_I2_J_0,axiom,
    c_Lambda_OdB_OdB__rec(V_f1,V_f2,V_f3,hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2),T_a) = hAPP(hAPP(hAPP(hAPP(V_f2,V_dB1),V_dB2),c_Lambda_OdB_OdB__rec(V_f1,V_f2,V_f3,V_dB1,T_a)),c_Lambda_OdB_OdB__rec(V_f1,V_f2,V_f3,V_dB2,T_a)),
    input ).

fof(cls_dB_Orecs_I2_J_0_0,plain,
    ! [T_a,V_dB1,V_dB2,V_f1,V_f2,V_f3] :
      ( c_Lambda_OdB_OdB__rec(V_f1,V_f2,V_f3,hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2),T_a) = hAPP(hAPP(hAPP(hAPP(V_f2,V_dB1),V_dB2),c_Lambda_OdB_OdB__rec(V_f1,V_f2,V_f3,V_dB1,T_a)),c_Lambda_OdB_OdB__rec(V_f1,V_f2,V_f3,V_dB2,T_a))
      | $false ),
    inference(orientation,[status(thm)],[cls_dB_Orecs_I2_J_0]) ).

cnf(cls_dB_Osimps_I11_J_0,axiom,
    c_Lambda_OdB_OdB__case(V_f1,V_f2,V_f3,hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2),T_a) = hAPP(hAPP(V_f2,V_dB1),V_dB2),
    input ).

fof(cls_dB_Osimps_I11_J_0_0,plain,
    ! [T_a,V_dB1,V_dB2,V_f1,V_f2,V_f3] :
      ( c_Lambda_OdB_OdB__case(V_f1,V_f2,V_f3,hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2),T_a) = hAPP(hAPP(V_f2,V_dB1),V_dB2)
      | $false ),
    inference(orientation,[status(thm)],[cls_dB_Osimps_I11_J_0]) ).

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

fof(cls_lift_Osimps_I2_J_0_0,plain,
    ! [V_k,V_s,V_t] :
      ( hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_t)),V_k) = hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_Olift,V_s),V_k)),hAPP(hAPP(c_Lambda_Olift,V_t),V_k))
      | $false ),
    inference(orientation,[status(thm)],[cls_lift_Osimps_I2_J_0]) ).

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

fof(cls_dB_Osimps_I9_J_0_0,plain,
    ! [V_dB1,V_dB2,V_dB_H] :
      ( c_Lambda_OdB_OAbs(V_dB_H) != hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2)
      | $false ),
    inference(orientation,[status(thm)],[cls_dB_Osimps_I9_J_0]) ).

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

fof(cls_dB_Osimps_I8_J_0_0,plain,
    ! [V_dB1,V_dB2,V_dB_H] :
      ( hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2) != c_Lambda_OdB_OAbs(V_dB_H)
      | $false ),
    inference(orientation,[status(thm)],[cls_dB_Osimps_I8_J_0]) ).

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

fof(cls_Nat_Oadd__0__right_0_0,plain,
    ! [V_m] :
      ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),c_HOL_Ozero__class_Ozero(tc_nat)) = V_m
      | $false ),
    inference(orientation,[status(thm)],[cls_Nat_Oadd__0__right_0]) ).

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

fof(cls_plus__nat_Oadd__0_0_0,plain,
    ! [V_n] :
      ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),V_n) = V_n
      | $false ),
    inference(orientation,[status(thm)],[cls_plus__nat_Oadd__0_0]) ).

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

fof(cls_natgb_Oadd__r0__iff_1_0,plain,
    ! [V_x] :
      ( V_x = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_x),c_HOL_Ozero__class_Ozero(tc_nat))
      | $false ),
    inference(orientation,[status(thm)],[cls_natgb_Oadd__r0__iff_1]) ).

cnf(cls_max__0L_0,axiom,
    c_Orderings_Oord__class_Omax(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) = V_n,
    input ).

fof(cls_max__0L_0_0,plain,
    ! [V_n] :
      ( c_Orderings_Oord__class_Omax(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) = V_n
      | $false ),
    inference(orientation,[status(thm)],[cls_max__0L_0]) ).

cnf(cls_max__0R_0,axiom,
    c_Orderings_Oord__class_Omax(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = V_n,
    input ).

fof(cls_max__0R_0_0,plain,
    ! [V_n] :
      ( c_Orderings_Oord__class_Omax(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = V_n
      | $false ),
    inference(orientation,[status(thm)],[cls_max__0R_0]) ).

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),
    input ).

fof(cls_replicate__eq__replicate_2_0,plain,
    ! [T_a,V_x,V_y] :
      ( 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)
      | 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) ),
    inference(orientation,[status(thm)],[cls_replicate__eq__replicate_2]) ).

cnf(cls_size__char_0,axiom,
    c_Nat_Osize__class_Osize(V_c,tc_String_Ochar) = c_HOL_Ozero__class_Ozero(tc_nat),
    input ).

fof(cls_size__char_0_0,plain,
    ! [V_c] :
      ( c_Nat_Osize__class_Osize(V_c,tc_String_Ochar) = c_HOL_Ozero__class_Ozero(tc_nat)
      | $false ),
    inference(orientation,[status(thm)],[cls_size__char_0]) ).

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),
    input ).

fof(cls_append__eq__append__conv2_5_0,plain,
    ! [T_a,V_ts,V_x,V_xs] :
      ( 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)
      | $false ),
    inference(orientation,[status(thm)],[cls_append__eq__append__conv2_5]) ).

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),
    input ).

fof(cls_append__eq__append__conv2_4_0,plain,
    ! [T_a,V_x,V_ys,V_zs] :
      ( 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)
      | $false ),
    inference(orientation,[status(thm)],[cls_append__eq__append__conv2_4]) ).

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),
    input ).

fof(cls_append__eq__appendI_0_0,plain,
    ! [T_a,V_us,V_xs,V_xs1] :
      ( 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)
      | $false ),
    inference(orientation,[status(thm)],[cls_append__eq__appendI_0]) ).

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),
    input ).

fof(cls_append__assoc_0_0,plain,
    ! [T_a,V_xs,V_ys,V_zs] :
      ( 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)
      | $false ),
    inference(orientation,[status(thm)],[cls_append__assoc_0]) ).

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),
    input ).

fof(cls_append__is__Nil__conv_2_0,plain,
    ! [T_a] :
      ( c_List_Oappend(c_List_Olist_ONil(T_a),c_List_Olist_ONil(T_a),T_a) = c_List_Olist_ONil(T_a)
      | $false ),
    inference(orientation,[status(thm)],[cls_append__is__Nil__conv_2]) ).

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),
    input ).

fof(cls_replicate__app__Cons__same_0_0,plain,
    ! [T_a,V_n,V_x,V_xs] :
      ( 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)
      | $false ),
    inference(orientation,[status(thm)],[cls_replicate__app__Cons__same_0]) ).

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),
    input ).

fof(cls_append__eq__Cons__conv_4_0,plain,
    ! [T_a,V_x,V_xs] :
      ( 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)
      | $false ),
    inference(orientation,[status(thm)],[cls_append__eq__Cons__conv_4]) ).

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

fof(cls_not__add__less2_0_0,plain,
    ! [V_i,V_j] :
      ( ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_j),V_i),V_i,tc_nat)
      | $false ),
    inference(orientation,[status(thm)],[cls_not__add__less2_0]) ).

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

fof(cls_not__add__less1_0_0,plain,
    ! [V_i,V_j] :
      ( ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_j),V_i,tc_nat)
      | $false ),
    inference(orientation,[status(thm)],[cls_not__add__less1_0]) ).

cnf(cls_conversep__conversep_0,axiom,
    c_Predicate_Oconversep(c_Predicate_Oconversep(V_r,T_a,T_b),T_b,T_a) = V_r,
    input ).

fof(cls_conversep__conversep_0_0,plain,
    ! [T_a,T_b,V_r] :
      ( c_Predicate_Oconversep(c_Predicate_Oconversep(V_r,T_a,T_b),T_b,T_a) = V_r
      | $false ),
    inference(orientation,[status(thm)],[cls_conversep__conversep_0]) ).

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

fof(cls_foldr_Osimps_I2_J_0_0,plain,
    ! [T_a,T_b,V_a,V_f,V_x,V_xs] :
      ( c_List_Ofoldr(V_f,c_List_Olist_OCons(V_x,V_xs,T_b),V_a,T_b,T_a) = hAPP(hAPP(V_f,V_x),c_List_Ofoldr(V_f,V_xs,V_a,T_b,T_a))
      | $false ),
    inference(orientation,[status(thm)],[cls_foldr_Osimps_I2_J_0]) ).

cnf(cls_dB_Orecs_I3_J_0,axiom,
    c_Lambda_OdB_OdB__rec(V_f1,V_f2,V_f3,c_Lambda_OdB_OAbs(V_dB),T_a) = hAPP(hAPP(V_f3,V_dB),c_Lambda_OdB_OdB__rec(V_f1,V_f2,V_f3,V_dB,T_a)),
    input ).

fof(cls_dB_Orecs_I3_J_0_0,plain,
    ! [T_a,V_dB,V_f1,V_f2,V_f3] :
      ( c_Lambda_OdB_OdB__rec(V_f1,V_f2,V_f3,c_Lambda_OdB_OAbs(V_dB),T_a) = hAPP(hAPP(V_f3,V_dB),c_Lambda_OdB_OdB__rec(V_f1,V_f2,V_f3,V_dB,T_a))
      | $false ),
    inference(orientation,[status(thm)],[cls_dB_Orecs_I3_J_0]) ).

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

fof(cls_lift__map_0_0,plain,
    ! [V_i,V_t,V_ts] :
      ( hAPP(hAPP(c_Lambda_Olift,c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB)),V_i) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_Olift,V_t),V_i),c_List_Omap(c_COMBC(c_Lambda_Olift,V_i,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)
      | $false ),
    inference(orientation,[status(thm)],[cls_lift__map_0]) ).

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

fof(cls_replicate__add_0_0,plain,
    ! [T_a,V_m,V_n,V_x] :
      ( c_List_Oreplicate(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_m),V_x,T_a) = c_List_Oappend(c_List_Oreplicate(V_n,V_x,T_a),c_List_Oreplicate(V_m,V_x,T_a),T_a)
      | $false ),
    inference(orientation,[status(thm)],[cls_replicate__add_0]) ).

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),
    input ).

fof(cls_list_Osimps_I2_J_0_0,plain,
    ! [T_a,V_a_H,V_list_H] :
      ( c_List_Olist_ONil(T_a) != c_List_Olist_OCons(V_a_H,V_list_H,T_a)
      | $false ),
    inference(orientation,[status(thm)],[cls_list_Osimps_I2_J_0]) ).

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),
    input ).

fof(cls_append__replicate__commute_0_0,plain,
    ! [T_a,V_k,V_n,V_x] :
      ( 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)
      | $false ),
    inference(orientation,[status(thm)],[cls_append__replicate__commute_0]) ).

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

fof(cls_map__append_0_0,plain,
    ! [T_a,T_b,V_f,V_xs,V_ys] :
      ( c_List_Omap(V_f,c_List_Oappend(V_xs,V_ys,T_b),T_b,T_a) = c_List_Oappend(c_List_Omap(V_f,V_xs,T_b,T_a),c_List_Omap(V_f,V_ys,T_b,T_a),T_a)
      | $false ),
    inference(orientation,[status(thm)],[cls_map__append_0]) ).

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

fof(cls_less__not__refl_0_0,plain,
    ! [V_n] :
      ( ~ c_HOL_Oord__class_Oless(V_n,V_n,tc_nat)
      | $false ),
    inference(orientation,[status(thm)],[cls_less__not__refl_0]) ).

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

fof(cls_nat__less__le_1_0,plain,
    ! [V_x] :
      ( ~ c_HOL_Oord__class_Oless(V_x,V_x,tc_nat)
      | $false ),
    inference(orientation,[status(thm)],[cls_nat__less__le_1]) ).

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),
    input ).

fof(cls_empty__replicate_1_0,plain,
    ! [T_a,V_x] :
      ( c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),V_x,T_a) = c_List_Olist_ONil(T_a)
      | $false ),
    inference(orientation,[status(thm)],[cls_empty__replicate_1]) ).

cnf(cls_conversep__eq_0,axiom,
    c_Predicate_Oconversep(c_fequal(T_a),T_a,T_a) = c_fequal(T_a),
    input ).

fof(cls_conversep__eq_0_0,plain,
    ! [T_a] :
      ( c_Predicate_Oconversep(c_fequal(T_a),T_a,T_a) = c_fequal(T_a)
      | $false ),
    inference(orientation,[status(thm)],[cls_conversep__eq_0]) ).

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

fof(cls_not__less0_0_0,plain,
    ! [V_n] :
      ( ~ c_HOL_Oord__class_Oless(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
      | $false ),
    inference(orientation,[status(thm)],[cls_not__less0_0]) ).

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

fof(cls_gr__implies__not0_0_0,plain,
    ! [V_m] :
      ( ~ c_HOL_Oord__class_Oless(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
      | $false ),
    inference(orientation,[status(thm)],[cls_gr__implies__not0_0]) ).

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

fof(cls_add__is__0_2_0,plain,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Ozero__class_Ozero(tc_nat)
    | $false ),
    inference(orientation,[status(thm)],[cls_add__is__0_2]) ).

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

fof(cls_liftn__0_0_0,plain,
    ! [V_k,V_t] :
      ( c_Lambda_Oliftn(c_HOL_Ozero__class_Ozero(tc_nat),V_t,V_k) = V_t
      | $false ),
    inference(orientation,[status(thm)],[cls_liftn__0_0]) ).

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

fof(cls_neq0__conv_1_0,plain,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
    | $false ),
    inference(orientation,[status(thm)],[cls_neq0__conv_1]) ).

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),
    input ).

fof(cls_replicate__append__same_0_0,plain,
    ! [T_a,V_i,V_x] :
      ( 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)
      | $false ),
    inference(orientation,[status(thm)],[cls_replicate__append__same_0]) ).

cnf(cls_rtranclp__idemp_0,axiom,
    c_Transitive__Closure_Ortranclp(c_Transitive__Closure_Ortranclp(V_r,T_a),T_a) = c_Transitive__Closure_Ortranclp(V_r,T_a),
    input ).

fof(cls_rtranclp__idemp_0_0,plain,
    ! [T_a,V_r] :
      ( c_Transitive__Closure_Ortranclp(c_Transitive__Closure_Ortranclp(V_r,T_a),T_a) = c_Transitive__Closure_Ortranclp(V_r,T_a)
      | $false ),
    inference(orientation,[status(thm)],[cls_rtranclp__idemp_0]) ).

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),
    input ).

fof(cls_Nil__is__append__conv_2_0,plain,
    ! [T_a] :
      ( c_List_Olist_ONil(T_a) = c_List_Oappend(c_List_Olist_ONil(T_a),c_List_Olist_ONil(T_a),T_a)
      | $false ),
    inference(orientation,[status(thm)],[cls_Nil__is__append__conv_2]) ).

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

fof(cls_Nil__is__map__conv_1_0,plain,
    ! [T_a,T_b,V_f] :
      ( c_List_Omap(V_f,c_List_Olist_ONil(T_b),T_b,T_a) = c_List_Olist_ONil(T_a)
      | $false ),
    inference(orientation,[status(thm)],[cls_Nil__is__map__conv_1]) ).

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),
    input ).

fof(cls_Cons__eq__append__conv_4_0,plain,
    ! [T_a,V_x,V_xs] :
      ( 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)
      | $false ),
    inference(orientation,[status(thm)],[cls_Cons__eq__append__conv_4]) ).

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

fof(cls_not__Cons__self_0_0,plain,
    ! [T_a,V_x,V_xs] :
      ( V_xs != c_List_Olist_OCons(V_x,V_xs,T_a)
      | $false ),
    inference(orientation,[status(thm)],[cls_not__Cons__self_0]) ).

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

fof(cls_not__Cons__self2_0_0,plain,
    ! [T_a,V_t,V_x] :
      ( c_List_Olist_OCons(V_x,V_t,T_a) != V_t
      | $false ),
    inference(orientation,[status(thm)],[cls_not__Cons__self2_0]) ).

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),
    input ).

fof(cls_replicate__empty_1_0,plain,
    ! [T_a,V_x] :
      ( c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),V_x,T_a) = c_List_Olist_ONil(T_a)
      | $false ),
    inference(orientation,[status(thm)],[cls_replicate__empty_1]) ).

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),
    input ).

fof(cls_list_Osimps_I3_J_0_0,plain,
    ! [T_a,V_a_H,V_list_H] :
      ( c_List_Olist_OCons(V_a_H,V_list_H,T_a) != c_List_Olist_ONil(T_a)
      | $false ),
    inference(orientation,[status(thm)],[cls_list_Osimps_I3_J_0]) ).

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

fof(cls_neq__Nil__conv_1_0,plain,
    ! [T_a,V_x,V_xa] :
      ( c_List_Olist_OCons(V_x,V_xa,T_a) != c_List_Olist_ONil(T_a)
      | $false ),
    inference(orientation,[status(thm)],[cls_neq__Nil__conv_1]) ).

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),
    input ).

fof(cls_Cons__eq__appendI_0_0,plain,
    ! [T_a,V_x,V_xs1,V_zs] :
      ( 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)
      | $false ),
    inference(orientation,[status(thm)],[cls_Cons__eq__appendI_0]) ).

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),
    input ).

fof(cls_Cons__eq__append__conv_5_0,plain,
    ! [T_a,V_x,V_xa,V_zs] :
      ( 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)
      | $false ),
    inference(orientation,[status(thm)],[cls_Cons__eq__append__conv_5]) ).

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

fof(cls_not__step1__Nil_0_0,plain,
    ! [T_a,V_r,V_xs] :
      ( ~ c_ListOrder_Ostep1(V_r,V_xs,c_List_Olist_ONil(T_a),T_a)
      | $false ),
    inference(orientation,[status(thm)],[cls_not__step1__Nil_0]) ).

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

fof(cls_not__Nil__step1_0_0,plain,
    ! [T_a,V_r,V_xs] :
      ( ~ c_ListOrder_Ostep1(V_r,c_List_Olist_ONil(T_a),V_xs,T_a)
      | $false ),
    inference(orientation,[status(thm)],[cls_not__Nil__step1_0]) ).

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

fof(cls_foldr__append_0_0,plain,
    ! [T_a,T_b,V_a,V_f,V_xs,V_ys] :
      ( c_List_Ofoldr(V_f,c_List_Oappend(V_xs,V_ys,T_b),V_a,T_b,T_a) = c_List_Ofoldr(V_f,V_xs,c_List_Ofoldr(V_f,V_ys,V_a,T_b,T_a),T_b,T_a)
      | $false ),
    inference(orientation,[status(thm)],[cls_foldr__append_0]) ).

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

fof(cls_nat__add__commute_0_0,plain,
    ! [V_m,V_n] :
      ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_m)
      | $false ),
    inference(orientation,[status(thm)],[cls_nat__add__commute_0]) ).

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

fof(cls_map__replicate_0_0,plain,
    ! [T_a,T_b,V_f,V_n,V_x] :
      ( c_List_Omap(V_f,c_List_Oreplicate(V_n,V_x,T_b),T_b,T_a) = c_List_Oreplicate(V_n,hAPP(V_f,V_x),T_a)
      | $false ),
    inference(orientation,[status(thm)],[cls_map__replicate_0]) ).

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

fof(cls_self__append__conv2_1_0,plain,
    ! [T_a,V_ys] :
      ( c_List_Oappend(c_List_Olist_ONil(T_a),V_ys,T_a) = V_ys
      | $false ),
    inference(orientation,[status(thm)],[cls_self__append__conv2_1]) ).

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

fof(cls_append__Nil_0_0,plain,
    ! [T_a,V_ys] :
      ( c_List_Oappend(c_List_Olist_ONil(T_a),V_ys,T_a) = V_ys
      | $false ),
    inference(orientation,[status(thm)],[cls_append__Nil_0]) ).

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

fof(cls_self__append__conv_1_0,plain,
    ! [T_a,V_xs] :
      ( c_List_Oappend(V_xs,c_List_Olist_ONil(T_a),T_a) = V_xs
      | $false ),
    inference(orientation,[status(thm)],[cls_self__append__conv_1]) ).

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

fof(cls_eq__Nil__appendI_0_0,plain,
    ! [T_a,V_x] :
      ( c_List_Oappend(c_List_Olist_ONil(T_a),V_x,T_a) = V_x
      | $false ),
    inference(orientation,[status(thm)],[cls_eq__Nil__appendI_0]) ).

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

fof(cls_append__Nil2_0_0,plain,
    ! [T_a,V_xs] :
      ( c_List_Oappend(V_xs,c_List_Olist_ONil(T_a),T_a) = V_xs
      | $false ),
    inference(orientation,[status(thm)],[cls_append__Nil2_0]) ).

cnf(cls_Nitpick_Ortranclp__def_1,axiom,
    hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_x),V_x)),
    input ).

fof(cls_Nitpick_Ortranclp__def_1_0,plain,
    ! [T_a,V_r,V_x] :
      ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_x),V_x))
      | $false ),
    inference(orientation,[status(thm)],[cls_Nitpick_Ortranclp__def_1]) ).

cnf(cls_rtranclp_Ortrancl__refl_0,axiom,
    hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_a),V_a)),
    input ).

fof(cls_rtranclp_Ortrancl__refl_0_0,plain,
    ! [T_a,V_a,V_r] :
      ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_a),V_a))
      | $false ),
    inference(orientation,[status(thm)],[cls_rtranclp_Ortrancl__refl_0]) ).

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

fof(cls_listsp_ONil_0_0,plain,
    ! [T_a,V_A] :
      ( c_List_Olistsp(V_A,c_List_Olist_ONil(T_a),T_a)
      | $false ),
    inference(orientation,[status(thm)],[cls_listsp_ONil_0]) ).

cnf(cls_dB_Osimps_I12_J_0,axiom,
    c_Lambda_OdB_OdB__case(V_f1,V_f2,V_f3,c_Lambda_OdB_OAbs(V_dB),T_a) = hAPP(V_f3,V_dB),
    input ).

fof(cls_dB_Osimps_I12_J_0_0,plain,
    ! [T_a,V_dB,V_f1,V_f2,V_f3] :
      ( c_Lambda_OdB_OdB__case(V_f1,V_f2,V_f3,c_Lambda_OdB_OAbs(V_dB),T_a) = hAPP(V_f3,V_dB)
      | $false ),
    inference(orientation,[status(thm)],[cls_dB_Osimps_I12_J_0]) ).

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

fof(cls_nat__add__left__commute_0_0,plain,
    ! [V_x,V_y,V_z] :
      ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_x),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_y),V_z)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_y),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_x),V_z))
      | $false ),
    inference(orientation,[status(thm)],[cls_nat__add__left__commute_0]) ).

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

fof(cls_nat__add__assoc_0_0,plain,
    ! [V_k,V_m,V_n] :
      ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)),V_k) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_k))
      | $false ),
    inference(orientation,[status(thm)],[cls_nat__add__assoc_0]) ).

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

fof(cls_COMBC__def_0_0,plain,
    ! [T_a,T_b,T_c,V_P,V_Q,V_R] :
      ( hAPP(c_COMBC(V_P,V_Q,T_b,T_c,T_a),V_R) = hAPP(hAPP(V_P,V_R),V_Q)
      | $false ),
    inference(orientation,[status(thm)],[cls_COMBC__def_0]) ).

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

fof(cls_foldr_Osimps_I1_J_0_0,plain,
    ! [T_a,T_b,V_a,V_f] :
      ( c_List_Ofoldr(V_f,c_List_Olist_ONil(T_b),V_a,T_b,T_a) = V_a
      | $false ),
    inference(orientation,[status(thm)],[cls_foldr_Osimps_I1_J_0]) ).

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

fof(cls_map__is__Nil__conv_1_0,plain,
    ! [T_a,T_b,V_f] :
      ( c_List_Omap(V_f,c_List_Olist_ONil(T_b),T_b,T_a) = c_List_Olist_ONil(T_a)
      | $false ),
    inference(orientation,[status(thm)],[cls_map__is__Nil__conv_1]) ).

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),
    input ).

fof(cls_append__eq__Cons__conv_5_0,plain,
    ! [T_a,V_x,V_xa,V_zs] :
      ( 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)
      | $false ),
    inference(orientation,[status(thm)],[cls_append__eq__Cons__conv_5]) ).

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),
    input ).

fof(cls_append__Cons_0_0,plain,
    ! [T_a,V_x,V_xs,V_ys] :
      ( 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)
      | $false ),
    inference(orientation,[status(thm)],[cls_append__Cons_0]) ).

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

fof(cls_map__eq__Cons__conv_3_0,plain,
    ! [T_a,T_b,V_f,V_x,V_xa] :
      ( c_List_Omap(V_f,c_List_Olist_OCons(V_x,V_xa,T_b),T_b,T_a) = c_List_Olist_OCons(hAPP(V_f,V_x),c_List_Omap(V_f,V_xa,T_b,T_a),T_a)
      | $false ),
    inference(orientation,[status(thm)],[cls_map__eq__Cons__conv_3]) ).

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

fof(cls_Cons__eq__map__conv_3_0,plain,
    ! [T_a,T_b,V_f,V_xa,V_xb] :
      ( c_List_Olist_OCons(hAPP(V_f,V_xa),c_List_Omap(V_f,V_xb,T_b,T_a),T_a) = c_List_Omap(V_f,c_List_Olist_OCons(V_xa,V_xb,T_b),T_b,T_a)
      | $false ),
    inference(orientation,[status(thm)],[cls_Cons__eq__map__conv_3]) ).

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

fof(cls_map_Osimps_I2_J_0_0,plain,
    ! [T_a,T_b,V_f,V_x,V_xs] :
      ( c_List_Omap(V_f,c_List_Olist_OCons(V_x,V_xs,T_b),T_b,T_a) = c_List_Olist_OCons(hAPP(V_f,V_x),c_List_Omap(V_f,V_xs,T_b,T_a),T_a)
      | $false ),
    inference(orientation,[status(thm)],[cls_map_Osimps_I2_J_0]) ).

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

fof(cls_subst__Abs_0_0,plain,
    ! [V_k,V_s,V_t] :
      ( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OAbs(V_t)),V_s),V_k) = c_Lambda_OdB_OAbs(hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),hAPP(hAPP(c_Lambda_Olift,V_s),c_HOL_Ozero__class_Ozero(tc_nat))),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),c_HOL_Oone__class_Oone(tc_nat))))
      | $false ),
    inference(orientation,[status(thm)],[cls_subst__Abs_0]) ).

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

fof(cls_substn_Osimps_I3_J_0_0,plain,
    ! [V_k,V_s,V_t] :
      ( c_Lambda_Osubstn(c_Lambda_OdB_OAbs(V_t),V_s,V_k) = c_Lambda_OdB_OAbs(c_Lambda_Osubstn(V_t,V_s,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),c_HOL_Oone__class_Oone(tc_nat))))
      | $false ),
    inference(orientation,[status(thm)],[cls_substn_Osimps_I3_J_0]) ).

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

fof(cls_liftn_Osimps_I3_J_0_0,plain,
    ! [V_k,V_n,V_s] :
      ( c_Lambda_Oliftn(V_n,c_Lambda_OdB_OAbs(V_s),V_k) = c_Lambda_OdB_OAbs(c_Lambda_Oliftn(V_n,V_s,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),c_HOL_Oone__class_Oone(tc_nat))))
      | $false ),
    inference(orientation,[status(thm)],[cls_liftn_Osimps_I3_J_0]) ).

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

fof(cls_lift_Osimps_I3_J_0_0,plain,
    ! [V_k,V_s] :
      ( hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OAbs(V_s)),V_k) = c_Lambda_OdB_OAbs(hAPP(hAPP(c_Lambda_Olift,V_s),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),c_HOL_Oone__class_Oone(tc_nat))))
      | $false ),
    inference(orientation,[status(thm)],[cls_lift_Osimps_I3_J_0]) ).

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

fof(cls_shift__eq_0_0,plain,
    ! [T_a,V_T,V_e,V_x] :
      ( hAPP(c_Type_Oshift(V_e,V_x,V_T,T_a),V_x) = V_T
      | $false ),
    inference(orientation,[status(thm)],[cls_shift__eq_0]) ).

fof(def_lhs_atom1,axiom,
    ! [V_x,V_e,V_T,T_a] :
      ( lhs_atom1(V_x,V_e,V_T,T_a)
    <=> hAPP(c_Type_Oshift(V_e,V_x,V_T,T_a),V_x) = V_T ),
    inference(definition,[],]) ).

fof(to_be_clausified_0,plain,
    ! [T_a,V_T,V_e,V_x] :
      ( lhs_atom1(V_x,V_e,V_T,T_a)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_shift__eq_0_0,def_lhs_atom1]) ).

fof(def_lhs_atom2,axiom,
    ! [V_s,V_k] :
      ( lhs_atom2(V_s,V_k)
    <=> hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OAbs(V_s)),V_k) = c_Lambda_OdB_OAbs(hAPP(hAPP(c_Lambda_Olift,V_s),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),c_HOL_Oone__class_Oone(tc_nat)))) ),
    inference(definition,[],]) ).

fof(to_be_clausified_1,plain,
    ! [V_k,V_s] :
      ( lhs_atom2(V_s,V_k)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_lift_Osimps_I3_J_0_0,def_lhs_atom2]) ).

fof(def_lhs_atom3,axiom,
    ! [V_s,V_n,V_k] :
      ( lhs_atom3(V_s,V_n,V_k)
    <=> c_Lambda_Oliftn(V_n,c_Lambda_OdB_OAbs(V_s),V_k) = c_Lambda_OdB_OAbs(c_Lambda_Oliftn(V_n,V_s,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),c_HOL_Oone__class_Oone(tc_nat)))) ),
    inference(definition,[],]) ).

fof(to_be_clausified_2,plain,
    ! [V_k,V_n,V_s] :
      ( lhs_atom3(V_s,V_n,V_k)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_liftn_Osimps_I3_J_0_0,def_lhs_atom3]) ).

fof(def_lhs_atom4,axiom,
    ! [V_t,V_s,V_k] :
      ( lhs_atom4(V_t,V_s,V_k)
    <=> c_Lambda_Osubstn(c_Lambda_OdB_OAbs(V_t),V_s,V_k) = c_Lambda_OdB_OAbs(c_Lambda_Osubstn(V_t,V_s,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),c_HOL_Oone__class_Oone(tc_nat)))) ),
    inference(definition,[],]) ).

fof(to_be_clausified_3,plain,
    ! [V_k,V_s,V_t] :
      ( lhs_atom4(V_t,V_s,V_k)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_substn_Osimps_I3_J_0_0,def_lhs_atom4]) ).

fof(def_lhs_atom5,axiom,
    ! [V_t,V_s,V_k] :
      ( lhs_atom5(V_t,V_s,V_k)
    <=> hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OAbs(V_t)),V_s),V_k) = c_Lambda_OdB_OAbs(hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),hAPP(hAPP(c_Lambda_Olift,V_s),c_HOL_Ozero__class_Ozero(tc_nat))),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),c_HOL_Oone__class_Oone(tc_nat)))) ),
    inference(definition,[],]) ).

fof(to_be_clausified_4,plain,
    ! [V_k,V_s,V_t] :
      ( lhs_atom5(V_t,V_s,V_k)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_subst__Abs_0_0,def_lhs_atom5]) ).

fof(def_lhs_atom6,axiom,
    ! [V_xs,V_x,V_f,T_b,T_a] :
      ( lhs_atom6(V_xs,V_x,V_f,T_b,T_a)
    <=> c_List_Omap(V_f,c_List_Olist_OCons(V_x,V_xs,T_b),T_b,T_a) = c_List_Olist_OCons(hAPP(V_f,V_x),c_List_Omap(V_f,V_xs,T_b,T_a),T_a) ),
    inference(definition,[],]) ).

fof(to_be_clausified_5,plain,
    ! [T_a,T_b,V_f,V_x,V_xs] :
      ( lhs_atom6(V_xs,V_x,V_f,T_b,T_a)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_map_Osimps_I2_J_0_0,def_lhs_atom6]) ).

fof(def_lhs_atom7,axiom,
    ! [V_xb,V_xa,V_f,T_b,T_a] :
      ( lhs_atom7(V_xb,V_xa,V_f,T_b,T_a)
    <=> c_List_Olist_OCons(hAPP(V_f,V_xa),c_List_Omap(V_f,V_xb,T_b,T_a),T_a) = c_List_Omap(V_f,c_List_Olist_OCons(V_xa,V_xb,T_b),T_b,T_a) ),
    inference(definition,[],]) ).

fof(to_be_clausified_6,plain,
    ! [T_a,T_b,V_f,V_xa,V_xb] :
      ( lhs_atom7(V_xb,V_xa,V_f,T_b,T_a)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_Cons__eq__map__conv_3_0,def_lhs_atom7]) ).

fof(def_lhs_atom8,axiom,
    ! [V_xa,V_x,V_f,T_b,T_a] :
      ( lhs_atom8(V_xa,V_x,V_f,T_b,T_a)
    <=> c_List_Omap(V_f,c_List_Olist_OCons(V_x,V_xa,T_b),T_b,T_a) = c_List_Olist_OCons(hAPP(V_f,V_x),c_List_Omap(V_f,V_xa,T_b,T_a),T_a) ),
    inference(definition,[],]) ).

fof(to_be_clausified_7,plain,
    ! [T_a,T_b,V_f,V_x,V_xa] :
      ( lhs_atom8(V_xa,V_x,V_f,T_b,T_a)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_map__eq__Cons__conv_3_0,def_lhs_atom8]) ).

fof(def_lhs_atom9,axiom,
    ! [V_ys,V_xs,V_x,T_a] :
      ( lhs_atom9(V_ys,V_xs,V_x,T_a)
    <=> 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) ),
    inference(definition,[],]) ).

fof(to_be_clausified_8,plain,
    ! [T_a,V_x,V_xs,V_ys] :
      ( lhs_atom9(V_ys,V_xs,V_x,T_a)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_append__Cons_0_0,def_lhs_atom9]) ).

fof(def_lhs_atom10,axiom,
    ! [V_zs,V_xa,V_x,T_a] :
      ( lhs_atom10(V_zs,V_xa,V_x,T_a)
    <=> 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) ),
    inference(definition,[],]) ).

fof(to_be_clausified_9,plain,
    ! [T_a,V_x,V_xa,V_zs] :
      ( lhs_atom10(V_zs,V_xa,V_x,T_a)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_append__eq__Cons__conv_5_0,def_lhs_atom10]) ).

fof(def_lhs_atom11,axiom,
    ! [V_f,T_b,T_a] :
      ( lhs_atom11(V_f,T_b,T_a)
    <=> c_List_Omap(V_f,c_List_Olist_ONil(T_b),T_b,T_a) = c_List_Olist_ONil(T_a) ),
    inference(definition,[],]) ).

fof(to_be_clausified_10,plain,
    ! [T_a,T_b,V_f] :
      ( lhs_atom11(V_f,T_b,T_a)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_map__is__Nil__conv_1_0,def_lhs_atom11]) ).

fof(def_lhs_atom12,axiom,
    ! [V_f,V_a,T_b,T_a] :
      ( lhs_atom12(V_f,V_a,T_b,T_a)
    <=> c_List_Ofoldr(V_f,c_List_Olist_ONil(T_b),V_a,T_b,T_a) = V_a ),
    inference(definition,[],]) ).

fof(to_be_clausified_11,plain,
    ! [T_a,T_b,V_a,V_f] :
      ( lhs_atom12(V_f,V_a,T_b,T_a)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_foldr_Osimps_I1_J_0_0,def_lhs_atom12]) ).

fof(def_lhs_atom13,axiom,
    ! [V_R,V_Q,V_P,T_c,T_b,T_a] :
      ( lhs_atom13(V_R,V_Q,V_P,T_c,T_b,T_a)
    <=> hAPP(c_COMBC(V_P,V_Q,T_b,T_c,T_a),V_R) = hAPP(hAPP(V_P,V_R),V_Q) ),
    inference(definition,[],]) ).

fof(to_be_clausified_12,plain,
    ! [T_a,T_b,T_c,V_P,V_Q,V_R] :
      ( lhs_atom13(V_R,V_Q,V_P,T_c,T_b,T_a)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_COMBC__def_0_0,def_lhs_atom13]) ).

fof(def_lhs_atom14,axiom,
    ! [V_n,V_m,V_k] :
      ( lhs_atom14(V_n,V_m,V_k)
    <=> hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)),V_k) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_k)) ),
    inference(definition,[],]) ).

fof(to_be_clausified_13,plain,
    ! [V_k,V_m,V_n] :
      ( lhs_atom14(V_n,V_m,V_k)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_nat__add__assoc_0_0,def_lhs_atom14]) ).

fof(def_lhs_atom15,axiom,
    ! [V_z,V_y,V_x] :
      ( lhs_atom15(V_z,V_y,V_x)
    <=> hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_x),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_y),V_z)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_y),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_x),V_z)) ),
    inference(definition,[],]) ).

fof(to_be_clausified_14,plain,
    ! [V_x,V_y,V_z] :
      ( lhs_atom15(V_z,V_y,V_x)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_nat__add__left__commute_0_0,def_lhs_atom15]) ).

fof(def_lhs_atom16,axiom,
    ! [V_f3,V_f2,V_f1,V_dB,T_a] :
      ( lhs_atom16(V_f3,V_f2,V_f1,V_dB,T_a)
    <=> c_Lambda_OdB_OdB__case(V_f1,V_f2,V_f3,c_Lambda_OdB_OAbs(V_dB),T_a) = hAPP(V_f3,V_dB) ),
    inference(definition,[],]) ).

fof(to_be_clausified_15,plain,
    ! [T_a,V_dB,V_f1,V_f2,V_f3] :
      ( lhs_atom16(V_f3,V_f2,V_f1,V_dB,T_a)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_dB_Osimps_I12_J_0_0,def_lhs_atom16]) ).

fof(def_lhs_atom17,axiom,
    ! [V_A,T_a] :
      ( lhs_atom17(V_A,T_a)
    <=> c_List_Olistsp(V_A,c_List_Olist_ONil(T_a),T_a) ),
    inference(definition,[],]) ).

fof(to_be_clausified_16,plain,
    ! [T_a,V_A] :
      ( lhs_atom17(V_A,T_a)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_listsp_ONil_0_0,def_lhs_atom17]) ).

fof(def_lhs_atom18,axiom,
    ! [V_r,V_a,T_a] :
      ( lhs_atom18(V_r,V_a,T_a)
    <=> hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_a),V_a)) ),
    inference(definition,[],]) ).

fof(to_be_clausified_17,plain,
    ! [T_a,V_a,V_r] :
      ( lhs_atom18(V_r,V_a,T_a)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_rtranclp_Ortrancl__refl_0_0,def_lhs_atom18]) ).

fof(def_lhs_atom19,axiom,
    ! [V_x,V_r,T_a] :
      ( lhs_atom19(V_x,V_r,T_a)
    <=> hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_x),V_x)) ),
    inference(definition,[],]) ).

fof(to_be_clausified_18,plain,
    ! [T_a,V_r,V_x] :
      ( lhs_atom19(V_x,V_r,T_a)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_Nitpick_Ortranclp__def_1_0,def_lhs_atom19]) ).

fof(def_lhs_atom20,axiom,
    ! [V_xs,T_a] :
      ( lhs_atom20(V_xs,T_a)
    <=> c_List_Oappend(V_xs,c_List_Olist_ONil(T_a),T_a) = V_xs ),
    inference(definition,[],]) ).

fof(to_be_clausified_19,plain,
    ! [T_a,V_xs] :
      ( lhs_atom20(V_xs,T_a)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_append__Nil2_0_0,def_lhs_atom20]) ).

fof(def_lhs_atom21,axiom,
    ! [V_x,T_a] :
      ( lhs_atom21(V_x,T_a)
    <=> c_List_Oappend(c_List_Olist_ONil(T_a),V_x,T_a) = V_x ),
    inference(definition,[],]) ).

fof(to_be_clausified_20,plain,
    ! [T_a,V_x] :
      ( lhs_atom21(V_x,T_a)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_eq__Nil__appendI_0_0,def_lhs_atom21]) ).

fof(to_be_clausified_21,plain,
    ! [T_a,V_xs] :
      ( lhs_atom20(V_xs,T_a)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_self__append__conv_1_0,def_lhs_atom20]) ).

fof(def_lhs_atom22,axiom,
    ! [V_ys,T_a] :
      ( lhs_atom22(V_ys,T_a)
    <=> c_List_Oappend(c_List_Olist_ONil(T_a),V_ys,T_a) = V_ys ),
    inference(definition,[],]) ).

fof(to_be_clausified_22,plain,
    ! [T_a,V_ys] :
      ( lhs_atom22(V_ys,T_a)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_append__Nil_0_0,def_lhs_atom22]) ).

fof(to_be_clausified_23,plain,
    ! [T_a,V_ys] :
      ( lhs_atom22(V_ys,T_a)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_self__append__conv2_1_0,def_lhs_atom22]) ).

fof(def_lhs_atom23,axiom,
    ! [V_x,V_n,V_f,T_b,T_a] :
      ( lhs_atom23(V_x,V_n,V_f,T_b,T_a)
    <=> c_List_Omap(V_f,c_List_Oreplicate(V_n,V_x,T_b),T_b,T_a) = c_List_Oreplicate(V_n,hAPP(V_f,V_x),T_a) ),
    inference(definition,[],]) ).

fof(to_be_clausified_24,plain,
    ! [T_a,T_b,V_f,V_n,V_x] :
      ( lhs_atom23(V_x,V_n,V_f,T_b,T_a)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_map__replicate_0_0,def_lhs_atom23]) ).

fof(def_lhs_atom24,axiom,
    ! [V_n,V_m] :
      ( lhs_atom24(V_n,V_m)
    <=> hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_m) ),
    inference(definition,[],]) ).

fof(to_be_clausified_25,plain,
    ! [V_m,V_n] :
      ( lhs_atom24(V_n,V_m)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_nat__add__commute_0_0,def_lhs_atom24]) ).

fof(def_lhs_atom25,axiom,
    ! [V_ys,V_xs,V_f,V_a,T_b,T_a] :
      ( lhs_atom25(V_ys,V_xs,V_f,V_a,T_b,T_a)
    <=> c_List_Ofoldr(V_f,c_List_Oappend(V_xs,V_ys,T_b),V_a,T_b,T_a) = c_List_Ofoldr(V_f,V_xs,c_List_Ofoldr(V_f,V_ys,V_a,T_b,T_a),T_b,T_a) ),
    inference(definition,[],]) ).

fof(to_be_clausified_26,plain,
    ! [T_a,T_b,V_a,V_f,V_xs,V_ys] :
      ( lhs_atom25(V_ys,V_xs,V_f,V_a,T_b,T_a)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_foldr__append_0_0,def_lhs_atom25]) ).

fof(def_lhs_atom26,axiom,
    ! [V_xs,V_r,T_a] :
      ( lhs_atom26(V_xs,V_r,T_a)
    <=> ~ c_ListOrder_Ostep1(V_r,c_List_Olist_ONil(T_a),V_xs,T_a) ),
    inference(definition,[],]) ).

fof(to_be_clausified_27,plain,
    ! [T_a,V_r,V_xs] :
      ( lhs_atom26(V_xs,V_r,T_a)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_not__Nil__step1_0_0,def_lhs_atom26]) ).

fof(def_lhs_atom27,axiom,
    ! [V_xs,V_r,T_a] :
      ( lhs_atom27(V_xs,V_r,T_a)
    <=> ~ c_ListOrder_Ostep1(V_r,V_xs,c_List_Olist_ONil(T_a),T_a) ),
    inference(definition,[],]) ).

fof(to_be_clausified_28,plain,
    ! [T_a,V_r,V_xs] :
      ( lhs_atom27(V_xs,V_r,T_a)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_not__step1__Nil_0_0,def_lhs_atom27]) ).

fof(def_lhs_atom28,axiom,
    ! [V_zs,V_xa,V_x,T_a] :
      ( lhs_atom28(V_zs,V_xa,V_x,T_a)
    <=> 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) ),
    inference(definition,[],]) ).

fof(to_be_clausified_29,plain,
    ! [T_a,V_x,V_xa,V_zs] :
      ( lhs_atom28(V_zs,V_xa,V_x,T_a)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_Cons__eq__append__conv_5_0,def_lhs_atom28]) ).

fof(def_lhs_atom29,axiom,
    ! [V_zs,V_xs1,V_x,T_a] :
      ( lhs_atom29(V_zs,V_xs1,V_x,T_a)
    <=> 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) ),
    inference(definition,[],]) ).

fof(to_be_clausified_30,plain,
    ! [T_a,V_x,V_xs1,V_zs] :
      ( lhs_atom29(V_zs,V_xs1,V_x,T_a)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_Cons__eq__appendI_0_0,def_lhs_atom29]) ).

fof(def_lhs_atom30,axiom,
    ! [V_xa,V_x,T_a] :
      ( lhs_atom30(V_xa,V_x,T_a)
    <=> c_List_Olist_OCons(V_x,V_xa,T_a) != c_List_Olist_ONil(T_a) ),
    inference(definition,[],]) ).

fof(to_be_clausified_31,plain,
    ! [T_a,V_x,V_xa] :
      ( lhs_atom30(V_xa,V_x,T_a)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_neq__Nil__conv_1_0,def_lhs_atom30]) ).

fof(def_lhs_atom31,axiom,
    ! [V_list_H,V_a_H,T_a] :
      ( lhs_atom31(V_list_H,V_a_H,T_a)
    <=> c_List_Olist_OCons(V_a_H,V_list_H,T_a) != c_List_Olist_ONil(T_a) ),
    inference(definition,[],]) ).

fof(to_be_clausified_32,plain,
    ! [T_a,V_a_H,V_list_H] :
      ( lhs_atom31(V_list_H,V_a_H,T_a)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_list_Osimps_I3_J_0_0,def_lhs_atom31]) ).

fof(def_lhs_atom32,axiom,
    ! [V_x,T_a] :
      ( lhs_atom32(V_x,T_a)
    <=> c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),V_x,T_a) = c_List_Olist_ONil(T_a) ),
    inference(definition,[],]) ).

fof(to_be_clausified_33,plain,
    ! [T_a,V_x] :
      ( lhs_atom32(V_x,T_a)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_replicate__empty_1_0,def_lhs_atom32]) ).

fof(def_lhs_atom33,axiom,
    ! [V_x,V_t,T_a] :
      ( lhs_atom33(V_x,V_t,T_a)
    <=> c_List_Olist_OCons(V_x,V_t,T_a) != V_t ),
    inference(definition,[],]) ).

fof(to_be_clausified_34,plain,
    ! [T_a,V_t,V_x] :
      ( lhs_atom33(V_x,V_t,T_a)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_not__Cons__self2_0_0,def_lhs_atom33]) ).

fof(def_lhs_atom34,axiom,
    ! [V_xs,V_x,T_a] :
      ( lhs_atom34(V_xs,V_x,T_a)
    <=> V_xs != c_List_Olist_OCons(V_x,V_xs,T_a) ),
    inference(definition,[],]) ).

fof(to_be_clausified_35,plain,
    ! [T_a,V_x,V_xs] :
      ( lhs_atom34(V_xs,V_x,T_a)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_not__Cons__self_0_0,def_lhs_atom34]) ).

fof(def_lhs_atom35,axiom,
    ! [V_xs,V_x,T_a] :
      ( lhs_atom35(V_xs,V_x,T_a)
    <=> 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) ),
    inference(definition,[],]) ).

fof(to_be_clausified_36,plain,
    ! [T_a,V_x,V_xs] :
      ( lhs_atom35(V_xs,V_x,T_a)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_Cons__eq__append__conv_4_0,def_lhs_atom35]) ).

fof(to_be_clausified_37,plain,
    ! [T_a,T_b,V_f] :
      ( lhs_atom11(V_f,T_b,T_a)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_Nil__is__map__conv_1_0,def_lhs_atom11]) ).

fof(def_lhs_atom36,axiom,
    ! [T_a] :
      ( lhs_atom36(T_a)
    <=> c_List_Olist_ONil(T_a) = c_List_Oappend(c_List_Olist_ONil(T_a),c_List_Olist_ONil(T_a),T_a) ),
    inference(definition,[],]) ).

fof(to_be_clausified_38,plain,
    ! [T_a] :
      ( lhs_atom36(T_a)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_Nil__is__append__conv_2_0,def_lhs_atom36]) ).

fof(def_lhs_atom37,axiom,
    ! [V_r,T_a] :
      ( lhs_atom37(V_r,T_a)
    <=> c_Transitive__Closure_Ortranclp(c_Transitive__Closure_Ortranclp(V_r,T_a),T_a) = c_Transitive__Closure_Ortranclp(V_r,T_a) ),
    inference(definition,[],]) ).

fof(to_be_clausified_39,plain,
    ! [T_a,V_r] :
      ( lhs_atom37(V_r,T_a)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_rtranclp__idemp_0_0,def_lhs_atom37]) ).

fof(def_lhs_atom38,axiom,
    ! [V_x,V_i,T_a] :
      ( lhs_atom38(V_x,V_i,T_a)
    <=> 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) ),
    inference(definition,[],]) ).

fof(to_be_clausified_40,plain,
    ! [T_a,V_i,V_x] :
      ( lhs_atom38(V_x,V_i,T_a)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_replicate__append__same_0_0,def_lhs_atom38]) ).

fof(def_lhs_atom39,axiom,
    ( lhs_atom39
  <=> ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_41,plain,
    ( lhs_atom39
    | $false ),
    inference(fold_definition,[status(thm)],[cls_neq0__conv_1_0,def_lhs_atom39]) ).

fof(def_lhs_atom40,axiom,
    ! [V_t,V_k] :
      ( lhs_atom40(V_t,V_k)
    <=> c_Lambda_Oliftn(c_HOL_Ozero__class_Ozero(tc_nat),V_t,V_k) = V_t ),
    inference(definition,[],]) ).

fof(to_be_clausified_42,plain,
    ! [V_k,V_t] :
      ( lhs_atom40(V_t,V_k)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_liftn__0_0_0,def_lhs_atom40]) ).

fof(def_lhs_atom41,axiom,
    ( lhs_atom41
  <=> hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_43,plain,
    ( lhs_atom41
    | $false ),
    inference(fold_definition,[status(thm)],[cls_add__is__0_2_0,def_lhs_atom41]) ).

fof(def_lhs_atom42,axiom,
    ! [V_m] :
      ( lhs_atom42(V_m)
    <=> ~ c_HOL_Oord__class_Oless(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_44,plain,
    ! [V_m] :
      ( lhs_atom42(V_m)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_gr__implies__not0_0_0,def_lhs_atom42]) ).

fof(def_lhs_atom43,axiom,
    ! [V_n] :
      ( lhs_atom43(V_n)
    <=> ~ c_HOL_Oord__class_Oless(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_45,plain,
    ! [V_n] :
      ( lhs_atom43(V_n)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_not__less0_0_0,def_lhs_atom43]) ).

fof(def_lhs_atom44,axiom,
    ! [T_a] :
      ( lhs_atom44(T_a)
    <=> c_Predicate_Oconversep(c_fequal(T_a),T_a,T_a) = c_fequal(T_a) ),
    inference(definition,[],]) ).

fof(to_be_clausified_46,plain,
    ! [T_a] :
      ( lhs_atom44(T_a)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_conversep__eq_0_0,def_lhs_atom44]) ).

fof(to_be_clausified_47,plain,
    ! [T_a,V_x] :
      ( lhs_atom32(V_x,T_a)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_empty__replicate_1_0,def_lhs_atom32]) ).

fof(def_lhs_atom45,axiom,
    ! [V_x] :
      ( lhs_atom45(V_x)
    <=> ~ c_HOL_Oord__class_Oless(V_x,V_x,tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_48,plain,
    ! [V_x] :
      ( lhs_atom45(V_x)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_nat__less__le_1_0,def_lhs_atom45]) ).

fof(def_lhs_atom46,axiom,
    ! [V_n] :
      ( lhs_atom46(V_n)
    <=> ~ c_HOL_Oord__class_Oless(V_n,V_n,tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_49,plain,
    ! [V_n] :
      ( lhs_atom46(V_n)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_less__not__refl_0_0,def_lhs_atom46]) ).

fof(def_lhs_atom47,axiom,
    ! [V_ys,V_xs,V_f,T_b,T_a] :
      ( lhs_atom47(V_ys,V_xs,V_f,T_b,T_a)
    <=> c_List_Omap(V_f,c_List_Oappend(V_xs,V_ys,T_b),T_b,T_a) = c_List_Oappend(c_List_Omap(V_f,V_xs,T_b,T_a),c_List_Omap(V_f,V_ys,T_b,T_a),T_a) ),
    inference(definition,[],]) ).

fof(to_be_clausified_50,plain,
    ! [T_a,T_b,V_f,V_xs,V_ys] :
      ( lhs_atom47(V_ys,V_xs,V_f,T_b,T_a)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_map__append_0_0,def_lhs_atom47]) ).

fof(def_lhs_atom48,axiom,
    ! [V_x,V_n,V_k,T_a] :
      ( lhs_atom48(V_x,V_n,V_k,T_a)
    <=> 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) ),
    inference(definition,[],]) ).

fof(to_be_clausified_51,plain,
    ! [T_a,V_k,V_n,V_x] :
      ( lhs_atom48(V_x,V_n,V_k,T_a)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_append__replicate__commute_0_0,def_lhs_atom48]) ).

fof(def_lhs_atom49,axiom,
    ! [V_list_H,V_a_H,T_a] :
      ( lhs_atom49(V_list_H,V_a_H,T_a)
    <=> c_List_Olist_ONil(T_a) != c_List_Olist_OCons(V_a_H,V_list_H,T_a) ),
    inference(definition,[],]) ).

fof(to_be_clausified_52,plain,
    ! [T_a,V_a_H,V_list_H] :
      ( lhs_atom49(V_list_H,V_a_H,T_a)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_list_Osimps_I2_J_0_0,def_lhs_atom49]) ).

fof(def_lhs_atom50,axiom,
    ! [V_x,V_n,V_m,T_a] :
      ( lhs_atom50(V_x,V_n,V_m,T_a)
    <=> c_List_Oreplicate(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_m),V_x,T_a) = c_List_Oappend(c_List_Oreplicate(V_n,V_x,T_a),c_List_Oreplicate(V_m,V_x,T_a),T_a) ),
    inference(definition,[],]) ).

fof(to_be_clausified_53,plain,
    ! [T_a,V_m,V_n,V_x] :
      ( lhs_atom50(V_x,V_n,V_m,T_a)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_replicate__add_0_0,def_lhs_atom50]) ).

fof(def_lhs_atom51,axiom,
    ! [V_ts,V_t,V_i] :
      ( lhs_atom51(V_ts,V_t,V_i)
    <=> hAPP(hAPP(c_Lambda_Olift,c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB)),V_i) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_Olift,V_t),V_i),c_List_Omap(c_COMBC(c_Lambda_Olift,V_i,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) ),
    inference(definition,[],]) ).

fof(to_be_clausified_54,plain,
    ! [V_i,V_t,V_ts] :
      ( lhs_atom51(V_ts,V_t,V_i)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_lift__map_0_0,def_lhs_atom51]) ).

fof(def_lhs_atom52,axiom,
    ! [V_f3,V_f2,V_f1,V_dB,T_a] :
      ( lhs_atom52(V_f3,V_f2,V_f1,V_dB,T_a)
    <=> c_Lambda_OdB_OdB__rec(V_f1,V_f2,V_f3,c_Lambda_OdB_OAbs(V_dB),T_a) = hAPP(hAPP(V_f3,V_dB),c_Lambda_OdB_OdB__rec(V_f1,V_f2,V_f3,V_dB,T_a)) ),
    inference(definition,[],]) ).

fof(to_be_clausified_55,plain,
    ! [T_a,V_dB,V_f1,V_f2,V_f3] :
      ( lhs_atom52(V_f3,V_f2,V_f1,V_dB,T_a)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_dB_Orecs_I3_J_0_0,def_lhs_atom52]) ).

fof(def_lhs_atom53,axiom,
    ! [V_xs,V_x,V_f,V_a,T_b,T_a] :
      ( lhs_atom53(V_xs,V_x,V_f,V_a,T_b,T_a)
    <=> c_List_Ofoldr(V_f,c_List_Olist_OCons(V_x,V_xs,T_b),V_a,T_b,T_a) = hAPP(hAPP(V_f,V_x),c_List_Ofoldr(V_f,V_xs,V_a,T_b,T_a)) ),
    inference(definition,[],]) ).

fof(to_be_clausified_56,plain,
    ! [T_a,T_b,V_a,V_f,V_x,V_xs] :
      ( lhs_atom53(V_xs,V_x,V_f,V_a,T_b,T_a)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_foldr_Osimps_I2_J_0_0,def_lhs_atom53]) ).

fof(def_lhs_atom54,axiom,
    ! [V_r,T_b,T_a] :
      ( lhs_atom54(V_r,T_b,T_a)
    <=> c_Predicate_Oconversep(c_Predicate_Oconversep(V_r,T_a,T_b),T_b,T_a) = V_r ),
    inference(definition,[],]) ).

fof(to_be_clausified_57,plain,
    ! [T_a,T_b,V_r] :
      ( lhs_atom54(V_r,T_b,T_a)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_conversep__conversep_0_0,def_lhs_atom54]) ).

fof(def_lhs_atom55,axiom,
    ! [V_j,V_i] :
      ( lhs_atom55(V_j,V_i)
    <=> ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_j),V_i,tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_58,plain,
    ! [V_i,V_j] :
      ( lhs_atom55(V_j,V_i)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_not__add__less1_0_0,def_lhs_atom55]) ).

fof(def_lhs_atom56,axiom,
    ! [V_j,V_i] :
      ( lhs_atom56(V_j,V_i)
    <=> ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_j),V_i),V_i,tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_59,plain,
    ! [V_i,V_j] :
      ( lhs_atom56(V_j,V_i)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_not__add__less2_0_0,def_lhs_atom56]) ).

fof(def_lhs_atom57,axiom,
    ! [V_xs,V_x,T_a] :
      ( lhs_atom57(V_xs,V_x,T_a)
    <=> 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) ),
    inference(definition,[],]) ).

fof(to_be_clausified_60,plain,
    ! [T_a,V_x,V_xs] :
      ( lhs_atom57(V_xs,V_x,T_a)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_append__eq__Cons__conv_4_0,def_lhs_atom57]) ).

fof(def_lhs_atom58,axiom,
    ! [V_xs,V_x,V_n,T_a] :
      ( lhs_atom58(V_xs,V_x,V_n,T_a)
    <=> 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) ),
    inference(definition,[],]) ).

fof(to_be_clausified_61,plain,
    ! [T_a,V_n,V_x,V_xs] :
      ( lhs_atom58(V_xs,V_x,V_n,T_a)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_replicate__app__Cons__same_0_0,def_lhs_atom58]) ).

fof(def_lhs_atom59,axiom,
    ! [T_a] :
      ( lhs_atom59(T_a)
    <=> c_List_Oappend(c_List_Olist_ONil(T_a),c_List_Olist_ONil(T_a),T_a) = c_List_Olist_ONil(T_a) ),
    inference(definition,[],]) ).

fof(to_be_clausified_62,plain,
    ! [T_a] :
      ( lhs_atom59(T_a)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_append__is__Nil__conv_2_0,def_lhs_atom59]) ).

fof(def_lhs_atom60,axiom,
    ! [V_zs,V_ys,V_xs,T_a] :
      ( lhs_atom60(V_zs,V_ys,V_xs,T_a)
    <=> 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) ),
    inference(definition,[],]) ).

fof(to_be_clausified_63,plain,
    ! [T_a,V_xs,V_ys,V_zs] :
      ( lhs_atom60(V_zs,V_ys,V_xs,T_a)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_append__assoc_0_0,def_lhs_atom60]) ).

fof(def_lhs_atom61,axiom,
    ! [V_xs1,V_xs,V_us,T_a] :
      ( lhs_atom61(V_xs1,V_xs,V_us,T_a)
    <=> 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) ),
    inference(definition,[],]) ).

fof(to_be_clausified_64,plain,
    ! [T_a,V_us,V_xs,V_xs1] :
      ( lhs_atom61(V_xs1,V_xs,V_us,T_a)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_append__eq__appendI_0_0,def_lhs_atom61]) ).

fof(def_lhs_atom62,axiom,
    ! [V_zs,V_ys,V_x,T_a] :
      ( lhs_atom62(V_zs,V_ys,V_x,T_a)
    <=> 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) ),
    inference(definition,[],]) ).

fof(to_be_clausified_65,plain,
    ! [T_a,V_x,V_ys,V_zs] :
      ( lhs_atom62(V_zs,V_ys,V_x,T_a)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_append__eq__append__conv2_4_0,def_lhs_atom62]) ).

fof(def_lhs_atom63,axiom,
    ! [V_xs,V_x,V_ts,T_a] :
      ( lhs_atom63(V_xs,V_x,V_ts,T_a)
    <=> 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) ),
    inference(definition,[],]) ).

fof(to_be_clausified_66,plain,
    ! [T_a,V_ts,V_x,V_xs] :
      ( lhs_atom63(V_xs,V_x,V_ts,T_a)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_append__eq__append__conv2_5_0,def_lhs_atom63]) ).

fof(def_lhs_atom64,axiom,
    ! [V_c] :
      ( lhs_atom64(V_c)
    <=> c_Nat_Osize__class_Osize(V_c,tc_String_Ochar) = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_67,plain,
    ! [V_c] :
      ( lhs_atom64(V_c)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_size__char_0_0,def_lhs_atom64]) ).

fof(def_lhs_atom65,axiom,
    ! [V_y,V_x,T_a] :
      ( lhs_atom65(V_y,V_x,T_a)
    <=> 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) ),
    inference(definition,[],]) ).

fof(to_be_clausified_68,plain,
    ! [T_a,V_x,V_y] :
      ( lhs_atom65(V_y,V_x,T_a)
      | 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) ),
    inference(fold_definition,[status(thm)],[cls_replicate__eq__replicate_2_0,def_lhs_atom65]) ).

fof(def_lhs_atom66,axiom,
    ! [V_n] :
      ( lhs_atom66(V_n)
    <=> c_Orderings_Oord__class_Omax(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = V_n ),
    inference(definition,[],]) ).

fof(to_be_clausified_69,plain,
    ! [V_n] :
      ( lhs_atom66(V_n)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_max__0R_0_0,def_lhs_atom66]) ).

fof(def_lhs_atom67,axiom,
    ! [V_n] :
      ( lhs_atom67(V_n)
    <=> c_Orderings_Oord__class_Omax(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) = V_n ),
    inference(definition,[],]) ).

fof(to_be_clausified_70,plain,
    ! [V_n] :
      ( lhs_atom67(V_n)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_max__0L_0_0,def_lhs_atom67]) ).

fof(def_lhs_atom68,axiom,
    ! [V_x] :
      ( lhs_atom68(V_x)
    <=> V_x = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_x),c_HOL_Ozero__class_Ozero(tc_nat)) ),
    inference(definition,[],]) ).

fof(to_be_clausified_71,plain,
    ! [V_x] :
      ( lhs_atom68(V_x)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_natgb_Oadd__r0__iff_1_0,def_lhs_atom68]) ).

fof(def_lhs_atom69,axiom,
    ! [V_n] :
      ( lhs_atom69(V_n)
    <=> hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),V_n) = V_n ),
    inference(definition,[],]) ).

fof(to_be_clausified_72,plain,
    ! [V_n] :
      ( lhs_atom69(V_n)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_plus__nat_Oadd__0_0_0,def_lhs_atom69]) ).

fof(def_lhs_atom70,axiom,
    ! [V_m] :
      ( lhs_atom70(V_m)
    <=> hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),c_HOL_Ozero__class_Ozero(tc_nat)) = V_m ),
    inference(definition,[],]) ).

fof(to_be_clausified_73,plain,
    ! [V_m] :
      ( lhs_atom70(V_m)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_Nat_Oadd__0__right_0_0,def_lhs_atom70]) ).

fof(def_lhs_atom71,axiom,
    ! [V_dB_H,V_dB2,V_dB1] :
      ( lhs_atom71(V_dB_H,V_dB2,V_dB1)
    <=> hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2) != c_Lambda_OdB_OAbs(V_dB_H) ),
    inference(definition,[],]) ).

fof(to_be_clausified_74,plain,
    ! [V_dB1,V_dB2,V_dB_H] :
      ( lhs_atom71(V_dB_H,V_dB2,V_dB1)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_dB_Osimps_I8_J_0_0,def_lhs_atom71]) ).

fof(def_lhs_atom72,axiom,
    ! [V_dB_H,V_dB2,V_dB1] :
      ( lhs_atom72(V_dB_H,V_dB2,V_dB1)
    <=> c_Lambda_OdB_OAbs(V_dB_H) != hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2) ),
    inference(definition,[],]) ).

fof(to_be_clausified_75,plain,
    ! [V_dB1,V_dB2,V_dB_H] :
      ( lhs_atom72(V_dB_H,V_dB2,V_dB1)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_dB_Osimps_I9_J_0_0,def_lhs_atom72]) ).

fof(def_lhs_atom73,axiom,
    ! [V_t,V_s,V_k] :
      ( lhs_atom73(V_t,V_s,V_k)
    <=> hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_t)),V_k) = hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_Olift,V_s),V_k)),hAPP(hAPP(c_Lambda_Olift,V_t),V_k)) ),
    inference(definition,[],]) ).

fof(to_be_clausified_76,plain,
    ! [V_k,V_s,V_t] :
      ( lhs_atom73(V_t,V_s,V_k)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_lift_Osimps_I2_J_0_0,def_lhs_atom73]) ).

fof(def_lhs_atom74,axiom,
    ! [V_f3,V_f2,V_f1,V_dB2,V_dB1,T_a] :
      ( lhs_atom74(V_f3,V_f2,V_f1,V_dB2,V_dB1,T_a)
    <=> c_Lambda_OdB_OdB__case(V_f1,V_f2,V_f3,hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2),T_a) = hAPP(hAPP(V_f2,V_dB1),V_dB2) ),
    inference(definition,[],]) ).

fof(to_be_clausified_77,plain,
    ! [T_a,V_dB1,V_dB2,V_f1,V_f2,V_f3] :
      ( lhs_atom74(V_f3,V_f2,V_f1,V_dB2,V_dB1,T_a)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_dB_Osimps_I11_J_0_0,def_lhs_atom74]) ).

fof(def_lhs_atom75,axiom,
    ! [V_f3,V_f2,V_f1,V_dB2,V_dB1,T_a] :
      ( lhs_atom75(V_f3,V_f2,V_f1,V_dB2,V_dB1,T_a)
    <=> c_Lambda_OdB_OdB__rec(V_f1,V_f2,V_f3,hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2),T_a) = hAPP(hAPP(hAPP(hAPP(V_f2,V_dB1),V_dB2),c_Lambda_OdB_OdB__rec(V_f1,V_f2,V_f3,V_dB1,T_a)),c_Lambda_OdB_OdB__rec(V_f1,V_f2,V_f3,V_dB2,T_a)) ),
    inference(definition,[],]) ).

fof(to_be_clausified_78,plain,
    ! [T_a,V_dB1,V_dB2,V_f1,V_f2,V_f3] :
      ( lhs_atom75(V_f3,V_f2,V_f1,V_dB2,V_dB1,T_a)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_dB_Orecs_I2_J_0_0,def_lhs_atom75]) ).

fof(def_lhs_atom76,axiom,
    ! [V_t,V_s,V_n,V_k] :
      ( lhs_atom76(V_t,V_s,V_n,V_k)
    <=> c_Lambda_Oliftn(V_n,hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_t),V_k) = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Oliftn(V_n,V_s,V_k)),c_Lambda_Oliftn(V_n,V_t,V_k)) ),
    inference(definition,[],]) ).

fof(to_be_clausified_79,plain,
    ! [V_k,V_n,V_s,V_t] :
      ( lhs_atom76(V_t,V_s,V_n,V_k)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_liftn_Osimps_I2_J_0_0,def_lhs_atom76]) ).

fof(def_lhs_atom77,axiom,
    ! [V_u,V_t,V_s,V_k] :
      ( lhs_atom77(V_u,V_t,V_s,V_k)
    <=> c_Lambda_Osubstn(hAPP(hAPP(c_Lambda_OdB_OApp,V_t),V_u),V_s,V_k) = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Osubstn(V_t,V_s,V_k)),c_Lambda_Osubstn(V_u,V_s,V_k)) ),
    inference(definition,[],]) ).

fof(to_be_clausified_80,plain,
    ! [V_k,V_s,V_t,V_u] :
      ( lhs_atom77(V_u,V_t,V_s,V_k)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_substn_Osimps_I2_J_0_0,def_lhs_atom77]) ).

fof(def_lhs_atom78,axiom,
    ! [V_t,V_s,V_n] :
      ( lhs_atom78(V_t,V_s,V_n)
    <=> c_Lambda_Osubstn(V_t,V_s,V_n) = hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),c_Lambda_Oliftn(V_n,V_s,c_HOL_Ozero__class_Ozero(tc_nat))),V_n) ),
    inference(definition,[],]) ).

fof(to_be_clausified_81,plain,
    ! [V_n,V_s,V_t] :
      ( lhs_atom78(V_t,V_s,V_n)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_substn__subst__n_0_0,def_lhs_atom78]) ).

fof(def_lhs_atom79,axiom,
    ! [V_r] :
      ( lhs_atom79(V_r)
    <=> c_Lambda_OdB_OAbs(V_r) = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_r),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) ),
    inference(definition,[],]) ).

fof(to_be_clausified_82,plain,
    ! [V_r] :
      ( lhs_atom79(V_r)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_Abs__eq__apps__conv_2_0,def_lhs_atom79]) ).

fof(def_lhs_atom80,axiom,
    ! [V_t] :
      ( lhs_atom80(V_t)
    <=> V_t = c_List_Ofoldl(c_Lambda_OdB_OApp,c_ListApplication_Osko__ListApplication__Xex__head__tail__1__2(V_t),c_ListApplication_Osko__ListApplication__Xex__head__tail__1__1(V_t),tc_Lambda_OdB,tc_Lambda_OdB) ),
    inference(definition,[],]) ).

fof(to_be_clausified_83,plain,
    ! [V_t] :
      ( lhs_atom80(V_t)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_ex__head__tail_0_0,def_lhs_atom80]) ).

fof(def_lhs_atom81,axiom,
    ! [V_r] :
      ( lhs_atom81(V_r)
    <=> c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_r),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) = c_Lambda_OdB_OAbs(V_r) ),
    inference(definition,[],]) ).

fof(to_be_clausified_84,plain,
    ! [V_r] :
      ( lhs_atom81(V_r)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_apps__eq__Abs__conv_2_0,def_lhs_atom81]) ).

fof(def_lhs_atom82,axiom,
    ! [V_f,V_a,T_b,T_a] :
      ( lhs_atom82(V_f,V_a,T_b,T_a)
    <=> c_List_Ofoldl(V_f,V_a,c_List_Olist_ONil(T_b),T_a,T_b) = V_a ),
    inference(definition,[],]) ).

fof(to_be_clausified_85,plain,
    ! [T_a,T_b,V_a,V_f] :
      ( lhs_atom82(V_f,V_a,T_b,T_a)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_foldl__Nil_0_0,def_lhs_atom82]) ).

fof(def_lhs_atom83,axiom,
    ! [V_xs,V_x,V_f,V_a,T_b,T_a] :
      ( lhs_atom83(V_xs,V_x,V_f,V_a,T_b,T_a)
    <=> c_List_Ofoldl(V_f,V_a,c_List_Olist_OCons(V_x,V_xs,T_b),T_a,T_b) = c_List_Ofoldl(V_f,hAPP(hAPP(V_f,V_a),V_x),V_xs,T_a,T_b) ),
    inference(definition,[],]) ).

fof(to_be_clausified_86,plain,
    ! [T_a,T_b,V_a,V_f,V_x,V_xs] :
      ( lhs_atom83(V_xs,V_x,V_f,V_a,T_b,T_a)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_foldl__Cons_0_0,def_lhs_atom83]) ).

fof(def_lhs_atom84,axiom,
    ! [V_ys,V_xs,V_f,V_a,T_b,T_a] :
      ( lhs_atom84(V_ys,V_xs,V_f,V_a,T_b,T_a)
    <=> c_List_Ofoldl(V_f,V_a,c_List_Oappend(V_xs,V_ys,T_b),T_a,T_b) = c_List_Ofoldl(V_f,c_List_Ofoldl(V_f,V_a,V_xs,T_a,T_b),V_ys,T_a,T_b) ),
    inference(definition,[],]) ).

fof(to_be_clausified_87,plain,
    ! [T_a,T_b,V_a,V_f,V_xs,V_ys] :
      ( lhs_atom84(V_ys,V_xs,V_f,V_a,T_b,T_a)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_foldl__append_0_0,def_lhs_atom84]) ).

fof(def_lhs_atom85,axiom,
    ! [V_u,V_ts,V_t,V_i] :
      ( lhs_atom85(V_u,V_ts,V_t,V_i)
    <=> hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB)),V_u),V_i) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_u),V_i),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,V_u,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),V_i,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) ),
    inference(definition,[],]) ).

fof(to_be_clausified_88,plain,
    ! [V_i,V_t,V_ts,V_u] :
      ( lhs_atom85(V_u,V_ts,V_t,V_i)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_subst__map_0_0,def_lhs_atom85]) ).

fof(def_lhs_atom86,axiom,
    ! [V_t,V_s,V_k] :
      ( lhs_atom86(V_t,V_s,V_k)
    <=> hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,V_t),V_k)),V_s),V_k) = V_t ),
    inference(definition,[],]) ).

fof(to_be_clausified_89,plain,
    ! [V_k,V_s,V_t] :
      ( lhs_atom86(V_t,V_s,V_k)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_subst__lift_0_0,def_lhs_atom86]) ).

fof(def_lhs_atom87,axiom,
    ! [V_nat,V_dB_H] :
      ( lhs_atom87(V_nat,V_dB_H)
    <=> c_Lambda_OdB_OAbs(V_dB_H) != c_Lambda_OdB_OVar(V_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_90,plain,
    ! [V_dB_H,V_nat] :
      ( lhs_atom87(V_nat,V_dB_H)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_dB_Osimps_I7_J_0_0,def_lhs_atom87]) ).

fof(def_lhs_atom88,axiom,
    ! [V_t,V_i] :
      ( lhs_atom88(V_t,V_i)
    <=> ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OVar(V_i)),V_t)) ),
    inference(definition,[],]) ).

fof(to_be_clausified_91,plain,
    ! [V_i,V_t] :
      ( lhs_atom88(V_t,V_i)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_beta__cases_I1_J_0_0,def_lhs_atom88]) ).

fof(def_lhs_atom89,axiom,
    ! [V_nat,V_f3,V_f2,V_f1,T_a] :
      ( lhs_atom89(V_nat,V_f3,V_f2,V_f1,T_a)
    <=> c_Lambda_OdB_OdB__rec(V_f1,V_f2,V_f3,c_Lambda_OdB_OVar(V_nat),T_a) = hAPP(V_f1,V_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_92,plain,
    ! [T_a,V_f1,V_f2,V_f3,V_nat] :
      ( lhs_atom89(V_nat,V_f3,V_f2,V_f1,T_a)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_dB_Orecs_I1_J_0_0,def_lhs_atom89]) ).

fof(def_lhs_atom90,axiom,
    ! [V_nat,V_dB_H] :
      ( lhs_atom90(V_nat,V_dB_H)
    <=> c_Lambda_OdB_OVar(V_nat) != c_Lambda_OdB_OAbs(V_dB_H) ),
    inference(definition,[],]) ).

fof(to_be_clausified_93,plain,
    ! [V_dB_H,V_nat] :
      ( lhs_atom90(V_nat,V_dB_H)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_dB_Osimps_I6_J_0_0,def_lhs_atom90]) ).

fof(def_lhs_atom91,axiom,
    ! [V_nat,V_f3,V_f2,V_f1,T_a] :
      ( lhs_atom91(V_nat,V_f3,V_f2,V_f1,T_a)
    <=> c_Lambda_OdB_OdB__case(V_f1,V_f2,V_f3,c_Lambda_OdB_OVar(V_nat),T_a) = hAPP(V_f1,V_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_94,plain,
    ! [T_a,V_f1,V_f2,V_f3,V_nat] :
      ( lhs_atom91(V_nat,V_f3,V_f2,V_f1,T_a)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_dB_Osimps_I10_J_0_0,def_lhs_atom91]) ).

fof(def_lhs_atom92,axiom,
    ! [V_x,V_env] :
      ( lhs_atom92(V_x,V_env)
    <=> c_Type_Otyping(V_env,c_Lambda_OdB_OVar(V_x),hAPP(V_env,V_x)) ),
    inference(definition,[],]) ).

fof(to_be_clausified_95,plain,
    ! [V_env,V_x] :
      ( lhs_atom92(V_x,V_env)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_typing_OVar_0_0,def_lhs_atom92]) ).

fof(def_lhs_atom93,axiom,
    ! [V_t,V_s] :
      ( lhs_atom93(V_t,V_s)
    <=> hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_s)),V_t)),hAPP(hAPP(hAPP(c_Lambda_Osubst,V_s),V_t),c_HOL_Ozero__class_Ozero(tc_nat)))) ),
    inference(definition,[],]) ).

fof(to_be_clausified_96,plain,
    ! [V_s,V_t] :
      ( lhs_atom93(V_t,V_s)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_beta_0_0,def_lhs_atom93]) ).

fof(def_lhs_atom94,axiom,
    ! [V_t,V_s] :
      ( lhs_atom94(V_t,V_s)
    <=> c_Lambda_Osubstn(V_t,V_s,c_HOL_Ozero__class_Ozero(tc_nat)) = hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_s),c_HOL_Ozero__class_Ozero(tc_nat)) ),
    inference(definition,[],]) ).

fof(to_be_clausified_97,plain,
    ! [V_s,V_t] :
      ( lhs_atom94(V_t,V_s)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_substn__subst__0_0_0,def_lhs_atom94]) ).

fof(def_lhs_atom95,axiom,
    ! [V_nat] :
      ( lhs_atom95(V_nat)
    <=> c_Nat_Osize__class_Osize(c_Lambda_OdB_OVar(V_nat),tc_Lambda_OdB) = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_98,plain,
    ! [V_nat] :
      ( lhs_atom95(V_nat)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_dB_Osize_I4_J_0_0,def_lhs_atom95]) ).

fof(def_lhs_atom96,axiom,
    ! [V_nat] :
      ( lhs_atom96(V_nat)
    <=> c_Lambda_OdB_OdB__size(c_Lambda_OdB_OVar(V_nat)) = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_99,plain,
    ! [V_nat] :
      ( lhs_atom96(V_nat)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_dB_Osize_I1_J_0_0,def_lhs_atom96]) ).

fof(def_lhs_atom97,axiom,
    ! [V_s,V_r] :
      ( lhs_atom97(V_s,V_r)
    <=> hAPP(hAPP(c_Lambda_OdB_OApp,V_r),V_s) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,V_r),V_s),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) ),
    inference(definition,[],]) ).

fof(to_be_clausified_100,plain,
    ! [V_r,V_s] :
      ( lhs_atom97(V_s,V_r)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_App__eq__foldl__conv_4_0,def_lhs_atom97]) ).

fof(def_lhs_atom98,axiom,
    ! [V_ts,V_ss,V_r,V_n] :
      ( lhs_atom98(V_ts,V_ss,V_r,V_n)
    <=> c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),V_ts,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_r),V_ss,tc_Lambda_OdB,tc_Lambda_OdB) ),
    inference(definition,[],]) ).

fof(to_be_clausified_101,plain,
    ! [V_n,V_r,V_ss,V_ts] :
      ( lhs_atom98(V_ts,V_ss,V_r,V_n)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_Var__apps__neq__Abs__apps_0_0,def_lhs_atom98]) ).

fof(def_lhs_atom99,axiom,
    ! [V_m] :
      ( lhs_atom99(V_m)
    <=> c_Lambda_OdB_OVar(V_m) = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_m),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) ),
    inference(definition,[],]) ).

fof(to_be_clausified_102,plain,
    ! [V_m] :
      ( lhs_atom99(V_m)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_Var__eq__apps__conv_2_0,def_lhs_atom99]) ).

fof(def_lhs_atom100,axiom,
    ! [V_t,V_ss,V_s,V_n] :
      ( lhs_atom100(V_t,V_ss,V_s,V_n)
    <=> hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_s)),V_t) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),V_ss,tc_Lambda_OdB,tc_Lambda_OdB) ),
    inference(definition,[],]) ).

fof(to_be_clausified_103,plain,
    ! [V_n,V_s,V_ss,V_t] :
      ( lhs_atom100(V_t,V_ss,V_s,V_n)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_Abs__App__neq__Var__apps_0_0,def_lhs_atom100]) ).

fof(def_lhs_atom101,axiom,
    ! [V_u,V_t,V_s,V_k] :
      ( lhs_atom101(V_u,V_t,V_s,V_k)
    <=> hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_OdB_OApp,V_t),V_u)),V_s),V_k) = hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_s),V_k)),hAPP(hAPP(hAPP(c_Lambda_Osubst,V_u),V_s),V_k)) ),
    inference(definition,[],]) ).

fof(to_be_clausified_104,plain,
    ! [V_k,V_s,V_t,V_u] :
      ( lhs_atom101(V_u,V_t,V_s,V_k)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_subst__App_0_0,def_lhs_atom101]) ).

fof(def_lhs_atom102,axiom,
    ! [V_u,V_k] :
      ( lhs_atom102(V_u,V_k)
    <=> hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(V_k)),V_u),V_k) = V_u ),
    inference(definition,[],]) ).

fof(to_be_clausified_105,plain,
    ! [V_k,V_u] :
      ( lhs_atom102(V_u,V_k)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_subst__eq_0_0,def_lhs_atom102]) ).

fof(def_lhs_atom103,axiom,
    ! [V_nat,V_dB2_H,V_dB1_H] :
      ( lhs_atom103(V_nat,V_dB2_H,V_dB1_H)
    <=> c_Lambda_OdB_OVar(V_nat) != hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1_H),V_dB2_H) ),
    inference(definition,[],]) ).

fof(to_be_clausified_106,plain,
    ! [V_dB1_H,V_dB2_H,V_nat] :
      ( lhs_atom103(V_nat,V_dB2_H,V_dB1_H)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_dB_Osimps_I4_J_0_0,def_lhs_atom103]) ).

fof(def_lhs_atom104,axiom,
    ! [V_n] :
      ( lhs_atom104(V_n)
    <=> hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(V_n))) ),
    inference(definition,[],]) ).

fof(to_be_clausified_107,plain,
    ! [V_n] :
      ( lhs_atom104(V_n)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_Var__IT_0_0,def_lhs_atom104]) ).

fof(def_lhs_atom105,axiom,
    ! [V_nat,V_dB2_H,V_dB1_H] :
      ( lhs_atom105(V_nat,V_dB2_H,V_dB1_H)
    <=> hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1_H),V_dB2_H) != c_Lambda_OdB_OVar(V_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_108,plain,
    ! [V_dB1_H,V_dB2_H,V_nat] :
      ( lhs_atom105(V_nat,V_dB2_H,V_dB1_H)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_dB_Osimps_I5_J_0_0,def_lhs_atom105]) ).

fof(def_lhs_atom106,axiom,
    ( lhs_atom106
  <=> class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_109,plain,
    ( lhs_atom106
    | $false ),
    inference(fold_definition,[status(thm)],[clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add_0,def_lhs_atom106]) ).

fof(def_lhs_atom107,axiom,
    ( lhs_atom107
  <=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_110,plain,
    ( lhs_atom107
    | $false ),
    inference(fold_definition,[status(thm)],[clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le_0,def_lhs_atom107]) ).

fof(def_lhs_atom108,axiom,
    ( lhs_atom108
  <=> class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_111,plain,
    ( lhs_atom108
    | $false ),
    inference(fold_definition,[status(thm)],[clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add_0,def_lhs_atom108]) ).

fof(def_lhs_atom109,axiom,
    ( lhs_atom109
  <=> class_OrderedGroup_Opordered__comm__monoid__add(tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_112,plain,
    ( lhs_atom109
    | $false ),
    inference(fold_definition,[status(thm)],[clsarity_nat__OrderedGroup_Opordered__comm__monoid__add_0,def_lhs_atom109]) ).

fof(def_lhs_atom110,axiom,
    ( lhs_atom110
  <=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_113,plain,
    ( lhs_atom110
    | $false ),
    inference(fold_definition,[status(thm)],[clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add_0,def_lhs_atom110]) ).

fof(def_lhs_atom111,axiom,
    ( lhs_atom111
  <=> class_OrderedGroup_Ocancel__semigroup__add(tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_114,plain,
    ( lhs_atom111
    | $false ),
    inference(fold_definition,[status(thm)],[clsarity_nat__OrderedGroup_Ocancel__semigroup__add_0,def_lhs_atom111]) ).

fof(def_lhs_atom112,axiom,
    ( lhs_atom112
  <=> class_Ring__and__Field_Ono__zero__divisors(tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_115,plain,
    ( lhs_atom112
    | $false ),
    inference(fold_definition,[status(thm)],[clsarity_nat__Ring__and__Field_Ono__zero__divisors_0,def_lhs_atom112]) ).

fof(def_lhs_atom113,axiom,
    ( lhs_atom113
  <=> class_Ring__and__Field_Oordered__semidom(tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_116,plain,
    ( lhs_atom113
    | $false ),
    inference(fold_definition,[status(thm)],[clsarity_nat__Ring__and__Field_Oordered__semidom_0,def_lhs_atom113]) ).

fof(def_lhs_atom114,axiom,
    ( lhs_atom114
  <=> class_Ring__and__Field_Ocomm__semiring__1(tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_117,plain,
    ( lhs_atom114
    | $false ),
    inference(fold_definition,[status(thm)],[clsarity_nat__Ring__and__Field_Ocomm__semiring__1_0,def_lhs_atom114]) ).

fof(def_lhs_atom115,axiom,
    ( lhs_atom115
  <=> class_OrderedGroup_Oab__semigroup__add(tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_118,plain,
    ( lhs_atom115
    | $false ),
    inference(fold_definition,[status(thm)],[clsarity_nat__OrderedGroup_Oab__semigroup__add_0,def_lhs_atom115]) ).

fof(def_lhs_atom116,axiom,
    ( lhs_atom116
  <=> class_OrderedGroup_Ocomm__monoid__add(tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_119,plain,
    ( lhs_atom116
    | $false ),
    inference(fold_definition,[status(thm)],[clsarity_nat__OrderedGroup_Ocomm__monoid__add_0,def_lhs_atom116]) ).

fof(def_lhs_atom117,axiom,
    ( lhs_atom117
  <=> class_Ring__and__Field_Ozero__neq__one(tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_120,plain,
    ( lhs_atom117
    | $false ),
    inference(fold_definition,[status(thm)],[clsarity_nat__Ring__and__Field_Ozero__neq__one_0,def_lhs_atom117]) ).

fof(def_lhs_atom118,axiom,
    ( lhs_atom118
  <=> class_OrderedGroup_Osemigroup__add(tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_121,plain,
    ( lhs_atom118
    | $false ),
    inference(fold_definition,[status(thm)],[clsarity_nat__OrderedGroup_Osemigroup__add_0,def_lhs_atom118]) ).

fof(def_lhs_atom119,axiom,
    ( lhs_atom119
  <=> class_Ring__and__Field_Osemiring__1(tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_122,plain,
    ( lhs_atom119
    | $false ),
    inference(fold_definition,[status(thm)],[clsarity_nat__Ring__and__Field_Osemiring__1_0,def_lhs_atom119]) ).

fof(def_lhs_atom120,axiom,
    ( lhs_atom120
  <=> class_Ring__and__Field_Osemiring__0(tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_123,plain,
    ( lhs_atom120
    | $false ),
    inference(fold_definition,[status(thm)],[clsarity_nat__Ring__and__Field_Osemiring__0_0,def_lhs_atom120]) ).

fof(def_lhs_atom121,axiom,
    ( lhs_atom121
  <=> class_Ring__and__Field_Omult__zero(tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_124,plain,
    ( lhs_atom121
    | $false ),
    inference(fold_definition,[status(thm)],[clsarity_nat__Ring__and__Field_Omult__zero_0,def_lhs_atom121]) ).

fof(def_lhs_atom122,axiom,
    ( lhs_atom122
  <=> class_OrderedGroup_Omonoid__mult(tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_125,plain,
    ( lhs_atom122
    | $false ),
    inference(fold_definition,[status(thm)],[clsarity_nat__OrderedGroup_Omonoid__mult_0,def_lhs_atom122]) ).

fof(def_lhs_atom123,axiom,
    ( lhs_atom123
  <=> class_OrderedGroup_Omonoid__add(tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_126,plain,
    ( lhs_atom123
    | $false ),
    inference(fold_definition,[status(thm)],[clsarity_nat__OrderedGroup_Omonoid__add_0,def_lhs_atom123]) ).

fof(def_lhs_atom124,axiom,
    ( lhs_atom124
  <=> class_Nat_Osemiring__char__0(tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_127,plain,
    ( lhs_atom124
    | $false ),
    inference(fold_definition,[status(thm)],[clsarity_nat__Nat_Osemiring__char__0_0,def_lhs_atom124]) ).

fof(def_lhs_atom125,axiom,
    ( lhs_atom125
  <=> class_Orderings_Opreorder(tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_128,plain,
    ( lhs_atom125
    | $false ),
    inference(fold_definition,[status(thm)],[clsarity_nat__Orderings_Opreorder_0,def_lhs_atom125]) ).

fof(def_lhs_atom126,axiom,
    ( lhs_atom126
  <=> class_Orderings_Olinorder(tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_129,plain,
    ( lhs_atom126
    | $false ),
    inference(fold_definition,[status(thm)],[clsarity_nat__Orderings_Olinorder_0,def_lhs_atom126]) ).

fof(def_lhs_atom127,axiom,
    ( lhs_atom127
  <=> class_Orderings_Oorder(tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_130,plain,
    ( lhs_atom127
    | $false ),
    inference(fold_definition,[status(thm)],[clsarity_nat__Orderings_Oorder_0,def_lhs_atom127]) ).

fof(def_lhs_atom128,axiom,
    ( lhs_atom128
  <=> class_Power_Opower(tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_131,plain,
    ( lhs_atom128
    | $false ),
    inference(fold_definition,[status(thm)],[clsarity_nat__Power_Opower_0,def_lhs_atom128]) ).

fof(def_lhs_atom129,axiom,
    ( lhs_atom129
  <=> class_Orderings_Opreorder(tc_bool) ),
    inference(definition,[],]) ).

fof(to_be_clausified_132,plain,
    ( lhs_atom129
    | $false ),
    inference(fold_definition,[status(thm)],[clsarity_bool__Orderings_Opreorder_0,def_lhs_atom129]) ).

fof(def_lhs_atom130,axiom,
    ( lhs_atom130
  <=> class_Orderings_Oorder(tc_bool) ),
    inference(definition,[],]) ).

fof(to_be_clausified_133,plain,
    ( lhs_atom130
    | $false ),
    inference(fold_definition,[status(thm)],[clsarity_bool__Orderings_Oorder_0,def_lhs_atom130]) ).

fof(def_lhs_atom131,axiom,
    ! [V_x,T_a] :
      ( lhs_atom131(V_x,T_a)
    <=> hBOOL(hAPP(hAPP(c_fequal(T_a),V_x),V_x)) ),
    inference(definition,[],]) ).

fof(to_be_clausified_134,plain,
    ! [T_a,V_x] :
      ( lhs_atom131(V_x,T_a)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_ATP__Linkup_Oequal__imp__fequal_0_0,def_lhs_atom131]) ).

% Start CNF derivation
fof(c_0_0,axiom,
    ! [X14,X9,X10,X16,X11,X4] :
      ( lhs_atom84(X14,X9,X10,X16,X11,X4)
      | ~ $true ),
    file('<stdin>',to_be_clausified_87) ).

fof(c_0_1,axiom,
    ! [X9,X1,X10,X16,X11,X4] :
      ( lhs_atom83(X9,X1,X10,X16,X11,X4)
      | ~ $true ),
    file('<stdin>',to_be_clausified_86) ).

fof(c_0_2,axiom,
    ! [X24,X25,X26,X39,X40,X4] :
      ( lhs_atom75(X24,X25,X26,X39,X40,X4)
      | ~ $true ),
    file('<stdin>',to_be_clausified_78) ).

fof(c_0_3,axiom,
    ! [X24,X25,X26,X39,X40,X4] :
      ( lhs_atom74(X24,X25,X26,X39,X40,X4)
      | ~ $true ),
    file('<stdin>',to_be_clausified_77) ).

fof(c_0_4,axiom,
    ! [X9,X1,X10,X16,X11,X4] :
      ( lhs_atom53(X9,X1,X10,X16,X11,X4)
      | ~ $true ),
    file('<stdin>',to_be_clausified_56) ).

fof(c_0_5,axiom,
    ! [X14,X9,X10,X16,X11,X4] :
      ( lhs_atom25(X14,X9,X10,X16,X11,X4)
      | ~ $true ),
    file('<stdin>',to_be_clausified_26) ).

fof(c_0_6,axiom,
    ! [X17,X18,X19,X20,X11,X4] :
      ( lhs_atom13(X17,X18,X19,X20,X11,X4)
      | ~ $true ),
    file('<stdin>',to_be_clausified_12) ).

fof(c_0_7,axiom,
    ! [X42,X24,X25,X26,X4] :
      ( lhs_atom91(X42,X24,X25,X26,X4)
      | ~ $true ),
    file('<stdin>',to_be_clausified_94) ).

fof(c_0_8,axiom,
    ! [X42,X24,X25,X26,X4] :
      ( lhs_atom89(X42,X24,X25,X26,X4)
      | ~ $true ),
    file('<stdin>',to_be_clausified_92) ).

fof(c_0_9,axiom,
    ! [X24,X25,X26,X27,X4] :
      ( lhs_atom52(X24,X25,X26,X27,X4)
      | ~ $true ),
    file('<stdin>',to_be_clausified_55) ).

fof(c_0_10,axiom,
    ! [X14,X9,X10,X11,X4] :
      ( lhs_atom47(X14,X9,X10,X11,X4)
      | ~ $true ),
    file('<stdin>',to_be_clausified_50) ).

fof(c_0_11,axiom,
    ! [X1,X7,X10,X11,X4] :
      ( lhs_atom23(X1,X7,X10,X11,X4)
      | ~ $true ),
    file('<stdin>',to_be_clausified_24) ).

fof(c_0_12,axiom,
    ! [X24,X25,X26,X27,X4] :
      ( lhs_atom16(X24,X25,X26,X27,X4)
      | ~ $true ),
    file('<stdin>',to_be_clausified_15) ).

fof(c_0_13,axiom,
    ! [X13,X1,X10,X11,X4] :
      ( lhs_atom8(X13,X1,X10,X11,X4)
      | ~ $true ),
    file('<stdin>',to_be_clausified_7) ).

fof(c_0_14,axiom,
    ! [X12,X13,X10,X11,X4] :
      ( lhs_atom7(X12,X13,X10,X11,X4)
      | ~ $true ),
    file('<stdin>',to_be_clausified_6) ).

fof(c_0_15,axiom,
    ! [X9,X1,X10,X11,X4] :
      ( lhs_atom6(X9,X1,X10,X11,X4)
      | ~ $true ),
    file('<stdin>',to_be_clausified_5) ).

fof(c_0_16,axiom,
    ! [X41,X8,X5,X6] :
      ( lhs_atom101(X41,X8,X5,X6)
      | ~ $true ),
    file('<stdin>',to_be_clausified_104) ).

fof(c_0_17,axiom,
    ! [X8,X44,X5,X7] :
      ( lhs_atom100(X8,X44,X5,X7)
      | ~ $true ),
    file('<stdin>',to_be_clausified_103) ).

fof(c_0_18,axiom,
    ! [X34,X44,X29,X7] :
      ( lhs_atom98(X34,X44,X29,X7)
      | ~ $true ),
    file('<stdin>',to_be_clausified_101) ).

fof(c_0_19,axiom,
    ! [X41,X34,X8,X33] :
      ( lhs_atom85(X41,X34,X8,X33)
      | ~ $true ),
    file('<stdin>',to_be_clausified_88) ).

fof(c_0_20,axiom,
    ! [X10,X16,X11,X4] :
      ( lhs_atom82(X10,X16,X11,X4)
      | ~ $true ),
    file('<stdin>',to_be_clausified_85) ).

fof(c_0_21,axiom,
    ! [X41,X8,X5,X6] :
      ( lhs_atom77(X41,X8,X5,X6)
      | ~ $true ),
    file('<stdin>',to_be_clausified_80) ).

fof(c_0_22,axiom,
    ! [X8,X5,X7,X6] :
      ( lhs_atom76(X8,X5,X7,X6)
      | ~ $true ),
    file('<stdin>',to_be_clausified_79) ).

fof(c_0_23,axiom,
    ! [X9,X1,X34,X4] :
      ( lhs_atom63(X9,X1,X34,X4)
      | ~ $true ),
    file('<stdin>',to_be_clausified_66) ).

fof(c_0_24,axiom,
    ! [X15,X14,X1,X4] :
      ( lhs_atom62(X15,X14,X1,X4)
      | ~ $true ),
    file('<stdin>',to_be_clausified_65) ).

fof(c_0_25,axiom,
    ! [X30,X9,X36,X4] :
      ( lhs_atom61(X30,X9,X36,X4)
      | ~ $true ),
    file('<stdin>',to_be_clausified_64) ).

fof(c_0_26,axiom,
    ! [X15,X14,X9,X4] :
      ( lhs_atom60(X15,X14,X9,X4)
      | ~ $true ),
    file('<stdin>',to_be_clausified_63) ).

fof(c_0_27,axiom,
    ! [X9,X1,X7,X4] :
      ( lhs_atom58(X9,X1,X7,X4)
      | ~ $true ),
    file('<stdin>',to_be_clausified_61) ).

fof(c_0_28,axiom,
    ! [X1,X7,X21,X4] :
      ( lhs_atom50(X1,X7,X21,X4)
      | ~ $true ),
    file('<stdin>',to_be_clausified_53) ).

fof(c_0_29,axiom,
    ! [X1,X7,X6,X4] :
      ( lhs_atom48(X1,X7,X6,X4)
      | ~ $true ),
    file('<stdin>',to_be_clausified_51) ).

fof(c_0_30,axiom,
    ! [X15,X30,X1,X4] :
      ( lhs_atom29(X15,X30,X1,X4)
      | ~ $true ),
    file('<stdin>',to_be_clausified_30) ).

fof(c_0_31,axiom,
    ! [X15,X13,X1,X4] :
      ( lhs_atom28(X15,X13,X1,X4)
      | ~ $true ),
    file('<stdin>',to_be_clausified_29) ).

fof(c_0_32,axiom,
    ! [X10,X16,X11,X4] :
      ( lhs_atom12(X10,X16,X11,X4)
      | ~ $true ),
    file('<stdin>',to_be_clausified_11) ).

fof(c_0_33,axiom,
    ! [X15,X13,X1,X4] :
      ( lhs_atom10(X15,X13,X1,X4)
      | ~ $true ),
    file('<stdin>',to_be_clausified_9) ).

fof(c_0_34,axiom,
    ! [X14,X9,X1,X4] :
      ( lhs_atom9(X14,X9,X1,X4)
      | ~ $true ),
    file('<stdin>',to_be_clausified_8) ).

fof(c_0_35,axiom,
    ! [X1,X2,X3,X4] :
      ( lhs_atom1(X1,X2,X3,X4)
      | ~ $true ),
    file('<stdin>',to_be_clausified_0) ).

fof(c_0_36,axiom,
    ! [X23,X1,X4] :
      ( lhs_atom65(X23,X1,X4)
      | c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),X1,X4) = c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),X23,X4) ),
    file('<stdin>',to_be_clausified_68) ).

fof(c_0_37,axiom,
    ! [X42,X45,X46] :
      ( lhs_atom105(X42,X45,X46)
      | ~ $true ),
    file('<stdin>',to_be_clausified_108) ).

fof(c_0_38,axiom,
    ! [X42,X45,X46] :
      ( lhs_atom103(X42,X45,X46)
      | ~ $true ),
    file('<stdin>',to_be_clausified_106) ).

fof(c_0_39,axiom,
    ! [X8,X5,X6] :
      ( lhs_atom86(X8,X5,X6)
      | ~ $true ),
    file('<stdin>',to_be_clausified_89) ).

fof(c_0_40,axiom,
    ! [X8,X5,X7] :
      ( lhs_atom78(X8,X5,X7)
      | ~ $true ),
    file('<stdin>',to_be_clausified_81) ).

fof(c_0_41,axiom,
    ! [X8,X5,X6] :
      ( lhs_atom73(X8,X5,X6)
      | ~ $true ),
    file('<stdin>',to_be_clausified_76) ).

fof(c_0_42,axiom,
    ! [X38,X39,X40] :
      ( lhs_atom72(X38,X39,X40)
      | ~ $true ),
    file('<stdin>',to_be_clausified_75) ).

fof(c_0_43,axiom,
    ! [X38,X39,X40] :
      ( lhs_atom71(X38,X39,X40)
      | ~ $true ),
    file('<stdin>',to_be_clausified_74) ).

fof(c_0_44,axiom,
    ! [X9,X1,X4] :
      ( lhs_atom57(X9,X1,X4)
      | ~ $true ),
    file('<stdin>',to_be_clausified_60) ).

fof(c_0_45,axiom,
    ! [X29,X11,X4] :
      ( lhs_atom54(X29,X11,X4)
      | ~ $true ),
    file('<stdin>',to_be_clausified_57) ).

fof(c_0_46,axiom,
    ! [X34,X8,X33] :
      ( lhs_atom51(X34,X8,X33)
      | ~ $true ),
    file('<stdin>',to_be_clausified_54) ).

fof(c_0_47,axiom,
    ! [X31,X32,X4] :
      ( lhs_atom49(X31,X32,X4)
      | ~ $true ),
    file('<stdin>',to_be_clausified_52) ).

fof(c_0_48,axiom,
    ! [X1,X33,X4] :
      ( lhs_atom38(X1,X33,X4)
      | ~ $true ),
    file('<stdin>',to_be_clausified_40) ).

fof(c_0_49,axiom,
    ! [X10,X11,X4] :
      ( lhs_atom11(X10,X11,X4)
      | ~ $true ),
    file('<stdin>',to_be_clausified_37) ).

fof(c_0_50,axiom,
    ! [X9,X1,X4] :
      ( lhs_atom35(X9,X1,X4)
      | ~ $true ),
    file('<stdin>',to_be_clausified_36) ).

fof(c_0_51,axiom,
    ! [X9,X1,X4] :
      ( lhs_atom34(X9,X1,X4)
      | ~ $true ),
    file('<stdin>',to_be_clausified_35) ).

fof(c_0_52,axiom,
    ! [X1,X8,X4] :
      ( lhs_atom33(X1,X8,X4)
      | ~ $true ),
    file('<stdin>',to_be_clausified_34) ).

fof(c_0_53,axiom,
    ! [X31,X32,X4] :
      ( lhs_atom31(X31,X32,X4)
      | ~ $true ),
    file('<stdin>',to_be_clausified_32) ).

fof(c_0_54,axiom,
    ! [X13,X1,X4] :
      ( lhs_atom30(X13,X1,X4)
      | ~ $true ),
    file('<stdin>',to_be_clausified_31) ).

fof(c_0_55,axiom,
    ! [X9,X29,X4] :
      ( lhs_atom27(X9,X29,X4)
      | ~ $true ),
    file('<stdin>',to_be_clausified_28) ).

fof(c_0_56,axiom,
    ! [X9,X29,X4] :
      ( lhs_atom26(X9,X29,X4)
      | ~ $true ),
    file('<stdin>',to_be_clausified_27) ).

fof(c_0_57,axiom,
    ! [X1,X29,X4] :
      ( lhs_atom19(X1,X29,X4)
      | ~ $true ),
    file('<stdin>',to_be_clausified_18) ).

fof(c_0_58,axiom,
    ! [X29,X16,X4] :
      ( lhs_atom18(X29,X16,X4)
      | ~ $true ),
    file('<stdin>',to_be_clausified_17) ).

fof(c_0_59,axiom,
    ! [X22,X23,X1] :
      ( lhs_atom15(X22,X23,X1)
      | ~ $true ),
    file('<stdin>',to_be_clausified_14) ).

fof(c_0_60,axiom,
    ! [X7,X21,X6] :
      ( lhs_atom14(X7,X21,X6)
      | ~ $true ),
    file('<stdin>',to_be_clausified_13) ).

fof(c_0_61,axiom,
    ! [X10,X11,X4] :
      ( lhs_atom11(X10,X11,X4)
      | ~ $true ),
    file('<stdin>',to_be_clausified_10) ).

fof(c_0_62,axiom,
    ! [X8,X5,X6] :
      ( lhs_atom5(X8,X5,X6)
      | ~ $true ),
    file('<stdin>',to_be_clausified_4) ).

fof(c_0_63,axiom,
    ! [X8,X5,X6] :
      ( lhs_atom4(X8,X5,X6)
      | ~ $true ),
    file('<stdin>',to_be_clausified_3) ).

fof(c_0_64,axiom,
    ! [X5,X7,X6] :
      ( lhs_atom3(X5,X7,X6)
      | ~ $true ),
    file('<stdin>',to_be_clausified_2) ).

fof(c_0_65,axiom,
    ! [X1,X4] :
      ( lhs_atom131(X1,X4)
      | ~ $true ),
    file('<stdin>',to_be_clausified_134) ).

fof(c_0_66,axiom,
    ! [X41,X6] :
      ( lhs_atom102(X41,X6)
      | ~ $true ),
    file('<stdin>',to_be_clausified_105) ).

fof(c_0_67,axiom,
    ! [X5,X29] :
      ( lhs_atom97(X5,X29)
      | ~ $true ),
    file('<stdin>',to_be_clausified_100) ).

fof(c_0_68,axiom,
    ! [X8,X5] :
      ( lhs_atom94(X8,X5)
      | ~ $true ),
    file('<stdin>',to_be_clausified_97) ).

fof(c_0_69,axiom,
    ! [X8,X5] :
      ( lhs_atom93(X8,X5)
      | ~ $true ),
    file('<stdin>',to_be_clausified_96) ).

fof(c_0_70,axiom,
    ! [X1,X43] :
      ( lhs_atom92(X1,X43)
      | ~ $true ),
    file('<stdin>',to_be_clausified_95) ).

fof(c_0_71,axiom,
    ! [X42,X38] :
      ( lhs_atom90(X42,X38)
      | ~ $true ),
    file('<stdin>',to_be_clausified_93) ).

fof(c_0_72,axiom,
    ! [X8,X33] :
      ( lhs_atom88(X8,X33)
      | ~ $true ),
    file('<stdin>',to_be_clausified_91) ).

fof(c_0_73,axiom,
    ! [X42,X38] :
      ( lhs_atom87(X42,X38)
      | ~ $true ),
    file('<stdin>',to_be_clausified_90) ).

fof(c_0_74,axiom,
    ! [X35,X33] :
      ( lhs_atom56(X35,X33)
      | ~ $true ),
    file('<stdin>',to_be_clausified_59) ).

fof(c_0_75,axiom,
    ! [X35,X33] :
      ( lhs_atom55(X35,X33)
      | ~ $true ),
    file('<stdin>',to_be_clausified_58) ).

fof(c_0_76,axiom,
    ! [X1,X4] :
      ( lhs_atom32(X1,X4)
      | ~ $true ),
    file('<stdin>',to_be_clausified_47) ).

fof(c_0_77,axiom,
    ! [X8,X6] :
      ( lhs_atom40(X8,X6)
      | ~ $true ),
    file('<stdin>',to_be_clausified_42) ).

fof(c_0_78,axiom,
    ! [X29,X4] :
      ( lhs_atom37(X29,X4)
      | ~ $true ),
    file('<stdin>',to_be_clausified_39) ).

fof(c_0_79,axiom,
    ! [X1,X4] :
      ( lhs_atom32(X1,X4)
      | ~ $true ),
    file('<stdin>',to_be_clausified_33) ).

fof(c_0_80,axiom,
    ! [X7,X21] :
      ( lhs_atom24(X7,X21)
      | ~ $true ),
    file('<stdin>',to_be_clausified_25) ).

fof(c_0_81,axiom,
    ! [X14,X4] :
      ( lhs_atom22(X14,X4)
      | ~ $true ),
    file('<stdin>',to_be_clausified_23) ).

fof(c_0_82,axiom,
    ! [X14,X4] :
      ( lhs_atom22(X14,X4)
      | ~ $true ),
    file('<stdin>',to_be_clausified_22) ).

fof(c_0_83,axiom,
    ! [X9,X4] :
      ( lhs_atom20(X9,X4)
      | ~ $true ),
    file('<stdin>',to_be_clausified_21) ).

fof(c_0_84,axiom,
    ! [X1,X4] :
      ( lhs_atom21(X1,X4)
      | ~ $true ),
    file('<stdin>',to_be_clausified_20) ).

fof(c_0_85,axiom,
    ! [X9,X4] :
      ( lhs_atom20(X9,X4)
      | ~ $true ),
    file('<stdin>',to_be_clausified_19) ).

fof(c_0_86,axiom,
    ! [X28,X4] :
      ( lhs_atom17(X28,X4)
      | ~ $true ),
    file('<stdin>',to_be_clausified_16) ).

fof(c_0_87,axiom,
    ! [X5,X6] :
      ( lhs_atom2(X5,X6)
      | ~ $true ),
    file('<stdin>',to_be_clausified_1) ).

fof(c_0_88,axiom,
    ! [X7] :
      ( lhs_atom104(X7)
      | ~ $true ),
    file('<stdin>',to_be_clausified_107) ).

fof(c_0_89,axiom,
    ! [X21] :
      ( lhs_atom99(X21)
      | ~ $true ),
    file('<stdin>',to_be_clausified_102) ).

fof(c_0_90,axiom,
    ! [X42] :
      ( lhs_atom96(X42)
      | ~ $true ),
    file('<stdin>',to_be_clausified_99) ).

fof(c_0_91,axiom,
    ! [X42] :
      ( lhs_atom95(X42)
      | ~ $true ),
    file('<stdin>',to_be_clausified_98) ).

fof(c_0_92,axiom,
    ! [X29] :
      ( lhs_atom81(X29)
      | ~ $true ),
    file('<stdin>',to_be_clausified_84) ).

fof(c_0_93,axiom,
    ! [X8] :
      ( lhs_atom80(X8)
      | ~ $true ),
    file('<stdin>',to_be_clausified_83) ).

fof(c_0_94,axiom,
    ! [X29] :
      ( lhs_atom79(X29)
      | ~ $true ),
    file('<stdin>',to_be_clausified_82) ).

fof(c_0_95,axiom,
    ! [X21] :
      ( lhs_atom70(X21)
      | ~ $true ),
    file('<stdin>',to_be_clausified_73) ).

fof(c_0_96,axiom,
    ! [X7] :
      ( lhs_atom69(X7)
      | ~ $true ),
    file('<stdin>',to_be_clausified_72) ).

fof(c_0_97,axiom,
    ! [X1] :
      ( lhs_atom68(X1)
      | ~ $true ),
    file('<stdin>',to_be_clausified_71) ).

fof(c_0_98,axiom,
    ! [X7] :
      ( lhs_atom67(X7)
      | ~ $true ),
    file('<stdin>',to_be_clausified_70) ).

fof(c_0_99,axiom,
    ! [X7] :
      ( lhs_atom66(X7)
      | ~ $true ),
    file('<stdin>',to_be_clausified_69) ).

fof(c_0_100,axiom,
    ! [X37] :
      ( lhs_atom64(X37)
      | ~ $true ),
    file('<stdin>',to_be_clausified_67) ).

fof(c_0_101,axiom,
    ! [X4] :
      ( lhs_atom59(X4)
      | ~ $true ),
    file('<stdin>',to_be_clausified_62) ).

fof(c_0_102,axiom,
    ! [X7] :
      ( lhs_atom46(X7)
      | ~ $true ),
    file('<stdin>',to_be_clausified_49) ).

fof(c_0_103,axiom,
    ! [X1] :
      ( lhs_atom45(X1)
      | ~ $true ),
    file('<stdin>',to_be_clausified_48) ).

fof(c_0_104,axiom,
    ! [X4] :
      ( lhs_atom44(X4)
      | ~ $true ),
    file('<stdin>',to_be_clausified_46) ).

fof(c_0_105,axiom,
    ! [X7] :
      ( lhs_atom43(X7)
      | ~ $true ),
    file('<stdin>',to_be_clausified_45) ).

fof(c_0_106,axiom,
    ! [X21] :
      ( lhs_atom42(X21)
      | ~ $true ),
    file('<stdin>',to_be_clausified_44) ).

fof(c_0_107,axiom,
    ! [X4] :
      ( lhs_atom36(X4)
      | ~ $true ),
    file('<stdin>',to_be_clausified_38) ).

fof(c_0_108,axiom,
    ( lhs_atom130
    | ~ $true ),
    file('<stdin>',to_be_clausified_133) ).

fof(c_0_109,axiom,
    ( lhs_atom129
    | ~ $true ),
    file('<stdin>',to_be_clausified_132) ).

fof(c_0_110,axiom,
    ( lhs_atom128
    | ~ $true ),
    file('<stdin>',to_be_clausified_131) ).

fof(c_0_111,axiom,
    ( lhs_atom127
    | ~ $true ),
    file('<stdin>',to_be_clausified_130) ).

fof(c_0_112,axiom,
    ( lhs_atom126
    | ~ $true ),
    file('<stdin>',to_be_clausified_129) ).

fof(c_0_113,axiom,
    ( lhs_atom125
    | ~ $true ),
    file('<stdin>',to_be_clausified_128) ).

fof(c_0_114,axiom,
    ( lhs_atom124
    | ~ $true ),
    file('<stdin>',to_be_clausified_127) ).

fof(c_0_115,axiom,
    ( lhs_atom123
    | ~ $true ),
    file('<stdin>',to_be_clausified_126) ).

fof(c_0_116,axiom,
    ( lhs_atom122
    | ~ $true ),
    file('<stdin>',to_be_clausified_125) ).

fof(c_0_117,axiom,
    ( lhs_atom121
    | ~ $true ),
    file('<stdin>',to_be_clausified_124) ).

fof(c_0_118,axiom,
    ( lhs_atom120
    | ~ $true ),
    file('<stdin>',to_be_clausified_123) ).

fof(c_0_119,axiom,
    ( lhs_atom119
    | ~ $true ),
    file('<stdin>',to_be_clausified_122) ).

fof(c_0_120,axiom,
    ( lhs_atom118
    | ~ $true ),
    file('<stdin>',to_be_clausified_121) ).

fof(c_0_121,axiom,
    ( lhs_atom117
    | ~ $true ),
    file('<stdin>',to_be_clausified_120) ).

fof(c_0_122,axiom,
    ( lhs_atom116
    | ~ $true ),
    file('<stdin>',to_be_clausified_119) ).

fof(c_0_123,axiom,
    ( lhs_atom115
    | ~ $true ),
    file('<stdin>',to_be_clausified_118) ).

fof(c_0_124,axiom,
    ( lhs_atom114
    | ~ $true ),
    file('<stdin>',to_be_clausified_117) ).

fof(c_0_125,axiom,
    ( lhs_atom113
    | ~ $true ),
    file('<stdin>',to_be_clausified_116) ).

fof(c_0_126,axiom,
    ( lhs_atom112
    | ~ $true ),
    file('<stdin>',to_be_clausified_115) ).

fof(c_0_127,axiom,
    ( lhs_atom111
    | ~ $true ),
    file('<stdin>',to_be_clausified_114) ).

fof(c_0_128,axiom,
    ( lhs_atom110
    | ~ $true ),
    file('<stdin>',to_be_clausified_113) ).

fof(c_0_129,axiom,
    ( lhs_atom109
    | ~ $true ),
    file('<stdin>',to_be_clausified_112) ).

fof(c_0_130,axiom,
    ( lhs_atom108
    | ~ $true ),
    file('<stdin>',to_be_clausified_111) ).

fof(c_0_131,axiom,
    ( lhs_atom107
    | ~ $true ),
    file('<stdin>',to_be_clausified_110) ).

fof(c_0_132,axiom,
    ( lhs_atom106
    | ~ $true ),
    file('<stdin>',to_be_clausified_109) ).

fof(c_0_133,axiom,
    ( lhs_atom41
    | ~ $true ),
    file('<stdin>',to_be_clausified_43) ).

fof(c_0_134,axiom,
    ( lhs_atom39
    | ~ $true ),
    file('<stdin>',to_be_clausified_41) ).

fof(c_0_135,plain,
    ! [X14,X9,X10,X16,X11,X4] : lhs_atom84(X14,X9,X10,X16,X11,X4),
    inference(fof_simplification,[status(thm)],[c_0_0]) ).

fof(c_0_136,plain,
    ! [X9,X1,X10,X16,X11,X4] : lhs_atom83(X9,X1,X10,X16,X11,X4),
    inference(fof_simplification,[status(thm)],[c_0_1]) ).

fof(c_0_137,plain,
    ! [X24,X25,X26,X39,X40,X4] : lhs_atom75(X24,X25,X26,X39,X40,X4),
    inference(fof_simplification,[status(thm)],[c_0_2]) ).

fof(c_0_138,plain,
    ! [X24,X25,X26,X39,X40,X4] : lhs_atom74(X24,X25,X26,X39,X40,X4),
    inference(fof_simplification,[status(thm)],[c_0_3]) ).

fof(c_0_139,plain,
    ! [X9,X1,X10,X16,X11,X4] : lhs_atom53(X9,X1,X10,X16,X11,X4),
    inference(fof_simplification,[status(thm)],[c_0_4]) ).

fof(c_0_140,plain,
    ! [X14,X9,X10,X16,X11,X4] : lhs_atom25(X14,X9,X10,X16,X11,X4),
    inference(fof_simplification,[status(thm)],[c_0_5]) ).

fof(c_0_141,plain,
    ! [X17,X18,X19,X20,X11,X4] : lhs_atom13(X17,X18,X19,X20,X11,X4),
    inference(fof_simplification,[status(thm)],[c_0_6]) ).

fof(c_0_142,plain,
    ! [X42,X24,X25,X26,X4] : lhs_atom91(X42,X24,X25,X26,X4),
    inference(fof_simplification,[status(thm)],[c_0_7]) ).

fof(c_0_143,plain,
    ! [X42,X24,X25,X26,X4] : lhs_atom89(X42,X24,X25,X26,X4),
    inference(fof_simplification,[status(thm)],[c_0_8]) ).

fof(c_0_144,plain,
    ! [X24,X25,X26,X27,X4] : lhs_atom52(X24,X25,X26,X27,X4),
    inference(fof_simplification,[status(thm)],[c_0_9]) ).

fof(c_0_145,plain,
    ! [X14,X9,X10,X11,X4] : lhs_atom47(X14,X9,X10,X11,X4),
    inference(fof_simplification,[status(thm)],[c_0_10]) ).

fof(c_0_146,plain,
    ! [X1,X7,X10,X11,X4] : lhs_atom23(X1,X7,X10,X11,X4),
    inference(fof_simplification,[status(thm)],[c_0_11]) ).

fof(c_0_147,plain,
    ! [X24,X25,X26,X27,X4] : lhs_atom16(X24,X25,X26,X27,X4),
    inference(fof_simplification,[status(thm)],[c_0_12]) ).

fof(c_0_148,plain,
    ! [X13,X1,X10,X11,X4] : lhs_atom8(X13,X1,X10,X11,X4),
    inference(fof_simplification,[status(thm)],[c_0_13]) ).

fof(c_0_149,plain,
    ! [X12,X13,X10,X11,X4] : lhs_atom7(X12,X13,X10,X11,X4),
    inference(fof_simplification,[status(thm)],[c_0_14]) ).

fof(c_0_150,plain,
    ! [X9,X1,X10,X11,X4] : lhs_atom6(X9,X1,X10,X11,X4),
    inference(fof_simplification,[status(thm)],[c_0_15]) ).

fof(c_0_151,plain,
    ! [X41,X8,X5,X6] : lhs_atom101(X41,X8,X5,X6),
    inference(fof_simplification,[status(thm)],[c_0_16]) ).

fof(c_0_152,plain,
    ! [X8,X44,X5,X7] : lhs_atom100(X8,X44,X5,X7),
    inference(fof_simplification,[status(thm)],[c_0_17]) ).

fof(c_0_153,plain,
    ! [X34,X44,X29,X7] : lhs_atom98(X34,X44,X29,X7),
    inference(fof_simplification,[status(thm)],[c_0_18]) ).

fof(c_0_154,plain,
    ! [X41,X34,X8,X33] : lhs_atom85(X41,X34,X8,X33),
    inference(fof_simplification,[status(thm)],[c_0_19]) ).

fof(c_0_155,plain,
    ! [X10,X16,X11,X4] : lhs_atom82(X10,X16,X11,X4),
    inference(fof_simplification,[status(thm)],[c_0_20]) ).

fof(c_0_156,plain,
    ! [X41,X8,X5,X6] : lhs_atom77(X41,X8,X5,X6),
    inference(fof_simplification,[status(thm)],[c_0_21]) ).

fof(c_0_157,plain,
    ! [X8,X5,X7,X6] : lhs_atom76(X8,X5,X7,X6),
    inference(fof_simplification,[status(thm)],[c_0_22]) ).

fof(c_0_158,plain,
    ! [X9,X1,X34,X4] : lhs_atom63(X9,X1,X34,X4),
    inference(fof_simplification,[status(thm)],[c_0_23]) ).

fof(c_0_159,plain,
    ! [X15,X14,X1,X4] : lhs_atom62(X15,X14,X1,X4),
    inference(fof_simplification,[status(thm)],[c_0_24]) ).

fof(c_0_160,plain,
    ! [X30,X9,X36,X4] : lhs_atom61(X30,X9,X36,X4),
    inference(fof_simplification,[status(thm)],[c_0_25]) ).

fof(c_0_161,plain,
    ! [X15,X14,X9,X4] : lhs_atom60(X15,X14,X9,X4),
    inference(fof_simplification,[status(thm)],[c_0_26]) ).

fof(c_0_162,plain,
    ! [X9,X1,X7,X4] : lhs_atom58(X9,X1,X7,X4),
    inference(fof_simplification,[status(thm)],[c_0_27]) ).

fof(c_0_163,plain,
    ! [X1,X7,X21,X4] : lhs_atom50(X1,X7,X21,X4),
    inference(fof_simplification,[status(thm)],[c_0_28]) ).

fof(c_0_164,plain,
    ! [X1,X7,X6,X4] : lhs_atom48(X1,X7,X6,X4),
    inference(fof_simplification,[status(thm)],[c_0_29]) ).

fof(c_0_165,plain,
    ! [X15,X30,X1,X4] : lhs_atom29(X15,X30,X1,X4),
    inference(fof_simplification,[status(thm)],[c_0_30]) ).

fof(c_0_166,plain,
    ! [X15,X13,X1,X4] : lhs_atom28(X15,X13,X1,X4),
    inference(fof_simplification,[status(thm)],[c_0_31]) ).

fof(c_0_167,plain,
    ! [X10,X16,X11,X4] : lhs_atom12(X10,X16,X11,X4),
    inference(fof_simplification,[status(thm)],[c_0_32]) ).

fof(c_0_168,plain,
    ! [X15,X13,X1,X4] : lhs_atom10(X15,X13,X1,X4),
    inference(fof_simplification,[status(thm)],[c_0_33]) ).

fof(c_0_169,plain,
    ! [X14,X9,X1,X4] : lhs_atom9(X14,X9,X1,X4),
    inference(fof_simplification,[status(thm)],[c_0_34]) ).

fof(c_0_170,plain,
    ! [X1,X2,X3,X4] : lhs_atom1(X1,X2,X3,X4),
    inference(fof_simplification,[status(thm)],[c_0_35]) ).

fof(c_0_171,axiom,
    ! [X23,X1,X4] :
      ( lhs_atom65(X23,X1,X4)
      | c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),X1,X4) = c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),X23,X4) ),
    c_0_36 ).

fof(c_0_172,plain,
    ! [X42,X45,X46] : lhs_atom105(X42,X45,X46),
    inference(fof_simplification,[status(thm)],[c_0_37]) ).

fof(c_0_173,plain,
    ! [X42,X45,X46] : lhs_atom103(X42,X45,X46),
    inference(fof_simplification,[status(thm)],[c_0_38]) ).

fof(c_0_174,plain,
    ! [X8,X5,X6] : lhs_atom86(X8,X5,X6),
    inference(fof_simplification,[status(thm)],[c_0_39]) ).

fof(c_0_175,plain,
    ! [X8,X5,X7] : lhs_atom78(X8,X5,X7),
    inference(fof_simplification,[status(thm)],[c_0_40]) ).

fof(c_0_176,plain,
    ! [X8,X5,X6] : lhs_atom73(X8,X5,X6),
    inference(fof_simplification,[status(thm)],[c_0_41]) ).

fof(c_0_177,plain,
    ! [X38,X39,X40] : lhs_atom72(X38,X39,X40),
    inference(fof_simplification,[status(thm)],[c_0_42]) ).

fof(c_0_178,plain,
    ! [X38,X39,X40] : lhs_atom71(X38,X39,X40),
    inference(fof_simplification,[status(thm)],[c_0_43]) ).

fof(c_0_179,plain,
    ! [X9,X1,X4] : lhs_atom57(X9,X1,X4),
    inference(fof_simplification,[status(thm)],[c_0_44]) ).

fof(c_0_180,plain,
    ! [X29,X11,X4] : lhs_atom54(X29,X11,X4),
    inference(fof_simplification,[status(thm)],[c_0_45]) ).

fof(c_0_181,plain,
    ! [X34,X8,X33] : lhs_atom51(X34,X8,X33),
    inference(fof_simplification,[status(thm)],[c_0_46]) ).

fof(c_0_182,plain,
    ! [X31,X32,X4] : lhs_atom49(X31,X32,X4),
    inference(fof_simplification,[status(thm)],[c_0_47]) ).

fof(c_0_183,plain,
    ! [X1,X33,X4] : lhs_atom38(X1,X33,X4),
    inference(fof_simplification,[status(thm)],[c_0_48]) ).

fof(c_0_184,plain,
    ! [X10,X11,X4] : lhs_atom11(X10,X11,X4),
    inference(fof_simplification,[status(thm)],[c_0_49]) ).

fof(c_0_185,plain,
    ! [X9,X1,X4] : lhs_atom35(X9,X1,X4),
    inference(fof_simplification,[status(thm)],[c_0_50]) ).

fof(c_0_186,plain,
    ! [X9,X1,X4] : lhs_atom34(X9,X1,X4),
    inference(fof_simplification,[status(thm)],[c_0_51]) ).

fof(c_0_187,plain,
    ! [X1,X8,X4] : lhs_atom33(X1,X8,X4),
    inference(fof_simplification,[status(thm)],[c_0_52]) ).

fof(c_0_188,plain,
    ! [X31,X32,X4] : lhs_atom31(X31,X32,X4),
    inference(fof_simplification,[status(thm)],[c_0_53]) ).

fof(c_0_189,plain,
    ! [X13,X1,X4] : lhs_atom30(X13,X1,X4),
    inference(fof_simplification,[status(thm)],[c_0_54]) ).

fof(c_0_190,plain,
    ! [X9,X29,X4] : lhs_atom27(X9,X29,X4),
    inference(fof_simplification,[status(thm)],[c_0_55]) ).

fof(c_0_191,plain,
    ! [X9,X29,X4] : lhs_atom26(X9,X29,X4),
    inference(fof_simplification,[status(thm)],[c_0_56]) ).

fof(c_0_192,plain,
    ! [X1,X29,X4] : lhs_atom19(X1,X29,X4),
    inference(fof_simplification,[status(thm)],[c_0_57]) ).

fof(c_0_193,plain,
    ! [X29,X16,X4] : lhs_atom18(X29,X16,X4),
    inference(fof_simplification,[status(thm)],[c_0_58]) ).

fof(c_0_194,plain,
    ! [X22,X23,X1] : lhs_atom15(X22,X23,X1),
    inference(fof_simplification,[status(thm)],[c_0_59]) ).

fof(c_0_195,plain,
    ! [X7,X21,X6] : lhs_atom14(X7,X21,X6),
    inference(fof_simplification,[status(thm)],[c_0_60]) ).

fof(c_0_196,plain,
    ! [X10,X11,X4] : lhs_atom11(X10,X11,X4),
    inference(fof_simplification,[status(thm)],[c_0_61]) ).

fof(c_0_197,plain,
    ! [X8,X5,X6] : lhs_atom5(X8,X5,X6),
    inference(fof_simplification,[status(thm)],[c_0_62]) ).

fof(c_0_198,plain,
    ! [X8,X5,X6] : lhs_atom4(X8,X5,X6),
    inference(fof_simplification,[status(thm)],[c_0_63]) ).

fof(c_0_199,plain,
    ! [X5,X7,X6] : lhs_atom3(X5,X7,X6),
    inference(fof_simplification,[status(thm)],[c_0_64]) ).

fof(c_0_200,plain,
    ! [X1,X4] : lhs_atom131(X1,X4),
    inference(fof_simplification,[status(thm)],[c_0_65]) ).

fof(c_0_201,plain,
    ! [X41,X6] : lhs_atom102(X41,X6),
    inference(fof_simplification,[status(thm)],[c_0_66]) ).

fof(c_0_202,plain,
    ! [X5,X29] : lhs_atom97(X5,X29),
    inference(fof_simplification,[status(thm)],[c_0_67]) ).

fof(c_0_203,plain,
    ! [X8,X5] : lhs_atom94(X8,X5),
    inference(fof_simplification,[status(thm)],[c_0_68]) ).

fof(c_0_204,plain,
    ! [X8,X5] : lhs_atom93(X8,X5),
    inference(fof_simplification,[status(thm)],[c_0_69]) ).

fof(c_0_205,plain,
    ! [X1,X43] : lhs_atom92(X1,X43),
    inference(fof_simplification,[status(thm)],[c_0_70]) ).

fof(c_0_206,plain,
    ! [X42,X38] : lhs_atom90(X42,X38),
    inference(fof_simplification,[status(thm)],[c_0_71]) ).

fof(c_0_207,plain,
    ! [X8,X33] : lhs_atom88(X8,X33),
    inference(fof_simplification,[status(thm)],[c_0_72]) ).

fof(c_0_208,plain,
    ! [X42,X38] : lhs_atom87(X42,X38),
    inference(fof_simplification,[status(thm)],[c_0_73]) ).

fof(c_0_209,plain,
    ! [X35,X33] : lhs_atom56(X35,X33),
    inference(fof_simplification,[status(thm)],[c_0_74]) ).

fof(c_0_210,plain,
    ! [X35,X33] : lhs_atom55(X35,X33),
    inference(fof_simplification,[status(thm)],[c_0_75]) ).

fof(c_0_211,plain,
    ! [X1,X4] : lhs_atom32(X1,X4),
    inference(fof_simplification,[status(thm)],[c_0_76]) ).

fof(c_0_212,plain,
    ! [X8,X6] : lhs_atom40(X8,X6),
    inference(fof_simplification,[status(thm)],[c_0_77]) ).

fof(c_0_213,plain,
    ! [X29,X4] : lhs_atom37(X29,X4),
    inference(fof_simplification,[status(thm)],[c_0_78]) ).

fof(c_0_214,plain,
    ! [X1,X4] : lhs_atom32(X1,X4),
    inference(fof_simplification,[status(thm)],[c_0_79]) ).

fof(c_0_215,plain,
    ! [X7,X21] : lhs_atom24(X7,X21),
    inference(fof_simplification,[status(thm)],[c_0_80]) ).

fof(c_0_216,plain,
    ! [X14,X4] : lhs_atom22(X14,X4),
    inference(fof_simplification,[status(thm)],[c_0_81]) ).

fof(c_0_217,plain,
    ! [X14,X4] : lhs_atom22(X14,X4),
    inference(fof_simplification,[status(thm)],[c_0_82]) ).

fof(c_0_218,plain,
    ! [X9,X4] : lhs_atom20(X9,X4),
    inference(fof_simplification,[status(thm)],[c_0_83]) ).

fof(c_0_219,plain,
    ! [X1,X4] : lhs_atom21(X1,X4),
    inference(fof_simplification,[status(thm)],[c_0_84]) ).

fof(c_0_220,plain,
    ! [X9,X4] : lhs_atom20(X9,X4),
    inference(fof_simplification,[status(thm)],[c_0_85]) ).

fof(c_0_221,plain,
    ! [X28,X4] : lhs_atom17(X28,X4),
    inference(fof_simplification,[status(thm)],[c_0_86]) ).

fof(c_0_222,plain,
    ! [X5,X6] : lhs_atom2(X5,X6),
    inference(fof_simplification,[status(thm)],[c_0_87]) ).

fof(c_0_223,plain,
    ! [X7] : lhs_atom104(X7),
    inference(fof_simplification,[status(thm)],[c_0_88]) ).

fof(c_0_224,plain,
    ! [X21] : lhs_atom99(X21),
    inference(fof_simplification,[status(thm)],[c_0_89]) ).

fof(c_0_225,plain,
    ! [X42] : lhs_atom96(X42),
    inference(fof_simplification,[status(thm)],[c_0_90]) ).

fof(c_0_226,plain,
    ! [X42] : lhs_atom95(X42),
    inference(fof_simplification,[status(thm)],[c_0_91]) ).

fof(c_0_227,plain,
    ! [X29] : lhs_atom81(X29),
    inference(fof_simplification,[status(thm)],[c_0_92]) ).

fof(c_0_228,plain,
    ! [X8] : lhs_atom80(X8),
    inference(fof_simplification,[status(thm)],[c_0_93]) ).

fof(c_0_229,plain,
    ! [X29] : lhs_atom79(X29),
    inference(fof_simplification,[status(thm)],[c_0_94]) ).

fof(c_0_230,plain,
    ! [X21] : lhs_atom70(X21),
    inference(fof_simplification,[status(thm)],[c_0_95]) ).

fof(c_0_231,plain,
    ! [X7] : lhs_atom69(X7),
    inference(fof_simplification,[status(thm)],[c_0_96]) ).

fof(c_0_232,plain,
    ! [X1] : lhs_atom68(X1),
    inference(fof_simplification,[status(thm)],[c_0_97]) ).

fof(c_0_233,plain,
    ! [X7] : lhs_atom67(X7),
    inference(fof_simplification,[status(thm)],[c_0_98]) ).

fof(c_0_234,plain,
    ! [X7] : lhs_atom66(X7),
    inference(fof_simplification,[status(thm)],[c_0_99]) ).

fof(c_0_235,plain,
    ! [X37] : lhs_atom64(X37),
    inference(fof_simplification,[status(thm)],[c_0_100]) ).

fof(c_0_236,plain,
    ! [X4] : lhs_atom59(X4),
    inference(fof_simplification,[status(thm)],[c_0_101]) ).

fof(c_0_237,plain,
    ! [X7] : lhs_atom46(X7),
    inference(fof_simplification,[status(thm)],[c_0_102]) ).

fof(c_0_238,plain,
    ! [X1] : lhs_atom45(X1),
    inference(fof_simplification,[status(thm)],[c_0_103]) ).

fof(c_0_239,plain,
    ! [X4] : lhs_atom44(X4),
    inference(fof_simplification,[status(thm)],[c_0_104]) ).

fof(c_0_240,plain,
    ! [X7] : lhs_atom43(X7),
    inference(fof_simplification,[status(thm)],[c_0_105]) ).

fof(c_0_241,plain,
    ! [X21] : lhs_atom42(X21),
    inference(fof_simplification,[status(thm)],[c_0_106]) ).

fof(c_0_242,plain,
    ! [X4] : lhs_atom36(X4),
    inference(fof_simplification,[status(thm)],[c_0_107]) ).

fof(c_0_243,plain,
    lhs_atom130,
    inference(fof_simplification,[status(thm)],[c_0_108]) ).

fof(c_0_244,plain,
    lhs_atom129,
    inference(fof_simplification,[status(thm)],[c_0_109]) ).

fof(c_0_245,plain,
    lhs_atom128,
    inference(fof_simplification,[status(thm)],[c_0_110]) ).

fof(c_0_246,plain,
    lhs_atom127,
    inference(fof_simplification,[status(thm)],[c_0_111]) ).

fof(c_0_247,plain,
    lhs_atom126,
    inference(fof_simplification,[status(thm)],[c_0_112]) ).

fof(c_0_248,plain,
    lhs_atom125,
    inference(fof_simplification,[status(thm)],[c_0_113]) ).

fof(c_0_249,plain,
    lhs_atom124,
    inference(fof_simplification,[status(thm)],[c_0_114]) ).

fof(c_0_250,plain,
    lhs_atom123,
    inference(fof_simplification,[status(thm)],[c_0_115]) ).

fof(c_0_251,plain,
    lhs_atom122,
    inference(fof_simplification,[status(thm)],[c_0_116]) ).

fof(c_0_252,plain,
    lhs_atom121,
    inference(fof_simplification,[status(thm)],[c_0_117]) ).

fof(c_0_253,plain,
    lhs_atom120,
    inference(fof_simplification,[status(thm)],[c_0_118]) ).

fof(c_0_254,plain,
    lhs_atom119,
    inference(fof_simplification,[status(thm)],[c_0_119]) ).

fof(c_0_255,plain,
    lhs_atom118,
    inference(fof_simplification,[status(thm)],[c_0_120]) ).

fof(c_0_256,plain,
    lhs_atom117,
    inference(fof_simplification,[status(thm)],[c_0_121]) ).

fof(c_0_257,plain,
    lhs_atom116,
    inference(fof_simplification,[status(thm)],[c_0_122]) ).

fof(c_0_258,plain,
    lhs_atom115,
    inference(fof_simplification,[status(thm)],[c_0_123]) ).

fof(c_0_259,plain,
    lhs_atom114,
    inference(fof_simplification,[status(thm)],[c_0_124]) ).

fof(c_0_260,plain,
    lhs_atom113,
    inference(fof_simplification,[status(thm)],[c_0_125]) ).

fof(c_0_261,plain,
    lhs_atom112,
    inference(fof_simplification,[status(thm)],[c_0_126]) ).

fof(c_0_262,plain,
    lhs_atom111,
    inference(fof_simplification,[status(thm)],[c_0_127]) ).

fof(c_0_263,plain,
    lhs_atom110,
    inference(fof_simplification,[status(thm)],[c_0_128]) ).

fof(c_0_264,plain,
    lhs_atom109,
    inference(fof_simplification,[status(thm)],[c_0_129]) ).

fof(c_0_265,plain,
    lhs_atom108,
    inference(fof_simplification,[status(thm)],[c_0_130]) ).

fof(c_0_266,plain,
    lhs_atom107,
    inference(fof_simplification,[status(thm)],[c_0_131]) ).

fof(c_0_267,plain,
    lhs_atom106,
    inference(fof_simplification,[status(thm)],[c_0_132]) ).

fof(c_0_268,plain,
    lhs_atom41,
    inference(fof_simplification,[status(thm)],[c_0_133]) ).

fof(c_0_269,plain,
    lhs_atom39,
    inference(fof_simplification,[status(thm)],[c_0_134]) ).

fof(c_0_270,plain,
    ! [X17,X18,X19,X20,X21,X22] : lhs_atom84(X17,X18,X19,X20,X21,X22),
    inference(variable_rename,[status(thm)],[c_0_135]) ).

fof(c_0_271,plain,
    ! [X17,X18,X19,X20,X21,X22] : lhs_atom83(X17,X18,X19,X20,X21,X22),
    inference(variable_rename,[status(thm)],[c_0_136]) ).

fof(c_0_272,plain,
    ! [X41,X42,X43,X44,X45,X46] : lhs_atom75(X41,X42,X43,X44,X45,X46),
    inference(variable_rename,[status(thm)],[c_0_137]) ).

fof(c_0_273,plain,
    ! [X41,X42,X43,X44,X45,X46] : lhs_atom74(X41,X42,X43,X44,X45,X46),
    inference(variable_rename,[status(thm)],[c_0_138]) ).

fof(c_0_274,plain,
    ! [X17,X18,X19,X20,X21,X22] : lhs_atom53(X17,X18,X19,X20,X21,X22),
    inference(variable_rename,[status(thm)],[c_0_139]) ).

fof(c_0_275,plain,
    ! [X17,X18,X19,X20,X21,X22] : lhs_atom25(X17,X18,X19,X20,X21,X22),
    inference(variable_rename,[status(thm)],[c_0_140]) ).

fof(c_0_276,plain,
    ! [X21,X22,X23,X24,X25,X26] : lhs_atom13(X21,X22,X23,X24,X25,X26),
    inference(variable_rename,[status(thm)],[c_0_141]) ).

fof(c_0_277,plain,
    ! [X43,X44,X45,X46,X47] : lhs_atom91(X43,X44,X45,X46,X47),
    inference(variable_rename,[status(thm)],[c_0_142]) ).

fof(c_0_278,plain,
    ! [X43,X44,X45,X46,X47] : lhs_atom89(X43,X44,X45,X46,X47),
    inference(variable_rename,[status(thm)],[c_0_143]) ).

fof(c_0_279,plain,
    ! [X28,X29,X30,X31,X32] : lhs_atom52(X28,X29,X30,X31,X32),
    inference(variable_rename,[status(thm)],[c_0_144]) ).

fof(c_0_280,plain,
    ! [X15,X16,X17,X18,X19] : lhs_atom47(X15,X16,X17,X18,X19),
    inference(variable_rename,[status(thm)],[c_0_145]) ).

fof(c_0_281,plain,
    ! [X12,X13,X14,X15,X16] : lhs_atom23(X12,X13,X14,X15,X16),
    inference(variable_rename,[status(thm)],[c_0_146]) ).

fof(c_0_282,plain,
    ! [X28,X29,X30,X31,X32] : lhs_atom16(X28,X29,X30,X31,X32),
    inference(variable_rename,[status(thm)],[c_0_147]) ).

fof(c_0_283,plain,
    ! [X14,X15,X16,X17,X18] : lhs_atom8(X14,X15,X16,X17,X18),
    inference(variable_rename,[status(thm)],[c_0_148]) ).

fof(c_0_284,plain,
    ! [X14,X15,X16,X17,X18] : lhs_atom7(X14,X15,X16,X17,X18),
    inference(variable_rename,[status(thm)],[c_0_149]) ).

fof(c_0_285,plain,
    ! [X12,X13,X14,X15,X16] : lhs_atom6(X12,X13,X14,X15,X16),
    inference(variable_rename,[status(thm)],[c_0_150]) ).

fof(c_0_286,plain,
    ! [X42,X43,X44,X45] : lhs_atom101(X42,X43,X44,X45),
    inference(variable_rename,[status(thm)],[c_0_151]) ).

fof(c_0_287,plain,
    ! [X45,X46,X47,X48] : lhs_atom100(X45,X46,X47,X48),
    inference(variable_rename,[status(thm)],[c_0_152]) ).

fof(c_0_288,plain,
    ! [X45,X46,X47,X48] : lhs_atom98(X45,X46,X47,X48),
    inference(variable_rename,[status(thm)],[c_0_153]) ).

fof(c_0_289,plain,
    ! [X42,X43,X44,X45] : lhs_atom85(X42,X43,X44,X45),
    inference(variable_rename,[status(thm)],[c_0_154]) ).

fof(c_0_290,plain,
    ! [X17,X18,X19,X20] : lhs_atom82(X17,X18,X19,X20),
    inference(variable_rename,[status(thm)],[c_0_155]) ).

fof(c_0_291,plain,
    ! [X42,X43,X44,X45] : lhs_atom77(X42,X43,X44,X45),
    inference(variable_rename,[status(thm)],[c_0_156]) ).

fof(c_0_292,plain,
    ! [X9,X10,X11,X12] : lhs_atom76(X9,X10,X11,X12),
    inference(variable_rename,[status(thm)],[c_0_157]) ).

fof(c_0_293,plain,
    ! [X35,X36,X37,X38] : lhs_atom63(X35,X36,X37,X38),
    inference(variable_rename,[status(thm)],[c_0_158]) ).

fof(c_0_294,plain,
    ! [X16,X17,X18,X19] : lhs_atom62(X16,X17,X18,X19),
    inference(variable_rename,[status(thm)],[c_0_159]) ).

fof(c_0_295,plain,
    ! [X37,X38,X39,X40] : lhs_atom61(X37,X38,X39,X40),
    inference(variable_rename,[status(thm)],[c_0_160]) ).

fof(c_0_296,plain,
    ! [X16,X17,X18,X19] : lhs_atom60(X16,X17,X18,X19),
    inference(variable_rename,[status(thm)],[c_0_161]) ).

fof(c_0_297,plain,
    ! [X10,X11,X12,X13] : lhs_atom58(X10,X11,X12,X13),
    inference(variable_rename,[status(thm)],[c_0_162]) ).

fof(c_0_298,plain,
    ! [X22,X23,X24,X25] : lhs_atom50(X22,X23,X24,X25),
    inference(variable_rename,[status(thm)],[c_0_163]) ).

fof(c_0_299,plain,
    ! [X8,X9,X10,X11] : lhs_atom48(X8,X9,X10,X11),
    inference(variable_rename,[status(thm)],[c_0_164]) ).

fof(c_0_300,plain,
    ! [X31,X32,X33,X34] : lhs_atom29(X31,X32,X33,X34),
    inference(variable_rename,[status(thm)],[c_0_165]) ).

fof(c_0_301,plain,
    ! [X16,X17,X18,X19] : lhs_atom28(X16,X17,X18,X19),
    inference(variable_rename,[status(thm)],[c_0_166]) ).

fof(c_0_302,plain,
    ! [X17,X18,X19,X20] : lhs_atom12(X17,X18,X19,X20),
    inference(variable_rename,[status(thm)],[c_0_167]) ).

fof(c_0_303,plain,
    ! [X16,X17,X18,X19] : lhs_atom10(X16,X17,X18,X19),
    inference(variable_rename,[status(thm)],[c_0_168]) ).

fof(c_0_304,plain,
    ! [X15,X16,X17,X18] : lhs_atom9(X15,X16,X17,X18),
    inference(variable_rename,[status(thm)],[c_0_169]) ).

fof(c_0_305,plain,
    ! [X5,X6,X7,X8] : lhs_atom1(X5,X6,X7,X8),
    inference(variable_rename,[status(thm)],[c_0_170]) ).

fof(c_0_306,plain,
    ! [X24,X25,X26] :
      ( lhs_atom65(X24,X25,X26)
      | c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),X25,X26) = c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),X24,X26) ),
    inference(variable_rename,[status(thm)],[c_0_171]) ).

fof(c_0_307,plain,
    ! [X47,X48,X49] : lhs_atom105(X47,X48,X49),
    inference(variable_rename,[status(thm)],[c_0_172]) ).

fof(c_0_308,plain,
    ! [X47,X48,X49] : lhs_atom103(X47,X48,X49),
    inference(variable_rename,[status(thm)],[c_0_173]) ).

fof(c_0_309,plain,
    ! [X9,X10,X11] : lhs_atom86(X9,X10,X11),
    inference(variable_rename,[status(thm)],[c_0_174]) ).

fof(c_0_310,plain,
    ! [X9,X10,X11] : lhs_atom78(X9,X10,X11),
    inference(variable_rename,[status(thm)],[c_0_175]) ).

fof(c_0_311,plain,
    ! [X9,X10,X11] : lhs_atom73(X9,X10,X11),
    inference(variable_rename,[status(thm)],[c_0_176]) ).

fof(c_0_312,plain,
    ! [X41,X42,X43] : lhs_atom72(X41,X42,X43),
    inference(variable_rename,[status(thm)],[c_0_177]) ).

fof(c_0_313,plain,
    ! [X41,X42,X43] : lhs_atom71(X41,X42,X43),
    inference(variable_rename,[status(thm)],[c_0_178]) ).

fof(c_0_314,plain,
    ! [X10,X11,X12] : lhs_atom57(X10,X11,X12),
    inference(variable_rename,[status(thm)],[c_0_179]) ).

fof(c_0_315,plain,
    ! [X30,X31,X32] : lhs_atom54(X30,X31,X32),
    inference(variable_rename,[status(thm)],[c_0_180]) ).

fof(c_0_316,plain,
    ! [X35,X36,X37] : lhs_atom51(X35,X36,X37),
    inference(variable_rename,[status(thm)],[c_0_181]) ).

fof(c_0_317,plain,
    ! [X33,X34,X35] : lhs_atom49(X33,X34,X35),
    inference(variable_rename,[status(thm)],[c_0_182]) ).

fof(c_0_318,plain,
    ! [X34,X35,X36] : lhs_atom38(X34,X35,X36),
    inference(variable_rename,[status(thm)],[c_0_183]) ).

fof(c_0_319,plain,
    ! [X12,X13,X14] : lhs_atom11(X12,X13,X14),
    inference(variable_rename,[status(thm)],[c_0_184]) ).

fof(c_0_320,plain,
    ! [X10,X11,X12] : lhs_atom35(X10,X11,X12),
    inference(variable_rename,[status(thm)],[c_0_185]) ).

fof(c_0_321,plain,
    ! [X10,X11,X12] : lhs_atom34(X10,X11,X12),
    inference(variable_rename,[status(thm)],[c_0_186]) ).

fof(c_0_322,plain,
    ! [X9,X10,X11] : lhs_atom33(X9,X10,X11),
    inference(variable_rename,[status(thm)],[c_0_187]) ).

fof(c_0_323,plain,
    ! [X33,X34,X35] : lhs_atom31(X33,X34,X35),
    inference(variable_rename,[status(thm)],[c_0_188]) ).

fof(c_0_324,plain,
    ! [X14,X15,X16] : lhs_atom30(X14,X15,X16),
    inference(variable_rename,[status(thm)],[c_0_189]) ).

fof(c_0_325,plain,
    ! [X30,X31,X32] : lhs_atom27(X30,X31,X32),
    inference(variable_rename,[status(thm)],[c_0_190]) ).

fof(c_0_326,plain,
    ! [X30,X31,X32] : lhs_atom26(X30,X31,X32),
    inference(variable_rename,[status(thm)],[c_0_191]) ).

fof(c_0_327,plain,
    ! [X30,X31,X32] : lhs_atom19(X30,X31,X32),
    inference(variable_rename,[status(thm)],[c_0_192]) ).

fof(c_0_328,plain,
    ! [X30,X31,X32] : lhs_atom18(X30,X31,X32),
    inference(variable_rename,[status(thm)],[c_0_193]) ).

fof(c_0_329,plain,
    ! [X24,X25,X26] : lhs_atom15(X24,X25,X26),
    inference(variable_rename,[status(thm)],[c_0_194]) ).

fof(c_0_330,plain,
    ! [X22,X23,X24] : lhs_atom14(X22,X23,X24),
    inference(variable_rename,[status(thm)],[c_0_195]) ).

fof(c_0_331,plain,
    ! [X12,X13,X14] : lhs_atom11(X12,X13,X14),
    inference(variable_rename,[status(thm)],[c_0_196]) ).

fof(c_0_332,plain,
    ! [X9,X10,X11] : lhs_atom5(X9,X10,X11),
    inference(variable_rename,[status(thm)],[c_0_197]) ).

fof(c_0_333,plain,
    ! [X9,X10,X11] : lhs_atom4(X9,X10,X11),
    inference(variable_rename,[status(thm)],[c_0_198]) ).

fof(c_0_334,plain,
    ! [X8,X9,X10] : lhs_atom3(X8,X9,X10),
    inference(variable_rename,[status(thm)],[c_0_199]) ).

fof(c_0_335,plain,
    ! [X5,X6] : lhs_atom131(X5,X6),
    inference(variable_rename,[status(thm)],[c_0_200]) ).

fof(c_0_336,plain,
    ! [X42,X43] : lhs_atom102(X42,X43),
    inference(variable_rename,[status(thm)],[c_0_201]) ).

fof(c_0_337,plain,
    ! [X30,X31] : lhs_atom97(X30,X31),
    inference(variable_rename,[status(thm)],[c_0_202]) ).

fof(c_0_338,plain,
    ! [X9,X10] : lhs_atom94(X9,X10),
    inference(variable_rename,[status(thm)],[c_0_203]) ).

fof(c_0_339,plain,
    ! [X9,X10] : lhs_atom93(X9,X10),
    inference(variable_rename,[status(thm)],[c_0_204]) ).

fof(c_0_340,plain,
    ! [X44,X45] : lhs_atom92(X44,X45),
    inference(variable_rename,[status(thm)],[c_0_205]) ).

fof(c_0_341,plain,
    ! [X43,X44] : lhs_atom90(X43,X44),
    inference(variable_rename,[status(thm)],[c_0_206]) ).

fof(c_0_342,plain,
    ! [X34,X35] : lhs_atom88(X34,X35),
    inference(variable_rename,[status(thm)],[c_0_207]) ).

fof(c_0_343,plain,
    ! [X43,X44] : lhs_atom87(X43,X44),
    inference(variable_rename,[status(thm)],[c_0_208]) ).

fof(c_0_344,plain,
    ! [X36,X37] : lhs_atom56(X36,X37),
    inference(variable_rename,[status(thm)],[c_0_209]) ).

fof(c_0_345,plain,
    ! [X36,X37] : lhs_atom55(X36,X37),
    inference(variable_rename,[status(thm)],[c_0_210]) ).

fof(c_0_346,plain,
    ! [X5,X6] : lhs_atom32(X5,X6),
    inference(variable_rename,[status(thm)],[c_0_211]) ).

fof(c_0_347,plain,
    ! [X9,X10] : lhs_atom40(X9,X10),
    inference(variable_rename,[status(thm)],[c_0_212]) ).

fof(c_0_348,plain,
    ! [X30,X31] : lhs_atom37(X30,X31),
    inference(variable_rename,[status(thm)],[c_0_213]) ).

fof(c_0_349,plain,
    ! [X5,X6] : lhs_atom32(X5,X6),
    inference(variable_rename,[status(thm)],[c_0_214]) ).

fof(c_0_350,plain,
    ! [X22,X23] : lhs_atom24(X22,X23),
    inference(variable_rename,[status(thm)],[c_0_215]) ).

fof(c_0_351,plain,
    ! [X15,X16] : lhs_atom22(X15,X16),
    inference(variable_rename,[status(thm)],[c_0_216]) ).

fof(c_0_352,plain,
    ! [X15,X16] : lhs_atom22(X15,X16),
    inference(variable_rename,[status(thm)],[c_0_217]) ).

fof(c_0_353,plain,
    ! [X10,X11] : lhs_atom20(X10,X11),
    inference(variable_rename,[status(thm)],[c_0_218]) ).

fof(c_0_354,plain,
    ! [X5,X6] : lhs_atom21(X5,X6),
    inference(variable_rename,[status(thm)],[c_0_219]) ).

fof(c_0_355,plain,
    ! [X10,X11] : lhs_atom20(X10,X11),
    inference(variable_rename,[status(thm)],[c_0_220]) ).

fof(c_0_356,plain,
    ! [X29,X30] : lhs_atom17(X29,X30),
    inference(variable_rename,[status(thm)],[c_0_221]) ).

fof(c_0_357,plain,
    ! [X7,X8] : lhs_atom2(X7,X8),
    inference(variable_rename,[status(thm)],[c_0_222]) ).

fof(c_0_358,plain,
    ! [X8] : lhs_atom104(X8),
    inference(variable_rename,[status(thm)],[c_0_223]) ).

fof(c_0_359,plain,
    ! [X22] : lhs_atom99(X22),
    inference(variable_rename,[status(thm)],[c_0_224]) ).

fof(c_0_360,plain,
    ! [X43] : lhs_atom96(X43),
    inference(variable_rename,[status(thm)],[c_0_225]) ).

fof(c_0_361,plain,
    ! [X43] : lhs_atom95(X43),
    inference(variable_rename,[status(thm)],[c_0_226]) ).

fof(c_0_362,plain,
    ! [X30] : lhs_atom81(X30),
    inference(variable_rename,[status(thm)],[c_0_227]) ).

fof(c_0_363,plain,
    ! [X9] : lhs_atom80(X9),
    inference(variable_rename,[status(thm)],[c_0_228]) ).

fof(c_0_364,plain,
    ! [X30] : lhs_atom79(X30),
    inference(variable_rename,[status(thm)],[c_0_229]) ).

fof(c_0_365,plain,
    ! [X22] : lhs_atom70(X22),
    inference(variable_rename,[status(thm)],[c_0_230]) ).

fof(c_0_366,plain,
    ! [X8] : lhs_atom69(X8),
    inference(variable_rename,[status(thm)],[c_0_231]) ).

fof(c_0_367,plain,
    ! [X2] : lhs_atom68(X2),
    inference(variable_rename,[status(thm)],[c_0_232]) ).

fof(c_0_368,plain,
    ! [X8] : lhs_atom67(X8),
    inference(variable_rename,[status(thm)],[c_0_233]) ).

fof(c_0_369,plain,
    ! [X8] : lhs_atom66(X8),
    inference(variable_rename,[status(thm)],[c_0_234]) ).

fof(c_0_370,plain,
    ! [X38] : lhs_atom64(X38),
    inference(variable_rename,[status(thm)],[c_0_235]) ).

fof(c_0_371,plain,
    ! [X5] : lhs_atom59(X5),
    inference(variable_rename,[status(thm)],[c_0_236]) ).

fof(c_0_372,plain,
    ! [X8] : lhs_atom46(X8),
    inference(variable_rename,[status(thm)],[c_0_237]) ).

fof(c_0_373,plain,
    ! [X2] : lhs_atom45(X2),
    inference(variable_rename,[status(thm)],[c_0_238]) ).

fof(c_0_374,plain,
    ! [X5] : lhs_atom44(X5),
    inference(variable_rename,[status(thm)],[c_0_239]) ).

fof(c_0_375,plain,
    ! [X8] : lhs_atom43(X8),
    inference(variable_rename,[status(thm)],[c_0_240]) ).

fof(c_0_376,plain,
    ! [X22] : lhs_atom42(X22),
    inference(variable_rename,[status(thm)],[c_0_241]) ).

fof(c_0_377,plain,
    ! [X5] : lhs_atom36(X5),
    inference(variable_rename,[status(thm)],[c_0_242]) ).

fof(c_0_378,plain,
    lhs_atom130,
    c_0_243 ).

fof(c_0_379,plain,
    lhs_atom129,
    c_0_244 ).

fof(c_0_380,plain,
    lhs_atom128,
    c_0_245 ).

fof(c_0_381,plain,
    lhs_atom127,
    c_0_246 ).

fof(c_0_382,plain,
    lhs_atom126,
    c_0_247 ).

fof(c_0_383,plain,
    lhs_atom125,
    c_0_248 ).

fof(c_0_384,plain,
    lhs_atom124,
    c_0_249 ).

fof(c_0_385,plain,
    lhs_atom123,
    c_0_250 ).

fof(c_0_386,plain,
    lhs_atom122,
    c_0_251 ).

fof(c_0_387,plain,
    lhs_atom121,
    c_0_252 ).

fof(c_0_388,plain,
    lhs_atom120,
    c_0_253 ).

fof(c_0_389,plain,
    lhs_atom119,
    c_0_254 ).

fof(c_0_390,plain,
    lhs_atom118,
    c_0_255 ).

fof(c_0_391,plain,
    lhs_atom117,
    c_0_256 ).

fof(c_0_392,plain,
    lhs_atom116,
    c_0_257 ).

fof(c_0_393,plain,
    lhs_atom115,
    c_0_258 ).

fof(c_0_394,plain,
    lhs_atom114,
    c_0_259 ).

fof(c_0_395,plain,
    lhs_atom113,
    c_0_260 ).

fof(c_0_396,plain,
    lhs_atom112,
    c_0_261 ).

fof(c_0_397,plain,
    lhs_atom111,
    c_0_262 ).

fof(c_0_398,plain,
    lhs_atom110,
    c_0_263 ).

fof(c_0_399,plain,
    lhs_atom109,
    c_0_264 ).

fof(c_0_400,plain,
    lhs_atom108,
    c_0_265 ).

fof(c_0_401,plain,
    lhs_atom107,
    c_0_266 ).

fof(c_0_402,plain,
    lhs_atom106,
    c_0_267 ).

fof(c_0_403,plain,
    lhs_atom41,
    c_0_268 ).

fof(c_0_404,plain,
    lhs_atom39,
    c_0_269 ).

cnf(c_0_405,plain,
    lhs_atom84(X1,X2,X3,X4,X5,X6),
    inference(split_conjunct,[status(thm)],[c_0_270]) ).

cnf(c_0_406,plain,
    lhs_atom83(X1,X2,X3,X4,X5,X6),
    inference(split_conjunct,[status(thm)],[c_0_271]) ).

cnf(c_0_407,plain,
    lhs_atom75(X1,X2,X3,X4,X5,X6),
    inference(split_conjunct,[status(thm)],[c_0_272]) ).

cnf(c_0_408,plain,
    lhs_atom74(X1,X2,X3,X4,X5,X6),
    inference(split_conjunct,[status(thm)],[c_0_273]) ).

cnf(c_0_409,plain,
    lhs_atom53(X1,X2,X3,X4,X5,X6),
    inference(split_conjunct,[status(thm)],[c_0_274]) ).

cnf(c_0_410,plain,
    lhs_atom25(X1,X2,X3,X4,X5,X6),
    inference(split_conjunct,[status(thm)],[c_0_275]) ).

cnf(c_0_411,plain,
    lhs_atom13(X1,X2,X3,X4,X5,X6),
    inference(split_conjunct,[status(thm)],[c_0_276]) ).

cnf(c_0_412,plain,
    lhs_atom91(X1,X2,X3,X4,X5),
    inference(split_conjunct,[status(thm)],[c_0_277]) ).

cnf(c_0_413,plain,
    lhs_atom89(X1,X2,X3,X4,X5),
    inference(split_conjunct,[status(thm)],[c_0_278]) ).

cnf(c_0_414,plain,
    lhs_atom52(X1,X2,X3,X4,X5),
    inference(split_conjunct,[status(thm)],[c_0_279]) ).

cnf(c_0_415,plain,
    lhs_atom47(X1,X2,X3,X4,X5),
    inference(split_conjunct,[status(thm)],[c_0_280]) ).

cnf(c_0_416,plain,
    lhs_atom23(X1,X2,X3,X4,X5),
    inference(split_conjunct,[status(thm)],[c_0_281]) ).

cnf(c_0_417,plain,
    lhs_atom16(X1,X2,X3,X4,X5),
    inference(split_conjunct,[status(thm)],[c_0_282]) ).

cnf(c_0_418,plain,
    lhs_atom8(X1,X2,X3,X4,X5),
    inference(split_conjunct,[status(thm)],[c_0_283]) ).

cnf(c_0_419,plain,
    lhs_atom7(X1,X2,X3,X4,X5),
    inference(split_conjunct,[status(thm)],[c_0_284]) ).

cnf(c_0_420,plain,
    lhs_atom6(X1,X2,X3,X4,X5),
    inference(split_conjunct,[status(thm)],[c_0_285]) ).

cnf(c_0_421,plain,
    lhs_atom101(X1,X2,X3,X4),
    inference(split_conjunct,[status(thm)],[c_0_286]) ).

cnf(c_0_422,plain,
    lhs_atom100(X1,X2,X3,X4),
    inference(split_conjunct,[status(thm)],[c_0_287]) ).

cnf(c_0_423,plain,
    lhs_atom98(X1,X2,X3,X4),
    inference(split_conjunct,[status(thm)],[c_0_288]) ).

cnf(c_0_424,plain,
    lhs_atom85(X1,X2,X3,X4),
    inference(split_conjunct,[status(thm)],[c_0_289]) ).

cnf(c_0_425,plain,
    lhs_atom82(X1,X2,X3,X4),
    inference(split_conjunct,[status(thm)],[c_0_290]) ).

cnf(c_0_426,plain,
    lhs_atom77(X1,X2,X3,X4),
    inference(split_conjunct,[status(thm)],[c_0_291]) ).

cnf(c_0_427,plain,
    lhs_atom76(X1,X2,X3,X4),
    inference(split_conjunct,[status(thm)],[c_0_292]) ).

cnf(c_0_428,plain,
    lhs_atom63(X1,X2,X3,X4),
    inference(split_conjunct,[status(thm)],[c_0_293]) ).

cnf(c_0_429,plain,
    lhs_atom62(X1,X2,X3,X4),
    inference(split_conjunct,[status(thm)],[c_0_294]) ).

cnf(c_0_430,plain,
    lhs_atom61(X1,X2,X3,X4),
    inference(split_conjunct,[status(thm)],[c_0_295]) ).

cnf(c_0_431,plain,
    lhs_atom60(X1,X2,X3,X4),
    inference(split_conjunct,[status(thm)],[c_0_296]) ).

cnf(c_0_432,plain,
    lhs_atom58(X1,X2,X3,X4),
    inference(split_conjunct,[status(thm)],[c_0_297]) ).

cnf(c_0_433,plain,
    lhs_atom50(X1,X2,X3,X4),
    inference(split_conjunct,[status(thm)],[c_0_298]) ).

cnf(c_0_434,plain,
    lhs_atom48(X1,X2,X3,X4),
    inference(split_conjunct,[status(thm)],[c_0_299]) ).

cnf(c_0_435,plain,
    lhs_atom29(X1,X2,X3,X4),
    inference(split_conjunct,[status(thm)],[c_0_300]) ).

cnf(c_0_436,plain,
    lhs_atom28(X1,X2,X3,X4),
    inference(split_conjunct,[status(thm)],[c_0_301]) ).

cnf(c_0_437,plain,
    lhs_atom12(X1,X2,X3,X4),
    inference(split_conjunct,[status(thm)],[c_0_302]) ).

cnf(c_0_438,plain,
    lhs_atom10(X1,X2,X3,X4),
    inference(split_conjunct,[status(thm)],[c_0_303]) ).

cnf(c_0_439,plain,
    lhs_atom9(X1,X2,X3,X4),
    inference(split_conjunct,[status(thm)],[c_0_304]) ).

cnf(c_0_440,plain,
    lhs_atom1(X1,X2,X3,X4),
    inference(split_conjunct,[status(thm)],[c_0_305]) ).

cnf(c_0_441,plain,
    ( c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),X1,X2) = c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),X3,X2)
    | lhs_atom65(X3,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_306]) ).

cnf(c_0_442,plain,
    lhs_atom105(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_307]) ).

cnf(c_0_443,plain,
    lhs_atom103(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_308]) ).

cnf(c_0_444,plain,
    lhs_atom86(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_309]) ).

cnf(c_0_445,plain,
    lhs_atom78(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_310]) ).

cnf(c_0_446,plain,
    lhs_atom73(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_311]) ).

cnf(c_0_447,plain,
    lhs_atom72(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_312]) ).

cnf(c_0_448,plain,
    lhs_atom71(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_313]) ).

cnf(c_0_449,plain,
    lhs_atom57(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_314]) ).

cnf(c_0_450,plain,
    lhs_atom54(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_315]) ).

cnf(c_0_451,plain,
    lhs_atom51(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_316]) ).

cnf(c_0_452,plain,
    lhs_atom49(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_317]) ).

cnf(c_0_453,plain,
    lhs_atom38(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_318]) ).

cnf(c_0_454,plain,
    lhs_atom11(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_319]) ).

cnf(c_0_455,plain,
    lhs_atom35(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_320]) ).

cnf(c_0_456,plain,
    lhs_atom34(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_321]) ).

cnf(c_0_457,plain,
    lhs_atom33(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_322]) ).

cnf(c_0_458,plain,
    lhs_atom31(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_323]) ).

cnf(c_0_459,plain,
    lhs_atom30(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_324]) ).

cnf(c_0_460,plain,
    lhs_atom27(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_325]) ).

cnf(c_0_461,plain,
    lhs_atom26(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_326]) ).

cnf(c_0_462,plain,
    lhs_atom19(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_327]) ).

cnf(c_0_463,plain,
    lhs_atom18(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_328]) ).

cnf(c_0_464,plain,
    lhs_atom15(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_329]) ).

cnf(c_0_465,plain,
    lhs_atom14(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_330]) ).

cnf(c_0_466,plain,
    lhs_atom11(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_331]) ).

cnf(c_0_467,plain,
    lhs_atom5(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_332]) ).

cnf(c_0_468,plain,
    lhs_atom4(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_333]) ).

cnf(c_0_469,plain,
    lhs_atom3(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_334]) ).

cnf(c_0_470,plain,
    lhs_atom131(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_335]) ).

cnf(c_0_471,plain,
    lhs_atom102(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_336]) ).

cnf(c_0_472,plain,
    lhs_atom97(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_337]) ).

cnf(c_0_473,plain,
    lhs_atom94(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_338]) ).

cnf(c_0_474,plain,
    lhs_atom93(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_339]) ).

cnf(c_0_475,plain,
    lhs_atom92(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_340]) ).

cnf(c_0_476,plain,
    lhs_atom90(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_341]) ).

cnf(c_0_477,plain,
    lhs_atom88(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_342]) ).

cnf(c_0_478,plain,
    lhs_atom87(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_343]) ).

cnf(c_0_479,plain,
    lhs_atom56(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_344]) ).

cnf(c_0_480,plain,
    lhs_atom55(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_345]) ).

cnf(c_0_481,plain,
    lhs_atom32(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_346]) ).

cnf(c_0_482,plain,
    lhs_atom40(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_347]) ).

cnf(c_0_483,plain,
    lhs_atom37(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_348]) ).

cnf(c_0_484,plain,
    lhs_atom32(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_349]) ).

cnf(c_0_485,plain,
    lhs_atom24(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_350]) ).

cnf(c_0_486,plain,
    lhs_atom22(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_351]) ).

cnf(c_0_487,plain,
    lhs_atom22(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_352]) ).

cnf(c_0_488,plain,
    lhs_atom20(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_353]) ).

cnf(c_0_489,plain,
    lhs_atom21(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_354]) ).

cnf(c_0_490,plain,
    lhs_atom20(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_355]) ).

cnf(c_0_491,plain,
    lhs_atom17(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_356]) ).

cnf(c_0_492,plain,
    lhs_atom2(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_357]) ).

cnf(c_0_493,plain,
    lhs_atom104(X1),
    inference(split_conjunct,[status(thm)],[c_0_358]) ).

cnf(c_0_494,plain,
    lhs_atom99(X1),
    inference(split_conjunct,[status(thm)],[c_0_359]) ).

cnf(c_0_495,plain,
    lhs_atom96(X1),
    inference(split_conjunct,[status(thm)],[c_0_360]) ).

cnf(c_0_496,plain,
    lhs_atom95(X1),
    inference(split_conjunct,[status(thm)],[c_0_361]) ).

cnf(c_0_497,plain,
    lhs_atom81(X1),
    inference(split_conjunct,[status(thm)],[c_0_362]) ).

cnf(c_0_498,plain,
    lhs_atom80(X1),
    inference(split_conjunct,[status(thm)],[c_0_363]) ).

cnf(c_0_499,plain,
    lhs_atom79(X1),
    inference(split_conjunct,[status(thm)],[c_0_364]) ).

cnf(c_0_500,plain,
    lhs_atom70(X1),
    inference(split_conjunct,[status(thm)],[c_0_365]) ).

cnf(c_0_501,plain,
    lhs_atom69(X1),
    inference(split_conjunct,[status(thm)],[c_0_366]) ).

cnf(c_0_502,plain,
    lhs_atom68(X1),
    inference(split_conjunct,[status(thm)],[c_0_367]) ).

cnf(c_0_503,plain,
    lhs_atom67(X1),
    inference(split_conjunct,[status(thm)],[c_0_368]) ).

cnf(c_0_504,plain,
    lhs_atom66(X1),
    inference(split_conjunct,[status(thm)],[c_0_369]) ).

cnf(c_0_505,plain,
    lhs_atom64(X1),
    inference(split_conjunct,[status(thm)],[c_0_370]) ).

cnf(c_0_506,plain,
    lhs_atom59(X1),
    inference(split_conjunct,[status(thm)],[c_0_371]) ).

cnf(c_0_507,plain,
    lhs_atom46(X1),
    inference(split_conjunct,[status(thm)],[c_0_372]) ).

cnf(c_0_508,plain,
    lhs_atom45(X1),
    inference(split_conjunct,[status(thm)],[c_0_373]) ).

cnf(c_0_509,plain,
    lhs_atom44(X1),
    inference(split_conjunct,[status(thm)],[c_0_374]) ).

cnf(c_0_510,plain,
    lhs_atom43(X1),
    inference(split_conjunct,[status(thm)],[c_0_375]) ).

cnf(c_0_511,plain,
    lhs_atom42(X1),
    inference(split_conjunct,[status(thm)],[c_0_376]) ).

cnf(c_0_512,plain,
    lhs_atom36(X1),
    inference(split_conjunct,[status(thm)],[c_0_377]) ).

cnf(c_0_513,plain,
    lhs_atom130,
    inference(split_conjunct,[status(thm)],[c_0_378]) ).

cnf(c_0_514,plain,
    lhs_atom129,
    inference(split_conjunct,[status(thm)],[c_0_379]) ).

cnf(c_0_515,plain,
    lhs_atom128,
    inference(split_conjunct,[status(thm)],[c_0_380]) ).

cnf(c_0_516,plain,
    lhs_atom127,
    inference(split_conjunct,[status(thm)],[c_0_381]) ).

cnf(c_0_517,plain,
    lhs_atom126,
    inference(split_conjunct,[status(thm)],[c_0_382]) ).

cnf(c_0_518,plain,
    lhs_atom125,
    inference(split_conjunct,[status(thm)],[c_0_383]) ).

cnf(c_0_519,plain,
    lhs_atom124,
    inference(split_conjunct,[status(thm)],[c_0_384]) ).

cnf(c_0_520,plain,
    lhs_atom123,
    inference(split_conjunct,[status(thm)],[c_0_385]) ).

cnf(c_0_521,plain,
    lhs_atom122,
    inference(split_conjunct,[status(thm)],[c_0_386]) ).

cnf(c_0_522,plain,
    lhs_atom121,
    inference(split_conjunct,[status(thm)],[c_0_387]) ).

cnf(c_0_523,plain,
    lhs_atom120,
    inference(split_conjunct,[status(thm)],[c_0_388]) ).

cnf(c_0_524,plain,
    lhs_atom119,
    inference(split_conjunct,[status(thm)],[c_0_389]) ).

cnf(c_0_525,plain,
    lhs_atom118,
    inference(split_conjunct,[status(thm)],[c_0_390]) ).

cnf(c_0_526,plain,
    lhs_atom117,
    inference(split_conjunct,[status(thm)],[c_0_391]) ).

cnf(c_0_527,plain,
    lhs_atom116,
    inference(split_conjunct,[status(thm)],[c_0_392]) ).

cnf(c_0_528,plain,
    lhs_atom115,
    inference(split_conjunct,[status(thm)],[c_0_393]) ).

cnf(c_0_529,plain,
    lhs_atom114,
    inference(split_conjunct,[status(thm)],[c_0_394]) ).

cnf(c_0_530,plain,
    lhs_atom113,
    inference(split_conjunct,[status(thm)],[c_0_395]) ).

cnf(c_0_531,plain,
    lhs_atom112,
    inference(split_conjunct,[status(thm)],[c_0_396]) ).

cnf(c_0_532,plain,
    lhs_atom111,
    inference(split_conjunct,[status(thm)],[c_0_397]) ).

cnf(c_0_533,plain,
    lhs_atom110,
    inference(split_conjunct,[status(thm)],[c_0_398]) ).

cnf(c_0_534,plain,
    lhs_atom109,
    inference(split_conjunct,[status(thm)],[c_0_399]) ).

cnf(c_0_535,plain,
    lhs_atom108,
    inference(split_conjunct,[status(thm)],[c_0_400]) ).

cnf(c_0_536,plain,
    lhs_atom107,
    inference(split_conjunct,[status(thm)],[c_0_401]) ).

cnf(c_0_537,plain,
    lhs_atom106,
    inference(split_conjunct,[status(thm)],[c_0_402]) ).

cnf(c_0_538,plain,
    lhs_atom41,
    inference(split_conjunct,[status(thm)],[c_0_403]) ).

cnf(c_0_539,plain,
    lhs_atom39,
    inference(split_conjunct,[status(thm)],[c_0_404]) ).

cnf(c_0_540,plain,
    lhs_atom84(X1,X2,X3,X4,X5,X6),
    c_0_405,
    [final] ).

cnf(c_0_541,plain,
    lhs_atom83(X1,X2,X3,X4,X5,X6),
    c_0_406,
    [final] ).

cnf(c_0_542,plain,
    lhs_atom75(X1,X2,X3,X4,X5,X6),
    c_0_407,
    [final] ).

cnf(c_0_543,plain,
    lhs_atom74(X1,X2,X3,X4,X5,X6),
    c_0_408,
    [final] ).

cnf(c_0_544,plain,
    lhs_atom53(X1,X2,X3,X4,X5,X6),
    c_0_409,
    [final] ).

cnf(c_0_545,plain,
    lhs_atom25(X1,X2,X3,X4,X5,X6),
    c_0_410,
    [final] ).

cnf(c_0_546,plain,
    lhs_atom13(X1,X2,X3,X4,X5,X6),
    c_0_411,
    [final] ).

cnf(c_0_547,plain,
    lhs_atom91(X1,X2,X3,X4,X5),
    c_0_412,
    [final] ).

cnf(c_0_548,plain,
    lhs_atom89(X1,X2,X3,X4,X5),
    c_0_413,
    [final] ).

cnf(c_0_549,plain,
    lhs_atom52(X1,X2,X3,X4,X5),
    c_0_414,
    [final] ).

cnf(c_0_550,plain,
    lhs_atom47(X1,X2,X3,X4,X5),
    c_0_415,
    [final] ).

cnf(c_0_551,plain,
    lhs_atom23(X1,X2,X3,X4,X5),
    c_0_416,
    [final] ).

cnf(c_0_552,plain,
    lhs_atom16(X1,X2,X3,X4,X5),
    c_0_417,
    [final] ).

cnf(c_0_553,plain,
    lhs_atom8(X1,X2,X3,X4,X5),
    c_0_418,
    [final] ).

cnf(c_0_554,plain,
    lhs_atom7(X1,X2,X3,X4,X5),
    c_0_419,
    [final] ).

cnf(c_0_555,plain,
    lhs_atom6(X1,X2,X3,X4,X5),
    c_0_420,
    [final] ).

cnf(c_0_556,plain,
    lhs_atom101(X1,X2,X3,X4),
    c_0_421,
    [final] ).

cnf(c_0_557,plain,
    lhs_atom100(X1,X2,X3,X4),
    c_0_422,
    [final] ).

cnf(c_0_558,plain,
    lhs_atom98(X1,X2,X3,X4),
    c_0_423,
    [final] ).

cnf(c_0_559,plain,
    lhs_atom85(X1,X2,X3,X4),
    c_0_424,
    [final] ).

cnf(c_0_560,plain,
    lhs_atom82(X1,X2,X3,X4),
    c_0_425,
    [final] ).

cnf(c_0_561,plain,
    lhs_atom77(X1,X2,X3,X4),
    c_0_426,
    [final] ).

cnf(c_0_562,plain,
    lhs_atom76(X1,X2,X3,X4),
    c_0_427,
    [final] ).

cnf(c_0_563,plain,
    lhs_atom63(X1,X2,X3,X4),
    c_0_428,
    [final] ).

cnf(c_0_564,plain,
    lhs_atom62(X1,X2,X3,X4),
    c_0_429,
    [final] ).

cnf(c_0_565,plain,
    lhs_atom61(X1,X2,X3,X4),
    c_0_430,
    [final] ).

cnf(c_0_566,plain,
    lhs_atom60(X1,X2,X3,X4),
    c_0_431,
    [final] ).

cnf(c_0_567,plain,
    lhs_atom58(X1,X2,X3,X4),
    c_0_432,
    [final] ).

cnf(c_0_568,plain,
    lhs_atom50(X1,X2,X3,X4),
    c_0_433,
    [final] ).

cnf(c_0_569,plain,
    lhs_atom48(X1,X2,X3,X4),
    c_0_434,
    [final] ).

cnf(c_0_570,plain,
    lhs_atom29(X1,X2,X3,X4),
    c_0_435,
    [final] ).

cnf(c_0_571,plain,
    lhs_atom28(X1,X2,X3,X4),
    c_0_436,
    [final] ).

cnf(c_0_572,plain,
    lhs_atom12(X1,X2,X3,X4),
    c_0_437,
    [final] ).

cnf(c_0_573,plain,
    lhs_atom10(X1,X2,X3,X4),
    c_0_438,
    [final] ).

cnf(c_0_574,plain,
    lhs_atom9(X1,X2,X3,X4),
    c_0_439,
    [final] ).

cnf(c_0_575,plain,
    lhs_atom1(X1,X2,X3,X4),
    c_0_440,
    [final] ).

cnf(c_0_576,plain,
    ( c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),X1,X2) = c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),X3,X2)
    | lhs_atom65(X3,X1,X2) ),
    c_0_441,
    [final] ).

cnf(c_0_577,plain,
    lhs_atom105(X1,X2,X3),
    c_0_442,
    [final] ).

cnf(c_0_578,plain,
    lhs_atom103(X1,X2,X3),
    c_0_443,
    [final] ).

cnf(c_0_579,plain,
    lhs_atom86(X1,X2,X3),
    c_0_444,
    [final] ).

cnf(c_0_580,plain,
    lhs_atom78(X1,X2,X3),
    c_0_445,
    [final] ).

cnf(c_0_581,plain,
    lhs_atom73(X1,X2,X3),
    c_0_446,
    [final] ).

cnf(c_0_582,plain,
    lhs_atom72(X1,X2,X3),
    c_0_447,
    [final] ).

cnf(c_0_583,plain,
    lhs_atom71(X1,X2,X3),
    c_0_448,
    [final] ).

cnf(c_0_584,plain,
    lhs_atom57(X1,X2,X3),
    c_0_449,
    [final] ).

cnf(c_0_585,plain,
    lhs_atom54(X1,X2,X3),
    c_0_450,
    [final] ).

cnf(c_0_586,plain,
    lhs_atom51(X1,X2,X3),
    c_0_451,
    [final] ).

cnf(c_0_587,plain,
    lhs_atom49(X1,X2,X3),
    c_0_452,
    [final] ).

cnf(c_0_588,plain,
    lhs_atom38(X1,X2,X3),
    c_0_453,
    [final] ).

cnf(c_0_589,plain,
    lhs_atom11(X1,X2,X3),
    c_0_454,
    [final] ).

cnf(c_0_590,plain,
    lhs_atom35(X1,X2,X3),
    c_0_455,
    [final] ).

cnf(c_0_591,plain,
    lhs_atom34(X1,X2,X3),
    c_0_456,
    [final] ).

cnf(c_0_592,plain,
    lhs_atom33(X1,X2,X3),
    c_0_457,
    [final] ).

cnf(c_0_593,plain,
    lhs_atom31(X1,X2,X3),
    c_0_458,
    [final] ).

cnf(c_0_594,plain,
    lhs_atom30(X1,X2,X3),
    c_0_459,
    [final] ).

cnf(c_0_595,plain,
    lhs_atom27(X1,X2,X3),
    c_0_460,
    [final] ).

cnf(c_0_596,plain,
    lhs_atom26(X1,X2,X3),
    c_0_461,
    [final] ).

cnf(c_0_597,plain,
    lhs_atom19(X1,X2,X3),
    c_0_462,
    [final] ).

cnf(c_0_598,plain,
    lhs_atom18(X1,X2,X3),
    c_0_463,
    [final] ).

cnf(c_0_599,plain,
    lhs_atom15(X1,X2,X3),
    c_0_464,
    [final] ).

cnf(c_0_600,plain,
    lhs_atom14(X1,X2,X3),
    c_0_465,
    [final] ).

cnf(c_0_601,plain,
    lhs_atom11(X1,X2,X3),
    c_0_466,
    [final] ).

cnf(c_0_602,plain,
    lhs_atom5(X1,X2,X3),
    c_0_467,
    [final] ).

cnf(c_0_603,plain,
    lhs_atom4(X1,X2,X3),
    c_0_468,
    [final] ).

cnf(c_0_604,plain,
    lhs_atom3(X1,X2,X3),
    c_0_469,
    [final] ).

cnf(c_0_605,plain,
    lhs_atom131(X1,X2),
    c_0_470,
    [final] ).

cnf(c_0_606,plain,
    lhs_atom102(X1,X2),
    c_0_471,
    [final] ).

cnf(c_0_607,plain,
    lhs_atom97(X1,X2),
    c_0_472,
    [final] ).

cnf(c_0_608,plain,
    lhs_atom94(X1,X2),
    c_0_473,
    [final] ).

cnf(c_0_609,plain,
    lhs_atom93(X1,X2),
    c_0_474,
    [final] ).

cnf(c_0_610,plain,
    lhs_atom92(X1,X2),
    c_0_475,
    [final] ).

cnf(c_0_611,plain,
    lhs_atom90(X1,X2),
    c_0_476,
    [final] ).

cnf(c_0_612,plain,
    lhs_atom88(X1,X2),
    c_0_477,
    [final] ).

cnf(c_0_613,plain,
    lhs_atom87(X1,X2),
    c_0_478,
    [final] ).

cnf(c_0_614,plain,
    lhs_atom56(X1,X2),
    c_0_479,
    [final] ).

cnf(c_0_615,plain,
    lhs_atom55(X1,X2),
    c_0_480,
    [final] ).

cnf(c_0_616,plain,
    lhs_atom32(X1,X2),
    c_0_481,
    [final] ).

cnf(c_0_617,plain,
    lhs_atom40(X1,X2),
    c_0_482,
    [final] ).

cnf(c_0_618,plain,
    lhs_atom37(X1,X2),
    c_0_483,
    [final] ).

cnf(c_0_619,plain,
    lhs_atom32(X1,X2),
    c_0_484,
    [final] ).

cnf(c_0_620,plain,
    lhs_atom24(X1,X2),
    c_0_485,
    [final] ).

cnf(c_0_621,plain,
    lhs_atom22(X1,X2),
    c_0_486,
    [final] ).

cnf(c_0_622,plain,
    lhs_atom22(X1,X2),
    c_0_487,
    [final] ).

cnf(c_0_623,plain,
    lhs_atom20(X1,X2),
    c_0_488,
    [final] ).

cnf(c_0_624,plain,
    lhs_atom21(X1,X2),
    c_0_489,
    [final] ).

cnf(c_0_625,plain,
    lhs_atom20(X1,X2),
    c_0_490,
    [final] ).

cnf(c_0_626,plain,
    lhs_atom17(X1,X2),
    c_0_491,
    [final] ).

cnf(c_0_627,plain,
    lhs_atom2(X1,X2),
    c_0_492,
    [final] ).

cnf(c_0_628,plain,
    lhs_atom104(X1),
    c_0_493,
    [final] ).

cnf(c_0_629,plain,
    lhs_atom99(X1),
    c_0_494,
    [final] ).

cnf(c_0_630,plain,
    lhs_atom96(X1),
    c_0_495,
    [final] ).

cnf(c_0_631,plain,
    lhs_atom95(X1),
    c_0_496,
    [final] ).

cnf(c_0_632,plain,
    lhs_atom81(X1),
    c_0_497,
    [final] ).

cnf(c_0_633,plain,
    lhs_atom80(X1),
    c_0_498,
    [final] ).

cnf(c_0_634,plain,
    lhs_atom79(X1),
    c_0_499,
    [final] ).

cnf(c_0_635,plain,
    lhs_atom70(X1),
    c_0_500,
    [final] ).

cnf(c_0_636,plain,
    lhs_atom69(X1),
    c_0_501,
    [final] ).

cnf(c_0_637,plain,
    lhs_atom68(X1),
    c_0_502,
    [final] ).

cnf(c_0_638,plain,
    lhs_atom67(X1),
    c_0_503,
    [final] ).

cnf(c_0_639,plain,
    lhs_atom66(X1),
    c_0_504,
    [final] ).

cnf(c_0_640,plain,
    lhs_atom64(X1),
    c_0_505,
    [final] ).

cnf(c_0_641,plain,
    lhs_atom59(X1),
    c_0_506,
    [final] ).

cnf(c_0_642,plain,
    lhs_atom46(X1),
    c_0_507,
    [final] ).

cnf(c_0_643,plain,
    lhs_atom45(X1),
    c_0_508,
    [final] ).

cnf(c_0_644,plain,
    lhs_atom44(X1),
    c_0_509,
    [final] ).

cnf(c_0_645,plain,
    lhs_atom43(X1),
    c_0_510,
    [final] ).

cnf(c_0_646,plain,
    lhs_atom42(X1),
    c_0_511,
    [final] ).

cnf(c_0_647,plain,
    lhs_atom36(X1),
    c_0_512,
    [final] ).

cnf(c_0_648,plain,
    lhs_atom130,
    c_0_513,
    [final] ).

cnf(c_0_649,plain,
    lhs_atom129,
    c_0_514,
    [final] ).

cnf(c_0_650,plain,
    lhs_atom128,
    c_0_515,
    [final] ).

cnf(c_0_651,plain,
    lhs_atom127,
    c_0_516,
    [final] ).

cnf(c_0_652,plain,
    lhs_atom126,
    c_0_517,
    [final] ).

cnf(c_0_653,plain,
    lhs_atom125,
    c_0_518,
    [final] ).

cnf(c_0_654,plain,
    lhs_atom124,
    c_0_519,
    [final] ).

cnf(c_0_655,plain,
    lhs_atom123,
    c_0_520,
    [final] ).

cnf(c_0_656,plain,
    lhs_atom122,
    c_0_521,
    [final] ).

cnf(c_0_657,plain,
    lhs_atom121,
    c_0_522,
    [final] ).

cnf(c_0_658,plain,
    lhs_atom120,
    c_0_523,
    [final] ).

cnf(c_0_659,plain,
    lhs_atom119,
    c_0_524,
    [final] ).

cnf(c_0_660,plain,
    lhs_atom118,
    c_0_525,
    [final] ).

cnf(c_0_661,plain,
    lhs_atom117,
    c_0_526,
    [final] ).

cnf(c_0_662,plain,
    lhs_atom116,
    c_0_527,
    [final] ).

cnf(c_0_663,plain,
    lhs_atom115,
    c_0_528,
    [final] ).

cnf(c_0_664,plain,
    lhs_atom114,
    c_0_529,
    [final] ).

cnf(c_0_665,plain,
    lhs_atom113,
    c_0_530,
    [final] ).

cnf(c_0_666,plain,
    lhs_atom112,
    c_0_531,
    [final] ).

cnf(c_0_667,plain,
    lhs_atom111,
    c_0_532,
    [final] ).

cnf(c_0_668,plain,
    lhs_atom110,
    c_0_533,
    [final] ).

cnf(c_0_669,plain,
    lhs_atom109,
    c_0_534,
    [final] ).

cnf(c_0_670,plain,
    lhs_atom108,
    c_0_535,
    [final] ).

cnf(c_0_671,plain,
    lhs_atom107,
    c_0_536,
    [final] ).

cnf(c_0_672,plain,
    lhs_atom106,
    c_0_537,
    [final] ).

cnf(c_0_673,plain,
    lhs_atom41,
    c_0_538,
    [final] ).

cnf(c_0_674,plain,
    lhs_atom39,
    c_0_539,
    [final] ).

% End CNF derivation
cnf(c_0_576_0,axiom,
    ( c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),X1,X2) = c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),X3,X2)
    | c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),X1,X2) = c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),X3,X2) ),
    inference(unfold_definition,[status(thm)],[c_0_576,def_lhs_atom65]) ).

cnf(c_0_540_0,axiom,
    c_List_Ofoldl(X3,X4,c_List_Oappend(X2,X1,X5),X6,X5) = c_List_Ofoldl(X3,c_List_Ofoldl(X3,X4,X2,X6,X5),X1,X6,X5),
    inference(unfold_definition,[status(thm)],[c_0_540,def_lhs_atom84]) ).

cnf(c_0_541_0,axiom,
    c_List_Ofoldl(X3,X4,c_List_Olist_OCons(X2,X1,X5),X6,X5) = c_List_Ofoldl(X3,hAPP(hAPP(X3,X4),X2),X1,X6,X5),
    inference(unfold_definition,[status(thm)],[c_0_541,def_lhs_atom83]) ).

cnf(c_0_542_0,axiom,
    c_Lambda_OdB_OdB__rec(X3,X2,X1,hAPP(hAPP(c_Lambda_OdB_OApp,X5),X4),X6) = hAPP(hAPP(hAPP(hAPP(X2,X5),X4),c_Lambda_OdB_OdB__rec(X3,X2,X1,X5,X6)),c_Lambda_OdB_OdB__rec(X3,X2,X1,X4,X6)),
    inference(unfold_definition,[status(thm)],[c_0_542,def_lhs_atom75]) ).

cnf(c_0_543_0,axiom,
    c_Lambda_OdB_OdB__case(X3,X2,X1,hAPP(hAPP(c_Lambda_OdB_OApp,X5),X4),X6) = hAPP(hAPP(X2,X5),X4),
    inference(unfold_definition,[status(thm)],[c_0_543,def_lhs_atom74]) ).

cnf(c_0_544_0,axiom,
    c_List_Ofoldr(X3,c_List_Olist_OCons(X2,X1,X5),X4,X5,X6) = hAPP(hAPP(X3,X2),c_List_Ofoldr(X3,X1,X4,X5,X6)),
    inference(unfold_definition,[status(thm)],[c_0_544,def_lhs_atom53]) ).

cnf(c_0_545_0,axiom,
    c_List_Ofoldr(X3,c_List_Oappend(X2,X1,X5),X4,X5,X6) = c_List_Ofoldr(X3,X2,c_List_Ofoldr(X3,X1,X4,X5,X6),X5,X6),
    inference(unfold_definition,[status(thm)],[c_0_545,def_lhs_atom25]) ).

cnf(c_0_546_0,axiom,
    hAPP(c_COMBC(X3,X2,X5,X4,X6),X1) = hAPP(hAPP(X3,X1),X2),
    inference(unfold_definition,[status(thm)],[c_0_546,def_lhs_atom13]) ).

cnf(c_0_547_0,axiom,
    c_Lambda_OdB_OdB__case(X4,X3,X2,c_Lambda_OdB_OVar(X1),X5) = hAPP(X4,X1),
    inference(unfold_definition,[status(thm)],[c_0_547,def_lhs_atom91]) ).

cnf(c_0_548_0,axiom,
    c_Lambda_OdB_OdB__rec(X4,X3,X2,c_Lambda_OdB_OVar(X1),X5) = hAPP(X4,X1),
    inference(unfold_definition,[status(thm)],[c_0_548,def_lhs_atom89]) ).

cnf(c_0_549_0,axiom,
    c_Lambda_OdB_OdB__rec(X3,X2,X1,c_Lambda_OdB_OAbs(X4),X5) = hAPP(hAPP(X1,X4),c_Lambda_OdB_OdB__rec(X3,X2,X1,X4,X5)),
    inference(unfold_definition,[status(thm)],[c_0_549,def_lhs_atom52]) ).

cnf(c_0_550_0,axiom,
    c_List_Omap(X3,c_List_Oappend(X2,X1,X4),X4,X5) = c_List_Oappend(c_List_Omap(X3,X2,X4,X5),c_List_Omap(X3,X1,X4,X5),X5),
    inference(unfold_definition,[status(thm)],[c_0_550,def_lhs_atom47]) ).

cnf(c_0_551_0,axiom,
    c_List_Omap(X3,c_List_Oreplicate(X2,X1,X4),X4,X5) = c_List_Oreplicate(X2,hAPP(X3,X1),X5),
    inference(unfold_definition,[status(thm)],[c_0_551,def_lhs_atom23]) ).

cnf(c_0_552_0,axiom,
    c_Lambda_OdB_OdB__case(X3,X2,X1,c_Lambda_OdB_OAbs(X4),X5) = hAPP(X1,X4),
    inference(unfold_definition,[status(thm)],[c_0_552,def_lhs_atom16]) ).

cnf(c_0_553_0,axiom,
    c_List_Omap(X3,c_List_Olist_OCons(X2,X1,X4),X4,X5) = c_List_Olist_OCons(hAPP(X3,X2),c_List_Omap(X3,X1,X4,X5),X5),
    inference(unfold_definition,[status(thm)],[c_0_553,def_lhs_atom8]) ).

cnf(c_0_554_0,axiom,
    c_List_Olist_OCons(hAPP(X3,X2),c_List_Omap(X3,X1,X4,X5),X5) = c_List_Omap(X3,c_List_Olist_OCons(X2,X1,X4),X4,X5),
    inference(unfold_definition,[status(thm)],[c_0_554,def_lhs_atom7]) ).

cnf(c_0_555_0,axiom,
    c_List_Omap(X3,c_List_Olist_OCons(X2,X1,X4),X4,X5) = c_List_Olist_OCons(hAPP(X3,X2),c_List_Omap(X3,X1,X4,X5),X5),
    inference(unfold_definition,[status(thm)],[c_0_555,def_lhs_atom6]) ).

cnf(c_0_556_0,axiom,
    hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_OdB_OApp,X2),X1)),X3),X4) = hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X2),X3),X4)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X3),X4)),
    inference(unfold_definition,[status(thm)],[c_0_556,def_lhs_atom101]) ).

cnf(c_0_557_0,axiom,
    hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X3)),X1) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X4),X2,tc_Lambda_OdB,tc_Lambda_OdB),
    inference(unfold_definition,[status(thm)],[c_0_557,def_lhs_atom100]) ).

cnf(c_0_558_0,axiom,
    c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X4),X1,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X3),X2,tc_Lambda_OdB,tc_Lambda_OdB),
    inference(unfold_definition,[status(thm)],[c_0_558,def_lhs_atom98]) ).

cnf(c_0_559_0,axiom,
    hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X2,tc_Lambda_OdB,tc_Lambda_OdB)),X1),X4) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X3),X1),X4),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,X1,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),X4,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X2,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
    inference(unfold_definition,[status(thm)],[c_0_559,def_lhs_atom85]) ).

cnf(c_0_560_0,axiom,
    c_List_Ofoldl(X1,X2,c_List_Olist_ONil(X3),X4,X3) = X2,
    inference(unfold_definition,[status(thm)],[c_0_560,def_lhs_atom82]) ).

cnf(c_0_561_0,axiom,
    c_Lambda_Osubstn(hAPP(hAPP(c_Lambda_OdB_OApp,X2),X1),X3,X4) = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Osubstn(X2,X3,X4)),c_Lambda_Osubstn(X1,X3,X4)),
    inference(unfold_definition,[status(thm)],[c_0_561,def_lhs_atom77]) ).

cnf(c_0_562_0,axiom,
    c_Lambda_Oliftn(X3,hAPP(hAPP(c_Lambda_OdB_OApp,X2),X1),X4) = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Oliftn(X3,X2,X4)),c_Lambda_Oliftn(X3,X1,X4)),
    inference(unfold_definition,[status(thm)],[c_0_562,def_lhs_atom76]) ).

cnf(c_0_563_0,axiom,
    c_List_Oappend(X1,c_List_Oappend(X2,X3,X4),X4) = c_List_Oappend(c_List_Oappend(X1,X2,X4),X3,X4),
    inference(unfold_definition,[status(thm)],[c_0_563,def_lhs_atom63]) ).

cnf(c_0_564_0,axiom,
    c_List_Oappend(c_List_Oappend(X1,X3,X4),X2,X4) = c_List_Oappend(X1,c_List_Oappend(X3,X2,X4),X4),
    inference(unfold_definition,[status(thm)],[c_0_564,def_lhs_atom62]) ).

cnf(c_0_565_0,axiom,
    c_List_Oappend(X2,c_List_Oappend(X1,X3,X4),X4) = c_List_Oappend(c_List_Oappend(X2,X1,X4),X3,X4),
    inference(unfold_definition,[status(thm)],[c_0_565,def_lhs_atom61]) ).

cnf(c_0_566_0,axiom,
    c_List_Oappend(c_List_Oappend(X3,X2,X4),X1,X4) = c_List_Oappend(X3,c_List_Oappend(X2,X1,X4),X4),
    inference(unfold_definition,[status(thm)],[c_0_566,def_lhs_atom60]) ).

cnf(c_0_567_0,axiom,
    c_List_Oappend(c_List_Oreplicate(X3,X2,X4),c_List_Olist_OCons(X2,X1,X4),X4) = c_List_Olist_OCons(X2,c_List_Oappend(c_List_Oreplicate(X3,X2,X4),X1,X4),X4),
    inference(unfold_definition,[status(thm)],[c_0_567,def_lhs_atom58]) ).

cnf(c_0_568_0,axiom,
    c_List_Oreplicate(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),X1,X4) = c_List_Oappend(c_List_Oreplicate(X2,X1,X4),c_List_Oreplicate(X3,X1,X4),X4),
    inference(unfold_definition,[status(thm)],[c_0_568,def_lhs_atom50]) ).

cnf(c_0_569_0,axiom,
    c_List_Oappend(c_List_Oreplicate(X2,X1,X4),c_List_Oreplicate(X3,X1,X4),X4) = c_List_Oappend(c_List_Oreplicate(X3,X1,X4),c_List_Oreplicate(X2,X1,X4),X4),
    inference(unfold_definition,[status(thm)],[c_0_569,def_lhs_atom48]) ).

cnf(c_0_570_0,axiom,
    c_List_Olist_OCons(X3,c_List_Oappend(X2,X1,X4),X4) = c_List_Oappend(c_List_Olist_OCons(X3,X2,X4),X1,X4),
    inference(unfold_definition,[status(thm)],[c_0_570,def_lhs_atom29]) ).

cnf(c_0_571_0,axiom,
    c_List_Olist_OCons(X3,c_List_Oappend(X2,X1,X4),X4) = c_List_Oappend(c_List_Olist_OCons(X3,X2,X4),X1,X4),
    inference(unfold_definition,[status(thm)],[c_0_571,def_lhs_atom28]) ).

cnf(c_0_572_0,axiom,
    c_List_Ofoldr(X1,c_List_Olist_ONil(X3),X2,X3,X4) = X2,
    inference(unfold_definition,[status(thm)],[c_0_572,def_lhs_atom12]) ).

cnf(c_0_573_0,axiom,
    c_List_Oappend(c_List_Olist_OCons(X3,X2,X4),X1,X4) = c_List_Olist_OCons(X3,c_List_Oappend(X2,X1,X4),X4),
    inference(unfold_definition,[status(thm)],[c_0_573,def_lhs_atom10]) ).

cnf(c_0_574_0,axiom,
    c_List_Oappend(c_List_Olist_OCons(X3,X2,X4),X1,X4) = c_List_Olist_OCons(X3,c_List_Oappend(X2,X1,X4),X4),
    inference(unfold_definition,[status(thm)],[c_0_574,def_lhs_atom9]) ).

cnf(c_0_575_0,axiom,
    hAPP(c_Type_Oshift(X2,X1,X3,X4),X1) = X3,
    inference(unfold_definition,[status(thm)],[c_0_575,def_lhs_atom1]) ).

cnf(c_0_577_0,axiom,
    hAPP(hAPP(c_Lambda_OdB_OApp,X3),X2) != c_Lambda_OdB_OVar(X1),
    inference(unfold_definition,[status(thm)],[c_0_577,def_lhs_atom105]) ).

cnf(c_0_578_0,axiom,
    c_Lambda_OdB_OVar(X1) != hAPP(hAPP(c_Lambda_OdB_OApp,X3),X2),
    inference(unfold_definition,[status(thm)],[c_0_578,def_lhs_atom103]) ).

cnf(c_0_579_0,axiom,
    hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,X1),X3)),X2),X3) = X1,
    inference(unfold_definition,[status(thm)],[c_0_579,def_lhs_atom86]) ).

cnf(c_0_580_0,axiom,
    c_Lambda_Osubstn(X1,X2,X3) = hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),c_Lambda_Oliftn(X3,X2,c_HOL_Ozero__class_Ozero(tc_nat))),X3),
    inference(unfold_definition,[status(thm)],[c_0_580,def_lhs_atom78]) ).

cnf(c_0_581_0,axiom,
    hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_OdB_OApp,X2),X1)),X3) = hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_Olift,X2),X3)),hAPP(hAPP(c_Lambda_Olift,X1),X3)),
    inference(unfold_definition,[status(thm)],[c_0_581,def_lhs_atom73]) ).

cnf(c_0_582_0,axiom,
    c_Lambda_OdB_OAbs(X1) != hAPP(hAPP(c_Lambda_OdB_OApp,X3),X2),
    inference(unfold_definition,[status(thm)],[c_0_582,def_lhs_atom72]) ).

cnf(c_0_583_0,axiom,
    hAPP(hAPP(c_Lambda_OdB_OApp,X3),X2) != c_Lambda_OdB_OAbs(X1),
    inference(unfold_definition,[status(thm)],[c_0_583,def_lhs_atom71]) ).

cnf(c_0_584_0,axiom,
    c_List_Oappend(c_List_Olist_ONil(X3),c_List_Olist_OCons(X2,X1,X3),X3) = c_List_Olist_OCons(X2,X1,X3),
    inference(unfold_definition,[status(thm)],[c_0_584,def_lhs_atom57]) ).

cnf(c_0_585_0,axiom,
    c_Predicate_Oconversep(c_Predicate_Oconversep(X1,X3,X2),X2,X3) = X1,
    inference(unfold_definition,[status(thm)],[c_0_585,def_lhs_atom54]) ).

cnf(c_0_586_0,axiom,
    hAPP(hAPP(c_Lambda_Olift,c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X1,tc_Lambda_OdB,tc_Lambda_OdB)),X3) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_Olift,X2),X3),c_List_Omap(c_COMBC(c_Lambda_Olift,X3,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X1,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
    inference(unfold_definition,[status(thm)],[c_0_586,def_lhs_atom51]) ).

cnf(c_0_587_0,axiom,
    c_List_Olist_ONil(X3) != c_List_Olist_OCons(X2,X1,X3),
    inference(unfold_definition,[status(thm)],[c_0_587,def_lhs_atom49]) ).

cnf(c_0_588_0,axiom,
    c_List_Oappend(c_List_Oreplicate(X2,X1,X3),c_List_Olist_OCons(X1,c_List_Olist_ONil(X3),X3),X3) = c_List_Olist_OCons(X1,c_List_Oreplicate(X2,X1,X3),X3),
    inference(unfold_definition,[status(thm)],[c_0_588,def_lhs_atom38]) ).

cnf(c_0_589_0,axiom,
    c_List_Omap(X1,c_List_Olist_ONil(X2),X2,X3) = c_List_Olist_ONil(X3),
    inference(unfold_definition,[status(thm)],[c_0_589,def_lhs_atom11]) ).

cnf(c_0_590_0,axiom,
    c_List_Olist_OCons(X2,X1,X3) = c_List_Oappend(c_List_Olist_ONil(X3),c_List_Olist_OCons(X2,X1,X3),X3),
    inference(unfold_definition,[status(thm)],[c_0_590,def_lhs_atom35]) ).

cnf(c_0_591_0,axiom,
    X1 != c_List_Olist_OCons(X2,X1,X3),
    inference(unfold_definition,[status(thm)],[c_0_591,def_lhs_atom34]) ).

cnf(c_0_592_0,axiom,
    c_List_Olist_OCons(X1,X2,X3) != X2,
    inference(unfold_definition,[status(thm)],[c_0_592,def_lhs_atom33]) ).

cnf(c_0_593_0,axiom,
    c_List_Olist_OCons(X2,X1,X3) != c_List_Olist_ONil(X3),
    inference(unfold_definition,[status(thm)],[c_0_593,def_lhs_atom31]) ).

cnf(c_0_594_0,axiom,
    c_List_Olist_OCons(X2,X1,X3) != c_List_Olist_ONil(X3),
    inference(unfold_definition,[status(thm)],[c_0_594,def_lhs_atom30]) ).

cnf(c_0_595_0,axiom,
    ~ c_ListOrder_Ostep1(X2,X1,c_List_Olist_ONil(X3),X3),
    inference(unfold_definition,[status(thm)],[c_0_595,def_lhs_atom27]) ).

cnf(c_0_596_0,axiom,
    ~ c_ListOrder_Ostep1(X2,c_List_Olist_ONil(X3),X1,X3),
    inference(unfold_definition,[status(thm)],[c_0_596,def_lhs_atom26]) ).

cnf(c_0_597_0,axiom,
    hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X2,X3),X1),X1)),
    inference(unfold_definition,[status(thm)],[c_0_597,def_lhs_atom19]) ).

cnf(c_0_598_0,axiom,
    hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X3),X2),X2)),
    inference(unfold_definition,[status(thm)],[c_0_598,def_lhs_atom18]) ).

cnf(c_0_599_0,axiom,
    hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X1)),
    inference(unfold_definition,[status(thm)],[c_0_599,def_lhs_atom15]) ).

cnf(c_0_600_0,axiom,
    hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1)),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3)),
    inference(unfold_definition,[status(thm)],[c_0_600,def_lhs_atom14]) ).

cnf(c_0_601_0,axiom,
    c_List_Omap(X1,c_List_Olist_ONil(X2),X2,X3) = c_List_Olist_ONil(X3),
    inference(unfold_definition,[status(thm)],[c_0_601,def_lhs_atom11]) ).

cnf(c_0_602_0,axiom,
    hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OAbs(X1)),X2),X3) = c_Lambda_OdB_OAbs(hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),hAPP(hAPP(c_Lambda_Olift,X2),c_HOL_Ozero__class_Ozero(tc_nat))),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat)))),
    inference(unfold_definition,[status(thm)],[c_0_602,def_lhs_atom5]) ).

cnf(c_0_603_0,axiom,
    c_Lambda_Osubstn(c_Lambda_OdB_OAbs(X1),X2,X3) = c_Lambda_OdB_OAbs(c_Lambda_Osubstn(X1,X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat)))),
    inference(unfold_definition,[status(thm)],[c_0_603,def_lhs_atom4]) ).

cnf(c_0_604_0,axiom,
    c_Lambda_Oliftn(X2,c_Lambda_OdB_OAbs(X1),X3) = c_Lambda_OdB_OAbs(c_Lambda_Oliftn(X2,X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat)))),
    inference(unfold_definition,[status(thm)],[c_0_604,def_lhs_atom3]) ).

cnf(c_0_605_0,axiom,
    hBOOL(hAPP(hAPP(c_fequal(X2),X1),X1)),
    inference(unfold_definition,[status(thm)],[c_0_605,def_lhs_atom131]) ).

cnf(c_0_606_0,axiom,
    hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X2)),X1),X2) = X1,
    inference(unfold_definition,[status(thm)],[c_0_606,def_lhs_atom102]) ).

cnf(c_0_607_0,axiom,
    hAPP(hAPP(c_Lambda_OdB_OApp,X2),X1) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,X2),X1),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
    inference(unfold_definition,[status(thm)],[c_0_607,def_lhs_atom97]) ).

cnf(c_0_608_0,axiom,
    c_Lambda_Osubstn(X1,X2,c_HOL_Ozero__class_Ozero(tc_nat)) = hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X2),c_HOL_Ozero__class_Ozero(tc_nat)),
    inference(unfold_definition,[status(thm)],[c_0_608,def_lhs_atom94]) ).

cnf(c_0_609_0,axiom,
    hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X2)),X1)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X2),X1),c_HOL_Ozero__class_Ozero(tc_nat)))),
    inference(unfold_definition,[status(thm)],[c_0_609,def_lhs_atom93]) ).

cnf(c_0_610_0,axiom,
    c_Type_Otyping(X2,c_Lambda_OdB_OVar(X1),hAPP(X2,X1)),
    inference(unfold_definition,[status(thm)],[c_0_610,def_lhs_atom92]) ).

cnf(c_0_611_0,axiom,
    c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OAbs(X2),
    inference(unfold_definition,[status(thm)],[c_0_611,def_lhs_atom90]) ).

cnf(c_0_612_0,axiom,
    ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OVar(X2)),X1)),
    inference(unfold_definition,[status(thm)],[c_0_612,def_lhs_atom88]) ).

cnf(c_0_613_0,axiom,
    c_Lambda_OdB_OAbs(X2) != c_Lambda_OdB_OVar(X1),
    inference(unfold_definition,[status(thm)],[c_0_613,def_lhs_atom87]) ).

cnf(c_0_614_0,axiom,
    ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X2,tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_614,def_lhs_atom56]) ).

cnf(c_0_615_0,axiom,
    ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1),X2,tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_615,def_lhs_atom55]) ).

cnf(c_0_616_0,axiom,
    c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),X1,X2) = c_List_Olist_ONil(X2),
    inference(unfold_definition,[status(thm)],[c_0_616,def_lhs_atom32]) ).

cnf(c_0_617_0,axiom,
    c_Lambda_Oliftn(c_HOL_Ozero__class_Ozero(tc_nat),X1,X2) = X1,
    inference(unfold_definition,[status(thm)],[c_0_617,def_lhs_atom40]) ).

cnf(c_0_618_0,axiom,
    c_Transitive__Closure_Ortranclp(c_Transitive__Closure_Ortranclp(X1,X2),X2) = c_Transitive__Closure_Ortranclp(X1,X2),
    inference(unfold_definition,[status(thm)],[c_0_618,def_lhs_atom37]) ).

cnf(c_0_619_0,axiom,
    c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),X1,X2) = c_List_Olist_ONil(X2),
    inference(unfold_definition,[status(thm)],[c_0_619,def_lhs_atom32]) ).

cnf(c_0_620_0,axiom,
    hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),
    inference(unfold_definition,[status(thm)],[c_0_620,def_lhs_atom24]) ).

cnf(c_0_621_0,axiom,
    c_List_Oappend(c_List_Olist_ONil(X2),X1,X2) = X1,
    inference(unfold_definition,[status(thm)],[c_0_621,def_lhs_atom22]) ).

cnf(c_0_622_0,axiom,
    c_List_Oappend(c_List_Olist_ONil(X2),X1,X2) = X1,
    inference(unfold_definition,[status(thm)],[c_0_622,def_lhs_atom22]) ).

cnf(c_0_623_0,axiom,
    c_List_Oappend(X1,c_List_Olist_ONil(X2),X2) = X1,
    inference(unfold_definition,[status(thm)],[c_0_623,def_lhs_atom20]) ).

cnf(c_0_624_0,axiom,
    c_List_Oappend(c_List_Olist_ONil(X2),X1,X2) = X1,
    inference(unfold_definition,[status(thm)],[c_0_624,def_lhs_atom21]) ).

cnf(c_0_625_0,axiom,
    c_List_Oappend(X1,c_List_Olist_ONil(X2),X2) = X1,
    inference(unfold_definition,[status(thm)],[c_0_625,def_lhs_atom20]) ).

cnf(c_0_626_0,axiom,
    c_List_Olistsp(X1,c_List_Olist_ONil(X2),X2),
    inference(unfold_definition,[status(thm)],[c_0_626,def_lhs_atom17]) ).

cnf(c_0_627_0,axiom,
    hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OAbs(X1)),X2) = c_Lambda_OdB_OAbs(hAPP(hAPP(c_Lambda_Olift,X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)))),
    inference(unfold_definition,[status(thm)],[c_0_627,def_lhs_atom2]) ).

cnf(c_0_628_0,axiom,
    hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(X1))),
    inference(unfold_definition,[status(thm)],[c_0_628,def_lhs_atom104]) ).

cnf(c_0_629_0,axiom,
    c_Lambda_OdB_OVar(X1) = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
    inference(unfold_definition,[status(thm)],[c_0_629,def_lhs_atom99]) ).

cnf(c_0_630_0,axiom,
    c_Lambda_OdB_OdB__size(c_Lambda_OdB_OVar(X1)) = c_HOL_Ozero__class_Ozero(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_630,def_lhs_atom96]) ).

cnf(c_0_631_0,axiom,
    c_Nat_Osize__class_Osize(c_Lambda_OdB_OVar(X1),tc_Lambda_OdB) = c_HOL_Ozero__class_Ozero(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_631,def_lhs_atom95]) ).

cnf(c_0_632_0,axiom,
    c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) = c_Lambda_OdB_OAbs(X1),
    inference(unfold_definition,[status(thm)],[c_0_632,def_lhs_atom81]) ).

cnf(c_0_633_0,axiom,
    X1 = c_List_Ofoldl(c_Lambda_OdB_OApp,c_ListApplication_Osko__ListApplication__Xex__head__tail__1__2(X1),c_ListApplication_Osko__ListApplication__Xex__head__tail__1__1(X1),tc_Lambda_OdB,tc_Lambda_OdB),
    inference(unfold_definition,[status(thm)],[c_0_633,def_lhs_atom80]) ).

cnf(c_0_634_0,axiom,
    c_Lambda_OdB_OAbs(X1) = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
    inference(unfold_definition,[status(thm)],[c_0_634,def_lhs_atom79]) ).

cnf(c_0_635_0,axiom,
    hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Ozero__class_Ozero(tc_nat)) = X1,
    inference(unfold_definition,[status(thm)],[c_0_635,def_lhs_atom70]) ).

cnf(c_0_636_0,axiom,
    hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X1) = X1,
    inference(unfold_definition,[status(thm)],[c_0_636,def_lhs_atom69]) ).

cnf(c_0_637_0,axiom,
    X1 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Ozero__class_Ozero(tc_nat)),
    inference(unfold_definition,[status(thm)],[c_0_637,def_lhs_atom68]) ).

cnf(c_0_638_0,axiom,
    c_Orderings_Oord__class_Omax(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = X1,
    inference(unfold_definition,[status(thm)],[c_0_638,def_lhs_atom67]) ).

cnf(c_0_639_0,axiom,
    c_Orderings_Oord__class_Omax(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X1,
    inference(unfold_definition,[status(thm)],[c_0_639,def_lhs_atom66]) ).

cnf(c_0_640_0,axiom,
    c_Nat_Osize__class_Osize(X1,tc_String_Ochar) = c_HOL_Ozero__class_Ozero(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_640,def_lhs_atom64]) ).

cnf(c_0_641_0,axiom,
    c_List_Oappend(c_List_Olist_ONil(X1),c_List_Olist_ONil(X1),X1) = c_List_Olist_ONil(X1),
    inference(unfold_definition,[status(thm)],[c_0_641,def_lhs_atom59]) ).

cnf(c_0_642_0,axiom,
    ~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_642,def_lhs_atom46]) ).

cnf(c_0_643_0,axiom,
    ~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_643,def_lhs_atom45]) ).

cnf(c_0_644_0,axiom,
    c_Predicate_Oconversep(c_fequal(X1),X1,X1) = c_fequal(X1),
    inference(unfold_definition,[status(thm)],[c_0_644,def_lhs_atom44]) ).

cnf(c_0_645_0,axiom,
    ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_645,def_lhs_atom43]) ).

cnf(c_0_646_0,axiom,
    ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_646,def_lhs_atom42]) ).

cnf(c_0_647_0,axiom,
    c_List_Olist_ONil(X1) = c_List_Oappend(c_List_Olist_ONil(X1),c_List_Olist_ONil(X1),X1),
    inference(unfold_definition,[status(thm)],[c_0_647,def_lhs_atom36]) ).

cnf(c_0_648_0,axiom,
    class_Orderings_Oorder(tc_bool),
    inference(unfold_definition,[status(thm)],[c_0_648,def_lhs_atom130]) ).

cnf(c_0_649_0,axiom,
    class_Orderings_Opreorder(tc_bool),
    inference(unfold_definition,[status(thm)],[c_0_649,def_lhs_atom129]) ).

cnf(c_0_650_0,axiom,
    class_Power_Opower(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_650,def_lhs_atom128]) ).

cnf(c_0_651_0,axiom,
    class_Orderings_Oorder(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_651,def_lhs_atom127]) ).

cnf(c_0_652_0,axiom,
    class_Orderings_Olinorder(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_652,def_lhs_atom126]) ).

cnf(c_0_653_0,axiom,
    class_Orderings_Opreorder(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_653,def_lhs_atom125]) ).

cnf(c_0_654_0,axiom,
    class_Nat_Osemiring__char__0(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_654,def_lhs_atom124]) ).

cnf(c_0_655_0,axiom,
    class_OrderedGroup_Omonoid__add(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_655,def_lhs_atom123]) ).

cnf(c_0_656_0,axiom,
    class_OrderedGroup_Omonoid__mult(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_656,def_lhs_atom122]) ).

cnf(c_0_657_0,axiom,
    class_Ring__and__Field_Omult__zero(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_657,def_lhs_atom121]) ).

cnf(c_0_658_0,axiom,
    class_Ring__and__Field_Osemiring__0(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_658,def_lhs_atom120]) ).

cnf(c_0_659_0,axiom,
    class_Ring__and__Field_Osemiring__1(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_659,def_lhs_atom119]) ).

cnf(c_0_660_0,axiom,
    class_OrderedGroup_Osemigroup__add(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_660,def_lhs_atom118]) ).

cnf(c_0_661_0,axiom,
    class_Ring__and__Field_Ozero__neq__one(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_661,def_lhs_atom117]) ).

cnf(c_0_662_0,axiom,
    class_OrderedGroup_Ocomm__monoid__add(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_662,def_lhs_atom116]) ).

cnf(c_0_663_0,axiom,
    class_OrderedGroup_Oab__semigroup__add(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_663,def_lhs_atom115]) ).

cnf(c_0_664_0,axiom,
    class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_664,def_lhs_atom114]) ).

cnf(c_0_665_0,axiom,
    class_Ring__and__Field_Oordered__semidom(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_665,def_lhs_atom113]) ).

cnf(c_0_666_0,axiom,
    class_Ring__and__Field_Ono__zero__divisors(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_666,def_lhs_atom112]) ).

cnf(c_0_667_0,axiom,
    class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_667,def_lhs_atom111]) ).

cnf(c_0_668_0,axiom,
    class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_668,def_lhs_atom110]) ).

cnf(c_0_669_0,axiom,
    class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_669,def_lhs_atom109]) ).

cnf(c_0_670_0,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_670,def_lhs_atom108]) ).

cnf(c_0_671_0,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_671,def_lhs_atom107]) ).

cnf(c_0_672_0,axiom,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_672,def_lhs_atom106]) ).

cnf(c_0_673_0,axiom,
    hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Ozero__class_Ozero(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_673,def_lhs_atom41]) ).

cnf(c_0_674_0,axiom,
    ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_674,def_lhs_atom39]) ).

% Orienting (remaining) axiom formulas using strategy ClausalAll
% CNF of (remaining) axioms:
% Start CNF derivation
fof(c_0_0_001,axiom,
    ! [X30,X17,X18] :
      ( X30 = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X18),c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(X18,X17,X30),tc_Lambda_OdB,tc_Lambda_OdB)
      | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X18),X17,tc_Lambda_OdB,tc_Lambda_OdB)),X30)) ),
    file('<stdin>',cls_head__Var__reduction_1) ).

fof(c_0_1_002,axiom,
    ! [X26,X6,X16,X21,X37,X23] :
      ( c_Type_Otypings(X21,c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,X26,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),X16,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X6,tc_Lambda_OdB,tc_Lambda_OdB),X37)
      | ~ c_Type_Otypings(c_Type_Oshift(X21,X16,X23,tc_Type_Otype),X6,X37)
      | ~ c_Type_Otyping(X21,X26,X23) ),
    file('<stdin>',cls_substs__lemma_0) ).

fof(c_0_2_003,axiom,
    ! [X36,X6,X16,X21,X22,X37,X23] :
      ( c_Type_Otypings(X21,X36,c_Type_Osko__Type__Xvar__app__types__1__1(X23,X22,X21,X36))
      | ~ c_Type_Otyping(X21,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X16),X6,tc_Lambda_OdB,tc_Lambda_OdB),X22)
      | ~ c_Type_Otypings(X21,X6,X37)
      | ~ c_Type_Otyping(X21,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X16),X6,tc_Lambda_OdB,tc_Lambda_OdB),X36,tc_Lambda_OdB,tc_Lambda_OdB),X23) ),
    file('<stdin>',cls_var__app__types_1) ).

fof(c_0_3_004,axiom,
    ! [X30,X17,X18] :
      ( c_ListOrder_Ostep1(c_Lambda_Obeta,X17,c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(X18,X17,X30),tc_Lambda_OdB)
      | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X18),X17,tc_Lambda_OdB,tc_Lambda_OdB)),X30)) ),
    file('<stdin>',cls_head__Var__reduction_0) ).

fof(c_0_4_005,axiom,
    ! [X27,X34] :
      ( hBOOL(hAPP(X34,X27))
      | ~ hBOOL(hAPP(X34,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3(X34)),c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__4(X34),tc_Lambda_OdB,tc_Lambda_OdB)))
      | ~ hBOOL(hAPP(X34,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1(X34)),c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2(X34),tc_Lambda_OdB,tc_Lambda_OdB))) ),
    file('<stdin>',cls_Apps__dB__induct_5) ).

fof(c_0_5_006,axiom,
    ! [X27,X34] :
      ( ~ hBOOL(hAPP(X34,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(c_ListApplication_Osko__ListApplication__Xlem__1__3(X34)),c_ListApplication_Osko__ListApplication__Xlem__1__4(X34),tc_Lambda_OdB,tc_Lambda_OdB)))
      | ~ hBOOL(hAPP(X34,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_ListApplication_Osko__ListApplication__Xlem__1__1(X34)),c_ListApplication_Osko__ListApplication__Xlem__1__2(X34),tc_Lambda_OdB,tc_Lambda_OdB)))
      | hBOOL(hAPP(X34,X27)) ),
    file('<stdin>',cls_lem_5) ).

fof(c_0_6_007,axiom,
    ! [X9,X17,X8] :
      ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,X8,X17,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X8,X9,tc_Lambda_OdB,tc_Lambda_OdB)))
      | ~ c_ListOrder_Ostep1(c_Lambda_Obeta,X17,X9,tc_Lambda_OdB) ),
    file('<stdin>',cls_apps__preserves__betas_0) ).

fof(c_0_7_008,axiom,
    ! [X9,X7,X8] :
      ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,X8,X9,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X7,X9,tc_Lambda_OdB,tc_Lambda_OdB)))
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X8),X7)) ),
    file('<stdin>',cls_apps__preserves__beta2_0) ).

fof(c_0_8_009,axiom,
    ! [X9,X7,X8] :
      ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,X8,X9,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X7,X9,tc_Lambda_OdB,tc_Lambda_OdB)))
      | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X8),X7)) ),
    file('<stdin>',cls_apps__preserves__beta_0) ).

fof(c_0_9_010,axiom,
    ! [X9,X7,X8] :
      ( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X8)),X7),X9,tc_Lambda_OdB,tc_Lambda_OdB)))
      | ~ hBOOL(hAPP(c_InductTermi_OIT,X7))
      | ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X8),X7),c_HOL_Ozero__class_Ozero(tc_nat)),X9,tc_Lambda_OdB,tc_Lambda_OdB))) ),
    file('<stdin>',cls_Beta_0) ).

fof(c_0_10_011,axiom,
    ! [X66,X67,X44,X45,X46,X47,X68,X69,X48,X3] :
      ( hAPP(hAPP(X47,hAPP(hAPP(X47,X69),X68)),hAPP(hAPP(X47,X67),X66)) = hAPP(hAPP(X47,X67),hAPP(hAPP(X47,hAPP(hAPP(X47,X69),X68)),X66))
      | ~ c_Groebner__Basis_Ogb__semiring(X48,X47,X46,X45,X44,X3) ),
    file('<stdin>',cls_gb__semiring_Osemiring__rules_I15_J_0) ).

fof(c_0_11_012,axiom,
    ! [X44,X45,X46,X47,X62,X50,X49,X48,X29,X3] :
      ( hAPP(hAPP(X48,hAPP(hAPP(X48,X29),X49)),hAPP(hAPP(X48,X50),X62)) = hAPP(hAPP(X48,hAPP(hAPP(X48,X29),X50)),hAPP(hAPP(X48,X49),X62))
      | ~ c_Groebner__Basis_Ogb__semiring(X48,X47,X46,X45,X44,X3) ),
    file('<stdin>',cls_gb__semiring_Osemiring__rules_I20_J_0) ).

fof(c_0_12_013,axiom,
    ! [X66,X67,X44,X45,X46,X47,X68,X69,X48,X3] :
      ( hAPP(hAPP(X47,hAPP(hAPP(X47,X69),X68)),hAPP(hAPP(X47,X67),X66)) = hAPP(hAPP(X47,X69),hAPP(hAPP(X47,X68),hAPP(hAPP(X47,X67),X66)))
      | ~ c_Groebner__Basis_Ogb__semiring(X48,X47,X46,X45,X44,X3) ),
    file('<stdin>',cls_gb__semiring_Osemiring__rules_I14_J_0) ).

fof(c_0_13_014,axiom,
    ! [X66,X67,X44,X45,X46,X47,X68,X69,X48,X3] :
      ( hAPP(hAPP(X47,hAPP(hAPP(X47,X69),X68)),hAPP(hAPP(X47,X67),X66)) = hAPP(hAPP(X47,hAPP(hAPP(X47,X69),X67)),hAPP(hAPP(X47,X68),X66))
      | ~ c_Groebner__Basis_Ogb__semiring(X48,X47,X46,X45,X44,X3) ),
    file('<stdin>',cls_gb__semiring_Osemiring__rules_I13_J_0) ).

fof(c_0_14_015,axiom,
    ! [X40,X24,X44,X45,X70,X46,X47,X48,X3] :
      ( hAPP(hAPP(X46,hAPP(hAPP(X47,X24),X40)),X70) = hAPP(hAPP(X47,hAPP(hAPP(X46,X24),X70)),hAPP(hAPP(X46,X40),X70))
      | ~ c_Groebner__Basis_Ogb__semiring(X48,X47,X46,X45,X44,X3) ),
    file('<stdin>',cls_gb__semiring_Opwr__mul_0) ).

fof(c_0_15_016,axiom,
    ! [X44,X45,X46,X47,X50,X49,X48,X29,X3] :
      ( hAPP(hAPP(X47,hAPP(hAPP(X48,X29),X49)),X50) = hAPP(hAPP(X48,hAPP(hAPP(X47,X29),X50)),hAPP(hAPP(X47,X49),X50))
      | ~ c_Groebner__Basis_Ogb__semiring(X48,X47,X46,X45,X44,X3) ),
    file('<stdin>',cls_gb__semiring_Osemiring__rules_I8_J_0) ).

fof(c_0_16_017,axiom,
    ! [X44,X45,X46,X47,X10,X49,X48,X29,X3] :
      ( hAPP(hAPP(X48,hAPP(hAPP(X47,X29),X10)),hAPP(hAPP(X47,X49),X10)) = hAPP(hAPP(X47,hAPP(hAPP(X48,X29),X49)),X10)
      | ~ c_Groebner__Basis_Ogb__semiring(X48,X47,X46,X45,X44,X3) ),
    file('<stdin>',cls_gb__semiring_Osemiring__rules_I1_J_0) ).

fof(c_0_17_018,axiom,
    ! [X24,X44,X45,X70,X46,X71,X47,X48,X3] :
      ( hAPP(hAPP(X47,hAPP(hAPP(X46,X24),X71)),hAPP(hAPP(X46,X24),X70)) = hAPP(hAPP(X46,X24),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X71),X70))
      | ~ c_Groebner__Basis_Ogb__semiring(X48,X47,X46,X45,X44,X3) ),
    file('<stdin>',cls_gb__semiring_Omul__pwr_0) ).

fof(c_0_18_019,axiom,
    ! [X64,X40,X24,X44,X45,X46,X47,X48,X3] :
      ( hAPP(hAPP(X47,X24),hAPP(hAPP(X48,X40),X64)) = hAPP(hAPP(X48,hAPP(hAPP(X47,X24),X40)),hAPP(hAPP(X47,X24),X64))
      | ~ c_Groebner__Basis_Ogb__semiring(X48,X47,X46,X45,X44,X3) ),
    file('<stdin>',cls_gb__semiring_Omul__d_0) ).

fof(c_0_19_020,axiom,
    ! [X44,X45,X46,X47,X50,X49,X48,X29,X3] :
      ( hAPP(hAPP(X48,hAPP(hAPP(X48,X29),X49)),X50) = hAPP(hAPP(X48,hAPP(hAPP(X48,X29),X50)),X49)
      | ~ c_Groebner__Basis_Ogb__semiring(X48,X47,X46,X45,X44,X3) ),
    file('<stdin>',cls_gb__semiring_Osemiring__rules_I23_J_0) ).

fof(c_0_20_021,axiom,
    ! [X67,X44,X45,X46,X47,X68,X69,X48,X3] :
      ( hAPP(hAPP(X47,hAPP(hAPP(X47,X69),X68)),X67) = hAPP(hAPP(X47,hAPP(hAPP(X47,X69),X67)),X68)
      | ~ c_Groebner__Basis_Ogb__semiring(X48,X47,X46,X45,X44,X3) ),
    file('<stdin>',cls_gb__semiring_Osemiring__rules_I16_J_0) ).

fof(c_0_21_022,axiom,
    ! [X44,X45,X46,X47,X10,X48,X29,X3] :
      ( hAPP(hAPP(X48,hAPP(hAPP(X47,X29),X10)),X10) = hAPP(hAPP(X47,hAPP(hAPP(X48,X29),X44)),X10)
      | ~ c_Groebner__Basis_Ogb__semiring(X48,X47,X46,X45,X44,X3) ),
    file('<stdin>',cls_gb__semiring_Osemiring__rules_I2_J_0) ).

fof(c_0_22_023,axiom,
    ! [X64,X40,X24,X44,X45,X46,X47,X48,X3] :
      ( hAPP(hAPP(X47,X24),hAPP(hAPP(X47,X40),X64)) = hAPP(hAPP(X47,hAPP(hAPP(X47,X24),X40)),X64)
      | ~ c_Groebner__Basis_Ogb__semiring(X48,X47,X46,X45,X44,X3) ),
    file('<stdin>',cls_gb__semiring_Omul__a_0) ).

fof(c_0_23_024,axiom,
    ! [X64,X40,X24,X44,X45,X46,X47,X48,X3] :
      ( hAPP(hAPP(X48,X24),hAPP(hAPP(X48,X40),X64)) = hAPP(hAPP(X48,hAPP(hAPP(X48,X24),X40)),X64)
      | ~ c_Groebner__Basis_Ogb__semiring(X48,X47,X46,X45,X44,X3) ),
    file('<stdin>',cls_gb__semiring_Oadd__a_0) ).

fof(c_0_24_025,axiom,
    ! [X44,X45,X46,X47,X62,X50,X48,X29,X3] :
      ( hAPP(hAPP(X48,X29),hAPP(hAPP(X48,X50),X62)) = hAPP(hAPP(X48,hAPP(hAPP(X48,X29),X50)),X62)
      | ~ c_Groebner__Basis_Ogb__semiring(X48,X47,X46,X45,X44,X3) ),
    file('<stdin>',cls_gb__semiring_Osemiring__rules_I25_J_0) ).

fof(c_0_25_026,axiom,
    ! [X44,X45,X46,X47,X50,X49,X48,X29,X3] :
      ( hAPP(hAPP(X48,hAPP(hAPP(X48,X29),X49)),X50) = hAPP(hAPP(X48,X29),hAPP(hAPP(X48,X49),X50))
      | ~ c_Groebner__Basis_Ogb__semiring(X48,X47,X46,X45,X44,X3) ),
    file('<stdin>',cls_gb__semiring_Osemiring__rules_I21_J_0) ).

fof(c_0_26_027,axiom,
    ! [X66,X67,X44,X45,X46,X47,X69,X48,X3] :
      ( hAPP(hAPP(X47,X69),hAPP(hAPP(X47,X67),X66)) = hAPP(hAPP(X47,hAPP(hAPP(X47,X69),X67)),X66)
      | ~ c_Groebner__Basis_Ogb__semiring(X48,X47,X46,X45,X44,X3) ),
    file('<stdin>',cls_gb__semiring_Osemiring__rules_I18_J_0) ).

fof(c_0_27_028,axiom,
    ! [X67,X44,X45,X46,X47,X68,X69,X48,X3] :
      ( hAPP(hAPP(X47,hAPP(hAPP(X47,X69),X68)),X67) = hAPP(hAPP(X47,X69),hAPP(hAPP(X47,X68),X67))
      | ~ c_Groebner__Basis_Ogb__semiring(X48,X47,X46,X45,X44,X3) ),
    file('<stdin>',cls_gb__semiring_Osemiring__rules_I17_J_0) ).

fof(c_0_28_029,axiom,
    ! [X44,X45,X46,X47,X10,X48,X29,X3] :
      ( hAPP(hAPP(X48,X10),hAPP(hAPP(X47,X29),X10)) = hAPP(hAPP(X47,hAPP(hAPP(X48,X29),X44)),X10)
      | ~ c_Groebner__Basis_Ogb__semiring(X48,X47,X46,X45,X44,X3) ),
    file('<stdin>',cls_gb__semiring_Osemiring__rules_I3_J_0) ).

fof(c_0_29_030,axiom,
    ! [X44,X45,X46,X47,X62,X50,X48,X29,X3] :
      ( hAPP(hAPP(X48,X29),hAPP(hAPP(X48,X50),X62)) = hAPP(hAPP(X48,X50),hAPP(hAPP(X48,X29),X62))
      | ~ c_Groebner__Basis_Ogb__semiring(X48,X47,X46,X45,X44,X3) ),
    file('<stdin>',cls_gb__semiring_Osemiring__rules_I22_J_0) ).

fof(c_0_30_031,axiom,
    ! [X66,X67,X44,X45,X46,X47,X69,X48,X3] :
      ( hAPP(hAPP(X47,X69),hAPP(hAPP(X47,X67),X66)) = hAPP(hAPP(X47,X67),hAPP(hAPP(X47,X69),X66))
      | ~ c_Groebner__Basis_Ogb__semiring(X48,X47,X46,X45,X44,X3) ),
    file('<stdin>',cls_gb__semiring_Osemiring__rules_I19_J_0) ).

fof(c_0_31_032,axiom,
    ! [X44,X45,X46,X47,X10,X48,X3] :
      ( hAPP(hAPP(X48,X10),X10) = hAPP(hAPP(X47,hAPP(hAPP(X48,X44),X44)),X10)
      | ~ c_Groebner__Basis_Ogb__semiring(X48,X47,X46,X45,X44,X3) ),
    file('<stdin>',cls_gb__semiring_Osemiring__rules_I4_J_0) ).

fof(c_0_32_033,axiom,
    ! [X40,X24,X44,X45,X46,X47,X48,X3] :
      ( hAPP(hAPP(X47,X24),X40) = hAPP(hAPP(X47,X40),X24)
      | ~ c_Groebner__Basis_Ogb__semiring(X48,X47,X46,X45,X44,X3) ),
    file('<stdin>',cls_gb__semiring_Omul__c_0) ).

fof(c_0_33_034,axiom,
    ! [X40,X24,X44,X45,X46,X47,X48,X3] :
      ( hAPP(hAPP(X48,X24),X40) = hAPP(hAPP(X48,X40),X24)
      | ~ c_Groebner__Basis_Ogb__semiring(X48,X47,X46,X45,X44,X3) ),
    file('<stdin>',cls_gb__semiring_Oadd__c_0) ).

fof(c_0_34_035,axiom,
    ! [X44,X45,X46,X47,X50,X48,X29,X3] :
      ( hAPP(hAPP(X48,X29),X50) = hAPP(hAPP(X48,X50),X29)
      | ~ c_Groebner__Basis_Ogb__semiring(X48,X47,X46,X45,X44,X3) ),
    file('<stdin>',cls_gb__semiring_Osemiring__rules_I24_J_0) ).

fof(c_0_35_036,axiom,
    ! [X44,X45,X46,X47,X49,X48,X29,X3] :
      ( hAPP(hAPP(X47,X29),X49) = hAPP(hAPP(X47,X49),X29)
      | ~ c_Groebner__Basis_Ogb__semiring(X48,X47,X46,X45,X44,X3) ),
    file('<stdin>',cls_gb__semiring_Osemiring__rules_I7_J_0) ).

fof(c_0_36_037,axiom,
    ! [X24,X44,X45,X46,X47,X48,X3] :
      ( hAPP(hAPP(X46,X24),c_HOL_Oone__class_Oone(tc_nat)) = X24
      | ~ c_Groebner__Basis_Ogb__semiring(X48,X47,X46,X45,X44,X3) ),
    file('<stdin>',cls_gb__semiring_Osemiring__rules_I33_J_0) ).

fof(c_0_37_038,axiom,
    ! [X24,X44,X45,X46,X47,X48,X3] :
      ( hAPP(hAPP(X46,X24),c_HOL_Ozero__class_Ozero(tc_nat)) = X44
      | ~ c_Groebner__Basis_Ogb__semiring(X48,X47,X46,X45,X44,X3) ),
    file('<stdin>',cls_gb__semiring_Opwr__0_0) ).

fof(c_0_38_039,axiom,
    ! [X24,X44,X45,X46,X47,X48,X3] :
      ( hAPP(hAPP(X47,X44),X24) = X24
      | ~ c_Groebner__Basis_Ogb__semiring(X48,X47,X46,X45,X44,X3) ),
    file('<stdin>',cls_gb__semiring_Omul__1_0) ).

fof(c_0_39_040,axiom,
    ! [X24,X44,X45,X46,X47,X48,X3] :
      ( hAPP(hAPP(X47,X45),X24) = X45
      | ~ c_Groebner__Basis_Ogb__semiring(X48,X47,X46,X45,X44,X3) ),
    file('<stdin>',cls_gb__semiring_Omul__0_0) ).

fof(c_0_40_041,axiom,
    ! [X24,X44,X45,X46,X47,X48,X3] :
      ( hAPP(hAPP(X48,X45),X24) = X24
      | ~ c_Groebner__Basis_Ogb__semiring(X48,X47,X46,X45,X44,X3) ),
    file('<stdin>',cls_gb__semiring_Oadd__0_0) ).

fof(c_0_41_042,axiom,
    ! [X44,X45,X46,X47,X48,X29,X3] :
      ( hAPP(hAPP(X47,X29),X44) = X29
      | ~ c_Groebner__Basis_Ogb__semiring(X48,X47,X46,X45,X44,X3) ),
    file('<stdin>',cls_gb__semiring_Osemiring__rules_I12_J_0) ).

fof(c_0_42_043,axiom,
    ! [X44,X45,X46,X47,X48,X29,X3] :
      ( hAPP(hAPP(X47,X44),X29) = X29
      | ~ c_Groebner__Basis_Ogb__semiring(X48,X47,X46,X45,X44,X3) ),
    file('<stdin>',cls_gb__semiring_Osemiring__rules_I11_J_0) ).

fof(c_0_43_044,axiom,
    ! [X44,X45,X46,X47,X48,X29,X3] :
      ( hAPP(hAPP(X47,X29),X45) = X45
      | ~ c_Groebner__Basis_Ogb__semiring(X48,X47,X46,X45,X44,X3) ),
    file('<stdin>',cls_gb__semiring_Osemiring__rules_I10_J_0) ).

fof(c_0_44_045,axiom,
    ! [X44,X45,X46,X47,X48,X29,X3] :
      ( hAPP(hAPP(X47,X45),X29) = X45
      | ~ c_Groebner__Basis_Ogb__semiring(X48,X47,X46,X45,X44,X3) ),
    file('<stdin>',cls_gb__semiring_Osemiring__rules_I9_J_0) ).

fof(c_0_45_046,axiom,
    ! [X44,X45,X46,X47,X48,X29,X3] :
      ( hAPP(hAPP(X48,X29),X45) = X29
      | ~ c_Groebner__Basis_Ogb__semiring(X48,X47,X46,X45,X44,X3) ),
    file('<stdin>',cls_gb__semiring_Osemiring__rules_I6_J_0) ).

fof(c_0_46_047,axiom,
    ! [X44,X45,X46,X47,X48,X29,X3] :
      ( hAPP(hAPP(X48,X45),X29) = X29
      | ~ c_Groebner__Basis_Ogb__semiring(X48,X47,X46,X45,X44,X3) ),
    file('<stdin>',cls_gb__semiring_Osemiring__rules_I5_J_0) ).

fof(c_0_47_048,axiom,
    ! [X41,X42,X31,X32,X33,X34] :
      ( ~ hBOOL(hAPP(X34,c_Lambda_OdB_OdB__case(X33,X32,X31,hAPP(hAPP(c_Lambda_OdB_OApp,X42),X41),t_a)))
      | hBOOL(hAPP(X34,hAPP(hAPP(X32,X42),X41))) ),
    file('<stdin>',cls_dB_Osplit__asm_1) ).

fof(c_0_48_049,axiom,
    ! [X31,X32,X33,X12,X14,X34] :
      ( ~ hBOOL(hAPP(X34,c_Lambda_OdB_OdB__case(X33,X32,X31,hAPP(hAPP(c_Lambda_OdB_OApp,X14),X12),t_a)))
      | hBOOL(hAPP(X34,hAPP(hAPP(X32,X14),X12))) ),
    file('<stdin>',cls_dB_Osplit_1) ).

fof(c_0_49_050,axiom,
    ! [X27,X34] :
      ( hBOOL(hAPP(X34,c_ListApplication_Osko__ListApplication__Xlem__1__3(X34)))
      | ~ hBOOL(hAPP(X34,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_ListApplication_Osko__ListApplication__Xlem__1__1(X34)),c_ListApplication_Osko__ListApplication__Xlem__1__2(X34),tc_Lambda_OdB,tc_Lambda_OdB)))
      | hBOOL(hAPP(X34,X27)) ),
    file('<stdin>',cls_lem_3) ).

fof(c_0_50_051,axiom,
    ! [X27,X34] :
      ( hBOOL(hAPP(X34,X27))
      | hBOOL(hAPP(X34,c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3(X34)))
      | ~ hBOOL(hAPP(X34,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1(X34)),c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2(X34),tc_Lambda_OdB,tc_Lambda_OdB))) ),
    file('<stdin>',cls_Apps__dB__induct_3) ).

fof(c_0_51_052,axiom,
    ! [X6,X16,X21,X22,X23] :
      ( X23 = X22
      | ~ c_Type_Otyping(X21,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X16),X6,tc_Lambda_OdB,tc_Lambda_OdB),X22)
      | ~ c_Type_Otyping(X21,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X16),X6,tc_Lambda_OdB,tc_Lambda_OdB),X23) ),
    file('<stdin>',cls_var__app__type__eq_0) ).

fof(c_0_52_053,axiom,
    ! [X31,X32,X33,X59,X34] :
      ( ~ hBOOL(hAPP(X34,c_Lambda_OdB_OdB__case(X33,X32,X31,c_Lambda_OdB_OAbs(X59),t_a)))
      | hBOOL(hAPP(X34,hAPP(X31,X59))) ),
    file('<stdin>',cls_dB_Osplit_2) ).

fof(c_0_53_054,axiom,
    ! [X58,X31,X32,X33,X34] :
      ( ~ hBOOL(hAPP(X34,c_Lambda_OdB_OdB__case(X33,X32,X31,c_Lambda_OdB_OAbs(X58),t_a)))
      | hBOOL(hAPP(X34,hAPP(X31,X58))) ),
    file('<stdin>',cls_dB_Osplit__asm_2) ).

fof(c_0_54_055,axiom,
    ! [X35,X31,X32,X33,X34] :
      ( ~ hBOOL(hAPP(X34,c_Lambda_OdB_OdB__case(X33,X32,X31,c_Lambda_OdB_OVar(X35),t_a)))
      | hBOOL(hAPP(X34,hAPP(X33,X35))) ),
    file('<stdin>',cls_dB_Osplit__asm_0) ).

fof(c_0_55_056,axiom,
    ! [X20,X31,X32,X33,X34] :
      ( ~ hBOOL(hAPP(X34,c_Lambda_OdB_OdB__case(X33,X32,X31,c_Lambda_OdB_OVar(X20),t_a)))
      | hBOOL(hAPP(X34,hAPP(X33,X20))) ),
    file('<stdin>',cls_dB_Osplit_0) ).

fof(c_0_56_057,axiom,
    ! [X9,X7,X8] :
      ( ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X8),X7),c_HOL_Ozero__class_Ozero(tc_nat)),X9,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)
      | ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X7,tc_Lambda_OdB)
      | c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X8)),X7),X9,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB) ),
    file('<stdin>',cls_double__induction__lemma_0) ).

fof(c_0_57_058,axiom,
    ! [X29] :
      ( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_sko__InductTermi__XIT__Xcases__4(X29)),v_sko__InductTermi__XIT__Xcases__5(X29)),c_HOL_Ozero__class_Ozero(tc_nat)),v_sko__InductTermi__XIT__Xcases__6(X29),tc_Lambda_OdB,tc_Lambda_OdB)))
      | hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X29)))
      | X29 = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X29)),v_sko__InductTermi__XIT__Xcases__1(X29),tc_Lambda_OdB,tc_Lambda_OdB)
      | ~ hBOOL(hAPP(c_InductTermi_OIT,X29)) ),
    file('<stdin>',cls_IT_Ocases_4) ).

fof(c_0_58_059,axiom,
    ! [X29] :
      ( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_sko__InductTermi__XIT__Xcases__4(X29)),v_sko__InductTermi__XIT__Xcases__5(X29)),c_HOL_Ozero__class_Ozero(tc_nat)),v_sko__InductTermi__XIT__Xcases__6(X29),tc_Lambda_OdB,tc_Lambda_OdB)))
      | X29 = c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X29))
      | X29 = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X29)),v_sko__InductTermi__XIT__Xcases__1(X29),tc_Lambda_OdB,tc_Lambda_OdB)
      | ~ hBOOL(hAPP(c_InductTermi_OIT,X29)) ),
    file('<stdin>',cls_IT_Ocases_1) ).

fof(c_0_59_060,axiom,
    ! [X29] :
      ( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_sko__InductTermi__XIT__Xcases__4(X29)),v_sko__InductTermi__XIT__Xcases__5(X29)),c_HOL_Ozero__class_Ozero(tc_nat)),v_sko__InductTermi__XIT__Xcases__6(X29),tc_Lambda_OdB,tc_Lambda_OdB)))
      | hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X29)))
      | c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X29),tc_Lambda_OdB)
      | ~ hBOOL(hAPP(c_InductTermi_OIT,X29)) ),
    file('<stdin>',cls_IT_Ocases_10) ).

fof(c_0_60_061,axiom,
    ! [X29] :
      ( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_sko__InductTermi__XIT__Xcases__4(X29)),v_sko__InductTermi__XIT__Xcases__5(X29)),c_HOL_Ozero__class_Ozero(tc_nat)),v_sko__InductTermi__XIT__Xcases__6(X29),tc_Lambda_OdB,tc_Lambda_OdB)))
      | X29 = c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X29))
      | c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X29),tc_Lambda_OdB)
      | ~ hBOOL(hAPP(c_InductTermi_OIT,X29)) ),
    file('<stdin>',cls_IT_Ocases_7) ).

fof(c_0_61_062,axiom,
    ! [X6,X16,X21,X22,X37] :
      ( c_Type_Otypings(c_Type_Oshift(X21,X16,X22,tc_Type_Otype),c_List_Omap(c_COMBC(c_Lambda_Olift,X16,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X6,tc_Lambda_OdB,tc_Lambda_OdB),X37)
      | ~ c_Type_Otypings(X21,X6,X37) ),
    file('<stdin>',cls_lift__types_0) ).

fof(c_0_62_063,axiom,
    ! [X6] :
      ( c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X6,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)
      | ~ c_List_Olistsp(c_InductTermi_OIT,X6,tc_Lambda_OdB) ),
    file('<stdin>',cls_lifts__IT_0) ).

fof(c_0_63_064,axiom,
    ! [X17,X18] :
      ( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X18),X17,tc_Lambda_OdB,tc_Lambda_OdB)))
      | ~ c_List_Olistsp(c_InductTermi_OIT,X17,tc_Lambda_OdB) ),
    file('<stdin>',cls_IT_OVar_0) ).

fof(c_0_64_065,axiom,
    ! [X6,X16,X21,X23] :
      ( c_Type_Otypings(X21,X6,c_Type_Osko__Type__Xvar__app__typesE__1__1(X23,X21,X16,X6))
      | ~ c_Type_Otyping(X21,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X16),X6,tc_Lambda_OdB,tc_Lambda_OdB),X23) ),
    file('<stdin>',cls_var__app__typesE_1) ).

fof(c_0_65_066,axiom,
    ! [X9,X7,X17,X8] :
      ( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X8),X17,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X7),X9,tc_Lambda_OdB,tc_Lambda_OdB)
      | X8 = X7 ),
    file('<stdin>',cls_Abs__apps__eq__Abs__apps__conv_0) ).

fof(c_0_66_067,axiom,
    ! [X9,X7,X17,X8] :
      ( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X8),X17,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X7),X9,tc_Lambda_OdB,tc_Lambda_OdB)
      | X17 = X9 ),
    file('<stdin>',cls_Abs__apps__eq__Abs__apps__conv_1) ).

fof(c_0_67_068,axiom,
    ! [X9,X17,X18,X10] :
      ( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X10),X17,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X18),X9,tc_Lambda_OdB,tc_Lambda_OdB)
      | X10 = X18 ),
    file('<stdin>',cls_Var__apps__eq__Var__apps__conv_0) ).

fof(c_0_68_069,axiom,
    ! [X9,X17,X18,X10] :
      ( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X10),X17,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X18),X9,tc_Lambda_OdB,tc_Lambda_OdB)
      | X17 = X9 ),
    file('<stdin>',cls_Var__apps__eq__Var__apps__conv_1) ).

fof(c_0_69_070,axiom,
    ! [X28,X40,X24,X3] :
      ( ~ class_OrderedGroup_Osemigroup__add(X3)
      | c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X24),X40),X28,X3,X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X24),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),X40,X28,X3,X3)) ),
    file('<stdin>',cls_foldl__assoc_0) ).

fof(c_0_70_071,axiom,
    ! [X6,X7,X8] :
      ( c_List_Ofoldl(c_Lambda_OdB_OApp,X8,X6,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,X7,X6,tc_Lambda_OdB,tc_Lambda_OdB)
      | X8 = X7 ),
    file('<stdin>',cls_apps__eq__tail__conv_0) ).

fof(c_0_71_072,axiom,
    ! [X28,X40,X24,X39,X3] :
      ( c_List_Ofoldl(X39,hAPP(hAPP(X39,X24),X40),X28,X3,X3) = hAPP(hAPP(X39,X24),c_List_Ofoldl(X39,X40,X28,X3,X3))
      | ~ c_OrderedGroup_Osemigroup__add(X39,X3) ),
    file('<stdin>',cls_semigroup__add_Ofoldl__assoc_0) ).

fof(c_0_72_073,axiom,
    ! [X28,X38,X24,X39,X3] :
      ( hAPP(hAPP(X39,X24),c_List_Ofoldl(X39,X38,X28,X3,X3)) = c_List_Ofoldl(X39,X24,X28,X3,X3)
      | ~ c_OrderedGroup_Omonoid__add(X38,X39,X3) ),
    file('<stdin>',cls_monoid__add_Ofoldl__absorb0_0) ).

fof(c_0_73_074,axiom,
    ! [X43,X29,X3] :
      ( ~ class_OrderedGroup_Omonoid__add(X3)
      | c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),X29,X43,X3,X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X3),X43,c_HOL_Ozero__class_Ozero(X3),X3,X3)) ),
    file('<stdin>',cls_foldl__foldr1__lemma_0) ).

fof(c_0_74_075,axiom,
    ! [X28,X24,X3] :
      ( ~ class_OrderedGroup_Omonoid__add(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X24),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3),X28,X3,X3)) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),X24,X28,X3,X3) ),
    file('<stdin>',cls_foldl__absorb0_0) ).

fof(c_0_75_076,axiom,
    ! [X6,X27,X7,X8] :
      ( hAPP(hAPP(c_Lambda_OdB_OApp,X8),X7) != c_List_Ofoldl(c_Lambda_OdB_OApp,X27,X6,tc_Lambda_OdB,tc_Lambda_OdB)
      | X8 = c_List_Ofoldl(c_Lambda_OdB_OApp,X27,c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1(X8,X7,X27,X6),tc_Lambda_OdB,tc_Lambda_OdB)
      | X6 = c_List_Olist_ONil(tc_Lambda_OdB) ),
    file('<stdin>',cls_App__eq__foldl__conv_2) ).

fof(c_0_76_077,axiom,
    ! [X29] :
      ( X29 = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__4(X29))),v_sko__InductTermi__XIT__Xcases__5(X29)),v_sko__InductTermi__XIT__Xcases__6(X29),tc_Lambda_OdB,tc_Lambda_OdB)
      | hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X29)))
      | X29 = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X29)),v_sko__InductTermi__XIT__Xcases__1(X29),tc_Lambda_OdB,tc_Lambda_OdB)
      | ~ hBOOL(hAPP(c_InductTermi_OIT,X29)) ),
    file('<stdin>',cls_IT_Ocases_3) ).

fof(c_0_77_078,axiom,
    ! [X29] :
      ( X29 = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__4(X29))),v_sko__InductTermi__XIT__Xcases__5(X29)),v_sko__InductTermi__XIT__Xcases__6(X29),tc_Lambda_OdB,tc_Lambda_OdB)
      | X29 = c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X29))
      | X29 = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X29)),v_sko__InductTermi__XIT__Xcases__1(X29),tc_Lambda_OdB,tc_Lambda_OdB)
      | ~ hBOOL(hAPP(c_InductTermi_OIT,X29)) ),
    file('<stdin>',cls_IT_Ocases_0) ).

fof(c_0_78_079,axiom,
    ! [X43,X3] :
      ( ~ class_OrderedGroup_Omonoid__add(X3)
      | c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3),X43,X3,X3) = c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X3),X43,c_HOL_Ozero__class_Ozero(X3),X3,X3) ),
    file('<stdin>',cls_foldl__foldr1_0) ).

fof(c_0_79_080,axiom,
    ! [X43,X29,X3] :
      ( ~ class_OrderedGroup_Oab__semigroup__add(X3)
      | c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X3),X43,X29,X3,X3) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),X29,X43,X3,X3) ),
    file('<stdin>',cls_foldr__conv__foldl_0) ).

fof(c_0_80_081,axiom,
    ! [X27,X7,X8] :
      ( hAPP(hAPP(c_Lambda_OdB_OApp,X8),X7) != c_List_Ofoldl(c_Lambda_OdB_OApp,X27,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)
      | hAPP(hAPP(c_Lambda_OdB_OApp,X8),X7) = X27 ),
    file('<stdin>',cls_App__eq__foldl__conv_0) ).

fof(c_0_81_082,axiom,
    ! [X9,X7,X8] :
      ( c_List_Ofoldl(c_Lambda_OdB_OApp,X7,X9,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X8)
      | X7 = c_Lambda_OdB_OAbs(X8) ),
    file('<stdin>',cls_apps__eq__Abs__conv_0) ).

fof(c_0_82_083,axiom,
    ! [X9,X7,X8] :
      ( c_Lambda_OdB_OAbs(X8) != c_List_Ofoldl(c_Lambda_OdB_OApp,X7,X9,tc_Lambda_OdB,tc_Lambda_OdB)
      | c_Lambda_OdB_OAbs(X8) = X7 ),
    file('<stdin>',cls_Abs__eq__apps__conv_0) ).

fof(c_0_83_084,axiom,
    ! [X9,X7,X10] :
      ( c_Lambda_OdB_OVar(X10) != c_List_Ofoldl(c_Lambda_OdB_OApp,X7,X9,tc_Lambda_OdB,tc_Lambda_OdB)
      | c_Lambda_OdB_OVar(X10) = X7 ),
    file('<stdin>',cls_Var__eq__apps__conv_0) ).

fof(c_0_84_085,axiom,
    ! [X27,X7,X15,X16] :
      ( hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(hAPP(c_Lambda_Osubst,X27),X7),X15)),X16) = hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,X27),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),c_HOL_Oone__class_Oone(tc_nat)))),hAPP(hAPP(c_Lambda_Olift,X7),X16)),X15)
      | ~ c_HOL_Oord__class_Oless(X15,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
    file('<stdin>',cls_lift__subst_0) ).

fof(c_0_85_086,axiom,
    ! [X9,X7,X8] :
      ( c_Lambda_OdB_OAbs(X8) != c_List_Ofoldl(c_Lambda_OdB_OApp,X7,X9,tc_Lambda_OdB,tc_Lambda_OdB)
      | X9 = c_List_Olist_ONil(tc_Lambda_OdB) ),
    file('<stdin>',cls_Abs__eq__apps__conv_1) ).

fof(c_0_86_087,axiom,
    ! [X9,X7,X8] :
      ( c_List_Ofoldl(c_Lambda_OdB_OApp,X7,X9,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X8)
      | X9 = c_List_Olist_ONil(tc_Lambda_OdB) ),
    file('<stdin>',cls_apps__eq__Abs__conv_1) ).

fof(c_0_87_088,axiom,
    ! [X9,X7,X10] :
      ( c_Lambda_OdB_OVar(X10) != c_List_Ofoldl(c_Lambda_OdB_OApp,X7,X9,tc_Lambda_OdB,tc_Lambda_OdB)
      | X9 = c_List_Olist_ONil(tc_Lambda_OdB) ),
    file('<stdin>',cls_Var__eq__apps__conv_1) ).

fof(c_0_88_089,axiom,
    ! [X40,X24,X8,X3] :
      ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X8,X3),X40),X24))
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Predicate_Oconversep(X8,X3,X3),X3),X24),X40)) ),
    file('<stdin>',cls_rtranclp__converseD_0) ).

fof(c_0_89_090,axiom,
    ! [X51,X40,X43,X24,X8,X3] :
      ( hBOOL(hAPP(hAPP(X8,X40),X24))
      | c_ListOrder_Ostep1(X8,X51,X43,X3)
      | ~ c_ListOrder_Ostep1(X8,c_List_Oappend(X51,c_List_Olist_OCons(X40,c_List_Olist_ONil(X3),X3),X3),c_List_Oappend(X43,c_List_Olist_OCons(X24,c_List_Olist_ONil(X3),X3),X3),X3) ),
    file('<stdin>',cls_Snoc__step1__SnocD_1) ).

fof(c_0_90_091,axiom,
    ! [X51,X40,X43,X24,X8,X3] :
      ( X51 = X43
      | c_ListOrder_Ostep1(X8,X51,X43,X3)
      | ~ c_ListOrder_Ostep1(X8,c_List_Oappend(X51,c_List_Olist_OCons(X40,c_List_Olist_ONil(X3),X3),X3),c_List_Oappend(X43,c_List_Olist_OCons(X24,c_List_Olist_ONil(X3),X3),X3),X3) ),
    file('<stdin>',cls_Snoc__step1__SnocD_0) ).

fof(c_0_91_092,axiom,
    ! [X51,X40,X43,X24,X8,X3] :
      ( hBOOL(hAPP(hAPP(X8,X40),X24))
      | X40 = X24
      | ~ c_ListOrder_Ostep1(X8,c_List_Oappend(X51,c_List_Olist_OCons(X40,c_List_Olist_ONil(X3),X3),X3),c_List_Oappend(X43,c_List_Olist_OCons(X24,c_List_Olist_ONil(X3),X3),X3),X3) ),
    file('<stdin>',cls_Snoc__step1__SnocD_3) ).

fof(c_0_92_093,axiom,
    ! [X29] :
      ( X29 = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__4(X29))),v_sko__InductTermi__XIT__Xcases__5(X29)),v_sko__InductTermi__XIT__Xcases__6(X29),tc_Lambda_OdB,tc_Lambda_OdB)
      | hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X29)))
      | c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X29),tc_Lambda_OdB)
      | ~ hBOOL(hAPP(c_InductTermi_OIT,X29)) ),
    file('<stdin>',cls_IT_Ocases_9) ).

fof(c_0_93_094,axiom,
    ! [X51,X40,X43,X24,X8,X3] :
      ( X51 = X43
      | X40 = X24
      | ~ c_ListOrder_Ostep1(X8,c_List_Oappend(X51,c_List_Olist_OCons(X40,c_List_Olist_ONil(X3),X3),X3),c_List_Oappend(X43,c_List_Olist_OCons(X24,c_List_Olist_ONil(X3),X3),X3),X3) ),
    file('<stdin>',cls_Snoc__step1__SnocD_2) ).

fof(c_0_94_095,axiom,
    ! [X29] :
      ( X29 = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__4(X29))),v_sko__InductTermi__XIT__Xcases__5(X29)),v_sko__InductTermi__XIT__Xcases__6(X29),tc_Lambda_OdB,tc_Lambda_OdB)
      | X29 = c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X29))
      | c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X29),tc_Lambda_OdB)
      | ~ hBOOL(hAPP(c_InductTermi_OIT,X29)) ),
    file('<stdin>',cls_IT_Ocases_6) ).

fof(c_0_95_096,axiom,
    ! [X27,X7,X8,X16] :
      ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,X8),X27),X16)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X7),X27),X16)))
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X8),X7)) ),
    file('<stdin>',cls_subst__preserves__beta_H_0) ).

fof(c_0_96_097,axiom,
    ! [X27,X7,X8,X16] :
      ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,X27),X8),X16)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X27),X7),X16)))
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X8),X7)) ),
    file('<stdin>',cls_subst__preserves__beta2_H_0) ).

fof(c_0_97_098,axiom,
    ! [X29] :
      ( hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__5(X29)))
      | hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X29)))
      | X29 = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X29)),v_sko__InductTermi__XIT__Xcases__1(X29),tc_Lambda_OdB,tc_Lambda_OdB)
      | ~ hBOOL(hAPP(c_InductTermi_OIT,X29)) ),
    file('<stdin>',cls_IT_Ocases_5) ).

fof(c_0_98_099,axiom,
    ! [X40,X24,X8,X3] :
      ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Predicate_Oconversep(X8,X3,X3),X3),X24),X40))
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X8,X3),X40),X24)) ),
    file('<stdin>',cls_rtranclp__converseI_0) ).

fof(c_0_99_100,axiom,
    ! [X29] :
      ( hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__5(X29)))
      | X29 = c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X29))
      | X29 = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X29)),v_sko__InductTermi__XIT__Xcases__1(X29),tc_Lambda_OdB,tc_Lambda_OdB)
      | ~ hBOOL(hAPP(c_InductTermi_OIT,X29)) ),
    file('<stdin>',cls_IT_Ocases_2) ).

fof(c_0_100_101,axiom,
    ! [X27,X7,X8,X16] :
      ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,X27),X8),X16)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X27),X7),X16)))
      | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X8),X7)) ),
    file('<stdin>',cls_subst__preserves__beta2_0) ).

fof(c_0_101_102,axiom,
    ! [X43,X3] :
      ( ~ class_OrderedGroup_Omonoid__add(X3)
      | c_List_Olistsum(X43,X3) = c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X3),X43,c_HOL_Ozero__class_Ozero(X3),X3,X3) ),
    file('<stdin>',cls_listsum__foldr_0) ).

fof(c_0_102_103,axiom,
    ! [X43,X3] :
      ( ~ class_OrderedGroup_Omonoid__add(X3)
      | c_List_Olistsum(X43,X3) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3),X43,X3,X3) ),
    file('<stdin>',cls_listsum_0) ).

fof(c_0_103_104,axiom,
    ! [X27,X7,X15,X16] :
      ( hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(hAPP(c_Lambda_Osubst,X27),X7),X15)),X16) = hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,X27),X16)),hAPP(hAPP(c_Lambda_Olift,X7),X16)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),c_HOL_Oone__class_Oone(tc_nat)))
      | ~ c_HOL_Oord__class_Oless(X16,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
    file('<stdin>',cls_lift__subst__lt_0) ).

fof(c_0_104_105,axiom,
    ! [X27,X7,X8,X16] :
      ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(hAPP(c_Lambda_Osubst,X8),X27),X16)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X7),X27),X16)))
      | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X8),X7)) ),
    file('<stdin>',cls_subst__preserves__beta_0) ).

fof(c_0_105_106,axiom,
    ! [X26,X27,X16,X76,X22,X23] :
      ( ~ c_Type_Otyping(X76,X26,X22)
      | ~ c_Type_Otyping(c_Type_Oshift(X76,X16,X22,tc_Type_Otype),X27,X23)
      | c_Type_Otyping(X76,hAPP(hAPP(hAPP(c_Lambda_Osubst,X27),X26),X16),X23) ),
    file('<stdin>',cls_subst__lemma_0) ).

fof(c_0_106_107,axiom,
    ! [X54,X27,X65,X7] :
      ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X7),X27)),hAPP(hAPP(c_Lambda_OdB_OApp,X65),X54)))
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X27),X54))
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X7),X65)) ),
    file('<stdin>',cls_rtrancl__beta__App_0) ).

fof(c_0_107_108,axiom,
    ! [X51,X40,X43,X24,X8,X3] :
      ( c_ListOrder_Ostep1(X8,X51,X43,X3)
      | hBOOL(hAPP(hAPP(X8,X40),X24))
      | ~ c_ListOrder_Ostep1(X8,c_List_Olist_OCons(X40,X51,X3),c_List_Olist_OCons(X24,X43,X3),X3) ),
    file('<stdin>',cls_Cons__step1__Cons_1) ).

fof(c_0_108_109,axiom,
    ! [X51,X40,X43,X24,X8,X3] :
      ( c_ListOrder_Ostep1(X8,X51,X43,X3)
      | X43 = X51
      | ~ c_ListOrder_Ostep1(X8,c_List_Olist_OCons(X40,X51,X3),c_List_Olist_OCons(X24,X43,X3),X3) ),
    file('<stdin>',cls_Cons__step1__Cons_3) ).

fof(c_0_109_110,axiom,
    ! [X8,X49,X29,X53,X3] :
      ( hBOOL(hAPP(hAPP(X8,X49),X29))
      | ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X8,X3,X53),X29),X49)) ),
    file('<stdin>',cls_conversepD_0) ).

fof(c_0_110_111,axiom,
    ! [X8,X73,X74,X53,X3] :
      ( hBOOL(hAPP(hAPP(X8,X73),X74))
      | ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X8,X3,X53),X74),X73)) ),
    file('<stdin>',cls_conversep_Ocases_0) ).

fof(c_0_111_112,axiom,
    ! [X51,X43,X24,X8,X3] :
      ( ~ c_ListOrder_Ostep1(X8,X51,X43,X3)
      | c_ListOrder_Ostep1(X8,c_List_Oappend(X51,X24,X3),c_List_Oappend(X43,X24,X3),X3) ),
    file('<stdin>',cls_append__step1I_0) ).

fof(c_0_112_113,axiom,
    ! [X24,X72,X36,X8,X3] :
      ( c_ListOrder_Ostep1(X8,c_List_Oappend(X24,X72,X3),c_List_Oappend(X24,X36,X3),X3)
      | ~ c_ListOrder_Ostep1(X8,X72,X36,X3) ),
    file('<stdin>',cls_append__step1I_1) ).

fof(c_0_113_114,axiom,
    ! [X51,X43,X24,X8,X3] :
      ( c_ListOrder_Ostep1(X8,c_List_Olist_OCons(X24,X51,X3),c_List_Olist_OCons(X24,X43,X3),X3)
      | ~ c_ListOrder_Ostep1(X8,X51,X43,X3) ),
    file('<stdin>',cls_Cons__step1__Cons_5) ).

fof(c_0_114_115,axiom,
    ! [X27,X65,X7] :
      ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X7),X27)),hAPP(hAPP(c_Lambda_OdB_OApp,X65),X27)))
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X7),X65)) ),
    file('<stdin>',cls_rtrancl__beta__AppL_0) ).

fof(c_0_115_116,axiom,
    ! [X54,X27,X7] :
      ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X7),X27)),hAPP(hAPP(c_Lambda_OdB_OApp,X7),X54)))
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X27),X54)) ),
    file('<stdin>',cls_rtrancl__beta__AppR_0) ).

fof(c_0_116_117,axiom,
    ! [X7,X8,X16] :
      ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_Olift,X8),X16)),hAPP(hAPP(c_Lambda_Olift,X7),X16)))
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X8),X7)) ),
    file('<stdin>',cls_lift__preserves__beta_H_0) ).

fof(c_0_117_118,axiom,
    ! [X51,X40,X43,X24,X8,X3] :
      ( X24 = X40
      | hBOOL(hAPP(hAPP(X8,X40),X24))
      | ~ c_ListOrder_Ostep1(X8,c_List_Olist_OCons(X40,X51,X3),c_List_Olist_OCons(X24,X43,X3),X3) ),
    file('<stdin>',cls_Cons__step1__Cons_0) ).

fof(c_0_118_119,axiom,
    ! [X64,X40,X24,X8,X3] :
      ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X8,X3),X24),X64))
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X8,X3),X40),X64))
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X8,X3),X24),X40)) ),
    file('<stdin>',cls_rtranclp__trans_0) ).

fof(c_0_119_120,axiom,
    ! [X51,X40,X43,X24,X8,X3] :
      ( X24 = X40
      | X43 = X51
      | ~ c_ListOrder_Ostep1(X8,c_List_Olist_OCons(X40,X51,X3),c_List_Olist_OCons(X24,X43,X3),X3) ),
    file('<stdin>',cls_Cons__step1__Cons_2) ).

fof(c_0_120_121,axiom,
    ! [X62,X50,X49,X29,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),X49)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X50),X62)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),X50)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X49),X62)) ),
    file('<stdin>',cls_class__semiring_Osemiring__rules_I20_J_0) ).

fof(c_0_121_122,axiom,
    ! [X27,X16,X21,X22,X23] :
      ( c_Type_Otyping(c_Type_Oshift(X21,X16,X22,tc_Type_Otype),hAPP(hAPP(c_Lambda_Olift,X27),X16),X23)
      | ~ c_Type_Otyping(X21,X27,X23) ),
    file('<stdin>',cls_lift__type_0) ).

fof(c_0_122_123,axiom,
    ! [X8,X49,X29,X53,X3] :
      ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X8,X3,X53),X29),X49))
      | ~ hBOOL(hAPP(hAPP(X8,X49),X29)) ),
    file('<stdin>',cls_conversep__iff_1) ).

fof(c_0_123_124,axiom,
    ! [X8,X49,X29,X53,X3] :
      ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X8,X3,X53),X49),X29))
      | ~ hBOOL(hAPP(hAPP(X8,X29),X49)) ),
    file('<stdin>',cls_conversep_Ointros_0) ).

fof(c_0_124_125,axiom,
    ! [X7,X8,X16] :
      ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_Olift,X8),X16)),hAPP(hAPP(c_Lambda_Olift,X7),X16)))
      | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X8),X7)) ),
    file('<stdin>',cls_lift__preserves__beta_0) ).

fof(c_0_125_126,axiom,
    ! [X26,X27,X7] :
      ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,X26),X7)),hAPP(hAPP(c_Lambda_OdB_OApp,X26),X27)))
      | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X7),X27)) ),
    file('<stdin>',cls_appR_0) ).

fof(c_0_126_127,axiom,
    ! [X26,X27,X7] :
      ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,X7),X26)),hAPP(hAPP(c_Lambda_OdB_OApp,X27),X26)))
      | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X7),X27)) ),
    file('<stdin>',cls_appL_0) ).

fof(c_0_127_128,axiom,
    ! [X8,X50,X49,X29,X3] :
      ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X8,X3),X29),X50))
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X8,X3),X49),X50))
      | ~ hBOOL(hAPP(hAPP(X8,X29),X49)) ),
    file('<stdin>',cls_converse__rtranclp__into__rtranclp_0) ).

fof(c_0_128_129,axiom,
    ! [X8,X50,X49,X29,X3] :
      ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X8,X3),X29),X50))
      | ~ hBOOL(hAPP(hAPP(X8,X49),X50))
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X8,X3),X29),X49)) ),
    file('<stdin>',cls_rtranclp_Ortrancl__into__rtrancl_0) ).

fof(c_0_129_130,axiom,
    ! [X15,X16,X21,X23,X3] :
      ( hAPP(c_Type_Oshift(X21,X16,X23,X3),X15) = hAPP(X21,X15)
      | ~ c_HOL_Oord__class_Oless(X15,X16,tc_nat) ),
    file('<stdin>',cls_shift__gt_0) ).

fof(c_0_130_131,axiom,
    ! [X40,X58,X24,X8,X3] :
      ( ~ hBOOL(hAPP(hAPP(X8,X40),X58))
      | c_ListOrder_Ostep1(X8,c_List_Olist_OCons(X40,X24,X3),c_List_Olist_OCons(X58,X24,X3),X3) ),
    file('<stdin>',cls_Cons__step1__Cons_4) ).

fof(c_0_131_132,axiom,
    ! [X18,X49,X29,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_HOL_Oord__class_Oless(X29,X49,X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X49,X3)
      | ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X29,X18,X3),c_Power_Opower__class_Opower(X49,X18,X3),X3) ),
    file('<stdin>',cls_power__less__imp__less__base_0) ).

fof(c_0_132_133,axiom,
    ! [X18,X10,X29,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_HOL_Oord__class_Oless(X10,X18,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X29,X10,X3),c_Power_Opower__class_Opower(X29,X18,X3),X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X29,X3) ),
    file('<stdin>',cls_power__less__imp__less__exp_0) ).

fof(c_0_133_134,axiom,
    ! [X40,X24,X49,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_HOL_Oord__class_Oless(X24,X40,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X49,X24,X3),c_Power_Opower__class_Opower(X49,X40,X3),X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X49,X3) ),
    file('<stdin>',cls_power__strict__increasing__iff_0) ).

fof(c_0_134_135,axiom,
    ! [X18,X29,X75,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X29,X75,X3),c_Power_Opower__class_Opower(X29,X18,X3),X3)
      | ~ c_HOL_Oord__class_Oless(X29,c_HOL_Oone__class_Oone(X3),X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X29,X3)
      | ~ c_HOL_Oord__class_Oless(X18,X75,tc_nat) ),
    file('<stdin>',cls_power__strict__decreasing_0) ).

fof(c_0_135_136,axiom,
    ! [X51,X40,X43,X24,X3] :
      ( c_List_Oappend(X43,c_List_Olist_OCons(X24,c_List_Olist_ONil(X3),X3),X3) != c_List_Oappend(X51,c_List_Olist_OCons(X40,c_List_Olist_ONil(X3),X3),X3)
      | X43 = X51 ),
    file('<stdin>',cls_append1__eq__conv_0) ).

fof(c_0_136_137,axiom,
    ! [X51,X40,X43,X24,X3] :
      ( c_List_Oappend(X43,c_List_Olist_OCons(X24,c_List_Olist_ONil(X3),X3),X3) != c_List_Oappend(X51,c_List_Olist_OCons(X40,c_List_Olist_ONil(X3),X3),X3)
      | X24 = X40 ),
    file('<stdin>',cls_append1__eq__conv_1) ).

fof(c_0_137_138,axiom,
    ! [X18,X49,X29,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X29,X18,X3),c_Power_Opower__class_Opower(X49,X18,X3),X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X18,tc_nat)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X29,X3)
      | ~ c_HOL_Oord__class_Oless(X29,X49,X3) ),
    file('<stdin>',cls_power__strict__mono_0) ).

fof(c_0_138_139,axiom,
    ! [X64,X40,X24,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_Orderings_Oord__class_Omax(X24,X40,X3)),X64) = c_Orderings_Oord__class_Omax(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X24),X64),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X40),X64),X3) ),
    file('<stdin>',cls_max__add__distrib__left_0) ).

fof(c_0_139_140,axiom,
    ! [X50,X49,X29,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),X49)),X50) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),X50)),X49) ),
    file('<stdin>',cls_class__semiring_Osemiring__rules_I23_J_0) ).

fof(c_0_140_141,axiom,
    ! [X62,X50,X49,X29,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
      | c_lessequals(X29,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X49),X62),X3)
      | ~ c_lessequals(X50,X62,X3)
      | ~ c_lessequals(X29,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X49),X50),X3) ),
    file('<stdin>',cls_le__add__right__mono_0) ).

fof(c_0_141_142,axiom,
    ! [X50,X49,X29,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
      | c_lessequals(X29,X49,X3)
      | ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X50),X29),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X50),X49),X3) ),
    file('<stdin>',cls_add__le__cancel__left_0) ).

fof(c_0_142_143,axiom,
    ! [X50,X49,X29,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
      | c_lessequals(X29,X49,X3)
      | ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),X50),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X49),X50),X3) ),
    file('<stdin>',cls_add__le__cancel__right_0) ).

fof(c_0_143_144,axiom,
    ! [X50,X49,X29,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
      | c_HOL_Oord__class_Oless(X29,X49,X3)
      | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),X50),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X49),X50),X3) ),
    file('<stdin>',cls_add__less__cancel__right_0) ).

fof(c_0_144_145,axiom,
    ! [X50,X49,X29,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
      | c_HOL_Oord__class_Oless(X29,X49,X3)
      | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X50),X29),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X50),X49),X3) ),
    file('<stdin>',cls_add__less__cancel__left_0) ).

fof(c_0_145_146,axiom,
    ! [X18,X49,X29,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_Power_Opower__class_Opower(X29,X18,X3) != c_Power_Opower__class_Opower(X49,X18,X3)
      | X29 = X49
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X18,tc_nat)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X49,X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X29,X3) ),
    file('<stdin>',cls_power__eq__imp__eq__base_0) ).

fof(c_0_146_147,axiom,
    ! [X8,X15,X16] :
      ( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,X8),c_Lambda_OdB_OVar(X16)),X15)))
      | ~ hBOOL(hAPP(c_InductTermi_OIT,X8)) ),
    file('<stdin>',cls_subst__Var__IT_0) ).

fof(c_0_147_148,axiom,
    ! [X18,X49,X29,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_lessequals(c_Power_Opower__class_Opower(X29,X18,X3),c_Power_Opower__class_Opower(X49,X18,X3),X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X29,X3)
      | ~ c_lessequals(X29,X49,X3) ),
    file('<stdin>',cls_power__mono_0) ).

fof(c_0_148_149,axiom,
    ! [X18,X29,X75,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X29,X18,X3),c_Power_Opower__class_Opower(X29,X75,X3),X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X29,X3)
      | ~ c_HOL_Oord__class_Oless(X18,X75,tc_nat) ),
    file('<stdin>',cls_power__strict__increasing_0) ).

fof(c_0_149_150,axiom,
    ! [X40,X24,X49,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X49,X24,X3),c_Power_Opower__class_Opower(X49,X40,X3),X3)
      | ~ c_HOL_Oord__class_Oless(X24,X40,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X49,X3) ),
    file('<stdin>',cls_power__strict__increasing__iff_1) ).

fof(c_0_150_151,axiom,
    ! [X65,X7] :
      ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_OdB_OAbs(X7)),c_Lambda_OdB_OAbs(X65)))
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X7),X65)) ),
    file('<stdin>',cls_rtrancl__beta__Abs_0) ).

fof(c_0_151_152,axiom,
    ! [X62,X50,X49,X29,X3] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),X50),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X49),X62),X3)
      | ~ c_HOL_Oord__class_Oless(X50,X62,X3)
      | ~ c_lessequals(X29,X49,X3) ),
    file('<stdin>',cls_add__le__less__mono_0) ).

fof(c_0_152_153,axiom,
    ! [X62,X50,X49,X29,X3] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),X50),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X49),X62),X3)
      | ~ c_lessequals(X50,X62,X3)
      | ~ c_HOL_Oord__class_Oless(X29,X49,X3) ),
    file('<stdin>',cls_add__less__le__mono_0) ).

fof(c_0_153_154,axiom,
    ! [X62,X50,X49,X29,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3)
      | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),X50),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X49),X62),X3)
      | ~ c_lessequals(X50,X62,X3)
      | ~ c_lessequals(X29,X49,X3) ),
    file('<stdin>',cls_add__mono_0) ).

fof(c_0_154_155,axiom,
    ! [X62,X50,X49,X29,X3] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),X50),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X49),X62),X3)
      | ~ c_HOL_Oord__class_Oless(X50,X62,X3)
      | ~ c_HOL_Oord__class_Oless(X29,X49,X3) ),
    file('<stdin>',cls_add__strict__mono_0) ).

fof(c_0_155_156,axiom,
    ! [X8,X49,X29,X3] :
      ( c_Wellfounded_Oaccp(X8,X49,X3)
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X8,X3),X49),X29))
      | ~ c_Wellfounded_Oaccp(X8,X29,X3) ),
    file('<stdin>',cls_accp__downwards_0) ).

fof(c_0_156_157,axiom,
    ! [X8,X49,X29,X3] :
      ( c_Wellfounded_Oaccp(X8,X49,X3)
      | ~ c_Wellfounded_Oaccp(X8,X29,X3)
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X8,X3),X49),X29)) ),
    file('<stdin>',cls_accp__downwards__aux_0) ).

fof(c_0_157_158,axiom,
    ! [X18,X10,X25] :
      ( c_HOL_Oord__class_Oless(X10,X18,tc_nat)
      | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X25),X10),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X25),X18),tc_nat) ),
    file('<stdin>',cls_nat__add__left__cancel__less_0) ).

fof(c_0_158_159,axiom,
    ! [X50,X49,X29,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),X49)),X50) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X49),X50)) ),
    file('<stdin>',cls_class__semiring_Osemiring__rules_I21_J_0) ).

fof(c_0_159_160,axiom,
    ! [X62,X50,X29,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X50),X62)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),X50)),X62) ),
    file('<stdin>',cls_class__semiring_Osemiring__rules_I25_J_0) ).

fof(c_0_160_161,axiom,
    ! [X50,X49,X29,X3] :
      ( ~ class_OrderedGroup_Oab__semigroup__add(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),X49)),X50) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X49),X50)) ),
    file('<stdin>',cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) ).

fof(c_0_161_162,axiom,
    ! [X50,X49,X29,X3] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),X49)),X50) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X49),X50)) ),
    file('<stdin>',cls_comm__monoid__add_Omult__assoc_0) ).

fof(c_0_162_163,axiom,
    ! [X64,X40,X24,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X24),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X40),X64)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X24),X40)),X64) ),
    file('<stdin>',cls_class__semiring_Oadd__a_0) ).

fof(c_0_163_164,axiom,
    ! [X61,X25,X15,X16] :
      ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),X25),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X61),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X25,X61,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X16,X15,tc_nat) ),
    file('<stdin>',cls_add__less__mono_0) ).

fof(c_0_164_165,axiom,
    ! [X43,X52,X53,X3] :
      ( c_List_Olist_ONil(X3) != c_List_Omap(X52,X43,X53,X3)
      | X43 = c_List_Olist_ONil(X53) ),
    file('<stdin>',cls_Nil__is__map__conv_0) ).

fof(c_0_165_166,axiom,
    ! [X43,X52,X53,X3] :
      ( c_List_Omap(X52,X43,X53,X3) != c_List_Olist_ONil(X3)
      | X43 = c_List_Olist_ONil(X53) ),
    file('<stdin>',cls_map__is__Nil__conv_0) ).

fof(c_0_166_167,axiom,
    ! [X54,X27,X21,X23] :
      ( c_Type_Otyping(X21,X54,X23)
      | ~ c_Type_Otyping(X21,X27,X23)
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X27),X54)) ),
    file('<stdin>',cls_subject__reduction_H_0) ).

fof(c_0_167_168,axiom,
    ! [X64,X40,X24,X26,X3] :
      ( ~ class_OrderedGroup_Oab__group__add(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X24),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X40),X64)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X40),X26)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X24),X64) = X26 ),
    file('<stdin>',cls_add__cancel__21_0) ).

fof(c_0_168_169,axiom,
    ! [X64,X40,X24,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_lessequals(X64,X40,X3)
      | c_lessequals(X64,X24,X3)
      | ~ c_lessequals(X64,c_Orderings_Oord__class_Omax(X24,X40,X3),X3) ),
    file('<stdin>',cls_le__max__iff__disj_0) ).

fof(c_0_169_170,axiom,
    ! [X64,X40,X24,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_HOL_Oord__class_Oless(X64,X40,X3)
      | c_HOL_Oord__class_Oless(X64,X24,X3)
      | ~ c_HOL_Oord__class_Oless(X64,c_Orderings_Oord__class_Omax(X24,X40,X3),X3) ),
    file('<stdin>',cls_less__max__iff__disj_0) ).

fof(c_0_170_171,axiom,
    ! [X49,X29,X3] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
      | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),X49),c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_lessequals(X49,c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_lessequals(X29,c_HOL_Ozero__class_Ozero(X3),X3) ),
    file('<stdin>',cls_add__nonpos__nonpos_0) ).

fof(c_0_171_172,axiom,
    ! [X49,X29,X3] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),X49),X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X49,X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X29,X3) ),
    file('<stdin>',cls_add__nonneg__nonneg_0) ).

fof(c_0_172_173,axiom,
    ! [X49,X29,X3] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),X49),c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_lessequals(X49,c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_HOL_Oord__class_Oless(X29,c_HOL_Ozero__class_Ozero(X3),X3) ),
    file('<stdin>',cls_add__neg__nonpos_0) ).

fof(c_0_173_174,axiom,
    ! [X49,X29,X3] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),X49),c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_HOL_Oord__class_Oless(X49,c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_lessequals(X29,c_HOL_Ozero__class_Ozero(X3),X3) ),
    file('<stdin>',cls_add__nonpos__neg_0) ).

fof(c_0_174_175,axiom,
    ! [X49,X29,X3] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),X49),X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X49,X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X29,X3) ),
    file('<stdin>',cls_add__nonneg__pos_0) ).

fof(c_0_175_176,axiom,
    ! [X49,X29,X3] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),X49),X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X49,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X29,X3) ),
    file('<stdin>',cls_add__pos__nonneg_0) ).

fof(c_0_176_177,axiom,
    ! [X49,X29,X3] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),X49),c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_HOL_Oord__class_Oless(X49,c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_HOL_Oord__class_Oless(X29,c_HOL_Ozero__class_Ozero(X3),X3) ),
    file('<stdin>',cls_add__neg__neg_0) ).

fof(c_0_177_178,axiom,
    ! [X49,X29,X3] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),X49),X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X49,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X29,X3) ),
    file('<stdin>',cls_add__pos__pos_0) ).

fof(c_0_178_179,axiom,
    ! [X18,X29,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),c_Power_Opower__class_Opower(X29,X18,X3),X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X18,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X29,X3) ),
    file('<stdin>',cls_one__less__power_0) ).

fof(c_0_179_180,axiom,
    ! [X50,X49,X29,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
      | ~ class_OrderedGroup_Ocomm__monoid__add(X3)
      | c_lessequals(X49,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),X50),X3)
      | ~ c_lessequals(X49,X29,X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X50,X3) ),
    file('<stdin>',cls_add__increasing2_0) ).

fof(c_0_180_181,axiom,
    ! [X50,X49,X29,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
      | ~ class_OrderedGroup_Ocomm__monoid__add(X3)
      | c_lessequals(X49,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),X50),X3)
      | ~ c_lessequals(X49,X50,X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X29,X3) ),
    file('<stdin>',cls_add__increasing_0) ).

fof(c_0_181_182,axiom,
    ! [X50,X49,X29,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
      | ~ class_OrderedGroup_Ocomm__monoid__add(X3)
      | c_HOL_Oord__class_Oless(X49,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),X50),X3)
      | ~ c_lessequals(X49,X50,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X29,X3) ),
    file('<stdin>',cls_add__strict__increasing_0) ).

fof(c_0_182_183,axiom,
    ! [X50,X49,X29,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
      | ~ class_OrderedGroup_Ocomm__monoid__add(X3)
      | c_HOL_Oord__class_Oless(X49,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),X50),X3)
      | ~ c_HOL_Oord__class_Oless(X49,X50,X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X29,X3) ),
    file('<stdin>',cls_add__strict__increasing2_0) ).

fof(c_0_183_184,axiom,
    ! [X50,X49,X29,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3)
      | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X50),X29),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X50),X49),X3)
      | ~ c_lessequals(X29,X49,X3) ),
    file('<stdin>',cls_add__left__mono_0) ).

fof(c_0_184_185,axiom,
    ! [X50,X49,X29,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3)
      | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),X50),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X49),X50),X3)
      | ~ c_lessequals(X29,X49,X3) ),
    file('<stdin>',cls_add__right__mono_0) ).

fof(c_0_185_186,axiom,
    ! [X50,X49,X29,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
      | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X50),X29),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X50),X49),X3)
      | ~ c_lessequals(X29,X49,X3) ),
    file('<stdin>',cls_add__le__cancel__left_1) ).

fof(c_0_186_187,axiom,
    ! [X50,X49,X29,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
      | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),X50),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X49),X50),X3)
      | ~ c_lessequals(X29,X49,X3) ),
    file('<stdin>',cls_add__le__cancel__right_1) ).

fof(c_0_187_188,axiom,
    ! [X50,X49,X29,X3] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),X50),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X49),X50),X3)
      | ~ c_HOL_Oord__class_Oless(X29,X49,X3) ),
    file('<stdin>',cls_add__strict__right__mono_0) ).

fof(c_0_188_189,axiom,
    ! [X50,X49,X29,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),X50),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X49),X50),X3)
      | ~ c_HOL_Oord__class_Oless(X29,X49,X3) ),
    file('<stdin>',cls_add__less__cancel__right_1) ).

fof(c_0_189_190,axiom,
    ! [X50,X49,X29,X3] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X50),X29),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X50),X49),X3)
      | ~ c_HOL_Oord__class_Oless(X29,X49,X3) ),
    file('<stdin>',cls_add__strict__left__mono_0) ).

fof(c_0_190_191,axiom,
    ! [X50,X49,X29,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X50),X29),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X50),X49),X3)
      | ~ c_HOL_Oord__class_Oless(X29,X49,X3) ),
    file('<stdin>',cls_add__less__cancel__left_1) ).

fof(c_0_191_192,axiom,
    ! [X50,X49,X29,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_HOL_Oord__class_Oless(X49,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),X50),X3)
      | ~ c_HOL_Oord__class_Oless(X49,X50,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X29,X3) ),
    file('<stdin>',cls_pos__add__strict_0) ).

fof(c_0_192_193,axiom,
    ! [X18,X10] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X18,tc_nat)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X10,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X10),X18),tc_nat) ),
    file('<stdin>',cls_add__gr__0_0) ).

fof(c_0_193_194,axiom,
    ! [X24,X49,X29,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_lessequals(c_Orderings_Oord__class_Omax(X29,X49,X3),X24,X3)
      | ~ c_lessequals(X49,X24,X3)
      | ~ c_lessequals(X29,X24,X3) ),
    file('<stdin>',cls_min__max_Ole__supI_0) ).

fof(c_0_194_195,axiom,
    ! [X64,X40,X24,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_lessequals(c_Orderings_Oord__class_Omax(X40,X64,X3),X24,X3)
      | ~ c_lessequals(X64,X24,X3)
      | ~ c_lessequals(X40,X24,X3) ),
    file('<stdin>',cls_min__max_Osup__least_0) ).

fof(c_0_195_196,axiom,
    ! [X64,X40,X24,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_lessequals(c_Orderings_Oord__class_Omax(X24,X40,X3),X64,X3)
      | ~ c_lessequals(X40,X64,X3)
      | ~ c_lessequals(X24,X64,X3) ),
    file('<stdin>',cls_min__max_Ole__sup__iff_2) ).

fof(c_0_196_197,axiom,
    ! [X64,X40,X24,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X24,X40,X3),X64,X3)
      | ~ c_HOL_Oord__class_Oless(X40,X64,X3)
      | ~ c_HOL_Oord__class_Oless(X24,X64,X3) ),
    file('<stdin>',cls_max__less__iff__conj_2) ).

fof(c_0_197_198,axiom,
    ! [X39,X50,X49,X29,X3] :
      ( hAPP(hAPP(X39,hAPP(hAPP(X39,X29),X49)),X50) = hAPP(hAPP(X39,X29),hAPP(hAPP(X39,X49),X50))
      | ~ c_OrderedGroup_Osemigroup__add(X39,X3) ),
    file('<stdin>',cls_semigroup__add_Oadd__assoc_0) ).

fof(c_0_198_199,axiom,
    ! [X51,X43,X60,X3] :
      ( c_List_Olistsp(X60,c_List_Oappend(X43,X51,X3),X3)
      | ~ c_List_Olistsp(X60,X51,X3)
      | ~ c_List_Olistsp(X60,X43,X3) ),
    file('<stdin>',cls_append__in__listsp__conv_2) ).

fof(c_0_199_200,axiom,
    ! [X64,X40,X24,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omax(X24,X40,X3),X64,X3) = c_Orderings_Oord__class_Omax(X24,c_Orderings_Oord__class_Omax(X40,X64,X3),X3) ),
    file('<stdin>',cls_min__max_Osup__assoc_0) ).

fof(c_0_200_201,axiom,
    ! [X64,X40,X24,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_Orderings_Oord__class_Omax(X24,c_Orderings_Oord__class_Omax(X40,X64,X3),X3) = c_Orderings_Oord__class_Omax(X40,c_Orderings_Oord__class_Omax(X24,X64,X3),X3) ),
    file('<stdin>',cls_min__max_Osup__left__commute_0) ).

fof(c_0_201_202,axiom,
    ! [X29,X3] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
      | c_lessequals(X29,c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),X29),c_HOL_Ozero__class_Ozero(X3),X3) ),
    file('<stdin>',cls_double__add__le__zero__iff__single__add__le__zero_0) ).

fof(c_0_202_203,axiom,
    ! [X29,X3] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X3),X29,X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),X29),X3) ),
    file('<stdin>',cls_zero__le__double__add__iff__zero__le__single__add_0) ).

fof(c_0_203_204,axiom,
    ! [X29,X3] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
      | c_HOL_Oord__class_Oless(X29,c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),X29),c_HOL_Ozero__class_Ozero(X3),X3) ),
    file('<stdin>',cls_double__add__less__zero__iff__single__less__zero_0) ).

fof(c_0_204_205,axiom,
    ! [X29,X3] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X29,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),X29),X3) ),
    file('<stdin>',cls_zero__less__double__add__iff__zero__less__single__add_0) ).

fof(c_0_205_206,axiom,
    ! [X29,X3] :
      ( ~ class_Ring__and__Field_Oordered__idom(X3)
      | c_HOL_Oord__class_Oless(X29,c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),X29),c_HOL_Ozero__class_Ozero(X3),X3) ),
    file('<stdin>',cls_even__less__0__iff_0) ).

fof(c_0_206_207,axiom,
    ! [X25,X15,X16] :
      ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),X25),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X25),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X16,X15,tc_nat) ),
    file('<stdin>',cls_add__less__mono1_0) ).

fof(c_0_207_208,axiom,
    ! [X18,X10,X25] :
      ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X25),X10),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X25),X18),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X10,X18,tc_nat) ),
    file('<stdin>',cls_nat__add__left__cancel__less_1) ).

fof(c_0_208_209,axiom,
    ! [X24,X49,X29,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_lessequals(X29,X24,X3)
      | ~ c_lessequals(c_Orderings_Oord__class_Omax(X29,X49,X3),X24,X3) ),
    file('<stdin>',cls_min__max_Ole__supE_0) ).

fof(c_0_209_210,axiom,
    ! [X24,X49,X29,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_lessequals(X49,X24,X3)
      | ~ c_lessequals(c_Orderings_Oord__class_Omax(X29,X49,X3),X24,X3) ),
    file('<stdin>',cls_min__max_Ole__supE_1) ).

fof(c_0_210_211,axiom,
    ! [X64,X40,X24,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_lessequals(X24,X64,X3)
      | ~ c_lessequals(c_Orderings_Oord__class_Omax(X24,X40,X3),X64,X3) ),
    file('<stdin>',cls_min__max_Ole__sup__iff_0) ).

fof(c_0_211_212,axiom,
    ! [X64,X40,X24,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_lessequals(X40,X64,X3)
      | ~ c_lessequals(c_Orderings_Oord__class_Omax(X24,X40,X3),X64,X3) ),
    file('<stdin>',cls_min__max_Ole__sup__iff_1) ).

fof(c_0_212_213,axiom,
    ! [X64,X40,X24,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_HOL_Oord__class_Oless(X40,X64,X3)
      | ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X24,X40,X3),X64,X3) ),
    file('<stdin>',cls_max__less__iff__conj_1) ).

fof(c_0_213_214,axiom,
    ! [X64,X40,X24,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_HOL_Oord__class_Oless(X24,X64,X3)
      | ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X24,X40,X3),X64,X3) ),
    file('<stdin>',cls_max__less__iff__conj_0) ).

fof(c_0_214_215,axiom,
    ! [X62,X50,X29,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X50),X62)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X50),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),X62)) ),
    file('<stdin>',cls_class__semiring_Osemiring__rules_I22_J_0) ).

fof(c_0_215_216,axiom,
    ! [X50,X49,X29,X3] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X49),X50)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X49),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),X50)) ),
    file('<stdin>',cls_comm__monoid__add_Omult__left__commute_0) ).

fof(c_0_216_217,axiom,
    ! [X64,X40,X24,X3] :
      ( ~ class_OrderedGroup_Oab__group__add(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X24),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X40),X64)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X40),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X24),X64)) ),
    file('<stdin>',cls_add__cancel__21_1) ).

fof(c_0_217_218,axiom,
    ! [X40,X24,X8,X3] :
      ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X8,X3),X24),X40))
      | ~ hBOOL(hAPP(hAPP(X8,X24),X40)) ),
    file('<stdin>',cls_r__into__rtranclp_0) ).

fof(c_0_218_219,axiom,
    ! [X51,X43,X60,X3] :
      ( c_List_Olistsp(X60,X43,X3)
      | ~ c_List_Olistsp(X60,c_List_Oappend(X43,X51,X3),X3) ),
    file('<stdin>',cls_append__in__listsp__conv_0) ).

fof(c_0_219_220,axiom,
    ! [X51,X43,X60,X3] :
      ( c_List_Olistsp(X60,X51,X3)
      | ~ c_List_Olistsp(X60,c_List_Oappend(X43,X51,X3),X3) ),
    file('<stdin>',cls_append__in__listsp__conv_1) ).

fof(c_0_220_221,axiom,
    ! [X40,X24,X3] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X24),X40) != c_HOL_Ozero__class_Ozero(X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X40,X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X24,X3)
      | X24 = c_HOL_Ozero__class_Ozero(X3) ),
    file('<stdin>',cls_add__nonneg__eq__0__iff_0) ).

fof(c_0_221_222,axiom,
    ! [X40,X24,X3] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X24),X40) != c_HOL_Ozero__class_Ozero(X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X40,X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X24,X3)
      | X40 = c_HOL_Ozero__class_Ozero(X3) ),
    file('<stdin>',cls_add__nonneg__eq__0__iff_1) ).

fof(c_0_222_223,axiom,
    ! [X3] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(X3),X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3)),c_HOL_Ozero__class_Ozero(X3)) = c_HOL_Ozero__class_Ozero(X3) ),
    file('<stdin>',cls_add__nonneg__eq__0__iff_2) ).

fof(c_0_223_224,axiom,
    ! [X18,X10,X61,X25] :
      ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X10),X61) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X25),X18)
      | ~ c_HOL_Oord__class_Oless(X25,X61,tc_nat)
      | c_HOL_Oord__class_Oless(X10,X18,tc_nat) ),
    file('<stdin>',cls_less__add__eq__less_0) ).

fof(c_0_224_225,axiom,
    ! [X25,X15,X16] :
      ( c_HOL_Oord__class_Oless(X16,X25,tc_nat)
      | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),X15),X25,tc_nat) ),
    file('<stdin>',cls_add__lessD1_0) ).

fof(c_0_225_226,axiom,
    ! [X18,X10,X29,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_Power_Opower__class_Opower(X29,X10,X3) != c_Power_Opower__class_Opower(X29,X18,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X29,X3)
      | X10 = X18 ),
    file('<stdin>',cls_power__inject__exp_0) ).

fof(c_0_226_227,axiom,
    ! [X18,X29,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_Power_Opower__class_Opower(X29,X18,X3),X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X29,X3) ),
    file('<stdin>',cls_zero__le__power_0) ).

fof(c_0_227_228,axiom,
    ! [X18,X29,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_lessequals(c_HOL_Oone__class_Oone(X3),c_Power_Opower__class_Opower(X29,X18,X3),X3)
      | ~ c_lessequals(c_HOL_Oone__class_Oone(X3),X29,X3) ),
    file('<stdin>',cls_one__le__power_0) ).

fof(c_0_228_229,axiom,
    ! [X18,X29,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Power_Opower__class_Opower(X29,X18,X3),X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X29,X3) ),
    file('<stdin>',cls_zero__less__power_0) ).

fof(c_0_229_230,axiom,
    ! [X40,X8,X29,X3] :
      ( c_Wellfounded_Oaccp(X8,X40,X3)
      | ~ hBOOL(hAPP(hAPP(X8,X40),X29))
      | ~ c_Wellfounded_Oaccp(X8,X29,X3) ),
    file('<stdin>',cls_accp_Ocases_0) ).

fof(c_0_230_231,axiom,
    ! [X8,X49,X29,X3] :
      ( c_Wellfounded_Oaccp(X8,X29,X3)
      | ~ hBOOL(hAPP(hAPP(X8,X29),X49))
      | ~ c_Wellfounded_Oaccp(X8,X49,X3) ),
    file('<stdin>',cls_accp__downward_0) ).

fof(c_0_231_232,axiom,
    ! [X29,X3] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
      | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),X29),c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_lessequals(X29,c_HOL_Ozero__class_Ozero(X3),X3) ),
    file('<stdin>',cls_double__add__le__zero__iff__single__add__le__zero_1) ).

fof(c_0_232_233,axiom,
    ! [X29,X3] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),X29),X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X29,X3) ),
    file('<stdin>',cls_zero__le__double__add__iff__zero__le__single__add_1) ).

fof(c_0_233_234,axiom,
    ! [X29,X3] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),X29),c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_HOL_Oord__class_Oless(X29,c_HOL_Ozero__class_Ozero(X3),X3) ),
    file('<stdin>',cls_double__add__less__zero__iff__single__less__zero_1) ).

fof(c_0_234_235,axiom,
    ! [X29,X3] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),X29),X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X29,X3) ),
    file('<stdin>',cls_zero__less__double__add__iff__zero__less__single__add_1) ).

fof(c_0_235_236,axiom,
    ! [X29,X3] :
      ( ~ class_Ring__and__Field_Oordered__idom(X3)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),X29),c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_HOL_Oord__class_Oless(X29,c_HOL_Ozero__class_Ozero(X3),X3) ),
    file('<stdin>',cls_even__less__0__iff_1) ).

fof(c_0_236_237,axiom,
    ! [X8] :
      ( hBOOL(hAPP(c_InductTermi_OIT,X8))
      | ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X8,tc_Lambda_OdB) ),
    file('<stdin>',cls_termi__implies__IT_0) ).

fof(c_0_237_238,axiom,
    ! [X54,X27,X21,X23] :
      ( c_Type_Otyping(X21,X54,X23)
      | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X27),X54))
      | ~ c_Type_Otyping(X21,X27,X23) ),
    file('<stdin>',cls_subject__reduction_0) ).

fof(c_0_238_239,axiom,
    ! [X51,X43,X3] :
      ( ~ class_OrderedGroup_Omonoid__add(X3)
      | c_List_Olistsum(c_List_Oappend(X43,X51,X3),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_List_Olistsum(X43,X3)),c_List_Olistsum(X51,X3)) ),
    file('<stdin>',cls_listsum__append_0) ).

fof(c_0_239_240,axiom,
    ! [X24,X49,X29,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_lessequals(X24,c_Orderings_Oord__class_Omax(X29,X49,X3),X3)
      | ~ c_lessequals(X24,X29,X3) ),
    file('<stdin>',cls_min__max_Ole__supI1_0) ).

fof(c_0_240_241,axiom,
    ! [X24,X49,X29,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_lessequals(X24,c_Orderings_Oord__class_Omax(X29,X49,X3),X3)
      | ~ c_lessequals(X24,X49,X3) ),
    file('<stdin>',cls_min__max_Ole__supI2_0) ).

fof(c_0_241_242,axiom,
    ! [X64,X40,X24,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_lessequals(X64,c_Orderings_Oord__class_Omax(X24,X40,X3),X3)
      | ~ c_lessequals(X64,X24,X3) ),
    file('<stdin>',cls_le__max__iff__disj_1) ).

fof(c_0_242_243,axiom,
    ! [X64,X40,X24,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_lessequals(X64,c_Orderings_Oord__class_Omax(X24,X40,X3),X3)
      | ~ c_lessequals(X64,X40,X3) ),
    file('<stdin>',cls_le__max__iff__disj_2) ).

fof(c_0_243_244,axiom,
    ! [X64,X40,X24,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_HOL_Oord__class_Oless(X64,c_Orderings_Oord__class_Omax(X24,X40,X3),X3)
      | ~ c_HOL_Oord__class_Oless(X64,X40,X3) ),
    file('<stdin>',cls_less__max__iff__disj_2) ).

fof(c_0_244_245,axiom,
    ! [X64,X40,X24,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_HOL_Oord__class_Oless(X64,c_Orderings_Oord__class_Omax(X24,X40,X3),X3)
      | ~ c_HOL_Oord__class_Oless(X64,X24,X3) ),
    file('<stdin>',cls_less__max__iff__disj_1) ).

fof(c_0_245_246,axiom,
    ! [X24,X49,X29,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_HOL_Oord__class_Oless(X24,c_Orderings_Oord__class_Omax(X29,X49,X3),X3)
      | ~ c_HOL_Oord__class_Oless(X24,X49,X3) ),
    file('<stdin>',cls_min__max_Oless__supI2_0) ).

fof(c_0_246_247,axiom,
    ! [X24,X49,X29,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_HOL_Oord__class_Oless(X24,c_Orderings_Oord__class_Omax(X29,X49,X3),X3)
      | ~ c_HOL_Oord__class_Oless(X24,X29,X3) ),
    file('<stdin>',cls_min__max_Oless__supI1_0) ).

fof(c_0_247_248,axiom,
    ! [X18,X10,X3] :
      ( ~ class_Ring__and__Field_Osemiring__1(X3)
      | c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X10),X18),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_Nat_Osemiring__1__class_Oof__nat(X10,X3)),c_Nat_Osemiring__1__class_Oof__nat(X18,X3)) ),
    file('<stdin>',cls_of__nat__add_0) ).

fof(c_0_248_249,axiom,
    ! [X18,X10] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X10),X18),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X18,tc_nat) ),
    file('<stdin>',cls_add__gr__0_2) ).

fof(c_0_249_250,axiom,
    ! [X18,X10] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X10),X18),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X10,tc_nat) ),
    file('<stdin>',cls_add__gr__0_1) ).

fof(c_0_250_251,axiom,
    ! [X64,X40,X24,X3] :
      ( ~ class_Orderings_Opreorder(X3)
      | c_HOL_Oord__class_Oless(X24,X64,X3)
      | ~ c_lessequals(X40,X64,X3)
      | ~ c_HOL_Oord__class_Oless(X24,X40,X3) ),
    file('<stdin>',cls_order__less__le__trans_0) ).

fof(c_0_251_252,axiom,
    ! [X64,X40,X24,X3] :
      ( ~ class_Orderings_Opreorder(X3)
      | c_HOL_Oord__class_Oless(X24,X64,X3)
      | ~ c_HOL_Oord__class_Oless(X40,X64,X3)
      | ~ c_lessequals(X24,X40,X3) ),
    file('<stdin>',cls_order__le__less__trans_0) ).

fof(c_0_252_253,axiom,
    ! [X64,X40,X24,X3] :
      ( ~ class_Orderings_Opreorder(X3)
      | c_lessequals(X24,X64,X3)
      | ~ c_lessequals(X40,X64,X3)
      | ~ c_lessequals(X24,X40,X3) ),
    file('<stdin>',cls_order__trans_0) ).

fof(c_0_253_254,axiom,
    ! [X64,X40,X24,X3] :
      ( ~ class_Orderings_Oorder(X3)
      | c_HOL_Oord__class_Oless(X64,X24,X3)
      | ~ c_HOL_Oord__class_Oless(X64,X40,X3)
      | ~ c_lessequals(X40,X24,X3) ),
    file('<stdin>',cls_xt1_I8_J_0) ).

fof(c_0_254_255,axiom,
    ! [X64,X40,X24,X3] :
      ( ~ class_Orderings_Oorder(X3)
      | c_HOL_Oord__class_Oless(X64,X24,X3)
      | ~ c_lessequals(X64,X40,X3)
      | ~ c_HOL_Oord__class_Oless(X40,X24,X3) ),
    file('<stdin>',cls_xt1_I7_J_0) ).

fof(c_0_255_256,axiom,
    ! [X64,X40,X24,X3] :
      ( ~ class_Orderings_Oorder(X3)
      | c_lessequals(X64,X24,X3)
      | ~ c_lessequals(X64,X40,X3)
      | ~ c_lessequals(X40,X24,X3) ),
    file('<stdin>',cls_xt1_I6_J_0) ).

fof(c_0_256_257,axiom,
    ! [X64,X40,X24,X3] :
      ( ~ class_Orderings_Oorder(X3)
      | c_HOL_Oord__class_Oless(X64,X24,X3)
      | ~ c_HOL_Oord__class_Oless(X64,X40,X3)
      | ~ c_HOL_Oord__class_Oless(X40,X24,X3) ),
    file('<stdin>',cls_xt1_I10_J_0) ).

fof(c_0_257_258,axiom,
    ! [X64,X40,X24,X3] :
      ( ~ class_Orderings_Opreorder(X3)
      | c_HOL_Oord__class_Oless(X24,X64,X3)
      | ~ c_HOL_Oord__class_Oless(X40,X64,X3)
      | ~ c_HOL_Oord__class_Oless(X24,X40,X3) ),
    file('<stdin>',cls_order__less__trans_0) ).

fof(c_0_258_259,axiom,
    ! [X27,X7] :
      ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OAbs(X7)),c_Lambda_OdB_OAbs(X27)))
      | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X7),X27)) ),
    file('<stdin>',cls_abs_0) ).

fof(c_0_259_260,axiom,
    ! [X18,X10,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_HOL_Oord__class_Oless(X10,X18,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X10,X3),c_Nat_Osemiring__1__class_Oof__nat(X18,X3),X3) ),
    file('<stdin>',cls_of__nat__less__iff_0) ).

fof(c_0_260_261,axiom,
    ! [X64,X40,X24] :
      ( c_HOL_Oord__class_Oless(X24,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X40),X64),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X24,X40,tc_nat) ),
    file('<stdin>',cls_termination__basic__simps_I1_J_0) ).

fof(c_0_261_262,axiom,
    ! [X64,X40,X24] :
      ( c_HOL_Oord__class_Oless(X24,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X40),X64),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X24,X64,tc_nat) ),
    file('<stdin>',cls_termination__basic__simps_I2_J_0) ).

fof(c_0_262_263,axiom,
    ! [X10,X15,X16] :
      ( c_HOL_Oord__class_Oless(X16,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X10),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X16,X15,tc_nat) ),
    file('<stdin>',cls_trans__less__add1_0) ).

fof(c_0_263_264,axiom,
    ! [X10,X15,X16] :
      ( c_HOL_Oord__class_Oless(X16,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X10),X15),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X16,X15,tc_nat) ),
    file('<stdin>',cls_trans__less__add2_0) ).

fof(c_0_264_265,axiom,
    ! [X40,X24,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_Orderings_Oord__class_Omax(X24,c_Orderings_Oord__class_Omax(X24,X40,X3),X3) = c_Orderings_Oord__class_Omax(X24,X40,X3) ),
    file('<stdin>',cls_min__max_Osup__left__idem_0) ).

fof(c_0_265_266,axiom,
    ! [X27,X16] :
      ( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_Olift,X27),X16)))
      | ~ hBOOL(hAPP(c_InductTermi_OIT,X27)) ),
    file('<stdin>',cls_lift__IT_0) ).

fof(c_0_266_267,axiom,
    ! [X18,X25,X16] :
      ( c_Lambda_Oliftn(X18,c_Lambda_OdB_OVar(X16),X25) = c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),X18))
      | c_HOL_Oord__class_Oless(X16,X25,tc_nat) ),
    file('<stdin>',cls_liftn_Osimps_I1_J_1) ).

fof(c_0_267_268,axiom,
    ! [X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Oone__class_Oone(X3)),c_HOL_Oone__class_Oone(X3)),X3) ),
    file('<stdin>',cls_zero__less__two_0) ).

fof(c_0_268_269,axiom,
    ! [X43,X24,X3] :
      ( ~ class_OrderedGroup_Omonoid__add(X3)
      | c_List_Olistsum(c_List_Olist_OCons(X24,X43,X3),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X24),c_List_Olistsum(X43,X3)) ),
    file('<stdin>',cls_listsum_Osimps_I2_J_0) ).

fof(c_0_269_270,axiom,
    ! [X40,X24,X3] :
      ( ~ class_Orderings_Opreorder(X3)
      | c_HOL_Oord__class_Oless(X24,X40,X3)
      | c_lessequals(X40,X24,X3)
      | ~ c_lessequals(X24,X40,X3) ),
    file('<stdin>',cls_less__le__not__le_2) ).

fof(c_0_270_271,axiom,
    ! [X25,X16] :
      ( hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(X16)),X25) = c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),c_HOL_Oone__class_Oone(tc_nat)))
      | c_HOL_Oord__class_Oless(X16,X25,tc_nat) ),
    file('<stdin>',cls_lift_Osimps_I1_J_1) ).

fof(c_0_271_272,axiom,
    ! [X18,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X18,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Nat_Osemiring__1__class_Oof__nat(X18,X3),X3) ),
    file('<stdin>',cls_of__nat__0__less__iff_0) ).

fof(c_0_272_273,axiom,
    ! [X26,X15,X16] :
      ( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X15)),X26),X16) = c_Lambda_OdB_OVar(X15)
      | ~ c_HOL_Oord__class_Oless(X15,X16,tc_nat) ),
    file('<stdin>',cls_subst__lt_0) ).

fof(c_0_273_274,axiom,
    ! [X18,X10,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X10,X3),c_Nat_Osemiring__1__class_Oof__nat(X18,X3),X3)
      | ~ c_HOL_Oord__class_Oless(X10,X18,tc_nat) ),
    file('<stdin>',cls_of__nat__less__iff_1) ).

fof(c_0_274_275,axiom,
    ! [X27] :
      ( c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X27,tc_Lambda_OdB)
      | ~ hBOOL(hAPP(c_InductTermi_OIT,X27)) ),
    file('<stdin>',cls_IT__implies__termi_0) ).

fof(c_0_275_276,axiom,
    ! [X18,X10,X34] :
      ( hBOOL(hAPP(hAPP(X34,X18),X10))
      | c_HOL_Oord__class_Oless(X18,X10,tc_nat)
      | X10 = X18
      | c_HOL_Oord__class_Oless(X10,X18,tc_nat) ),
    file('<stdin>',cls_nat__less__cases_0) ).

fof(c_0_276_277,axiom,
    ! [X18,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Nat_Osemiring__1__class_Oof__nat(X18,X3),X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X18,tc_nat) ),
    file('<stdin>',cls_of__nat__0__less__iff_1) ).

fof(c_0_277_278,axiom,
    ! [X40,X24,X3] :
      ( ~ class_Orderings_Oorder(X3)
      | X24 = X40
      | ~ c_lessequals(X24,X40,X3)
      | ~ c_lessequals(X40,X24,X3) ),
    file('<stdin>',cls_order__antisym__conv_0) ).

fof(c_0_278_279,axiom,
    ! [X40,X24,X3] :
      ( ~ class_Orderings_Oorder(X3)
      | X24 = X40
      | ~ c_lessequals(X40,X24,X3)
      | ~ c_lessequals(X24,X40,X3) ),
    file('<stdin>',cls_order__antisym_0) ).

fof(c_0_279_280,axiom,
    ! [X40,X24,X3] :
      ( ~ class_Orderings_Oorder(X3)
      | X24 = X40
      | ~ c_lessequals(X40,X24,X3)
      | ~ c_lessequals(X24,X40,X3) ),
    file('<stdin>',cls_order__eq__iff_2) ).

fof(c_0_280_281,axiom,
    ! [X64,X40,X24,X3] :
      ( ~ class_Ring__and__Field_Oidom(X3)
      | ~ class_Int_Onumber__ring(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X24),X40) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X24),X64)
      | X40 = X64 ),
    file('<stdin>',cls_class__ringb_Oadd__cancel_0) ).

fof(c_0_281_282,axiom,
    ! [X29] :
      ( hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__5(X29)))
      | hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X29)))
      | c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X29),tc_Lambda_OdB)
      | ~ hBOOL(hAPP(c_InductTermi_OIT,X29)) ),
    file('<stdin>',cls_IT_Ocases_11) ).

fof(c_0_282_283,axiom,
    ! [X24,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | ~ c_lessequals(X24,X24,X3)
      | ~ c_HOL_Oord__class_Oless(X24,X24,X3) ),
    file('<stdin>',cls_linorder__antisym__conv2_1) ).

fof(c_0_283_284,axiom,
    ! [X40,X24,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | ~ c_HOL_Oord__class_Oless(X24,X40,X3)
      | ~ c_lessequals(X40,X24,X3) ),
    file('<stdin>',cls_linorder__not__less_1) ).

fof(c_0_284_285,axiom,
    ! [X40,X24,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | ~ c_lessequals(X24,X40,X3)
      | ~ c_HOL_Oord__class_Oless(X40,X24,X3) ),
    file('<stdin>',cls_linorder__not__le_1) ).

fof(c_0_285_286,axiom,
    ! [X40,X24,X3] :
      ( ~ class_Orderings_Opreorder(X3)
      | ~ c_lessequals(X40,X24,X3)
      | ~ c_HOL_Oord__class_Oless(X24,X40,X3) ),
    file('<stdin>',cls_less__le__not__le_1) ).

fof(c_0_286_287,axiom,
    ! [X49,X29,X3] :
      ( ~ class_Orderings_Oorder(X3)
      | ~ c_HOL_Oord__class_Oless(X29,X49,X3)
      | ~ c_HOL_Oord__class_Oless(X49,X29,X3) ),
    file('<stdin>',cls_xt1_I9_J_0) ).

fof(c_0_287_288,axiom,
    ! [X40,X24,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | ~ c_HOL_Oord__class_Oless(X24,X40,X3)
      | ~ c_HOL_Oord__class_Oless(X40,X24,X3) ),
    file('<stdin>',cls_not__less__iff__gr__or__eq_1) ).

fof(c_0_288_289,axiom,
    ! [X40,X24,X3] :
      ( ~ class_Orderings_Opreorder(X3)
      | ~ c_HOL_Oord__class_Oless(X40,X24,X3)
      | ~ c_HOL_Oord__class_Oless(X24,X40,X3) ),
    file('<stdin>',cls_order__less__asym_0) ).

fof(c_0_289_290,axiom,
    ! [X49,X29,X3] :
      ( ~ class_Orderings_Opreorder(X3)
      | ~ c_HOL_Oord__class_Oless(X49,X29,X3)
      | ~ c_HOL_Oord__class_Oless(X29,X49,X3) ),
    file('<stdin>',cls_order__less__asym_H_0) ).

fof(c_0_290_291,axiom,
    ! [X40,X24,X18,X10,X3] :
      ( c_List_Oreplicate(X10,X24,X3) != c_List_Oreplicate(X18,X40,X3)
      | X24 = X40
      | X10 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('<stdin>',cls_replicate__eq__replicate_1) ).

fof(c_0_291_292,axiom,
    ! [X29,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_HOL_Oord__class_Oless(X29,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),c_HOL_Oone__class_Oone(X3)),X3) ),
    file('<stdin>',cls_less__add__one_0) ).

fof(c_0_292_293,axiom,
    ! [X40,X24,X18,X10,X3] :
      ( c_List_Oreplicate(X10,X24,X3) != c_List_Oreplicate(X18,X40,X3)
      | X10 = X18 ),
    file('<stdin>',cls_replicate__eq__replicate_0) ).

fof(c_0_293_294,axiom,
    ! [X28,X51,X43,X3] :
      ( c_List_Oappend(X51,X43,X3) != c_List_Oappend(X28,X43,X3)
      | X51 = X28 ),
    file('<stdin>',cls_append__same__eq_0) ).

fof(c_0_294_295,axiom,
    ! [X28,X51,X43,X3] :
      ( c_List_Oappend(X43,X51,X3) != c_List_Oappend(X43,X28,X3)
      | X51 = X28 ),
    file('<stdin>',cls_same__append__eq_0) ).

fof(c_0_295_296,axiom,
    ! [X50,X49,X29,X3] :
      ( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),X49) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),X50)
      | X49 = X50 ),
    file('<stdin>',cls_add__imp__eq_0) ).

fof(c_0_296_297,axiom,
    ! [X50,X49,X29,X3] :
      ( ~ class_OrderedGroup_Ocancel__semigroup__add(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),X49) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),X50)
      | X49 = X50 ),
    file('<stdin>',cls_add__left__cancel_0) ).

fof(c_0_297_298,axiom,
    ! [X50,X49,X29,X3] :
      ( ~ class_OrderedGroup_Ocancel__semigroup__add(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X49),X29) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X50),X29)
      | X49 = X50 ),
    file('<stdin>',cls_add__right__cancel_0) ).

fof(c_0_298_299,axiom,
    ! [X55,X56,X57,X29,X3] :
      ( c_List_Olist_OCons(X29,X56,X3) != c_List_Olist_OCons(X57,X55,X3)
      | X29 = X57 ),
    file('<stdin>',cls_list_Oinject_0) ).

fof(c_0_299_300,axiom,
    ! [X55,X56,X57,X29,X3] :
      ( c_List_Olist_OCons(X29,X56,X3) != c_List_Olist_OCons(X57,X55,X3)
      | X56 = X55 ),
    file('<stdin>',cls_list_Oinject_1) ).

fof(c_0_300_301,axiom,
    ! [X24,X7] :
      ( c_HOL_Oord__class_Oless(X24,X24,tc_nat)
      | c_Lambda_Osubstn(c_Lambda_OdB_OVar(X24),X7,X24) = c_Lambda_Oliftn(X24,X7,c_HOL_Ozero__class_Ozero(tc_nat)) ),
    file('<stdin>',cls_substn_Osimps_I1_J_1) ).

fof(c_0_301_302,axiom,
    ! [X7,X25,X16] :
      ( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X16)),X7),X25) = c_Lambda_OdB_OVar(X16)
      | X16 = X25
      | c_HOL_Oord__class_Oless(X25,X16,tc_nat) ),
    file('<stdin>',cls_subst__Var_2) ).

fof(c_0_302_303,axiom,
    ! [X1,X2,X3] :
      ( X2 = X1
      | ~ hBOOL(hAPP(hAPP(c_fequal(X3),X2),X1)) ),
    file('<stdin>',cls_ATP__Linkup_Ofequal__imp__equal_0) ).

fof(c_0_303_304,axiom,
    ! [X40,X24,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_lessequals(X40,c_Orderings_Oord__class_Omax(X24,X40,X3),X3) ),
    file('<stdin>',cls_le__maxI2_0) ).

fof(c_0_304_305,axiom,
    ! [X40,X24,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_lessequals(X24,c_Orderings_Oord__class_Omax(X24,X40,X3),X3) ),
    file('<stdin>',cls_le__maxI1_0) ).

fof(c_0_305_306,axiom,
    ! [X24,X7] :
      ( c_HOL_Oord__class_Oless(X24,X24,tc_nat)
      | hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X24)),X7),X24) = X7 ),
    file('<stdin>',cls_subst__Var_1) ).

fof(c_0_306_307,axiom,
    ! [X29] :
      ( hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__5(X29)))
      | X29 = c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X29))
      | c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X29),tc_Lambda_OdB)
      | ~ hBOOL(hAPP(c_InductTermi_OIT,X29)) ),
    file('<stdin>',cls_IT_Ocases_8) ).

fof(c_0_307_308,axiom,
    ! [X40,X24,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | X24 = X40
      | c_HOL_Oord__class_Oless(X24,X40,X3)
      | ~ c_lessequals(X24,X40,X3) ),
    file('<stdin>',cls_linorder__antisym__conv2_0) ).

fof(c_0_308_309,axiom,
    ! [X40,X24,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | X24 = X40
      | ~ c_lessequals(X24,X40,X3)
      | c_HOL_Oord__class_Oless(X24,X40,X3) ),
    file('<stdin>',cls_linorder__antisym__conv1_0) ).

fof(c_0_309_310,axiom,
    ! [X49,X29,X3] :
      ( ~ class_Orderings_Oorder(X3)
      | c_HOL_Oord__class_Oless(X29,X49,X3)
      | ~ c_lessequals(X29,X49,X3)
      | X29 = X49 ),
    file('<stdin>',cls_order__neq__le__trans_0) ).

fof(c_0_310_311,axiom,
    ! [X49,X29,X3] :
      ( ~ class_Orderings_Oorder(X3)
      | c_HOL_Oord__class_Oless(X29,X49,X3)
      | X29 = X49
      | ~ c_lessequals(X29,X49,X3) ),
    file('<stdin>',cls_order__le__neq__trans_0) ).

fof(c_0_311_312,axiom,
    ! [X40,X24,X3] :
      ( ~ class_Orderings_Oorder(X3)
      | c_HOL_Oord__class_Oless(X24,X40,X3)
      | X24 = X40
      | ~ c_lessequals(X24,X40,X3) ),
    file('<stdin>',cls_order__less__le_2) ).

fof(c_0_312_313,axiom,
    ! [X40,X24,X3] :
      ( ~ class_Orderings_Oorder(X3)
      | X24 = X40
      | c_HOL_Oord__class_Oless(X24,X40,X3)
      | ~ c_lessequals(X24,X40,X3) ),
    file('<stdin>',cls_order__le__less_0) ).

fof(c_0_313_314,axiom,
    ! [X49,X29,X3] :
      ( ~ class_Orderings_Oorder(X3)
      | c_HOL_Oord__class_Oless(X49,X29,X3)
      | ~ c_lessequals(X49,X29,X3)
      | X29 = X49 ),
    file('<stdin>',cls_xt1_I12_J_0) ).

fof(c_0_314_315,axiom,
    ! [X49,X29,X3] :
      ( ~ class_Orderings_Oorder(X3)
      | c_HOL_Oord__class_Oless(X49,X29,X3)
      | X29 = X49
      | ~ c_lessequals(X49,X29,X3) ),
    file('<stdin>',cls_xt1_I11_J_0) ).

fof(c_0_315_316,axiom,
    ! [X40,X24,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_Orderings_Oord__class_Omax(X24,X40,X3) != X40
      | c_lessequals(X24,X40,X3) ),
    file('<stdin>',cls_min__max_Ole__iff__sup_1) ).

fof(c_0_316_317,axiom,
    ! [X40,X24,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_Orderings_Oord__class_Omax(X24,X40,X3) = X40
      | ~ c_lessequals(X24,X40,X3) ),
    file('<stdin>',cls_min__max_Ole__iff__sup_0) ).

fof(c_0_317_318,axiom,
    ! [X40,X24,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_Orderings_Oord__class_Omax(X24,X40,X3) = X24
      | ~ c_lessequals(X40,X24,X3) ),
    file('<stdin>',cls_min__max_Osup__absorb1_0) ).

fof(c_0_318_319,axiom,
    ! [X18,X25,X16] :
      ( c_Lambda_Oliftn(X18,c_Lambda_OdB_OVar(X16),X25) = c_Lambda_OdB_OVar(X16)
      | ~ c_HOL_Oord__class_Oless(X16,X25,tc_nat) ),
    file('<stdin>',cls_liftn_Osimps_I1_J_0) ).

fof(c_0_319_320,axiom,
    ! [X40,X24,X3] :
      ( ~ class_Orderings_Opreorder(X3)
      | c_lessequals(X24,X40,X3)
      | ~ c_HOL_Oord__class_Oless(X24,X40,X3) ),
    file('<stdin>',cls_order__less__imp__le_0) ).

fof(c_0_320_321,axiom,
    ! [X40,X24,X3] :
      ( ~ class_Orderings_Oorder(X3)
      | c_lessequals(X24,X40,X3)
      | ~ c_HOL_Oord__class_Oless(X24,X40,X3) ),
    file('<stdin>',cls_order__le__less_1) ).

fof(c_0_321_322,axiom,
    ! [X18,X10,X25] :
      ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X10),X25) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X25)
      | X10 = X18 ),
    file('<stdin>',cls_nat__add__right__cancel_0) ).

fof(c_0_322_323,axiom,
    ! [X64,X40,X24] :
      ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X24),X40) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X24),X64)
      | X40 = X64 ),
    file('<stdin>',cls_natgb_Oadd__cancel_0) ).

fof(c_0_323_324,axiom,
    ! [X18,X10,X25] :
      ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X25),X10) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X25),X18)
      | X10 = X18 ),
    file('<stdin>',cls_nat__add__left__cancel_0) ).

fof(c_0_324_325,axiom,
    ! [X10,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X10,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
    file('<stdin>',cls_of__nat__less__0__iff_0) ).

fof(c_0_325_326,axiom,
    ! [X25,X16] :
      ( hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(X16)),X25) = c_Lambda_OdB_OVar(X16)
      | ~ c_HOL_Oord__class_Oless(X16,X25,tc_nat) ),
    file('<stdin>',cls_lift_Osimps_I1_J_0) ).

fof(c_0_326_327,axiom,
    ! [X38,X39,X29,X3] :
      ( hAPP(hAPP(X39,X29),X38) = X29
      | ~ c_OrderedGroup_Omonoid__add(X38,X39,X3) ),
    file('<stdin>',cls_monoid__add_Oadd__0__right_0) ).

fof(c_0_327_328,axiom,
    ! [X38,X39,X29,X3] :
      ( hAPP(hAPP(X39,X38),X29) = X29
      | ~ c_OrderedGroup_Omonoid__add(X38,X39,X3) ),
    file('<stdin>',cls_monoid__add_Oadd__0__left_0) ).

fof(c_0_328_329,axiom,
    ! [X18,X29,X3] :
      ( ~ class_Ring__and__Field_Ozero__neq__one(X3)
      | ~ class_Ring__and__Field_Ono__zero__divisors(X3)
      | ~ class_Ring__and__Field_Omult__zero(X3)
      | ~ class_Power_Opower(X3)
      | c_Power_Opower__class_Opower(X29,X18,X3) != c_HOL_Ozero__class_Ozero(X3)
      | X29 = c_HOL_Ozero__class_Ozero(X3) ),
    file('<stdin>',cls_power__eq__0__iff_0) ).

fof(c_0_329_330,axiom,
    ! [X29,X3] :
      ( ~ class_Ring__and__Field_Ozero__neq__one(X3)
      | ~ class_Ring__and__Field_Ono__zero__divisors(X3)
      | ~ class_Ring__and__Field_Omult__zero(X3)
      | ~ class_Power_Opower(X3)
      | c_Power_Opower__class_Opower(X29,c_HOL_Ozero__class_Ozero(tc_nat),X3) != c_HOL_Ozero__class_Ozero(X3) ),
    file('<stdin>',cls_power__eq__0__iff_1) ).

fof(c_0_330_331,axiom,
    ! [X7,X25,X16] :
      ( c_Lambda_Osubstn(c_Lambda_OdB_OVar(X16),X7,X25) = c_Lambda_OdB_OVar(X16)
      | X16 = X25
      | c_HOL_Oord__class_Oless(X25,X16,tc_nat) ),
    file('<stdin>',cls_substn_Osimps_I1_J_2) ).

fof(c_0_331_332,axiom,
    ! [X40,X24,X3] :
      ( ~ class_Ring__and__Field_Oordered__idom(X3)
      | c_HOL_Oord__class_Oless(X40,X24,X3)
      | c_HOL_Oord__class_Oless(X24,X40,X3)
      | X24 = X40 ),
    file('<stdin>',cls_linorder__neqE__ordered__idom_0) ).

fof(c_0_332_333,axiom,
    ! [X40,X24,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | X24 = X40
      | c_HOL_Oord__class_Oless(X40,X24,X3)
      | c_HOL_Oord__class_Oless(X24,X40,X3) ),
    file('<stdin>',cls_not__less__iff__gr__or__eq_0) ).

fof(c_0_333_334,axiom,
    ! [X40,X24,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_HOL_Oord__class_Oless(X40,X24,X3)
      | c_HOL_Oord__class_Oless(X24,X40,X3)
      | X24 = X40 ),
    file('<stdin>',cls_linorder__neqE_0) ).

fof(c_0_334_335,axiom,
    ! [X40,X24,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_HOL_Oord__class_Oless(X40,X24,X3)
      | X24 = X40
      | c_HOL_Oord__class_Oless(X24,X40,X3) ),
    file('<stdin>',cls_linorder__less__linear_0) ).

fof(c_0_335_336,axiom,
    ! [X40,X24,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | X24 = X40
      | c_HOL_Oord__class_Oless(X24,X40,X3)
      | c_HOL_Oord__class_Oless(X40,X24,X3) ),
    file('<stdin>',cls_linorder__antisym__conv3_0) ).

fof(c_0_336_337,axiom,
    ! [X11,X12,X13,X14] :
      ( hAPP(hAPP(c_Lambda_OdB_OApp,X14),X12) != hAPP(hAPP(c_Lambda_OdB_OApp,X13),X11)
      | X14 = X13 ),
    file('<stdin>',cls_dB_Osimps_I2_J_0) ).

fof(c_0_337_338,axiom,
    ! [X11,X12,X13,X14] :
      ( hAPP(hAPP(c_Lambda_OdB_OApp,X14),X12) != hAPP(hAPP(c_Lambda_OdB_OApp,X13),X11)
      | X12 = X11 ),
    file('<stdin>',cls_dB_Osimps_I2_J_1) ).

fof(c_0_338_339,axiom,
    ! [X40,X24,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_lessequals(X40,X24,X3)
      | c_lessequals(X24,X40,X3) ),
    file('<stdin>',cls_linorder__linear_0) ).

fof(c_0_339_340,axiom,
    ! [X40,X24,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_HOL_Oord__class_Oless(X24,X40,X3)
      | c_lessequals(X40,X24,X3) ),
    file('<stdin>',cls_not__leE_0) ).

fof(c_0_340_341,axiom,
    ! [X24,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_HOL_Oord__class_Oless(X24,X24,X3)
      | c_lessequals(X24,X24,X3) ),
    file('<stdin>',cls_linorder__antisym__conv1_1) ).

fof(c_0_341_342,axiom,
    ! [X40,X24,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_lessequals(X40,X24,X3)
      | c_HOL_Oord__class_Oless(X24,X40,X3) ),
    file('<stdin>',cls_linorder__not__less_0) ).

fof(c_0_342_343,axiom,
    ! [X40,X24,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_HOL_Oord__class_Oless(X40,X24,X3)
      | c_lessequals(X24,X40,X3) ),
    file('<stdin>',cls_linorder__not__le_0) ).

fof(c_0_343_344,axiom,
    ! [X40,X24,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_Orderings_Oord__class_Omax(X24,X40,X3) = c_Orderings_Oord__class_Omax(X40,X24,X3) ),
    file('<stdin>',cls_min__max_Osup__commute_0) ).

fof(c_0_344_345,axiom,
    ! [X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
    file('<stdin>',cls_not__one__less__zero_0) ).

fof(c_0_345_346,axiom,
    ! [X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | ~ c_lessequals(c_HOL_Oone__class_Oone(X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
    file('<stdin>',cls_not__one__le__zero_0) ).

fof(c_0_346_347,axiom,
    ! [X50,X29,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),X50) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X50),X29) ),
    file('<stdin>',cls_class__semiring_Osemiring__rules_I24_J_0) ).

fof(c_0_347_348,axiom,
    ! [X49,X29,X3] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),X49) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X49),X29) ),
    file('<stdin>',cls_comm__monoid__add_Omult__commute_0) ).

fof(c_0_348_349,axiom,
    ! [X40,X24,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X24),X40) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X40),X24) ),
    file('<stdin>',cls_class__semiring_Oadd__c_0) ).

fof(c_0_349_350,axiom,
    ! [X16,X21,X23] :
      ( hAPP(X21,X16) = X23
      | ~ c_Type_Otyping(X21,c_Lambda_OdB_OVar(X16),X23) ),
    file('<stdin>',cls_typing__elims_I1_J_0) ).

fof(c_0_350_351,axiom,
    ! [X18,X10] :
      ( c_HOL_Oord__class_Oless(X18,X10,tc_nat)
      | c_HOL_Oord__class_Oless(X10,X18,tc_nat)
      | X10 = X18 ),
    file('<stdin>',cls_nat__neq__iff_0) ).

fof(c_0_351_352,axiom,
    ! [X40,X24] :
      ( c_HOL_Oord__class_Oless(X40,X24,tc_nat)
      | c_HOL_Oord__class_Oless(X24,X40,tc_nat)
      | X24 = X40 ),
    file('<stdin>',cls_linorder__neqE__nat_0) ).

fof(c_0_352_353,axiom,
    ! [X18,X29,X3] :
      ( ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X3)
      | c_Power_Opower__class_Opower(X29,X18,X3) != c_HOL_Ozero__class_Ozero(X3)
      | X29 = c_HOL_Ozero__class_Ozero(X3) ),
    file('<stdin>',cls_field__power__not__zero_0) ).

fof(c_0_353_354,axiom,
    ! [X24,X29,X3] :
      ( ~ class_Ring__and__Field_Oidom(X3)
      | ~ class_Int_Onumber__ring(X3)
      | X24 != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X24),X29)
      | X29 = c_HOL_Ozero__class_Ozero(X3) ),
    file('<stdin>',cls_class__ringb_Oadd__r0__iff_0) ).

fof(c_0_354_355,axiom,
    ! [X29,X3] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),X29) != c_HOL_Ozero__class_Ozero(X3)
      | X29 = c_HOL_Ozero__class_Ozero(X3) ),
    file('<stdin>',cls_double__eq__0__iff_0) ).

fof(c_0_355_356,axiom,
    ! [X51,X43,X3] :
      ( c_List_Olist_ONil(X3) != c_List_Oappend(X43,X51,X3)
      | X43 = c_List_Olist_ONil(X3) ),
    file('<stdin>',cls_Nil__is__append__conv_0) ).

fof(c_0_356_357,axiom,
    ! [X51,X43,X3] :
      ( c_List_Olist_ONil(X3) != c_List_Oappend(X43,X51,X3)
      | X51 = c_List_Olist_ONil(X3) ),
    file('<stdin>',cls_Nil__is__append__conv_1) ).

fof(c_0_357_358,axiom,
    ! [X51,X43,X3] :
      ( c_List_Oappend(X43,X51,X3) != c_List_Olist_ONil(X3)
      | X43 = c_List_Olist_ONil(X3) ),
    file('<stdin>',cls_append__is__Nil__conv_0) ).

fof(c_0_358_359,axiom,
    ! [X51,X43,X3] :
      ( c_List_Oappend(X43,X51,X3) != c_List_Olist_ONil(X3)
      | X51 = c_List_Olist_ONil(X3) ),
    file('<stdin>',cls_append__is__Nil__conv_1) ).

fof(c_0_359_360,axiom,
    ! [X18,X3] :
      ( ~ class_Ring__and__Field_Ozero__neq__one(X3)
      | ~ class_Ring__and__Field_Ono__zero__divisors(X3)
      | ~ class_Ring__and__Field_Omult__zero(X3)
      | ~ class_Power_Opower(X3)
      | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X3),X18,X3) = c_HOL_Ozero__class_Ozero(X3)
      | X18 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('<stdin>',cls_power__eq__0__iff_2) ).

fof(c_0_360_361,axiom,
    ! [X24,X18,X3] :
      ( c_List_Oreplicate(X18,X24,X3) != c_List_Olist_ONil(X3)
      | X18 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('<stdin>',cls_replicate__empty_0) ).

fof(c_0_361_362,axiom,
    ! [X24,X18,X3] :
      ( c_List_Olist_ONil(X3) != c_List_Oreplicate(X18,X24,X3)
      | X18 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('<stdin>',cls_empty__replicate_0) ).

fof(c_0_362_363,axiom,
    ! [X10,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_Nat_Osemiring__1__class_Oof__nat(X10,X3),X3) ),
    file('<stdin>',cls_zero__le__imp__of__nat_0) ).

fof(c_0_363_364,axiom,
    ! [X18,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_Nat_Osemiring__1__class_Oof__nat(X18,X3),X3) ),
    file('<stdin>',cls_of__nat__0__le__iff_0) ).

fof(c_0_364_365,axiom,
    ! [X24,X3] :
      ( ~ class_Orderings_Oorder(X3)
      | ~ c_HOL_Oord__class_Oless(X24,X24,X3) ),
    file('<stdin>',cls_order__less__le_1) ).

fof(c_0_365_366,axiom,
    ! [X24,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | ~ c_HOL_Oord__class_Oless(X24,X24,X3) ),
    file('<stdin>',cls_linorder__neq__iff_1) ).

fof(c_0_366_367,axiom,
    ! [X24,X3] :
      ( ~ class_Orderings_Opreorder(X3)
      | ~ c_HOL_Oord__class_Oless(X24,X24,X3) ),
    file('<stdin>',cls_order__less__irrefl_0) ).

fof(c_0_367_368,axiom,
    ! [X51,X43,X3] :
      ( c_List_Oappend(X43,X51,X3) != X43
      | X51 = c_List_Olist_ONil(X3) ),
    file('<stdin>',cls_append__self__conv_0) ).

fof(c_0_368_369,axiom,
    ! [X51,X43,X3] :
      ( X43 != c_List_Oappend(X43,X51,X3)
      | X51 = c_List_Olist_ONil(X3) ),
    file('<stdin>',cls_self__append__conv_0) ).

fof(c_0_369_370,axiom,
    ! [X51,X43,X3] :
      ( c_List_Oappend(X43,X51,X3) != X51
      | X43 = c_List_Olist_ONil(X3) ),
    file('<stdin>',cls_append__self__conv2_0) ).

fof(c_0_370_371,axiom,
    ! [X51,X43,X3] :
      ( X51 != c_List_Oappend(X43,X51,X3)
      | X43 = c_List_Olist_ONil(X3) ),
    file('<stdin>',cls_self__append__conv2_0) ).

fof(c_0_371_372,axiom,
    ! [X18,X3] :
      ( ~ class_Ring__and__Field_Osemiring__0(X3)
      | ~ class_Power_Opower(X3)
      | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X3),X18,X3) = c_HOL_Ozero__class_Ozero(X3)
      | X18 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('<stdin>',cls_power__0__left_1) ).

fof(c_0_372_373,axiom,
    ! [X8] :
      ( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(X8)))
      | ~ hBOOL(hAPP(c_InductTermi_OIT,X8)) ),
    file('<stdin>',cls_Lambda_0) ).

fof(c_0_373_374,axiom,
    ! [X3] :
      ( ~ class_Ring__and__Field_Osemiring__0(X3)
      | ~ class_Power_Opower(X3)
      | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(tc_nat),X3) = c_HOL_Oone__class_Oone(X3) ),
    file('<stdin>',cls_power__0__left_0) ).

fof(c_0_374_375,axiom,
    ! [X3] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3)),c_HOL_Ozero__class_Ozero(X3)) = c_HOL_Ozero__class_Ozero(X3) ),
    file('<stdin>',cls_double__eq__0__iff_1) ).

fof(c_0_375_376,axiom,
    ! [X18,X10] :
      ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X10),X18) != c_HOL_Ozero__class_Ozero(tc_nat)
      | X18 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('<stdin>',cls_add__is__0_1) ).

fof(c_0_376_377,axiom,
    ! [X18,X10] :
      ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X10),X18) != c_HOL_Ozero__class_Ozero(tc_nat)
      | X10 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('<stdin>',cls_add__is__0_0) ).

fof(c_0_377_378,axiom,
    ! [X24,X29] :
      ( X24 != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X24),X29)
      | X29 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('<stdin>',cls_natgb_Oadd__r0__iff_0) ).

fof(c_0_378_379,axiom,
    ! [X18,X10] :
      ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X10),X18) != X10
      | X18 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('<stdin>',cls_add__eq__self__zero_0) ).

fof(c_0_379_380,axiom,
    ! [X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oone__class_Oone(X3),X3) ),
    file('<stdin>',cls_zero__less__one_0) ).

fof(c_0_380_381,axiom,
    ! [X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oone__class_Oone(X3),X3) ),
    file('<stdin>',cls_zero__le__one_0) ).

fof(c_0_381_382,axiom,
    ! [X24,X3] :
      ( ~ class_Ring__and__Field_Oidom(X3)
      | ~ class_Int_Onumber__ring(X3)
      | X24 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X24),c_HOL_Ozero__class_Ozero(X3)) ),
    file('<stdin>',cls_class__ringb_Oadd__r0__iff_1) ).

fof(c_0_382_383,axiom,
    ! [X24,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3)),X24) = X24 ),
    file('<stdin>',cls_class__semiring_Oadd__0_0) ).

fof(c_0_383_384,axiom,
    ! [X29,X3] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3)),X29) = X29 ),
    file('<stdin>',cls_comm__monoid__add_Omult__1_0) ).

fof(c_0_384_385,axiom,
    ! [X29,X3] :
      ( ~ class_OrderedGroup_Omonoid__add(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3)),X29) = X29 ),
    file('<stdin>',cls_add__0__left_0) ).

fof(c_0_385_386,axiom,
    ! [X29,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3)),X29) = X29 ),
    file('<stdin>',cls_class__semiring_Osemiring__rules_I5_J_0) ).

fof(c_0_386_387,axiom,
    ! [X18,X3] :
      ( ~ class_OrderedGroup_Omonoid__mult(X3)
      | c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X3),X18,X3) = c_HOL_Oone__class_Oone(X3) ),
    file('<stdin>',cls_power__one_0) ).

fof(c_0_387_388,axiom,
    ! [X29,X3] :
      ( ~ class_Power_Opower(X3)
      | c_Power_Opower__class_Opower(X29,c_HOL_Ozero__class_Ozero(tc_nat),X3) = c_HOL_Oone__class_Oone(X3) ),
    file('<stdin>',cls_power__0_0) ).

fof(c_0_388_389,axiom,
    ! [X24,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_Power_Opower__class_Opower(X24,c_HOL_Ozero__class_Ozero(tc_nat),X3) = c_HOL_Oone__class_Oone(X3) ),
    file('<stdin>',cls_class__semiring_Opwr__0_0) ).

fof(c_0_389_390,axiom,
    ! [X29,X3] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),c_HOL_Ozero__class_Ozero(X3)) = X29 ),
    file('<stdin>',cls_comm__monoid__add_Omult__1__right_0) ).

fof(c_0_390_391,axiom,
    ! [X29,X3] :
      ( ~ class_OrderedGroup_Omonoid__add(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),c_HOL_Ozero__class_Ozero(X3)) = X29 ),
    file('<stdin>',cls_monoid__add__class_Oadd__0__right_0) ).

fof(c_0_391_392,axiom,
    ! [X29,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),c_HOL_Ozero__class_Ozero(X3)) = X29 ),
    file('<stdin>',cls_class__semiring_Osemiring__rules_I6_J_0) ).

fof(c_0_392_393,axiom,
    ! [X29,X3] :
      ( ~ class_OrderedGroup_Omonoid__mult(X3)
      | c_Power_Opower__class_Opower(X29,c_HOL_Oone__class_Oone(tc_nat),X3) = X29 ),
    file('<stdin>',cls_power__one__right_0) ).

fof(c_0_393_394,axiom,
    ! [X24,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_Power_Opower__class_Opower(X24,c_HOL_Oone__class_Oone(tc_nat),X3) = X24 ),
    file('<stdin>',cls_class__semiring_Osemiring__rules_I33_J_0) ).

fof(c_0_394_395,axiom,
    ! [X24,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_Orderings_Oord__class_Omax(X24,X24,X3) = X24 ),
    file('<stdin>',cls_min__max_Osup__idem_0) ).

fof(c_0_395_396,axiom,
    ! [X24,X3] :
      ( ~ class_Orderings_Opreorder(X3)
      | c_lessequals(X24,X24,X3) ),
    file('<stdin>',cls_order__eq__refl_0) ).

fof(c_0_396_397,axiom,
    ! [X24,X3] :
      ( ~ class_Orderings_Oorder(X3)
      | c_lessequals(X24,X24,X3) ),
    file('<stdin>',cls_order__eq__iff_0) ).

fof(c_0_397_398,axiom,
    ! [X18] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X18,tc_nat)
      | X18 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('<stdin>',cls_gr0I_0) ).

fof(c_0_398_399,axiom,
    ! [X18,X10,X3] :
      ( ~ class_Nat_Osemiring__char__0(X3)
      | c_Nat_Osemiring__1__class_Oof__nat(X10,X3) != c_Nat_Osemiring__1__class_Oof__nat(X18,X3)
      | X10 = X18 ),
    file('<stdin>',cls_of__nat__eq__iff_0) ).

fof(c_0_399_400,axiom,
    ! [X4,X5] :
      ( class_Orderings_Opreorder(tc_fun(X4,X5))
      | ~ class_Orderings_Opreorder(X5) ),
    file('<stdin>',clsarity_fun__Orderings_Opreorder) ).

fof(c_0_400_401,axiom,
    ! [X4,X5] :
      ( class_Orderings_Oorder(tc_fun(X4,X5))
      | ~ class_Orderings_Oorder(X5) ),
    file('<stdin>',clsarity_fun__Orderings_Oorder) ).

fof(c_0_401_402,axiom,
    ! [X3] :
      ( ~ class_OrderedGroup_Omonoid__add(X3)
      | c_List_Olistsum(c_List_Olist_ONil(X3),X3) = c_HOL_Ozero__class_Ozero(X3) ),
    file('<stdin>',cls_listsum_Osimps_I1_J_0) ).

fof(c_0_402_403,axiom,
    ! [X3] :
      ( ~ class_Ring__and__Field_Osemiring__1(X3)
      | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),X3) = c_HOL_Oone__class_Oone(X3) ),
    file('<stdin>',cls_of__nat__1_0) ).

fof(c_0_403_404,axiom,
    ! [X3] :
      ( ~ class_Ring__and__Field_Osemiring__1(X3)
      | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X3) = c_HOL_Ozero__class_Ozero(X3) ),
    file('<stdin>',cls_of__nat__0_0) ).

fof(c_0_404_405,axiom,
    ! [X3] :
      ( ~ class_OrderedGroup_Osemigroup__add(X3)
      | c_OrderedGroup_Osemigroup__add(c_HOL_Oplus__class_Oplus(X3),X3) ),
    file('<stdin>',cls_semigroup__add__class_Oaxioms_0) ).

fof(c_0_405_406,axiom,
    ! [X3] :
      ( ~ class_Ring__and__Field_Ozero__neq__one(X3)
      | c_HOL_Oone__class_Oone(X3) != c_HOL_Ozero__class_Ozero(X3) ),
    file('<stdin>',cls_one__neq__zero_0) ).

fof(c_0_406_407,axiom,
    ! [X3] :
      ( ~ class_Ring__and__Field_Ozero__neq__one(X3)
      | c_HOL_Ozero__class_Ozero(X3) != c_HOL_Oone__class_Oone(X3) ),
    file('<stdin>',cls_zero__neq__one_0) ).

fof(c_0_407_408,axiom,
    ! [X63,X59] :
      ( c_Lambda_OdB_OAbs(X59) != c_Lambda_OdB_OAbs(X63)
      | X59 = X63 ),
    file('<stdin>',cls_dB_Osimps_I3_J_0) ).

fof(c_0_408_409,axiom,
    ! [X19,X20] :
      ( c_Lambda_OdB_OVar(X20) != c_Lambda_OdB_OVar(X19)
      | X20 = X19 ),
    file('<stdin>',cls_dB_Osimps_I1_J_0) ).

fof(c_0_409_410,plain,
    ! [X30,X17,X18] :
      ( X30 = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X18),c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(X18,X17,X30),tc_Lambda_OdB,tc_Lambda_OdB)
      | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X18),X17,tc_Lambda_OdB,tc_Lambda_OdB)),X30)) ),
    inference(fof_simplification,[status(thm)],[c_0_0]) ).

fof(c_0_410_411,plain,
    ! [X26,X6,X16,X21,X37,X23] :
      ( c_Type_Otypings(X21,c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,X26,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),X16,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X6,tc_Lambda_OdB,tc_Lambda_OdB),X37)
      | ~ c_Type_Otypings(c_Type_Oshift(X21,X16,X23,tc_Type_Otype),X6,X37)
      | ~ c_Type_Otyping(X21,X26,X23) ),
    inference(fof_simplification,[status(thm)],[c_0_1]) ).

fof(c_0_411_412,plain,
    ! [X36,X6,X16,X21,X22,X37,X23] :
      ( c_Type_Otypings(X21,X36,c_Type_Osko__Type__Xvar__app__types__1__1(X23,X22,X21,X36))
      | ~ c_Type_Otyping(X21,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X16),X6,tc_Lambda_OdB,tc_Lambda_OdB),X22)
      | ~ c_Type_Otypings(X21,X6,X37)
      | ~ c_Type_Otyping(X21,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X16),X6,tc_Lambda_OdB,tc_Lambda_OdB),X36,tc_Lambda_OdB,tc_Lambda_OdB),X23) ),
    inference(fof_simplification,[status(thm)],[c_0_2]) ).

fof(c_0_412_413,plain,
    ! [X30,X17,X18] :
      ( c_ListOrder_Ostep1(c_Lambda_Obeta,X17,c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(X18,X17,X30),tc_Lambda_OdB)
      | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X18),X17,tc_Lambda_OdB,tc_Lambda_OdB)),X30)) ),
    inference(fof_simplification,[status(thm)],[c_0_3]) ).

fof(c_0_413_414,plain,
    ! [X27,X34] :
      ( hBOOL(hAPP(X34,X27))
      | ~ hBOOL(hAPP(X34,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3(X34)),c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__4(X34),tc_Lambda_OdB,tc_Lambda_OdB)))
      | ~ hBOOL(hAPP(X34,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1(X34)),c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2(X34),tc_Lambda_OdB,tc_Lambda_OdB))) ),
    inference(fof_simplification,[status(thm)],[c_0_4]) ).

fof(c_0_414_415,plain,
    ! [X27,X34] :
      ( ~ hBOOL(hAPP(X34,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(c_ListApplication_Osko__ListApplication__Xlem__1__3(X34)),c_ListApplication_Osko__ListApplication__Xlem__1__4(X34),tc_Lambda_OdB,tc_Lambda_OdB)))
      | ~ hBOOL(hAPP(X34,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_ListApplication_Osko__ListApplication__Xlem__1__1(X34)),c_ListApplication_Osko__ListApplication__Xlem__1__2(X34),tc_Lambda_OdB,tc_Lambda_OdB)))
      | hBOOL(hAPP(X34,X27)) ),
    inference(fof_simplification,[status(thm)],[c_0_5]) ).

fof(c_0_415_416,plain,
    ! [X9,X17,X8] :
      ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,X8,X17,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X8,X9,tc_Lambda_OdB,tc_Lambda_OdB)))
      | ~ c_ListOrder_Ostep1(c_Lambda_Obeta,X17,X9,tc_Lambda_OdB) ),
    inference(fof_simplification,[status(thm)],[c_0_6]) ).

fof(c_0_416_417,plain,
    ! [X9,X7,X8] :
      ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,X8,X9,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X7,X9,tc_Lambda_OdB,tc_Lambda_OdB)))
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X8),X7)) ),
    inference(fof_simplification,[status(thm)],[c_0_7]) ).

fof(c_0_417_418,plain,
    ! [X9,X7,X8] :
      ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,X8,X9,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X7,X9,tc_Lambda_OdB,tc_Lambda_OdB)))
      | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X8),X7)) ),
    inference(fof_simplification,[status(thm)],[c_0_8]) ).

fof(c_0_418_419,plain,
    ! [X9,X7,X8] :
      ( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X8)),X7),X9,tc_Lambda_OdB,tc_Lambda_OdB)))
      | ~ hBOOL(hAPP(c_InductTermi_OIT,X7))
      | ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X8),X7),c_HOL_Ozero__class_Ozero(tc_nat)),X9,tc_Lambda_OdB,tc_Lambda_OdB))) ),
    inference(fof_simplification,[status(thm)],[c_0_9]) ).

fof(c_0_419_420,plain,
    ! [X66,X67,X44,X45,X46,X47,X68,X69,X48,X3] :
      ( hAPP(hAPP(X47,hAPP(hAPP(X47,X69),X68)),hAPP(hAPP(X47,X67),X66)) = hAPP(hAPP(X47,X67),hAPP(hAPP(X47,hAPP(hAPP(X47,X69),X68)),X66))
      | ~ c_Groebner__Basis_Ogb__semiring(X48,X47,X46,X45,X44,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_10]) ).

fof(c_0_420_421,plain,
    ! [X44,X45,X46,X47,X62,X50,X49,X48,X29,X3] :
      ( hAPP(hAPP(X48,hAPP(hAPP(X48,X29),X49)),hAPP(hAPP(X48,X50),X62)) = hAPP(hAPP(X48,hAPP(hAPP(X48,X29),X50)),hAPP(hAPP(X48,X49),X62))
      | ~ c_Groebner__Basis_Ogb__semiring(X48,X47,X46,X45,X44,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_11]) ).

fof(c_0_421_422,plain,
    ! [X66,X67,X44,X45,X46,X47,X68,X69,X48,X3] :
      ( hAPP(hAPP(X47,hAPP(hAPP(X47,X69),X68)),hAPP(hAPP(X47,X67),X66)) = hAPP(hAPP(X47,X69),hAPP(hAPP(X47,X68),hAPP(hAPP(X47,X67),X66)))
      | ~ c_Groebner__Basis_Ogb__semiring(X48,X47,X46,X45,X44,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_12]) ).

fof(c_0_422_423,plain,
    ! [X66,X67,X44,X45,X46,X47,X68,X69,X48,X3] :
      ( hAPP(hAPP(X47,hAPP(hAPP(X47,X69),X68)),hAPP(hAPP(X47,X67),X66)) = hAPP(hAPP(X47,hAPP(hAPP(X47,X69),X67)),hAPP(hAPP(X47,X68),X66))
      | ~ c_Groebner__Basis_Ogb__semiring(X48,X47,X46,X45,X44,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_13]) ).

fof(c_0_423_424,plain,
    ! [X40,X24,X44,X45,X70,X46,X47,X48,X3] :
      ( hAPP(hAPP(X46,hAPP(hAPP(X47,X24),X40)),X70) = hAPP(hAPP(X47,hAPP(hAPP(X46,X24),X70)),hAPP(hAPP(X46,X40),X70))
      | ~ c_Groebner__Basis_Ogb__semiring(X48,X47,X46,X45,X44,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_14]) ).

fof(c_0_424_425,plain,
    ! [X44,X45,X46,X47,X50,X49,X48,X29,X3] :
      ( hAPP(hAPP(X47,hAPP(hAPP(X48,X29),X49)),X50) = hAPP(hAPP(X48,hAPP(hAPP(X47,X29),X50)),hAPP(hAPP(X47,X49),X50))
      | ~ c_Groebner__Basis_Ogb__semiring(X48,X47,X46,X45,X44,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_15]) ).

fof(c_0_425_426,plain,
    ! [X44,X45,X46,X47,X10,X49,X48,X29,X3] :
      ( hAPP(hAPP(X48,hAPP(hAPP(X47,X29),X10)),hAPP(hAPP(X47,X49),X10)) = hAPP(hAPP(X47,hAPP(hAPP(X48,X29),X49)),X10)
      | ~ c_Groebner__Basis_Ogb__semiring(X48,X47,X46,X45,X44,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_16]) ).

fof(c_0_426_427,plain,
    ! [X24,X44,X45,X70,X46,X71,X47,X48,X3] :
      ( hAPP(hAPP(X47,hAPP(hAPP(X46,X24),X71)),hAPP(hAPP(X46,X24),X70)) = hAPP(hAPP(X46,X24),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X71),X70))
      | ~ c_Groebner__Basis_Ogb__semiring(X48,X47,X46,X45,X44,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_17]) ).

fof(c_0_427_428,plain,
    ! [X64,X40,X24,X44,X45,X46,X47,X48,X3] :
      ( hAPP(hAPP(X47,X24),hAPP(hAPP(X48,X40),X64)) = hAPP(hAPP(X48,hAPP(hAPP(X47,X24),X40)),hAPP(hAPP(X47,X24),X64))
      | ~ c_Groebner__Basis_Ogb__semiring(X48,X47,X46,X45,X44,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_18]) ).

fof(c_0_428_429,plain,
    ! [X44,X45,X46,X47,X50,X49,X48,X29,X3] :
      ( hAPP(hAPP(X48,hAPP(hAPP(X48,X29),X49)),X50) = hAPP(hAPP(X48,hAPP(hAPP(X48,X29),X50)),X49)
      | ~ c_Groebner__Basis_Ogb__semiring(X48,X47,X46,X45,X44,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_19]) ).

fof(c_0_429_430,plain,
    ! [X67,X44,X45,X46,X47,X68,X69,X48,X3] :
      ( hAPP(hAPP(X47,hAPP(hAPP(X47,X69),X68)),X67) = hAPP(hAPP(X47,hAPP(hAPP(X47,X69),X67)),X68)
      | ~ c_Groebner__Basis_Ogb__semiring(X48,X47,X46,X45,X44,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_20]) ).

fof(c_0_430_431,plain,
    ! [X44,X45,X46,X47,X10,X48,X29,X3] :
      ( hAPP(hAPP(X48,hAPP(hAPP(X47,X29),X10)),X10) = hAPP(hAPP(X47,hAPP(hAPP(X48,X29),X44)),X10)
      | ~ c_Groebner__Basis_Ogb__semiring(X48,X47,X46,X45,X44,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_21]) ).

fof(c_0_431_432,plain,
    ! [X64,X40,X24,X44,X45,X46,X47,X48,X3] :
      ( hAPP(hAPP(X47,X24),hAPP(hAPP(X47,X40),X64)) = hAPP(hAPP(X47,hAPP(hAPP(X47,X24),X40)),X64)
      | ~ c_Groebner__Basis_Ogb__semiring(X48,X47,X46,X45,X44,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_22]) ).

fof(c_0_432_433,plain,
    ! [X64,X40,X24,X44,X45,X46,X47,X48,X3] :
      ( hAPP(hAPP(X48,X24),hAPP(hAPP(X48,X40),X64)) = hAPP(hAPP(X48,hAPP(hAPP(X48,X24),X40)),X64)
      | ~ c_Groebner__Basis_Ogb__semiring(X48,X47,X46,X45,X44,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_23]) ).

fof(c_0_433_434,plain,
    ! [X44,X45,X46,X47,X62,X50,X48,X29,X3] :
      ( hAPP(hAPP(X48,X29),hAPP(hAPP(X48,X50),X62)) = hAPP(hAPP(X48,hAPP(hAPP(X48,X29),X50)),X62)
      | ~ c_Groebner__Basis_Ogb__semiring(X48,X47,X46,X45,X44,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_24]) ).

fof(c_0_434_435,plain,
    ! [X44,X45,X46,X47,X50,X49,X48,X29,X3] :
      ( hAPP(hAPP(X48,hAPP(hAPP(X48,X29),X49)),X50) = hAPP(hAPP(X48,X29),hAPP(hAPP(X48,X49),X50))
      | ~ c_Groebner__Basis_Ogb__semiring(X48,X47,X46,X45,X44,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_25]) ).

fof(c_0_435_436,plain,
    ! [X66,X67,X44,X45,X46,X47,X69,X48,X3] :
      ( hAPP(hAPP(X47,X69),hAPP(hAPP(X47,X67),X66)) = hAPP(hAPP(X47,hAPP(hAPP(X47,X69),X67)),X66)
      | ~ c_Groebner__Basis_Ogb__semiring(X48,X47,X46,X45,X44,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_26]) ).

fof(c_0_436_437,plain,
    ! [X67,X44,X45,X46,X47,X68,X69,X48,X3] :
      ( hAPP(hAPP(X47,hAPP(hAPP(X47,X69),X68)),X67) = hAPP(hAPP(X47,X69),hAPP(hAPP(X47,X68),X67))
      | ~ c_Groebner__Basis_Ogb__semiring(X48,X47,X46,X45,X44,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_27]) ).

fof(c_0_437_438,plain,
    ! [X44,X45,X46,X47,X10,X48,X29,X3] :
      ( hAPP(hAPP(X48,X10),hAPP(hAPP(X47,X29),X10)) = hAPP(hAPP(X47,hAPP(hAPP(X48,X29),X44)),X10)
      | ~ c_Groebner__Basis_Ogb__semiring(X48,X47,X46,X45,X44,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_28]) ).

fof(c_0_438_439,plain,
    ! [X44,X45,X46,X47,X62,X50,X48,X29,X3] :
      ( hAPP(hAPP(X48,X29),hAPP(hAPP(X48,X50),X62)) = hAPP(hAPP(X48,X50),hAPP(hAPP(X48,X29),X62))
      | ~ c_Groebner__Basis_Ogb__semiring(X48,X47,X46,X45,X44,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_29]) ).

fof(c_0_439_440,plain,
    ! [X66,X67,X44,X45,X46,X47,X69,X48,X3] :
      ( hAPP(hAPP(X47,X69),hAPP(hAPP(X47,X67),X66)) = hAPP(hAPP(X47,X67),hAPP(hAPP(X47,X69),X66))
      | ~ c_Groebner__Basis_Ogb__semiring(X48,X47,X46,X45,X44,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_30]) ).

fof(c_0_440_441,plain,
    ! [X44,X45,X46,X47,X10,X48,X3] :
      ( hAPP(hAPP(X48,X10),X10) = hAPP(hAPP(X47,hAPP(hAPP(X48,X44),X44)),X10)
      | ~ c_Groebner__Basis_Ogb__semiring(X48,X47,X46,X45,X44,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_31]) ).

fof(c_0_441_442,plain,
    ! [X40,X24,X44,X45,X46,X47,X48,X3] :
      ( hAPP(hAPP(X47,X24),X40) = hAPP(hAPP(X47,X40),X24)
      | ~ c_Groebner__Basis_Ogb__semiring(X48,X47,X46,X45,X44,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_32]) ).

fof(c_0_442_443,plain,
    ! [X40,X24,X44,X45,X46,X47,X48,X3] :
      ( hAPP(hAPP(X48,X24),X40) = hAPP(hAPP(X48,X40),X24)
      | ~ c_Groebner__Basis_Ogb__semiring(X48,X47,X46,X45,X44,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_33]) ).

fof(c_0_443_444,plain,
    ! [X44,X45,X46,X47,X50,X48,X29,X3] :
      ( hAPP(hAPP(X48,X29),X50) = hAPP(hAPP(X48,X50),X29)
      | ~ c_Groebner__Basis_Ogb__semiring(X48,X47,X46,X45,X44,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_34]) ).

fof(c_0_444_445,plain,
    ! [X44,X45,X46,X47,X49,X48,X29,X3] :
      ( hAPP(hAPP(X47,X29),X49) = hAPP(hAPP(X47,X49),X29)
      | ~ c_Groebner__Basis_Ogb__semiring(X48,X47,X46,X45,X44,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_35]) ).

fof(c_0_445_446,plain,
    ! [X24,X44,X45,X46,X47,X48,X3] :
      ( hAPP(hAPP(X46,X24),c_HOL_Oone__class_Oone(tc_nat)) = X24
      | ~ c_Groebner__Basis_Ogb__semiring(X48,X47,X46,X45,X44,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_36]) ).

fof(c_0_446_447,plain,
    ! [X24,X44,X45,X46,X47,X48,X3] :
      ( hAPP(hAPP(X46,X24),c_HOL_Ozero__class_Ozero(tc_nat)) = X44
      | ~ c_Groebner__Basis_Ogb__semiring(X48,X47,X46,X45,X44,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_37]) ).

fof(c_0_447_448,plain,
    ! [X24,X44,X45,X46,X47,X48,X3] :
      ( hAPP(hAPP(X47,X44),X24) = X24
      | ~ c_Groebner__Basis_Ogb__semiring(X48,X47,X46,X45,X44,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_38]) ).

fof(c_0_448_449,plain,
    ! [X24,X44,X45,X46,X47,X48,X3] :
      ( hAPP(hAPP(X47,X45),X24) = X45
      | ~ c_Groebner__Basis_Ogb__semiring(X48,X47,X46,X45,X44,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_39]) ).

fof(c_0_449_450,plain,
    ! [X24,X44,X45,X46,X47,X48,X3] :
      ( hAPP(hAPP(X48,X45),X24) = X24
      | ~ c_Groebner__Basis_Ogb__semiring(X48,X47,X46,X45,X44,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_40]) ).

fof(c_0_450_451,plain,
    ! [X44,X45,X46,X47,X48,X29,X3] :
      ( hAPP(hAPP(X47,X29),X44) = X29
      | ~ c_Groebner__Basis_Ogb__semiring(X48,X47,X46,X45,X44,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_41]) ).

fof(c_0_451_452,plain,
    ! [X44,X45,X46,X47,X48,X29,X3] :
      ( hAPP(hAPP(X47,X44),X29) = X29
      | ~ c_Groebner__Basis_Ogb__semiring(X48,X47,X46,X45,X44,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_42]) ).

fof(c_0_452_453,plain,
    ! [X44,X45,X46,X47,X48,X29,X3] :
      ( hAPP(hAPP(X47,X29),X45) = X45
      | ~ c_Groebner__Basis_Ogb__semiring(X48,X47,X46,X45,X44,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_43]) ).

fof(c_0_453_454,plain,
    ! [X44,X45,X46,X47,X48,X29,X3] :
      ( hAPP(hAPP(X47,X45),X29) = X45
      | ~ c_Groebner__Basis_Ogb__semiring(X48,X47,X46,X45,X44,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_44]) ).

fof(c_0_454_455,plain,
    ! [X44,X45,X46,X47,X48,X29,X3] :
      ( hAPP(hAPP(X48,X29),X45) = X29
      | ~ c_Groebner__Basis_Ogb__semiring(X48,X47,X46,X45,X44,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_45]) ).

fof(c_0_455_456,plain,
    ! [X44,X45,X46,X47,X48,X29,X3] :
      ( hAPP(hAPP(X48,X45),X29) = X29
      | ~ c_Groebner__Basis_Ogb__semiring(X48,X47,X46,X45,X44,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_46]) ).

fof(c_0_456_457,plain,
    ! [X41,X42,X31,X32,X33,X34] :
      ( ~ hBOOL(hAPP(X34,c_Lambda_OdB_OdB__case(X33,X32,X31,hAPP(hAPP(c_Lambda_OdB_OApp,X42),X41),t_a)))
      | hBOOL(hAPP(X34,hAPP(hAPP(X32,X42),X41))) ),
    inference(fof_simplification,[status(thm)],[c_0_47]) ).

fof(c_0_457_458,plain,
    ! [X31,X32,X33,X12,X14,X34] :
      ( ~ hBOOL(hAPP(X34,c_Lambda_OdB_OdB__case(X33,X32,X31,hAPP(hAPP(c_Lambda_OdB_OApp,X14),X12),t_a)))
      | hBOOL(hAPP(X34,hAPP(hAPP(X32,X14),X12))) ),
    inference(fof_simplification,[status(thm)],[c_0_48]) ).

fof(c_0_458_459,plain,
    ! [X27,X34] :
      ( hBOOL(hAPP(X34,c_ListApplication_Osko__ListApplication__Xlem__1__3(X34)))
      | ~ hBOOL(hAPP(X34,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_ListApplication_Osko__ListApplication__Xlem__1__1(X34)),c_ListApplication_Osko__ListApplication__Xlem__1__2(X34),tc_Lambda_OdB,tc_Lambda_OdB)))
      | hBOOL(hAPP(X34,X27)) ),
    inference(fof_simplification,[status(thm)],[c_0_49]) ).

fof(c_0_459_460,plain,
    ! [X27,X34] :
      ( hBOOL(hAPP(X34,X27))
      | hBOOL(hAPP(X34,c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3(X34)))
      | ~ hBOOL(hAPP(X34,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1(X34)),c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2(X34),tc_Lambda_OdB,tc_Lambda_OdB))) ),
    inference(fof_simplification,[status(thm)],[c_0_50]) ).

fof(c_0_460_461,plain,
    ! [X6,X16,X21,X22,X23] :
      ( X23 = X22
      | ~ c_Type_Otyping(X21,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X16),X6,tc_Lambda_OdB,tc_Lambda_OdB),X22)
      | ~ c_Type_Otyping(X21,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X16),X6,tc_Lambda_OdB,tc_Lambda_OdB),X23) ),
    inference(fof_simplification,[status(thm)],[c_0_51]) ).

fof(c_0_461_462,plain,
    ! [X31,X32,X33,X59,X34] :
      ( ~ hBOOL(hAPP(X34,c_Lambda_OdB_OdB__case(X33,X32,X31,c_Lambda_OdB_OAbs(X59),t_a)))
      | hBOOL(hAPP(X34,hAPP(X31,X59))) ),
    inference(fof_simplification,[status(thm)],[c_0_52]) ).

fof(c_0_462_463,plain,
    ! [X58,X31,X32,X33,X34] :
      ( ~ hBOOL(hAPP(X34,c_Lambda_OdB_OdB__case(X33,X32,X31,c_Lambda_OdB_OAbs(X58),t_a)))
      | hBOOL(hAPP(X34,hAPP(X31,X58))) ),
    inference(fof_simplification,[status(thm)],[c_0_53]) ).

fof(c_0_463_464,plain,
    ! [X35,X31,X32,X33,X34] :
      ( ~ hBOOL(hAPP(X34,c_Lambda_OdB_OdB__case(X33,X32,X31,c_Lambda_OdB_OVar(X35),t_a)))
      | hBOOL(hAPP(X34,hAPP(X33,X35))) ),
    inference(fof_simplification,[status(thm)],[c_0_54]) ).

fof(c_0_464_465,plain,
    ! [X20,X31,X32,X33,X34] :
      ( ~ hBOOL(hAPP(X34,c_Lambda_OdB_OdB__case(X33,X32,X31,c_Lambda_OdB_OVar(X20),t_a)))
      | hBOOL(hAPP(X34,hAPP(X33,X20))) ),
    inference(fof_simplification,[status(thm)],[c_0_55]) ).

fof(c_0_465_466,plain,
    ! [X9,X7,X8] :
      ( ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X8),X7),c_HOL_Ozero__class_Ozero(tc_nat)),X9,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)
      | ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X7,tc_Lambda_OdB)
      | c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X8)),X7),X9,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB) ),
    inference(fof_simplification,[status(thm)],[c_0_56]) ).

fof(c_0_466_467,plain,
    ! [X29] :
      ( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_sko__InductTermi__XIT__Xcases__4(X29)),v_sko__InductTermi__XIT__Xcases__5(X29)),c_HOL_Ozero__class_Ozero(tc_nat)),v_sko__InductTermi__XIT__Xcases__6(X29),tc_Lambda_OdB,tc_Lambda_OdB)))
      | hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X29)))
      | X29 = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X29)),v_sko__InductTermi__XIT__Xcases__1(X29),tc_Lambda_OdB,tc_Lambda_OdB)
      | ~ hBOOL(hAPP(c_InductTermi_OIT,X29)) ),
    inference(fof_simplification,[status(thm)],[c_0_57]) ).

fof(c_0_467_468,plain,
    ! [X29] :
      ( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_sko__InductTermi__XIT__Xcases__4(X29)),v_sko__InductTermi__XIT__Xcases__5(X29)),c_HOL_Ozero__class_Ozero(tc_nat)),v_sko__InductTermi__XIT__Xcases__6(X29),tc_Lambda_OdB,tc_Lambda_OdB)))
      | X29 = c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X29))
      | X29 = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X29)),v_sko__InductTermi__XIT__Xcases__1(X29),tc_Lambda_OdB,tc_Lambda_OdB)
      | ~ hBOOL(hAPP(c_InductTermi_OIT,X29)) ),
    inference(fof_simplification,[status(thm)],[c_0_58]) ).

fof(c_0_468_469,plain,
    ! [X29] :
      ( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_sko__InductTermi__XIT__Xcases__4(X29)),v_sko__InductTermi__XIT__Xcases__5(X29)),c_HOL_Ozero__class_Ozero(tc_nat)),v_sko__InductTermi__XIT__Xcases__6(X29),tc_Lambda_OdB,tc_Lambda_OdB)))
      | hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X29)))
      | c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X29),tc_Lambda_OdB)
      | ~ hBOOL(hAPP(c_InductTermi_OIT,X29)) ),
    inference(fof_simplification,[status(thm)],[c_0_59]) ).

fof(c_0_469_470,plain,
    ! [X29] :
      ( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_sko__InductTermi__XIT__Xcases__4(X29)),v_sko__InductTermi__XIT__Xcases__5(X29)),c_HOL_Ozero__class_Ozero(tc_nat)),v_sko__InductTermi__XIT__Xcases__6(X29),tc_Lambda_OdB,tc_Lambda_OdB)))
      | X29 = c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X29))
      | c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X29),tc_Lambda_OdB)
      | ~ hBOOL(hAPP(c_InductTermi_OIT,X29)) ),
    inference(fof_simplification,[status(thm)],[c_0_60]) ).

fof(c_0_470_471,plain,
    ! [X6,X16,X21,X22,X37] :
      ( c_Type_Otypings(c_Type_Oshift(X21,X16,X22,tc_Type_Otype),c_List_Omap(c_COMBC(c_Lambda_Olift,X16,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X6,tc_Lambda_OdB,tc_Lambda_OdB),X37)
      | ~ c_Type_Otypings(X21,X6,X37) ),
    inference(fof_simplification,[status(thm)],[c_0_61]) ).

fof(c_0_471_472,plain,
    ! [X6] :
      ( c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X6,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)
      | ~ c_List_Olistsp(c_InductTermi_OIT,X6,tc_Lambda_OdB) ),
    inference(fof_simplification,[status(thm)],[c_0_62]) ).

fof(c_0_472_473,plain,
    ! [X17,X18] :
      ( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X18),X17,tc_Lambda_OdB,tc_Lambda_OdB)))
      | ~ c_List_Olistsp(c_InductTermi_OIT,X17,tc_Lambda_OdB) ),
    inference(fof_simplification,[status(thm)],[c_0_63]) ).

fof(c_0_473_474,plain,
    ! [X6,X16,X21,X23] :
      ( c_Type_Otypings(X21,X6,c_Type_Osko__Type__Xvar__app__typesE__1__1(X23,X21,X16,X6))
      | ~ c_Type_Otyping(X21,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X16),X6,tc_Lambda_OdB,tc_Lambda_OdB),X23) ),
    inference(fof_simplification,[status(thm)],[c_0_64]) ).

fof(c_0_474_475,axiom,
    ! [X9,X7,X17,X8] :
      ( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X8),X17,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X7),X9,tc_Lambda_OdB,tc_Lambda_OdB)
      | X8 = X7 ),
    c_0_65 ).

fof(c_0_475_476,axiom,
    ! [X9,X7,X17,X8] :
      ( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X8),X17,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X7),X9,tc_Lambda_OdB,tc_Lambda_OdB)
      | X17 = X9 ),
    c_0_66 ).

fof(c_0_476_477,axiom,
    ! [X9,X17,X18,X10] :
      ( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X10),X17,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X18),X9,tc_Lambda_OdB,tc_Lambda_OdB)
      | X10 = X18 ),
    c_0_67 ).

fof(c_0_477_478,axiom,
    ! [X9,X17,X18,X10] :
      ( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X10),X17,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X18),X9,tc_Lambda_OdB,tc_Lambda_OdB)
      | X17 = X9 ),
    c_0_68 ).

fof(c_0_478_479,plain,
    ! [X28,X40,X24,X3] :
      ( ~ class_OrderedGroup_Osemigroup__add(X3)
      | c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X24),X40),X28,X3,X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X24),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),X40,X28,X3,X3)) ),
    inference(fof_simplification,[status(thm)],[c_0_69]) ).

fof(c_0_479_480,axiom,
    ! [X6,X7,X8] :
      ( c_List_Ofoldl(c_Lambda_OdB_OApp,X8,X6,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,X7,X6,tc_Lambda_OdB,tc_Lambda_OdB)
      | X8 = X7 ),
    c_0_70 ).

fof(c_0_480_481,plain,
    ! [X28,X40,X24,X39,X3] :
      ( c_List_Ofoldl(X39,hAPP(hAPP(X39,X24),X40),X28,X3,X3) = hAPP(hAPP(X39,X24),c_List_Ofoldl(X39,X40,X28,X3,X3))
      | ~ c_OrderedGroup_Osemigroup__add(X39,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_71]) ).

fof(c_0_481_482,plain,
    ! [X28,X38,X24,X39,X3] :
      ( hAPP(hAPP(X39,X24),c_List_Ofoldl(X39,X38,X28,X3,X3)) = c_List_Ofoldl(X39,X24,X28,X3,X3)
      | ~ c_OrderedGroup_Omonoid__add(X38,X39,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_72]) ).

fof(c_0_482_483,plain,
    ! [X43,X29,X3] :
      ( ~ class_OrderedGroup_Omonoid__add(X3)
      | c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),X29,X43,X3,X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X3),X43,c_HOL_Ozero__class_Ozero(X3),X3,X3)) ),
    inference(fof_simplification,[status(thm)],[c_0_73]) ).

fof(c_0_483_484,plain,
    ! [X28,X24,X3] :
      ( ~ class_OrderedGroup_Omonoid__add(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X24),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3),X28,X3,X3)) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),X24,X28,X3,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_74]) ).

fof(c_0_484_485,axiom,
    ! [X6,X27,X7,X8] :
      ( hAPP(hAPP(c_Lambda_OdB_OApp,X8),X7) != c_List_Ofoldl(c_Lambda_OdB_OApp,X27,X6,tc_Lambda_OdB,tc_Lambda_OdB)
      | X8 = c_List_Ofoldl(c_Lambda_OdB_OApp,X27,c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1(X8,X7,X27,X6),tc_Lambda_OdB,tc_Lambda_OdB)
      | X6 = c_List_Olist_ONil(tc_Lambda_OdB) ),
    c_0_75 ).

fof(c_0_485_486,plain,
    ! [X29] :
      ( X29 = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__4(X29))),v_sko__InductTermi__XIT__Xcases__5(X29)),v_sko__InductTermi__XIT__Xcases__6(X29),tc_Lambda_OdB,tc_Lambda_OdB)
      | hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X29)))
      | X29 = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X29)),v_sko__InductTermi__XIT__Xcases__1(X29),tc_Lambda_OdB,tc_Lambda_OdB)
      | ~ hBOOL(hAPP(c_InductTermi_OIT,X29)) ),
    inference(fof_simplification,[status(thm)],[c_0_76]) ).

fof(c_0_486_487,plain,
    ! [X29] :
      ( X29 = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__4(X29))),v_sko__InductTermi__XIT__Xcases__5(X29)),v_sko__InductTermi__XIT__Xcases__6(X29),tc_Lambda_OdB,tc_Lambda_OdB)
      | X29 = c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X29))
      | X29 = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X29)),v_sko__InductTermi__XIT__Xcases__1(X29),tc_Lambda_OdB,tc_Lambda_OdB)
      | ~ hBOOL(hAPP(c_InductTermi_OIT,X29)) ),
    inference(fof_simplification,[status(thm)],[c_0_77]) ).

fof(c_0_487_488,plain,
    ! [X43,X3] :
      ( ~ class_OrderedGroup_Omonoid__add(X3)
      | c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3),X43,X3,X3) = c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X3),X43,c_HOL_Ozero__class_Ozero(X3),X3,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_78]) ).

fof(c_0_488_489,plain,
    ! [X43,X29,X3] :
      ( ~ class_OrderedGroup_Oab__semigroup__add(X3)
      | c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X3),X43,X29,X3,X3) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),X29,X43,X3,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_79]) ).

fof(c_0_489_490,axiom,
    ! [X27,X7,X8] :
      ( hAPP(hAPP(c_Lambda_OdB_OApp,X8),X7) != c_List_Ofoldl(c_Lambda_OdB_OApp,X27,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)
      | hAPP(hAPP(c_Lambda_OdB_OApp,X8),X7) = X27 ),
    c_0_80 ).

fof(c_0_490_491,axiom,
    ! [X9,X7,X8] :
      ( c_List_Ofoldl(c_Lambda_OdB_OApp,X7,X9,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X8)
      | X7 = c_Lambda_OdB_OAbs(X8) ),
    c_0_81 ).

fof(c_0_491_492,axiom,
    ! [X9,X7,X8] :
      ( c_Lambda_OdB_OAbs(X8) != c_List_Ofoldl(c_Lambda_OdB_OApp,X7,X9,tc_Lambda_OdB,tc_Lambda_OdB)
      | c_Lambda_OdB_OAbs(X8) = X7 ),
    c_0_82 ).

fof(c_0_492_493,axiom,
    ! [X9,X7,X10] :
      ( c_Lambda_OdB_OVar(X10) != c_List_Ofoldl(c_Lambda_OdB_OApp,X7,X9,tc_Lambda_OdB,tc_Lambda_OdB)
      | c_Lambda_OdB_OVar(X10) = X7 ),
    c_0_83 ).

fof(c_0_493_494,plain,
    ! [X27,X7,X15,X16] :
      ( hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(hAPP(c_Lambda_Osubst,X27),X7),X15)),X16) = hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,X27),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),c_HOL_Oone__class_Oone(tc_nat)))),hAPP(hAPP(c_Lambda_Olift,X7),X16)),X15)
      | ~ c_HOL_Oord__class_Oless(X15,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_84]) ).

fof(c_0_494_495,axiom,
    ! [X9,X7,X8] :
      ( c_Lambda_OdB_OAbs(X8) != c_List_Ofoldl(c_Lambda_OdB_OApp,X7,X9,tc_Lambda_OdB,tc_Lambda_OdB)
      | X9 = c_List_Olist_ONil(tc_Lambda_OdB) ),
    c_0_85 ).

fof(c_0_495_496,axiom,
    ! [X9,X7,X8] :
      ( c_List_Ofoldl(c_Lambda_OdB_OApp,X7,X9,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X8)
      | X9 = c_List_Olist_ONil(tc_Lambda_OdB) ),
    c_0_86 ).

fof(c_0_496_497,axiom,
    ! [X9,X7,X10] :
      ( c_Lambda_OdB_OVar(X10) != c_List_Ofoldl(c_Lambda_OdB_OApp,X7,X9,tc_Lambda_OdB,tc_Lambda_OdB)
      | X9 = c_List_Olist_ONil(tc_Lambda_OdB) ),
    c_0_87 ).

fof(c_0_497_498,plain,
    ! [X40,X24,X8,X3] :
      ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X8,X3),X40),X24))
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Predicate_Oconversep(X8,X3,X3),X3),X24),X40)) ),
    inference(fof_simplification,[status(thm)],[c_0_88]) ).

fof(c_0_498_499,plain,
    ! [X51,X40,X43,X24,X8,X3] :
      ( hBOOL(hAPP(hAPP(X8,X40),X24))
      | c_ListOrder_Ostep1(X8,X51,X43,X3)
      | ~ c_ListOrder_Ostep1(X8,c_List_Oappend(X51,c_List_Olist_OCons(X40,c_List_Olist_ONil(X3),X3),X3),c_List_Oappend(X43,c_List_Olist_OCons(X24,c_List_Olist_ONil(X3),X3),X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_89]) ).

fof(c_0_499_500,plain,
    ! [X51,X40,X43,X24,X8,X3] :
      ( X51 = X43
      | c_ListOrder_Ostep1(X8,X51,X43,X3)
      | ~ c_ListOrder_Ostep1(X8,c_List_Oappend(X51,c_List_Olist_OCons(X40,c_List_Olist_ONil(X3),X3),X3),c_List_Oappend(X43,c_List_Olist_OCons(X24,c_List_Olist_ONil(X3),X3),X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_90]) ).

fof(c_0_500_501,plain,
    ! [X51,X40,X43,X24,X8,X3] :
      ( hBOOL(hAPP(hAPP(X8,X40),X24))
      | X40 = X24
      | ~ c_ListOrder_Ostep1(X8,c_List_Oappend(X51,c_List_Olist_OCons(X40,c_List_Olist_ONil(X3),X3),X3),c_List_Oappend(X43,c_List_Olist_OCons(X24,c_List_Olist_ONil(X3),X3),X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_91]) ).

fof(c_0_501_502,plain,
    ! [X29] :
      ( X29 = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__4(X29))),v_sko__InductTermi__XIT__Xcases__5(X29)),v_sko__InductTermi__XIT__Xcases__6(X29),tc_Lambda_OdB,tc_Lambda_OdB)
      | hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X29)))
      | c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X29),tc_Lambda_OdB)
      | ~ hBOOL(hAPP(c_InductTermi_OIT,X29)) ),
    inference(fof_simplification,[status(thm)],[c_0_92]) ).

fof(c_0_502_503,plain,
    ! [X51,X40,X43,X24,X8,X3] :
      ( X51 = X43
      | X40 = X24
      | ~ c_ListOrder_Ostep1(X8,c_List_Oappend(X51,c_List_Olist_OCons(X40,c_List_Olist_ONil(X3),X3),X3),c_List_Oappend(X43,c_List_Olist_OCons(X24,c_List_Olist_ONil(X3),X3),X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_93]) ).

fof(c_0_503_504,plain,
    ! [X29] :
      ( X29 = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__4(X29))),v_sko__InductTermi__XIT__Xcases__5(X29)),v_sko__InductTermi__XIT__Xcases__6(X29),tc_Lambda_OdB,tc_Lambda_OdB)
      | X29 = c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X29))
      | c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X29),tc_Lambda_OdB)
      | ~ hBOOL(hAPP(c_InductTermi_OIT,X29)) ),
    inference(fof_simplification,[status(thm)],[c_0_94]) ).

fof(c_0_504_505,plain,
    ! [X27,X7,X8,X16] :
      ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,X8),X27),X16)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X7),X27),X16)))
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X8),X7)) ),
    inference(fof_simplification,[status(thm)],[c_0_95]) ).

fof(c_0_505_506,plain,
    ! [X27,X7,X8,X16] :
      ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,X27),X8),X16)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X27),X7),X16)))
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X8),X7)) ),
    inference(fof_simplification,[status(thm)],[c_0_96]) ).

fof(c_0_506_507,plain,
    ! [X29] :
      ( hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__5(X29)))
      | hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X29)))
      | X29 = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X29)),v_sko__InductTermi__XIT__Xcases__1(X29),tc_Lambda_OdB,tc_Lambda_OdB)
      | ~ hBOOL(hAPP(c_InductTermi_OIT,X29)) ),
    inference(fof_simplification,[status(thm)],[c_0_97]) ).

fof(c_0_507_508,plain,
    ! [X40,X24,X8,X3] :
      ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Predicate_Oconversep(X8,X3,X3),X3),X24),X40))
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X8,X3),X40),X24)) ),
    inference(fof_simplification,[status(thm)],[c_0_98]) ).

fof(c_0_508_509,plain,
    ! [X29] :
      ( hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__5(X29)))
      | X29 = c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X29))
      | X29 = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X29)),v_sko__InductTermi__XIT__Xcases__1(X29),tc_Lambda_OdB,tc_Lambda_OdB)
      | ~ hBOOL(hAPP(c_InductTermi_OIT,X29)) ),
    inference(fof_simplification,[status(thm)],[c_0_99]) ).

fof(c_0_509_510,plain,
    ! [X27,X7,X8,X16] :
      ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,X27),X8),X16)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X27),X7),X16)))
      | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X8),X7)) ),
    inference(fof_simplification,[status(thm)],[c_0_100]) ).

fof(c_0_510_511,plain,
    ! [X43,X3] :
      ( ~ class_OrderedGroup_Omonoid__add(X3)
      | c_List_Olistsum(X43,X3) = c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X3),X43,c_HOL_Ozero__class_Ozero(X3),X3,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_101]) ).

fof(c_0_511_512,plain,
    ! [X43,X3] :
      ( ~ class_OrderedGroup_Omonoid__add(X3)
      | c_List_Olistsum(X43,X3) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3),X43,X3,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_102]) ).

fof(c_0_512_513,plain,
    ! [X27,X7,X15,X16] :
      ( hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(hAPP(c_Lambda_Osubst,X27),X7),X15)),X16) = hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,X27),X16)),hAPP(hAPP(c_Lambda_Olift,X7),X16)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),c_HOL_Oone__class_Oone(tc_nat)))
      | ~ c_HOL_Oord__class_Oless(X16,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_103]) ).

fof(c_0_513_514,plain,
    ! [X27,X7,X8,X16] :
      ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(hAPP(c_Lambda_Osubst,X8),X27),X16)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X7),X27),X16)))
      | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X8),X7)) ),
    inference(fof_simplification,[status(thm)],[c_0_104]) ).

fof(c_0_514_515,plain,
    ! [X26,X27,X16,X76,X22,X23] :
      ( ~ c_Type_Otyping(X76,X26,X22)
      | ~ c_Type_Otyping(c_Type_Oshift(X76,X16,X22,tc_Type_Otype),X27,X23)
      | c_Type_Otyping(X76,hAPP(hAPP(hAPP(c_Lambda_Osubst,X27),X26),X16),X23) ),
    inference(fof_simplification,[status(thm)],[c_0_105]) ).

fof(c_0_515_516,plain,
    ! [X54,X27,X65,X7] :
      ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X7),X27)),hAPP(hAPP(c_Lambda_OdB_OApp,X65),X54)))
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X27),X54))
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X7),X65)) ),
    inference(fof_simplification,[status(thm)],[c_0_106]) ).

fof(c_0_516_517,plain,
    ! [X51,X40,X43,X24,X8,X3] :
      ( c_ListOrder_Ostep1(X8,X51,X43,X3)
      | hBOOL(hAPP(hAPP(X8,X40),X24))
      | ~ c_ListOrder_Ostep1(X8,c_List_Olist_OCons(X40,X51,X3),c_List_Olist_OCons(X24,X43,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_107]) ).

fof(c_0_517_518,plain,
    ! [X51,X40,X43,X24,X8,X3] :
      ( c_ListOrder_Ostep1(X8,X51,X43,X3)
      | X43 = X51
      | ~ c_ListOrder_Ostep1(X8,c_List_Olist_OCons(X40,X51,X3),c_List_Olist_OCons(X24,X43,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_108]) ).

fof(c_0_518_519,plain,
    ! [X8,X49,X29,X53,X3] :
      ( hBOOL(hAPP(hAPP(X8,X49),X29))
      | ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X8,X3,X53),X29),X49)) ),
    inference(fof_simplification,[status(thm)],[c_0_109]) ).

fof(c_0_519_520,plain,
    ! [X8,X73,X74,X53,X3] :
      ( hBOOL(hAPP(hAPP(X8,X73),X74))
      | ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X8,X3,X53),X74),X73)) ),
    inference(fof_simplification,[status(thm)],[c_0_110]) ).

fof(c_0_520_521,plain,
    ! [X51,X43,X24,X8,X3] :
      ( ~ c_ListOrder_Ostep1(X8,X51,X43,X3)
      | c_ListOrder_Ostep1(X8,c_List_Oappend(X51,X24,X3),c_List_Oappend(X43,X24,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_111]) ).

fof(c_0_521_522,plain,
    ! [X24,X72,X36,X8,X3] :
      ( c_ListOrder_Ostep1(X8,c_List_Oappend(X24,X72,X3),c_List_Oappend(X24,X36,X3),X3)
      | ~ c_ListOrder_Ostep1(X8,X72,X36,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_112]) ).

fof(c_0_522_523,plain,
    ! [X51,X43,X24,X8,X3] :
      ( c_ListOrder_Ostep1(X8,c_List_Olist_OCons(X24,X51,X3),c_List_Olist_OCons(X24,X43,X3),X3)
      | ~ c_ListOrder_Ostep1(X8,X51,X43,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_113]) ).

fof(c_0_523_524,plain,
    ! [X27,X65,X7] :
      ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X7),X27)),hAPP(hAPP(c_Lambda_OdB_OApp,X65),X27)))
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X7),X65)) ),
    inference(fof_simplification,[status(thm)],[c_0_114]) ).

fof(c_0_524_525,plain,
    ! [X54,X27,X7] :
      ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X7),X27)),hAPP(hAPP(c_Lambda_OdB_OApp,X7),X54)))
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X27),X54)) ),
    inference(fof_simplification,[status(thm)],[c_0_115]) ).

fof(c_0_525_526,plain,
    ! [X7,X8,X16] :
      ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_Olift,X8),X16)),hAPP(hAPP(c_Lambda_Olift,X7),X16)))
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X8),X7)) ),
    inference(fof_simplification,[status(thm)],[c_0_116]) ).

fof(c_0_526_527,plain,
    ! [X51,X40,X43,X24,X8,X3] :
      ( X24 = X40
      | hBOOL(hAPP(hAPP(X8,X40),X24))
      | ~ c_ListOrder_Ostep1(X8,c_List_Olist_OCons(X40,X51,X3),c_List_Olist_OCons(X24,X43,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_117]) ).

fof(c_0_527_528,plain,
    ! [X64,X40,X24,X8,X3] :
      ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X8,X3),X24),X64))
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X8,X3),X40),X64))
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X8,X3),X24),X40)) ),
    inference(fof_simplification,[status(thm)],[c_0_118]) ).

fof(c_0_528_529,plain,
    ! [X51,X40,X43,X24,X8,X3] :
      ( X24 = X40
      | X43 = X51
      | ~ c_ListOrder_Ostep1(X8,c_List_Olist_OCons(X40,X51,X3),c_List_Olist_OCons(X24,X43,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_119]) ).

fof(c_0_529_530,plain,
    ! [X62,X50,X49,X29,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),X49)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X50),X62)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),X50)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X49),X62)) ),
    inference(fof_simplification,[status(thm)],[c_0_120]) ).

fof(c_0_530_531,plain,
    ! [X27,X16,X21,X22,X23] :
      ( c_Type_Otyping(c_Type_Oshift(X21,X16,X22,tc_Type_Otype),hAPP(hAPP(c_Lambda_Olift,X27),X16),X23)
      | ~ c_Type_Otyping(X21,X27,X23) ),
    inference(fof_simplification,[status(thm)],[c_0_121]) ).

fof(c_0_531_532,plain,
    ! [X8,X49,X29,X53,X3] :
      ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X8,X3,X53),X29),X49))
      | ~ hBOOL(hAPP(hAPP(X8,X49),X29)) ),
    inference(fof_simplification,[status(thm)],[c_0_122]) ).

fof(c_0_532_533,plain,
    ! [X8,X49,X29,X53,X3] :
      ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X8,X3,X53),X49),X29))
      | ~ hBOOL(hAPP(hAPP(X8,X29),X49)) ),
    inference(fof_simplification,[status(thm)],[c_0_123]) ).

fof(c_0_533_534,plain,
    ! [X7,X8,X16] :
      ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_Olift,X8),X16)),hAPP(hAPP(c_Lambda_Olift,X7),X16)))
      | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X8),X7)) ),
    inference(fof_simplification,[status(thm)],[c_0_124]) ).

fof(c_0_534_535,plain,
    ! [X26,X27,X7] :
      ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,X26),X7)),hAPP(hAPP(c_Lambda_OdB_OApp,X26),X27)))
      | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X7),X27)) ),
    inference(fof_simplification,[status(thm)],[c_0_125]) ).

fof(c_0_535_536,plain,
    ! [X26,X27,X7] :
      ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,X7),X26)),hAPP(hAPP(c_Lambda_OdB_OApp,X27),X26)))
      | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X7),X27)) ),
    inference(fof_simplification,[status(thm)],[c_0_126]) ).

fof(c_0_536_537,plain,
    ! [X8,X50,X49,X29,X3] :
      ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X8,X3),X29),X50))
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X8,X3),X49),X50))
      | ~ hBOOL(hAPP(hAPP(X8,X29),X49)) ),
    inference(fof_simplification,[status(thm)],[c_0_127]) ).

fof(c_0_537_538,plain,
    ! [X8,X50,X49,X29,X3] :
      ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X8,X3),X29),X50))
      | ~ hBOOL(hAPP(hAPP(X8,X49),X50))
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X8,X3),X29),X49)) ),
    inference(fof_simplification,[status(thm)],[c_0_128]) ).

fof(c_0_538_539,plain,
    ! [X15,X16,X21,X23,X3] :
      ( hAPP(c_Type_Oshift(X21,X16,X23,X3),X15) = hAPP(X21,X15)
      | ~ c_HOL_Oord__class_Oless(X15,X16,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_129]) ).

fof(c_0_539_540,plain,
    ! [X40,X58,X24,X8,X3] :
      ( ~ hBOOL(hAPP(hAPP(X8,X40),X58))
      | c_ListOrder_Ostep1(X8,c_List_Olist_OCons(X40,X24,X3),c_List_Olist_OCons(X58,X24,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_130]) ).

fof(c_0_540_541,plain,
    ! [X18,X49,X29,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_HOL_Oord__class_Oless(X29,X49,X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X49,X3)
      | ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X29,X18,X3),c_Power_Opower__class_Opower(X49,X18,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_131]) ).

fof(c_0_541_542,plain,
    ! [X18,X10,X29,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_HOL_Oord__class_Oless(X10,X18,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X29,X10,X3),c_Power_Opower__class_Opower(X29,X18,X3),X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X29,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_132]) ).

fof(c_0_542_543,plain,
    ! [X40,X24,X49,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_HOL_Oord__class_Oless(X24,X40,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X49,X24,X3),c_Power_Opower__class_Opower(X49,X40,X3),X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X49,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_133]) ).

fof(c_0_543_544,plain,
    ! [X18,X29,X75,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X29,X75,X3),c_Power_Opower__class_Opower(X29,X18,X3),X3)
      | ~ c_HOL_Oord__class_Oless(X29,c_HOL_Oone__class_Oone(X3),X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X29,X3)
      | ~ c_HOL_Oord__class_Oless(X18,X75,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_134]) ).

fof(c_0_544_545,axiom,
    ! [X51,X40,X43,X24,X3] :
      ( c_List_Oappend(X43,c_List_Olist_OCons(X24,c_List_Olist_ONil(X3),X3),X3) != c_List_Oappend(X51,c_List_Olist_OCons(X40,c_List_Olist_ONil(X3),X3),X3)
      | X43 = X51 ),
    c_0_135 ).

fof(c_0_545_546,axiom,
    ! [X51,X40,X43,X24,X3] :
      ( c_List_Oappend(X43,c_List_Olist_OCons(X24,c_List_Olist_ONil(X3),X3),X3) != c_List_Oappend(X51,c_List_Olist_OCons(X40,c_List_Olist_ONil(X3),X3),X3)
      | X24 = X40 ),
    c_0_136 ).

fof(c_0_546_547,plain,
    ! [X18,X49,X29,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X29,X18,X3),c_Power_Opower__class_Opower(X49,X18,X3),X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X18,tc_nat)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X29,X3)
      | ~ c_HOL_Oord__class_Oless(X29,X49,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_137]) ).

fof(c_0_547_548,plain,
    ! [X64,X40,X24,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_Orderings_Oord__class_Omax(X24,X40,X3)),X64) = c_Orderings_Oord__class_Omax(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X24),X64),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X40),X64),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_138]) ).

fof(c_0_548_549,plain,
    ! [X50,X49,X29,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),X49)),X50) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),X50)),X49) ),
    inference(fof_simplification,[status(thm)],[c_0_139]) ).

fof(c_0_549_550,plain,
    ! [X62,X50,X49,X29,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
      | c_lessequals(X29,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X49),X62),X3)
      | ~ c_lessequals(X50,X62,X3)
      | ~ c_lessequals(X29,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X49),X50),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_140]) ).

fof(c_0_550_551,plain,
    ! [X50,X49,X29,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
      | c_lessequals(X29,X49,X3)
      | ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X50),X29),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X50),X49),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_141]) ).

fof(c_0_551_552,plain,
    ! [X50,X49,X29,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
      | c_lessequals(X29,X49,X3)
      | ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),X50),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X49),X50),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_142]) ).

fof(c_0_552_553,plain,
    ! [X50,X49,X29,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
      | c_HOL_Oord__class_Oless(X29,X49,X3)
      | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),X50),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X49),X50),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_143]) ).

fof(c_0_553_554,plain,
    ! [X50,X49,X29,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
      | c_HOL_Oord__class_Oless(X29,X49,X3)
      | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X50),X29),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X50),X49),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_144]) ).

fof(c_0_554_555,plain,
    ! [X18,X49,X29,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_Power_Opower__class_Opower(X29,X18,X3) != c_Power_Opower__class_Opower(X49,X18,X3)
      | X29 = X49
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X18,tc_nat)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X49,X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X29,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_145]) ).

fof(c_0_555_556,plain,
    ! [X8,X15,X16] :
      ( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,X8),c_Lambda_OdB_OVar(X16)),X15)))
      | ~ hBOOL(hAPP(c_InductTermi_OIT,X8)) ),
    inference(fof_simplification,[status(thm)],[c_0_146]) ).

fof(c_0_556_557,plain,
    ! [X18,X49,X29,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_lessequals(c_Power_Opower__class_Opower(X29,X18,X3),c_Power_Opower__class_Opower(X49,X18,X3),X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X29,X3)
      | ~ c_lessequals(X29,X49,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_147]) ).

fof(c_0_557_558,plain,
    ! [X18,X29,X75,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X29,X18,X3),c_Power_Opower__class_Opower(X29,X75,X3),X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X29,X3)
      | ~ c_HOL_Oord__class_Oless(X18,X75,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_148]) ).

fof(c_0_558_559,plain,
    ! [X40,X24,X49,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X49,X24,X3),c_Power_Opower__class_Opower(X49,X40,X3),X3)
      | ~ c_HOL_Oord__class_Oless(X24,X40,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X49,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_149]) ).

fof(c_0_559_560,plain,
    ! [X65,X7] :
      ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_OdB_OAbs(X7)),c_Lambda_OdB_OAbs(X65)))
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X7),X65)) ),
    inference(fof_simplification,[status(thm)],[c_0_150]) ).

fof(c_0_560_561,plain,
    ! [X62,X50,X49,X29,X3] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),X50),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X49),X62),X3)
      | ~ c_HOL_Oord__class_Oless(X50,X62,X3)
      | ~ c_lessequals(X29,X49,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_151]) ).

fof(c_0_561_562,plain,
    ! [X62,X50,X49,X29,X3] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),X50),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X49),X62),X3)
      | ~ c_lessequals(X50,X62,X3)
      | ~ c_HOL_Oord__class_Oless(X29,X49,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_152]) ).

fof(c_0_562_563,plain,
    ! [X62,X50,X49,X29,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3)
      | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),X50),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X49),X62),X3)
      | ~ c_lessequals(X50,X62,X3)
      | ~ c_lessequals(X29,X49,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_153]) ).

fof(c_0_563_564,plain,
    ! [X62,X50,X49,X29,X3] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),X50),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X49),X62),X3)
      | ~ c_HOL_Oord__class_Oless(X50,X62,X3)
      | ~ c_HOL_Oord__class_Oless(X29,X49,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_154]) ).

fof(c_0_564_565,plain,
    ! [X8,X49,X29,X3] :
      ( c_Wellfounded_Oaccp(X8,X49,X3)
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X8,X3),X49),X29))
      | ~ c_Wellfounded_Oaccp(X8,X29,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_155]) ).

fof(c_0_565_566,plain,
    ! [X8,X49,X29,X3] :
      ( c_Wellfounded_Oaccp(X8,X49,X3)
      | ~ c_Wellfounded_Oaccp(X8,X29,X3)
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X8,X3),X49),X29)) ),
    inference(fof_simplification,[status(thm)],[c_0_156]) ).

fof(c_0_566_567,plain,
    ! [X18,X10,X25] :
      ( c_HOL_Oord__class_Oless(X10,X18,tc_nat)
      | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X25),X10),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X25),X18),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_157]) ).

fof(c_0_567_568,plain,
    ! [X50,X49,X29,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),X49)),X50) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X49),X50)) ),
    inference(fof_simplification,[status(thm)],[c_0_158]) ).

fof(c_0_568_569,plain,
    ! [X62,X50,X29,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X50),X62)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),X50)),X62) ),
    inference(fof_simplification,[status(thm)],[c_0_159]) ).

fof(c_0_569_570,plain,
    ! [X50,X49,X29,X3] :
      ( ~ class_OrderedGroup_Oab__semigroup__add(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),X49)),X50) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X49),X50)) ),
    inference(fof_simplification,[status(thm)],[c_0_160]) ).

fof(c_0_570_571,plain,
    ! [X50,X49,X29,X3] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),X49)),X50) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X49),X50)) ),
    inference(fof_simplification,[status(thm)],[c_0_161]) ).

fof(c_0_571_572,plain,
    ! [X64,X40,X24,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X24),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X40),X64)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X24),X40)),X64) ),
    inference(fof_simplification,[status(thm)],[c_0_162]) ).

fof(c_0_572_573,plain,
    ! [X61,X25,X15,X16] :
      ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),X25),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X61),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X25,X61,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X16,X15,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_163]) ).

fof(c_0_573_574,axiom,
    ! [X43,X52,X53,X3] :
      ( c_List_Olist_ONil(X3) != c_List_Omap(X52,X43,X53,X3)
      | X43 = c_List_Olist_ONil(X53) ),
    c_0_164 ).

fof(c_0_574_575,axiom,
    ! [X43,X52,X53,X3] :
      ( c_List_Omap(X52,X43,X53,X3) != c_List_Olist_ONil(X3)
      | X43 = c_List_Olist_ONil(X53) ),
    c_0_165 ).

fof(c_0_575_576,plain,
    ! [X54,X27,X21,X23] :
      ( c_Type_Otyping(X21,X54,X23)
      | ~ c_Type_Otyping(X21,X27,X23)
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X27),X54)) ),
    inference(fof_simplification,[status(thm)],[c_0_166]) ).

fof(c_0_576_577,plain,
    ! [X64,X40,X24,X26,X3] :
      ( ~ class_OrderedGroup_Oab__group__add(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X24),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X40),X64)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X40),X26)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X24),X64) = X26 ),
    inference(fof_simplification,[status(thm)],[c_0_167]) ).

fof(c_0_577_578,plain,
    ! [X64,X40,X24,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_lessequals(X64,X40,X3)
      | c_lessequals(X64,X24,X3)
      | ~ c_lessequals(X64,c_Orderings_Oord__class_Omax(X24,X40,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_168]) ).

fof(c_0_578_579,plain,
    ! [X64,X40,X24,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_HOL_Oord__class_Oless(X64,X40,X3)
      | c_HOL_Oord__class_Oless(X64,X24,X3)
      | ~ c_HOL_Oord__class_Oless(X64,c_Orderings_Oord__class_Omax(X24,X40,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_169]) ).

fof(c_0_579_580,plain,
    ! [X49,X29,X3] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
      | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),X49),c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_lessequals(X49,c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_lessequals(X29,c_HOL_Ozero__class_Ozero(X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_170]) ).

fof(c_0_580_581,plain,
    ! [X49,X29,X3] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),X49),X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X49,X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X29,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_171]) ).

fof(c_0_581_582,plain,
    ! [X49,X29,X3] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),X49),c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_lessequals(X49,c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_HOL_Oord__class_Oless(X29,c_HOL_Ozero__class_Ozero(X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_172]) ).

fof(c_0_582_583,plain,
    ! [X49,X29,X3] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),X49),c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_HOL_Oord__class_Oless(X49,c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_lessequals(X29,c_HOL_Ozero__class_Ozero(X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_173]) ).

fof(c_0_583_584,plain,
    ! [X49,X29,X3] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),X49),X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X49,X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X29,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_174]) ).

fof(c_0_584_585,plain,
    ! [X49,X29,X3] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),X49),X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X49,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X29,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_175]) ).

fof(c_0_585_586,plain,
    ! [X49,X29,X3] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),X49),c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_HOL_Oord__class_Oless(X49,c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_HOL_Oord__class_Oless(X29,c_HOL_Ozero__class_Ozero(X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_176]) ).

fof(c_0_586_587,plain,
    ! [X49,X29,X3] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),X49),X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X49,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X29,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_177]) ).

fof(c_0_587_588,plain,
    ! [X18,X29,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),c_Power_Opower__class_Opower(X29,X18,X3),X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X18,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X29,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_178]) ).

fof(c_0_588_589,plain,
    ! [X50,X49,X29,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
      | ~ class_OrderedGroup_Ocomm__monoid__add(X3)
      | c_lessequals(X49,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),X50),X3)
      | ~ c_lessequals(X49,X29,X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X50,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_179]) ).

fof(c_0_589_590,plain,
    ! [X50,X49,X29,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
      | ~ class_OrderedGroup_Ocomm__monoid__add(X3)
      | c_lessequals(X49,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),X50),X3)
      | ~ c_lessequals(X49,X50,X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X29,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_180]) ).

fof(c_0_590_591,plain,
    ! [X50,X49,X29,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
      | ~ class_OrderedGroup_Ocomm__monoid__add(X3)
      | c_HOL_Oord__class_Oless(X49,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),X50),X3)
      | ~ c_lessequals(X49,X50,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X29,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_181]) ).

fof(c_0_591_592,plain,
    ! [X50,X49,X29,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
      | ~ class_OrderedGroup_Ocomm__monoid__add(X3)
      | c_HOL_Oord__class_Oless(X49,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),X50),X3)
      | ~ c_HOL_Oord__class_Oless(X49,X50,X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X29,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_182]) ).

fof(c_0_592_593,plain,
    ! [X50,X49,X29,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3)
      | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X50),X29),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X50),X49),X3)
      | ~ c_lessequals(X29,X49,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_183]) ).

fof(c_0_593_594,plain,
    ! [X50,X49,X29,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3)
      | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),X50),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X49),X50),X3)
      | ~ c_lessequals(X29,X49,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_184]) ).

fof(c_0_594_595,plain,
    ! [X50,X49,X29,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
      | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X50),X29),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X50),X49),X3)
      | ~ c_lessequals(X29,X49,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_185]) ).

fof(c_0_595_596,plain,
    ! [X50,X49,X29,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
      | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),X50),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X49),X50),X3)
      | ~ c_lessequals(X29,X49,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_186]) ).

fof(c_0_596_597,plain,
    ! [X50,X49,X29,X3] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),X50),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X49),X50),X3)
      | ~ c_HOL_Oord__class_Oless(X29,X49,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_187]) ).

fof(c_0_597_598,plain,
    ! [X50,X49,X29,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),X50),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X49),X50),X3)
      | ~ c_HOL_Oord__class_Oless(X29,X49,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_188]) ).

fof(c_0_598_599,plain,
    ! [X50,X49,X29,X3] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X50),X29),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X50),X49),X3)
      | ~ c_HOL_Oord__class_Oless(X29,X49,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_189]) ).

fof(c_0_599_600,plain,
    ! [X50,X49,X29,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X50),X29),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X50),X49),X3)
      | ~ c_HOL_Oord__class_Oless(X29,X49,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_190]) ).

fof(c_0_600_601,plain,
    ! [X50,X49,X29,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_HOL_Oord__class_Oless(X49,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),X50),X3)
      | ~ c_HOL_Oord__class_Oless(X49,X50,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X29,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_191]) ).

fof(c_0_601_602,plain,
    ! [X18,X10] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X18,tc_nat)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X10,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X10),X18),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_192]) ).

fof(c_0_602_603,plain,
    ! [X24,X49,X29,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_lessequals(c_Orderings_Oord__class_Omax(X29,X49,X3),X24,X3)
      | ~ c_lessequals(X49,X24,X3)
      | ~ c_lessequals(X29,X24,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_193]) ).

fof(c_0_603_604,plain,
    ! [X64,X40,X24,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_lessequals(c_Orderings_Oord__class_Omax(X40,X64,X3),X24,X3)
      | ~ c_lessequals(X64,X24,X3)
      | ~ c_lessequals(X40,X24,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_194]) ).

fof(c_0_604_605,plain,
    ! [X64,X40,X24,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_lessequals(c_Orderings_Oord__class_Omax(X24,X40,X3),X64,X3)
      | ~ c_lessequals(X40,X64,X3)
      | ~ c_lessequals(X24,X64,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_195]) ).

fof(c_0_605_606,plain,
    ! [X64,X40,X24,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X24,X40,X3),X64,X3)
      | ~ c_HOL_Oord__class_Oless(X40,X64,X3)
      | ~ c_HOL_Oord__class_Oless(X24,X64,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_196]) ).

fof(c_0_606_607,plain,
    ! [X39,X50,X49,X29,X3] :
      ( hAPP(hAPP(X39,hAPP(hAPP(X39,X29),X49)),X50) = hAPP(hAPP(X39,X29),hAPP(hAPP(X39,X49),X50))
      | ~ c_OrderedGroup_Osemigroup__add(X39,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_197]) ).

fof(c_0_607_608,plain,
    ! [X51,X43,X60,X3] :
      ( c_List_Olistsp(X60,c_List_Oappend(X43,X51,X3),X3)
      | ~ c_List_Olistsp(X60,X51,X3)
      | ~ c_List_Olistsp(X60,X43,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_198]) ).

fof(c_0_608_609,plain,
    ! [X64,X40,X24,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omax(X24,X40,X3),X64,X3) = c_Orderings_Oord__class_Omax(X24,c_Orderings_Oord__class_Omax(X40,X64,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_199]) ).

fof(c_0_609_610,plain,
    ! [X64,X40,X24,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_Orderings_Oord__class_Omax(X24,c_Orderings_Oord__class_Omax(X40,X64,X3),X3) = c_Orderings_Oord__class_Omax(X40,c_Orderings_Oord__class_Omax(X24,X64,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_200]) ).

fof(c_0_610_611,plain,
    ! [X29,X3] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
      | c_lessequals(X29,c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),X29),c_HOL_Ozero__class_Ozero(X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_201]) ).

fof(c_0_611_612,plain,
    ! [X29,X3] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X3),X29,X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),X29),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_202]) ).

fof(c_0_612_613,plain,
    ! [X29,X3] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
      | c_HOL_Oord__class_Oless(X29,c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),X29),c_HOL_Ozero__class_Ozero(X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_203]) ).

fof(c_0_613_614,plain,
    ! [X29,X3] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X29,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),X29),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_204]) ).

fof(c_0_614_615,plain,
    ! [X29,X3] :
      ( ~ class_Ring__and__Field_Oordered__idom(X3)
      | c_HOL_Oord__class_Oless(X29,c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),X29),c_HOL_Ozero__class_Ozero(X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_205]) ).

fof(c_0_615_616,plain,
    ! [X25,X15,X16] :
      ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),X25),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X25),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X16,X15,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_206]) ).

fof(c_0_616_617,plain,
    ! [X18,X10,X25] :
      ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X25),X10),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X25),X18),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X10,X18,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_207]) ).

fof(c_0_617_618,plain,
    ! [X24,X49,X29,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_lessequals(X29,X24,X3)
      | ~ c_lessequals(c_Orderings_Oord__class_Omax(X29,X49,X3),X24,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_208]) ).

fof(c_0_618_619,plain,
    ! [X24,X49,X29,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_lessequals(X49,X24,X3)
      | ~ c_lessequals(c_Orderings_Oord__class_Omax(X29,X49,X3),X24,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_209]) ).

fof(c_0_619_620,plain,
    ! [X64,X40,X24,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_lessequals(X24,X64,X3)
      | ~ c_lessequals(c_Orderings_Oord__class_Omax(X24,X40,X3),X64,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_210]) ).

fof(c_0_620_621,plain,
    ! [X64,X40,X24,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_lessequals(X40,X64,X3)
      | ~ c_lessequals(c_Orderings_Oord__class_Omax(X24,X40,X3),X64,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_211]) ).

fof(c_0_621_622,plain,
    ! [X64,X40,X24,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_HOL_Oord__class_Oless(X40,X64,X3)
      | ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X24,X40,X3),X64,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_212]) ).

fof(c_0_622_623,plain,
    ! [X64,X40,X24,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_HOL_Oord__class_Oless(X24,X64,X3)
      | ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X24,X40,X3),X64,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_213]) ).

fof(c_0_623_624,plain,
    ! [X62,X50,X29,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X50),X62)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X50),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),X62)) ),
    inference(fof_simplification,[status(thm)],[c_0_214]) ).

fof(c_0_624_625,plain,
    ! [X50,X49,X29,X3] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X49),X50)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X49),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),X50)) ),
    inference(fof_simplification,[status(thm)],[c_0_215]) ).

fof(c_0_625_626,plain,
    ! [X64,X40,X24,X3] :
      ( ~ class_OrderedGroup_Oab__group__add(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X24),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X40),X64)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X40),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X24),X64)) ),
    inference(fof_simplification,[status(thm)],[c_0_216]) ).

fof(c_0_626_627,plain,
    ! [X40,X24,X8,X3] :
      ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X8,X3),X24),X40))
      | ~ hBOOL(hAPP(hAPP(X8,X24),X40)) ),
    inference(fof_simplification,[status(thm)],[c_0_217]) ).

fof(c_0_627_628,plain,
    ! [X51,X43,X60,X3] :
      ( c_List_Olistsp(X60,X43,X3)
      | ~ c_List_Olistsp(X60,c_List_Oappend(X43,X51,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_218]) ).

fof(c_0_628_629,plain,
    ! [X51,X43,X60,X3] :
      ( c_List_Olistsp(X60,X51,X3)
      | ~ c_List_Olistsp(X60,c_List_Oappend(X43,X51,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_219]) ).

fof(c_0_629_630,plain,
    ! [X40,X24,X3] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X24),X40) != c_HOL_Ozero__class_Ozero(X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X40,X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X24,X3)
      | X24 = c_HOL_Ozero__class_Ozero(X3) ),
    inference(fof_simplification,[status(thm)],[c_0_220]) ).

fof(c_0_630_631,plain,
    ! [X40,X24,X3] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X24),X40) != c_HOL_Ozero__class_Ozero(X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X40,X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X24,X3)
      | X40 = c_HOL_Ozero__class_Ozero(X3) ),
    inference(fof_simplification,[status(thm)],[c_0_221]) ).

fof(c_0_631_632,plain,
    ! [X3] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(X3),X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3)),c_HOL_Ozero__class_Ozero(X3)) = c_HOL_Ozero__class_Ozero(X3) ),
    inference(fof_simplification,[status(thm)],[c_0_222]) ).

fof(c_0_632_633,plain,
    ! [X18,X10,X61,X25] :
      ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X10),X61) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X25),X18)
      | ~ c_HOL_Oord__class_Oless(X25,X61,tc_nat)
      | c_HOL_Oord__class_Oless(X10,X18,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_223]) ).

fof(c_0_633_634,plain,
    ! [X25,X15,X16] :
      ( c_HOL_Oord__class_Oless(X16,X25,tc_nat)
      | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),X15),X25,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_224]) ).

fof(c_0_634_635,plain,
    ! [X18,X10,X29,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_Power_Opower__class_Opower(X29,X10,X3) != c_Power_Opower__class_Opower(X29,X18,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X29,X3)
      | X10 = X18 ),
    inference(fof_simplification,[status(thm)],[c_0_225]) ).

fof(c_0_635_636,plain,
    ! [X18,X29,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_Power_Opower__class_Opower(X29,X18,X3),X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X29,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_226]) ).

fof(c_0_636_637,plain,
    ! [X18,X29,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_lessequals(c_HOL_Oone__class_Oone(X3),c_Power_Opower__class_Opower(X29,X18,X3),X3)
      | ~ c_lessequals(c_HOL_Oone__class_Oone(X3),X29,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_227]) ).

fof(c_0_637_638,plain,
    ! [X18,X29,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Power_Opower__class_Opower(X29,X18,X3),X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X29,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_228]) ).

fof(c_0_638_639,plain,
    ! [X40,X8,X29,X3] :
      ( c_Wellfounded_Oaccp(X8,X40,X3)
      | ~ hBOOL(hAPP(hAPP(X8,X40),X29))
      | ~ c_Wellfounded_Oaccp(X8,X29,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_229]) ).

fof(c_0_639_640,plain,
    ! [X8,X49,X29,X3] :
      ( c_Wellfounded_Oaccp(X8,X29,X3)
      | ~ hBOOL(hAPP(hAPP(X8,X29),X49))
      | ~ c_Wellfounded_Oaccp(X8,X49,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_230]) ).

fof(c_0_640_641,plain,
    ! [X29,X3] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
      | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),X29),c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_lessequals(X29,c_HOL_Ozero__class_Ozero(X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_231]) ).

fof(c_0_641_642,plain,
    ! [X29,X3] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),X29),X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X29,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_232]) ).

fof(c_0_642_643,plain,
    ! [X29,X3] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),X29),c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_HOL_Oord__class_Oless(X29,c_HOL_Ozero__class_Ozero(X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_233]) ).

fof(c_0_643_644,plain,
    ! [X29,X3] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),X29),X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X29,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_234]) ).

fof(c_0_644_645,plain,
    ! [X29,X3] :
      ( ~ class_Ring__and__Field_Oordered__idom(X3)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),X29),c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_HOL_Oord__class_Oless(X29,c_HOL_Ozero__class_Ozero(X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_235]) ).

fof(c_0_645_646,plain,
    ! [X8] :
      ( hBOOL(hAPP(c_InductTermi_OIT,X8))
      | ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X8,tc_Lambda_OdB) ),
    inference(fof_simplification,[status(thm)],[c_0_236]) ).

fof(c_0_646_647,plain,
    ! [X54,X27,X21,X23] :
      ( c_Type_Otyping(X21,X54,X23)
      | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X27),X54))
      | ~ c_Type_Otyping(X21,X27,X23) ),
    inference(fof_simplification,[status(thm)],[c_0_237]) ).

fof(c_0_647_648,plain,
    ! [X51,X43,X3] :
      ( ~ class_OrderedGroup_Omonoid__add(X3)
      | c_List_Olistsum(c_List_Oappend(X43,X51,X3),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_List_Olistsum(X43,X3)),c_List_Olistsum(X51,X3)) ),
    inference(fof_simplification,[status(thm)],[c_0_238]) ).

fof(c_0_648_649,plain,
    ! [X24,X49,X29,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_lessequals(X24,c_Orderings_Oord__class_Omax(X29,X49,X3),X3)
      | ~ c_lessequals(X24,X29,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_239]) ).

fof(c_0_649_650,plain,
    ! [X24,X49,X29,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_lessequals(X24,c_Orderings_Oord__class_Omax(X29,X49,X3),X3)
      | ~ c_lessequals(X24,X49,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_240]) ).

fof(c_0_650_651,plain,
    ! [X64,X40,X24,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_lessequals(X64,c_Orderings_Oord__class_Omax(X24,X40,X3),X3)
      | ~ c_lessequals(X64,X24,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_241]) ).

fof(c_0_651_652,plain,
    ! [X64,X40,X24,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_lessequals(X64,c_Orderings_Oord__class_Omax(X24,X40,X3),X3)
      | ~ c_lessequals(X64,X40,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_242]) ).

fof(c_0_652_653,plain,
    ! [X64,X40,X24,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_HOL_Oord__class_Oless(X64,c_Orderings_Oord__class_Omax(X24,X40,X3),X3)
      | ~ c_HOL_Oord__class_Oless(X64,X40,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_243]) ).

fof(c_0_653_654,plain,
    ! [X64,X40,X24,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_HOL_Oord__class_Oless(X64,c_Orderings_Oord__class_Omax(X24,X40,X3),X3)
      | ~ c_HOL_Oord__class_Oless(X64,X24,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_244]) ).

fof(c_0_654_655,plain,
    ! [X24,X49,X29,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_HOL_Oord__class_Oless(X24,c_Orderings_Oord__class_Omax(X29,X49,X3),X3)
      | ~ c_HOL_Oord__class_Oless(X24,X49,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_245]) ).

fof(c_0_655_656,plain,
    ! [X24,X49,X29,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_HOL_Oord__class_Oless(X24,c_Orderings_Oord__class_Omax(X29,X49,X3),X3)
      | ~ c_HOL_Oord__class_Oless(X24,X29,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_246]) ).

fof(c_0_656_657,plain,
    ! [X18,X10,X3] :
      ( ~ class_Ring__and__Field_Osemiring__1(X3)
      | c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X10),X18),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_Nat_Osemiring__1__class_Oof__nat(X10,X3)),c_Nat_Osemiring__1__class_Oof__nat(X18,X3)) ),
    inference(fof_simplification,[status(thm)],[c_0_247]) ).

fof(c_0_657_658,plain,
    ! [X18,X10] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X10),X18),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X18,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_248]) ).

fof(c_0_658_659,plain,
    ! [X18,X10] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X10),X18),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X10,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_249]) ).

fof(c_0_659_660,plain,
    ! [X64,X40,X24,X3] :
      ( ~ class_Orderings_Opreorder(X3)
      | c_HOL_Oord__class_Oless(X24,X64,X3)
      | ~ c_lessequals(X40,X64,X3)
      | ~ c_HOL_Oord__class_Oless(X24,X40,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_250]) ).

fof(c_0_660_661,plain,
    ! [X64,X40,X24,X3] :
      ( ~ class_Orderings_Opreorder(X3)
      | c_HOL_Oord__class_Oless(X24,X64,X3)
      | ~ c_HOL_Oord__class_Oless(X40,X64,X3)
      | ~ c_lessequals(X24,X40,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_251]) ).

fof(c_0_661_662,plain,
    ! [X64,X40,X24,X3] :
      ( ~ class_Orderings_Opreorder(X3)
      | c_lessequals(X24,X64,X3)
      | ~ c_lessequals(X40,X64,X3)
      | ~ c_lessequals(X24,X40,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_252]) ).

fof(c_0_662_663,plain,
    ! [X64,X40,X24,X3] :
      ( ~ class_Orderings_Oorder(X3)
      | c_HOL_Oord__class_Oless(X64,X24,X3)
      | ~ c_HOL_Oord__class_Oless(X64,X40,X3)
      | ~ c_lessequals(X40,X24,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_253]) ).

fof(c_0_663_664,plain,
    ! [X64,X40,X24,X3] :
      ( ~ class_Orderings_Oorder(X3)
      | c_HOL_Oord__class_Oless(X64,X24,X3)
      | ~ c_lessequals(X64,X40,X3)
      | ~ c_HOL_Oord__class_Oless(X40,X24,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_254]) ).

fof(c_0_664_665,plain,
    ! [X64,X40,X24,X3] :
      ( ~ class_Orderings_Oorder(X3)
      | c_lessequals(X64,X24,X3)
      | ~ c_lessequals(X64,X40,X3)
      | ~ c_lessequals(X40,X24,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_255]) ).

fof(c_0_665_666,plain,
    ! [X64,X40,X24,X3] :
      ( ~ class_Orderings_Oorder(X3)
      | c_HOL_Oord__class_Oless(X64,X24,X3)
      | ~ c_HOL_Oord__class_Oless(X64,X40,X3)
      | ~ c_HOL_Oord__class_Oless(X40,X24,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_256]) ).

fof(c_0_666_667,plain,
    ! [X64,X40,X24,X3] :
      ( ~ class_Orderings_Opreorder(X3)
      | c_HOL_Oord__class_Oless(X24,X64,X3)
      | ~ c_HOL_Oord__class_Oless(X40,X64,X3)
      | ~ c_HOL_Oord__class_Oless(X24,X40,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_257]) ).

fof(c_0_667_668,plain,
    ! [X27,X7] :
      ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OAbs(X7)),c_Lambda_OdB_OAbs(X27)))
      | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X7),X27)) ),
    inference(fof_simplification,[status(thm)],[c_0_258]) ).

fof(c_0_668_669,plain,
    ! [X18,X10,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_HOL_Oord__class_Oless(X10,X18,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X10,X3),c_Nat_Osemiring__1__class_Oof__nat(X18,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_259]) ).

fof(c_0_669_670,plain,
    ! [X64,X40,X24] :
      ( c_HOL_Oord__class_Oless(X24,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X40),X64),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X24,X40,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_260]) ).

fof(c_0_670_671,plain,
    ! [X64,X40,X24] :
      ( c_HOL_Oord__class_Oless(X24,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X40),X64),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X24,X64,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_261]) ).

fof(c_0_671_672,plain,
    ! [X10,X15,X16] :
      ( c_HOL_Oord__class_Oless(X16,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X10),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X16,X15,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_262]) ).

fof(c_0_672_673,plain,
    ! [X10,X15,X16] :
      ( c_HOL_Oord__class_Oless(X16,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X10),X15),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X16,X15,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_263]) ).

fof(c_0_673_674,plain,
    ! [X40,X24,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_Orderings_Oord__class_Omax(X24,c_Orderings_Oord__class_Omax(X24,X40,X3),X3) = c_Orderings_Oord__class_Omax(X24,X40,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_264]) ).

fof(c_0_674_675,plain,
    ! [X27,X16] :
      ( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_Olift,X27),X16)))
      | ~ hBOOL(hAPP(c_InductTermi_OIT,X27)) ),
    inference(fof_simplification,[status(thm)],[c_0_265]) ).

fof(c_0_675,axiom,
    ! [X18,X25,X16] :
      ( c_Lambda_Oliftn(X18,c_Lambda_OdB_OVar(X16),X25) = c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),X18))
      | c_HOL_Oord__class_Oless(X16,X25,tc_nat) ),
    c_0_266 ).

fof(c_0_676,plain,
    ! [X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Oone__class_Oone(X3)),c_HOL_Oone__class_Oone(X3)),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_267]) ).

fof(c_0_677,plain,
    ! [X43,X24,X3] :
      ( ~ class_OrderedGroup_Omonoid__add(X3)
      | c_List_Olistsum(c_List_Olist_OCons(X24,X43,X3),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X24),c_List_Olistsum(X43,X3)) ),
    inference(fof_simplification,[status(thm)],[c_0_268]) ).

fof(c_0_678,plain,
    ! [X40,X24,X3] :
      ( ~ class_Orderings_Opreorder(X3)
      | c_HOL_Oord__class_Oless(X24,X40,X3)
      | c_lessequals(X40,X24,X3)
      | ~ c_lessequals(X24,X40,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_269]) ).

fof(c_0_679,axiom,
    ! [X25,X16] :
      ( hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(X16)),X25) = c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),c_HOL_Oone__class_Oone(tc_nat)))
      | c_HOL_Oord__class_Oless(X16,X25,tc_nat) ),
    c_0_270 ).

fof(c_0_680,plain,
    ! [X18,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X18,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Nat_Osemiring__1__class_Oof__nat(X18,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_271]) ).

fof(c_0_681,plain,
    ! [X26,X15,X16] :
      ( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X15)),X26),X16) = c_Lambda_OdB_OVar(X15)
      | ~ c_HOL_Oord__class_Oless(X15,X16,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_272]) ).

fof(c_0_682,plain,
    ! [X18,X10,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X10,X3),c_Nat_Osemiring__1__class_Oof__nat(X18,X3),X3)
      | ~ c_HOL_Oord__class_Oless(X10,X18,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_273]) ).

fof(c_0_683,plain,
    ! [X27] :
      ( c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X27,tc_Lambda_OdB)
      | ~ hBOOL(hAPP(c_InductTermi_OIT,X27)) ),
    inference(fof_simplification,[status(thm)],[c_0_274]) ).

fof(c_0_684,axiom,
    ! [X18,X10,X34] :
      ( hBOOL(hAPP(hAPP(X34,X18),X10))
      | c_HOL_Oord__class_Oless(X18,X10,tc_nat)
      | X10 = X18
      | c_HOL_Oord__class_Oless(X10,X18,tc_nat) ),
    c_0_275 ).

fof(c_0_685,plain,
    ! [X18,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Nat_Osemiring__1__class_Oof__nat(X18,X3),X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X18,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_276]) ).

fof(c_0_686,plain,
    ! [X40,X24,X3] :
      ( ~ class_Orderings_Oorder(X3)
      | X24 = X40
      | ~ c_lessequals(X24,X40,X3)
      | ~ c_lessequals(X40,X24,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_277]) ).

fof(c_0_687,plain,
    ! [X40,X24,X3] :
      ( ~ class_Orderings_Oorder(X3)
      | X24 = X40
      | ~ c_lessequals(X40,X24,X3)
      | ~ c_lessequals(X24,X40,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_278]) ).

fof(c_0_688,plain,
    ! [X40,X24,X3] :
      ( ~ class_Orderings_Oorder(X3)
      | X24 = X40
      | ~ c_lessequals(X40,X24,X3)
      | ~ c_lessequals(X24,X40,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_279]) ).

fof(c_0_689,plain,
    ! [X64,X40,X24,X3] :
      ( ~ class_Ring__and__Field_Oidom(X3)
      | ~ class_Int_Onumber__ring(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X24),X40) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X24),X64)
      | X40 = X64 ),
    inference(fof_simplification,[status(thm)],[c_0_280]) ).

fof(c_0_690,plain,
    ! [X29] :
      ( hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__5(X29)))
      | hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X29)))
      | c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X29),tc_Lambda_OdB)
      | ~ hBOOL(hAPP(c_InductTermi_OIT,X29)) ),
    inference(fof_simplification,[status(thm)],[c_0_281]) ).

fof(c_0_691,plain,
    ! [X24,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | ~ c_lessequals(X24,X24,X3)
      | ~ c_HOL_Oord__class_Oless(X24,X24,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_282]) ).

fof(c_0_692,plain,
    ! [X40,X24,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | ~ c_HOL_Oord__class_Oless(X24,X40,X3)
      | ~ c_lessequals(X40,X24,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_283]) ).

fof(c_0_693,plain,
    ! [X40,X24,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | ~ c_lessequals(X24,X40,X3)
      | ~ c_HOL_Oord__class_Oless(X40,X24,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_284]) ).

fof(c_0_694,plain,
    ! [X40,X24,X3] :
      ( ~ class_Orderings_Opreorder(X3)
      | ~ c_lessequals(X40,X24,X3)
      | ~ c_HOL_Oord__class_Oless(X24,X40,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_285]) ).

fof(c_0_695,plain,
    ! [X49,X29,X3] :
      ( ~ class_Orderings_Oorder(X3)
      | ~ c_HOL_Oord__class_Oless(X29,X49,X3)
      | ~ c_HOL_Oord__class_Oless(X49,X29,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_286]) ).

fof(c_0_696,plain,
    ! [X40,X24,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | ~ c_HOL_Oord__class_Oless(X24,X40,X3)
      | ~ c_HOL_Oord__class_Oless(X40,X24,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_287]) ).

fof(c_0_697,plain,
    ! [X40,X24,X3] :
      ( ~ class_Orderings_Opreorder(X3)
      | ~ c_HOL_Oord__class_Oless(X40,X24,X3)
      | ~ c_HOL_Oord__class_Oless(X24,X40,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_288]) ).

fof(c_0_698,plain,
    ! [X49,X29,X3] :
      ( ~ class_Orderings_Opreorder(X3)
      | ~ c_HOL_Oord__class_Oless(X49,X29,X3)
      | ~ c_HOL_Oord__class_Oless(X29,X49,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_289]) ).

fof(c_0_699,axiom,
    ! [X40,X24,X18,X10,X3] :
      ( c_List_Oreplicate(X10,X24,X3) != c_List_Oreplicate(X18,X40,X3)
      | X24 = X40
      | X10 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    c_0_290 ).

fof(c_0_700,plain,
    ! [X29,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_HOL_Oord__class_Oless(X29,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),c_HOL_Oone__class_Oone(X3)),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_291]) ).

fof(c_0_701,axiom,
    ! [X40,X24,X18,X10,X3] :
      ( c_List_Oreplicate(X10,X24,X3) != c_List_Oreplicate(X18,X40,X3)
      | X10 = X18 ),
    c_0_292 ).

fof(c_0_702,axiom,
    ! [X28,X51,X43,X3] :
      ( c_List_Oappend(X51,X43,X3) != c_List_Oappend(X28,X43,X3)
      | X51 = X28 ),
    c_0_293 ).

fof(c_0_703,axiom,
    ! [X28,X51,X43,X3] :
      ( c_List_Oappend(X43,X51,X3) != c_List_Oappend(X43,X28,X3)
      | X51 = X28 ),
    c_0_294 ).

fof(c_0_704,plain,
    ! [X50,X49,X29,X3] :
      ( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),X49) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),X50)
      | X49 = X50 ),
    inference(fof_simplification,[status(thm)],[c_0_295]) ).

fof(c_0_705,plain,
    ! [X50,X49,X29,X3] :
      ( ~ class_OrderedGroup_Ocancel__semigroup__add(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),X49) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),X50)
      | X49 = X50 ),
    inference(fof_simplification,[status(thm)],[c_0_296]) ).

fof(c_0_706,plain,
    ! [X50,X49,X29,X3] :
      ( ~ class_OrderedGroup_Ocancel__semigroup__add(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X49),X29) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X50),X29)
      | X49 = X50 ),
    inference(fof_simplification,[status(thm)],[c_0_297]) ).

fof(c_0_707,axiom,
    ! [X55,X56,X57,X29,X3] :
      ( c_List_Olist_OCons(X29,X56,X3) != c_List_Olist_OCons(X57,X55,X3)
      | X29 = X57 ),
    c_0_298 ).

fof(c_0_708,axiom,
    ! [X55,X56,X57,X29,X3] :
      ( c_List_Olist_OCons(X29,X56,X3) != c_List_Olist_OCons(X57,X55,X3)
      | X56 = X55 ),
    c_0_299 ).

fof(c_0_709,axiom,
    ! [X24,X7] :
      ( c_HOL_Oord__class_Oless(X24,X24,tc_nat)
      | c_Lambda_Osubstn(c_Lambda_OdB_OVar(X24),X7,X24) = c_Lambda_Oliftn(X24,X7,c_HOL_Ozero__class_Ozero(tc_nat)) ),
    c_0_300 ).

fof(c_0_710,axiom,
    ! [X7,X25,X16] :
      ( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X16)),X7),X25) = c_Lambda_OdB_OVar(X16)
      | X16 = X25
      | c_HOL_Oord__class_Oless(X25,X16,tc_nat) ),
    c_0_301 ).

fof(c_0_711,plain,
    ! [X1,X2,X3] :
      ( X2 = X1
      | ~ hBOOL(hAPP(hAPP(c_fequal(X3),X2),X1)) ),
    inference(fof_simplification,[status(thm)],[c_0_302]) ).

fof(c_0_712,plain,
    ! [X40,X24,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_lessequals(X40,c_Orderings_Oord__class_Omax(X24,X40,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_303]) ).

fof(c_0_713,plain,
    ! [X40,X24,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_lessequals(X24,c_Orderings_Oord__class_Omax(X24,X40,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_304]) ).

fof(c_0_714,axiom,
    ! [X24,X7] :
      ( c_HOL_Oord__class_Oless(X24,X24,tc_nat)
      | hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X24)),X7),X24) = X7 ),
    c_0_305 ).

fof(c_0_715,plain,
    ! [X29] :
      ( hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__5(X29)))
      | X29 = c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X29))
      | c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X29),tc_Lambda_OdB)
      | ~ hBOOL(hAPP(c_InductTermi_OIT,X29)) ),
    inference(fof_simplification,[status(thm)],[c_0_306]) ).

fof(c_0_716,plain,
    ! [X40,X24,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | X24 = X40
      | c_HOL_Oord__class_Oless(X24,X40,X3)
      | ~ c_lessequals(X24,X40,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_307]) ).

fof(c_0_717,plain,
    ! [X40,X24,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | X24 = X40
      | ~ c_lessequals(X24,X40,X3)
      | c_HOL_Oord__class_Oless(X24,X40,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_308]) ).

fof(c_0_718,plain,
    ! [X49,X29,X3] :
      ( ~ class_Orderings_Oorder(X3)
      | c_HOL_Oord__class_Oless(X29,X49,X3)
      | ~ c_lessequals(X29,X49,X3)
      | X29 = X49 ),
    inference(fof_simplification,[status(thm)],[c_0_309]) ).

fof(c_0_719,plain,
    ! [X49,X29,X3] :
      ( ~ class_Orderings_Oorder(X3)
      | c_HOL_Oord__class_Oless(X29,X49,X3)
      | X29 = X49
      | ~ c_lessequals(X29,X49,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_310]) ).

fof(c_0_720,plain,
    ! [X40,X24,X3] :
      ( ~ class_Orderings_Oorder(X3)
      | c_HOL_Oord__class_Oless(X24,X40,X3)
      | X24 = X40
      | ~ c_lessequals(X24,X40,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_311]) ).

fof(c_0_721,plain,
    ! [X40,X24,X3] :
      ( ~ class_Orderings_Oorder(X3)
      | X24 = X40
      | c_HOL_Oord__class_Oless(X24,X40,X3)
      | ~ c_lessequals(X24,X40,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_312]) ).

fof(c_0_722,plain,
    ! [X49,X29,X3] :
      ( ~ class_Orderings_Oorder(X3)
      | c_HOL_Oord__class_Oless(X49,X29,X3)
      | ~ c_lessequals(X49,X29,X3)
      | X29 = X49 ),
    inference(fof_simplification,[status(thm)],[c_0_313]) ).

fof(c_0_723,plain,
    ! [X49,X29,X3] :
      ( ~ class_Orderings_Oorder(X3)
      | c_HOL_Oord__class_Oless(X49,X29,X3)
      | X29 = X49
      | ~ c_lessequals(X49,X29,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_314]) ).

fof(c_0_724,plain,
    ! [X40,X24,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_Orderings_Oord__class_Omax(X24,X40,X3) != X40
      | c_lessequals(X24,X40,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_315]) ).

fof(c_0_725,plain,
    ! [X40,X24,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_Orderings_Oord__class_Omax(X24,X40,X3) = X40
      | ~ c_lessequals(X24,X40,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_316]) ).

fof(c_0_726,plain,
    ! [X40,X24,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_Orderings_Oord__class_Omax(X24,X40,X3) = X24
      | ~ c_lessequals(X40,X24,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_317]) ).

fof(c_0_727,plain,
    ! [X18,X25,X16] :
      ( c_Lambda_Oliftn(X18,c_Lambda_OdB_OVar(X16),X25) = c_Lambda_OdB_OVar(X16)
      | ~ c_HOL_Oord__class_Oless(X16,X25,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_318]) ).

fof(c_0_728,plain,
    ! [X40,X24,X3] :
      ( ~ class_Orderings_Opreorder(X3)
      | c_lessequals(X24,X40,X3)
      | ~ c_HOL_Oord__class_Oless(X24,X40,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_319]) ).

fof(c_0_729,plain,
    ! [X40,X24,X3] :
      ( ~ class_Orderings_Oorder(X3)
      | c_lessequals(X24,X40,X3)
      | ~ c_HOL_Oord__class_Oless(X24,X40,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_320]) ).

fof(c_0_730,axiom,
    ! [X18,X10,X25] :
      ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X10),X25) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X25)
      | X10 = X18 ),
    c_0_321 ).

fof(c_0_731,axiom,
    ! [X64,X40,X24] :
      ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X24),X40) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X24),X64)
      | X40 = X64 ),
    c_0_322 ).

fof(c_0_732,axiom,
    ! [X18,X10,X25] :
      ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X25),X10) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X25),X18)
      | X10 = X18 ),
    c_0_323 ).

fof(c_0_733,plain,
    ! [X10,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X10,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_324]) ).

fof(c_0_734,plain,
    ! [X25,X16] :
      ( hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(X16)),X25) = c_Lambda_OdB_OVar(X16)
      | ~ c_HOL_Oord__class_Oless(X16,X25,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_325]) ).

fof(c_0_735,plain,
    ! [X38,X39,X29,X3] :
      ( hAPP(hAPP(X39,X29),X38) = X29
      | ~ c_OrderedGroup_Omonoid__add(X38,X39,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_326]) ).

fof(c_0_736,plain,
    ! [X38,X39,X29,X3] :
      ( hAPP(hAPP(X39,X38),X29) = X29
      | ~ c_OrderedGroup_Omonoid__add(X38,X39,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_327]) ).

fof(c_0_737,plain,
    ! [X18,X29,X3] :
      ( ~ class_Ring__and__Field_Ozero__neq__one(X3)
      | ~ class_Ring__and__Field_Ono__zero__divisors(X3)
      | ~ class_Ring__and__Field_Omult__zero(X3)
      | ~ class_Power_Opower(X3)
      | c_Power_Opower__class_Opower(X29,X18,X3) != c_HOL_Ozero__class_Ozero(X3)
      | X29 = c_HOL_Ozero__class_Ozero(X3) ),
    inference(fof_simplification,[status(thm)],[c_0_328]) ).

fof(c_0_738,plain,
    ! [X29,X3] :
      ( ~ class_Ring__and__Field_Ozero__neq__one(X3)
      | ~ class_Ring__and__Field_Ono__zero__divisors(X3)
      | ~ class_Ring__and__Field_Omult__zero(X3)
      | ~ class_Power_Opower(X3)
      | c_Power_Opower__class_Opower(X29,c_HOL_Ozero__class_Ozero(tc_nat),X3) != c_HOL_Ozero__class_Ozero(X3) ),
    inference(fof_simplification,[status(thm)],[c_0_329]) ).

fof(c_0_739,axiom,
    ! [X7,X25,X16] :
      ( c_Lambda_Osubstn(c_Lambda_OdB_OVar(X16),X7,X25) = c_Lambda_OdB_OVar(X16)
      | X16 = X25
      | c_HOL_Oord__class_Oless(X25,X16,tc_nat) ),
    c_0_330 ).

fof(c_0_740,plain,
    ! [X40,X24,X3] :
      ( ~ class_Ring__and__Field_Oordered__idom(X3)
      | c_HOL_Oord__class_Oless(X40,X24,X3)
      | c_HOL_Oord__class_Oless(X24,X40,X3)
      | X24 = X40 ),
    inference(fof_simplification,[status(thm)],[c_0_331]) ).

fof(c_0_741,plain,
    ! [X40,X24,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | X24 = X40
      | c_HOL_Oord__class_Oless(X40,X24,X3)
      | c_HOL_Oord__class_Oless(X24,X40,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_332]) ).

fof(c_0_742,plain,
    ! [X40,X24,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_HOL_Oord__class_Oless(X40,X24,X3)
      | c_HOL_Oord__class_Oless(X24,X40,X3)
      | X24 = X40 ),
    inference(fof_simplification,[status(thm)],[c_0_333]) ).

fof(c_0_743,plain,
    ! [X40,X24,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_HOL_Oord__class_Oless(X40,X24,X3)
      | X24 = X40
      | c_HOL_Oord__class_Oless(X24,X40,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_334]) ).

fof(c_0_744,plain,
    ! [X40,X24,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | X24 = X40
      | c_HOL_Oord__class_Oless(X24,X40,X3)
      | c_HOL_Oord__class_Oless(X40,X24,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_335]) ).

fof(c_0_745,axiom,
    ! [X11,X12,X13,X14] :
      ( hAPP(hAPP(c_Lambda_OdB_OApp,X14),X12) != hAPP(hAPP(c_Lambda_OdB_OApp,X13),X11)
      | X14 = X13 ),
    c_0_336 ).

fof(c_0_746,axiom,
    ! [X11,X12,X13,X14] :
      ( hAPP(hAPP(c_Lambda_OdB_OApp,X14),X12) != hAPP(hAPP(c_Lambda_OdB_OApp,X13),X11)
      | X12 = X11 ),
    c_0_337 ).

fof(c_0_747,plain,
    ! [X40,X24,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_lessequals(X40,X24,X3)
      | c_lessequals(X24,X40,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_338]) ).

fof(c_0_748,plain,
    ! [X40,X24,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_HOL_Oord__class_Oless(X24,X40,X3)
      | c_lessequals(X40,X24,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_339]) ).

fof(c_0_749,plain,
    ! [X24,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_HOL_Oord__class_Oless(X24,X24,X3)
      | c_lessequals(X24,X24,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_340]) ).

fof(c_0_750,plain,
    ! [X40,X24,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_lessequals(X40,X24,X3)
      | c_HOL_Oord__class_Oless(X24,X40,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_341]) ).

fof(c_0_751,plain,
    ! [X40,X24,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_HOL_Oord__class_Oless(X40,X24,X3)
      | c_lessequals(X24,X40,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_342]) ).

fof(c_0_752,plain,
    ! [X40,X24,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_Orderings_Oord__class_Omax(X24,X40,X3) = c_Orderings_Oord__class_Omax(X40,X24,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_343]) ).

fof(c_0_753,plain,
    ! [X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_344]) ).

fof(c_0_754,plain,
    ! [X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | ~ c_lessequals(c_HOL_Oone__class_Oone(X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_345]) ).

fof(c_0_755,plain,
    ! [X50,X29,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),X50) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X50),X29) ),
    inference(fof_simplification,[status(thm)],[c_0_346]) ).

fof(c_0_756,plain,
    ! [X49,X29,X3] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),X49) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X49),X29) ),
    inference(fof_simplification,[status(thm)],[c_0_347]) ).

fof(c_0_757,plain,
    ! [X40,X24,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X24),X40) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X40),X24) ),
    inference(fof_simplification,[status(thm)],[c_0_348]) ).

fof(c_0_758,plain,
    ! [X16,X21,X23] :
      ( hAPP(X21,X16) = X23
      | ~ c_Type_Otyping(X21,c_Lambda_OdB_OVar(X16),X23) ),
    inference(fof_simplification,[status(thm)],[c_0_349]) ).

fof(c_0_759,axiom,
    ! [X18,X10] :
      ( c_HOL_Oord__class_Oless(X18,X10,tc_nat)
      | c_HOL_Oord__class_Oless(X10,X18,tc_nat)
      | X10 = X18 ),
    c_0_350 ).

fof(c_0_760,axiom,
    ! [X40,X24] :
      ( c_HOL_Oord__class_Oless(X40,X24,tc_nat)
      | c_HOL_Oord__class_Oless(X24,X40,tc_nat)
      | X24 = X40 ),
    c_0_351 ).

fof(c_0_761,plain,
    ! [X18,X29,X3] :
      ( ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X3)
      | c_Power_Opower__class_Opower(X29,X18,X3) != c_HOL_Ozero__class_Ozero(X3)
      | X29 = c_HOL_Ozero__class_Ozero(X3) ),
    inference(fof_simplification,[status(thm)],[c_0_352]) ).

fof(c_0_762,plain,
    ! [X24,X29,X3] :
      ( ~ class_Ring__and__Field_Oidom(X3)
      | ~ class_Int_Onumber__ring(X3)
      | X24 != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X24),X29)
      | X29 = c_HOL_Ozero__class_Ozero(X3) ),
    inference(fof_simplification,[status(thm)],[c_0_353]) ).

fof(c_0_763,plain,
    ! [X29,X3] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),X29) != c_HOL_Ozero__class_Ozero(X3)
      | X29 = c_HOL_Ozero__class_Ozero(X3) ),
    inference(fof_simplification,[status(thm)],[c_0_354]) ).

fof(c_0_764,axiom,
    ! [X51,X43,X3] :
      ( c_List_Olist_ONil(X3) != c_List_Oappend(X43,X51,X3)
      | X43 = c_List_Olist_ONil(X3) ),
    c_0_355 ).

fof(c_0_765,axiom,
    ! [X51,X43,X3] :
      ( c_List_Olist_ONil(X3) != c_List_Oappend(X43,X51,X3)
      | X51 = c_List_Olist_ONil(X3) ),
    c_0_356 ).

fof(c_0_766,axiom,
    ! [X51,X43,X3] :
      ( c_List_Oappend(X43,X51,X3) != c_List_Olist_ONil(X3)
      | X43 = c_List_Olist_ONil(X3) ),
    c_0_357 ).

fof(c_0_767,axiom,
    ! [X51,X43,X3] :
      ( c_List_Oappend(X43,X51,X3) != c_List_Olist_ONil(X3)
      | X51 = c_List_Olist_ONil(X3) ),
    c_0_358 ).

fof(c_0_768,plain,
    ! [X18,X3] :
      ( ~ class_Ring__and__Field_Ozero__neq__one(X3)
      | ~ class_Ring__and__Field_Ono__zero__divisors(X3)
      | ~ class_Ring__and__Field_Omult__zero(X3)
      | ~ class_Power_Opower(X3)
      | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X3),X18,X3) = c_HOL_Ozero__class_Ozero(X3)
      | X18 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_359]) ).

fof(c_0_769,axiom,
    ! [X24,X18,X3] :
      ( c_List_Oreplicate(X18,X24,X3) != c_List_Olist_ONil(X3)
      | X18 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    c_0_360 ).

fof(c_0_770,axiom,
    ! [X24,X18,X3] :
      ( c_List_Olist_ONil(X3) != c_List_Oreplicate(X18,X24,X3)
      | X18 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    c_0_361 ).

fof(c_0_771,plain,
    ! [X10,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_Nat_Osemiring__1__class_Oof__nat(X10,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_362]) ).

fof(c_0_772,plain,
    ! [X18,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_Nat_Osemiring__1__class_Oof__nat(X18,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_363]) ).

fof(c_0_773,plain,
    ! [X24,X3] :
      ( ~ class_Orderings_Oorder(X3)
      | ~ c_HOL_Oord__class_Oless(X24,X24,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_364]) ).

fof(c_0_774,plain,
    ! [X24,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | ~ c_HOL_Oord__class_Oless(X24,X24,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_365]) ).

fof(c_0_775,plain,
    ! [X24,X3] :
      ( ~ class_Orderings_Opreorder(X3)
      | ~ c_HOL_Oord__class_Oless(X24,X24,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_366]) ).

fof(c_0_776,axiom,
    ! [X51,X43,X3] :
      ( c_List_Oappend(X43,X51,X3) != X43
      | X51 = c_List_Olist_ONil(X3) ),
    c_0_367 ).

fof(c_0_777,axiom,
    ! [X51,X43,X3] :
      ( X43 != c_List_Oappend(X43,X51,X3)
      | X51 = c_List_Olist_ONil(X3) ),
    c_0_368 ).

fof(c_0_778,axiom,
    ! [X51,X43,X3] :
      ( c_List_Oappend(X43,X51,X3) != X51
      | X43 = c_List_Olist_ONil(X3) ),
    c_0_369 ).

fof(c_0_779,axiom,
    ! [X51,X43,X3] :
      ( X51 != c_List_Oappend(X43,X51,X3)
      | X43 = c_List_Olist_ONil(X3) ),
    c_0_370 ).

fof(c_0_780,plain,
    ! [X18,X3] :
      ( ~ class_Ring__and__Field_Osemiring__0(X3)
      | ~ class_Power_Opower(X3)
      | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X3),X18,X3) = c_HOL_Ozero__class_Ozero(X3)
      | X18 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_371]) ).

fof(c_0_781,plain,
    ! [X8] :
      ( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(X8)))
      | ~ hBOOL(hAPP(c_InductTermi_OIT,X8)) ),
    inference(fof_simplification,[status(thm)],[c_0_372]) ).

fof(c_0_782,plain,
    ! [X3] :
      ( ~ class_Ring__and__Field_Osemiring__0(X3)
      | ~ class_Power_Opower(X3)
      | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(tc_nat),X3) = c_HOL_Oone__class_Oone(X3) ),
    inference(fof_simplification,[status(thm)],[c_0_373]) ).

fof(c_0_783,plain,
    ! [X3] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3)),c_HOL_Ozero__class_Ozero(X3)) = c_HOL_Ozero__class_Ozero(X3) ),
    inference(fof_simplification,[status(thm)],[c_0_374]) ).

fof(c_0_784,axiom,
    ! [X18,X10] :
      ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X10),X18) != c_HOL_Ozero__class_Ozero(tc_nat)
      | X18 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    c_0_375 ).

fof(c_0_785,axiom,
    ! [X18,X10] :
      ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X10),X18) != c_HOL_Ozero__class_Ozero(tc_nat)
      | X10 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    c_0_376 ).

fof(c_0_786,axiom,
    ! [X24,X29] :
      ( X24 != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X24),X29)
      | X29 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    c_0_377 ).

fof(c_0_787,axiom,
    ! [X18,X10] :
      ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X10),X18) != X10
      | X18 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    c_0_378 ).

fof(c_0_788,plain,
    ! [X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oone__class_Oone(X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_379]) ).

fof(c_0_789,plain,
    ! [X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oone__class_Oone(X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_380]) ).

fof(c_0_790,plain,
    ! [X24,X3] :
      ( ~ class_Ring__and__Field_Oidom(X3)
      | ~ class_Int_Onumber__ring(X3)
      | X24 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X24),c_HOL_Ozero__class_Ozero(X3)) ),
    inference(fof_simplification,[status(thm)],[c_0_381]) ).

fof(c_0_791,plain,
    ! [X24,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3)),X24) = X24 ),
    inference(fof_simplification,[status(thm)],[c_0_382]) ).

fof(c_0_792,plain,
    ! [X29,X3] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3)),X29) = X29 ),
    inference(fof_simplification,[status(thm)],[c_0_383]) ).

fof(c_0_793,plain,
    ! [X29,X3] :
      ( ~ class_OrderedGroup_Omonoid__add(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3)),X29) = X29 ),
    inference(fof_simplification,[status(thm)],[c_0_384]) ).

fof(c_0_794,plain,
    ! [X29,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3)),X29) = X29 ),
    inference(fof_simplification,[status(thm)],[c_0_385]) ).

fof(c_0_795,plain,
    ! [X18,X3] :
      ( ~ class_OrderedGroup_Omonoid__mult(X3)
      | c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X3),X18,X3) = c_HOL_Oone__class_Oone(X3) ),
    inference(fof_simplification,[status(thm)],[c_0_386]) ).

fof(c_0_796,plain,
    ! [X29,X3] :
      ( ~ class_Power_Opower(X3)
      | c_Power_Opower__class_Opower(X29,c_HOL_Ozero__class_Ozero(tc_nat),X3) = c_HOL_Oone__class_Oone(X3) ),
    inference(fof_simplification,[status(thm)],[c_0_387]) ).

fof(c_0_797,plain,
    ! [X24,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_Power_Opower__class_Opower(X24,c_HOL_Ozero__class_Ozero(tc_nat),X3) = c_HOL_Oone__class_Oone(X3) ),
    inference(fof_simplification,[status(thm)],[c_0_388]) ).

fof(c_0_798,plain,
    ! [X29,X3] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),c_HOL_Ozero__class_Ozero(X3)) = X29 ),
    inference(fof_simplification,[status(thm)],[c_0_389]) ).

fof(c_0_799,plain,
    ! [X29,X3] :
      ( ~ class_OrderedGroup_Omonoid__add(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),c_HOL_Ozero__class_Ozero(X3)) = X29 ),
    inference(fof_simplification,[status(thm)],[c_0_390]) ).

fof(c_0_800,plain,
    ! [X29,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X29),c_HOL_Ozero__class_Ozero(X3)) = X29 ),
    inference(fof_simplification,[status(thm)],[c_0_391]) ).

fof(c_0_801,plain,
    ! [X29,X3] :
      ( ~ class_OrderedGroup_Omonoid__mult(X3)
      | c_Power_Opower__class_Opower(X29,c_HOL_Oone__class_Oone(tc_nat),X3) = X29 ),
    inference(fof_simplification,[status(thm)],[c_0_392]) ).

fof(c_0_802,plain,
    ! [X24,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_Power_Opower__class_Opower(X24,c_HOL_Oone__class_Oone(tc_nat),X3) = X24 ),
    inference(fof_simplification,[status(thm)],[c_0_393]) ).

fof(c_0_803,plain,
    ! [X24,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_Orderings_Oord__class_Omax(X24,X24,X3) = X24 ),
    inference(fof_simplification,[status(thm)],[c_0_394]) ).

fof(c_0_804,plain,
    ! [X24,X3] :
      ( ~ class_Orderings_Opreorder(X3)
      | c_lessequals(X24,X24,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_395]) ).

fof(c_0_805,plain,
    ! [X24,X3] :
      ( ~ class_Orderings_Oorder(X3)
      | c_lessequals(X24,X24,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_396]) ).

fof(c_0_806,axiom,
    ! [X18] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X18,tc_nat)
      | X18 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    c_0_397 ).

fof(c_0_807,plain,
    ! [X18,X10,X3] :
      ( ~ class_Nat_Osemiring__char__0(X3)
      | c_Nat_Osemiring__1__class_Oof__nat(X10,X3) != c_Nat_Osemiring__1__class_Oof__nat(X18,X3)
      | X10 = X18 ),
    inference(fof_simplification,[status(thm)],[c_0_398]) ).

fof(c_0_808,plain,
    ! [X4,X5] :
      ( class_Orderings_Opreorder(tc_fun(X4,X5))
      | ~ class_Orderings_Opreorder(X5) ),
    inference(fof_simplification,[status(thm)],[c_0_399]) ).

fof(c_0_809,plain,
    ! [X4,X5] :
      ( class_Orderings_Oorder(tc_fun(X4,X5))
      | ~ class_Orderings_Oorder(X5) ),
    inference(fof_simplification,[status(thm)],[c_0_400]) ).

fof(c_0_810,plain,
    ! [X3] :
      ( ~ class_OrderedGroup_Omonoid__add(X3)
      | c_List_Olistsum(c_List_Olist_ONil(X3),X3) = c_HOL_Ozero__class_Ozero(X3) ),
    inference(fof_simplification,[status(thm)],[c_0_401]) ).

fof(c_0_811,plain,
    ! [X3] :
      ( ~ class_Ring__and__Field_Osemiring__1(X3)
      | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),X3) = c_HOL_Oone__class_Oone(X3) ),
    inference(fof_simplification,[status(thm)],[c_0_402]) ).

fof(c_0_812,plain,
    ! [X3] :
      ( ~ class_Ring__and__Field_Osemiring__1(X3)
      | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X3) = c_HOL_Ozero__class_Ozero(X3) ),
    inference(fof_simplification,[status(thm)],[c_0_403]) ).

fof(c_0_813,plain,
    ! [X3] :
      ( ~ class_OrderedGroup_Osemigroup__add(X3)
      | c_OrderedGroup_Osemigroup__add(c_HOL_Oplus__class_Oplus(X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_404]) ).

fof(c_0_814,plain,
    ! [X3] :
      ( ~ class_Ring__and__Field_Ozero__neq__one(X3)
      | c_HOL_Oone__class_Oone(X3) != c_HOL_Ozero__class_Ozero(X3) ),
    inference(fof_simplification,[status(thm)],[c_0_405]) ).

fof(c_0_815,plain,
    ! [X3] :
      ( ~ class_Ring__and__Field_Ozero__neq__one(X3)
      | c_HOL_Ozero__class_Ozero(X3) != c_HOL_Oone__class_Oone(X3) ),
    inference(fof_simplification,[status(thm)],[c_0_406]) ).

fof(c_0_816,axiom,
    ! [X63,X59] :
      ( c_Lambda_OdB_OAbs(X59) != c_Lambda_OdB_OAbs(X63)
      | X59 = X63 ),
    c_0_407 ).

fof(c_0_817,axiom,
    ! [X19,X20] :
      ( c_Lambda_OdB_OVar(X20) != c_Lambda_OdB_OVar(X19)
      | X20 = X19 ),
    c_0_408 ).

fof(c_0_818,plain,
    ! [X31,X32,X33] :
      ( X31 = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X33),c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(X33,X32,X31),tc_Lambda_OdB,tc_Lambda_OdB)
      | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X33),X32,tc_Lambda_OdB,tc_Lambda_OdB)),X31)) ),
    inference(variable_rename,[status(thm)],[c_0_409]) ).

fof(c_0_819,plain,
    ! [X38,X39,X40,X41,X42,X43] :
      ( c_Type_Otypings(X41,c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,X38,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),X40,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X39,tc_Lambda_OdB,tc_Lambda_OdB),X42)
      | ~ c_Type_Otypings(c_Type_Oshift(X41,X40,X43,tc_Type_Otype),X39,X42)
      | ~ c_Type_Otyping(X41,X38,X43) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_410])])]) ).

fof(c_0_820,plain,
    ! [X38,X39,X40,X41,X42,X43,X44] :
      ( c_Type_Otypings(X41,X38,c_Type_Osko__Type__Xvar__app__types__1__1(X44,X42,X41,X38))
      | ~ c_Type_Otyping(X41,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X40),X39,tc_Lambda_OdB,tc_Lambda_OdB),X42)
      | ~ c_Type_Otypings(X41,X39,X43)
      | ~ c_Type_Otyping(X41,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X40),X39,tc_Lambda_OdB,tc_Lambda_OdB),X38,tc_Lambda_OdB,tc_Lambda_OdB),X44) ),
    inference(variable_rename,[status(thm)],[c_0_411]) ).

fof(c_0_821,plain,
    ! [X31,X32,X33] :
      ( c_ListOrder_Ostep1(c_Lambda_Obeta,X32,c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(X33,X32,X31),tc_Lambda_OdB)
      | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X33),X32,tc_Lambda_OdB,tc_Lambda_OdB)),X31)) ),
    inference(variable_rename,[status(thm)],[c_0_412]) ).

fof(c_0_822,plain,
    ! [X35,X36] :
      ( hBOOL(hAPP(X36,X35))
      | ~ hBOOL(hAPP(X36,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3(X36)),c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__4(X36),tc_Lambda_OdB,tc_Lambda_OdB)))
      | ~ hBOOL(hAPP(X36,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1(X36)),c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2(X36),tc_Lambda_OdB,tc_Lambda_OdB))) ),
    inference(variable_rename,[status(thm)],[c_0_413]) ).

fof(c_0_823,plain,
    ! [X35,X36] :
      ( ~ hBOOL(hAPP(X36,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(c_ListApplication_Osko__ListApplication__Xlem__1__3(X36)),c_ListApplication_Osko__ListApplication__Xlem__1__4(X36),tc_Lambda_OdB,tc_Lambda_OdB)))
      | ~ hBOOL(hAPP(X36,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_ListApplication_Osko__ListApplication__Xlem__1__1(X36)),c_ListApplication_Osko__ListApplication__Xlem__1__2(X36),tc_Lambda_OdB,tc_Lambda_OdB)))
      | hBOOL(hAPP(X36,X35)) ),
    inference(variable_rename,[status(thm)],[c_0_414]) ).

fof(c_0_824,plain,
    ! [X18,X19,X20] :
      ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,X20,X19,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X20,X18,tc_Lambda_OdB,tc_Lambda_OdB)))
      | ~ c_ListOrder_Ostep1(c_Lambda_Obeta,X19,X18,tc_Lambda_OdB) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_415])])]) ).

fof(c_0_825,plain,
    ! [X10,X11,X12] :
      ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,X12,X10,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X11,X10,tc_Lambda_OdB,tc_Lambda_OdB)))
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X12),X11)) ),
    inference(variable_rename,[status(thm)],[c_0_416]) ).

fof(c_0_826,plain,
    ! [X10,X11,X12] :
      ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,X12,X10,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X11,X10,tc_Lambda_OdB,tc_Lambda_OdB)))
      | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X12),X11)) ),
    inference(variable_rename,[status(thm)],[c_0_417]) ).

fof(c_0_827,plain,
    ! [X10,X11,X12] :
      ( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X12)),X11),X10,tc_Lambda_OdB,tc_Lambda_OdB)))
      | ~ hBOOL(hAPP(c_InductTermi_OIT,X11))
      | ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X12),X11),c_HOL_Ozero__class_Ozero(tc_nat)),X10,tc_Lambda_OdB,tc_Lambda_OdB))) ),
    inference(variable_rename,[status(thm)],[c_0_418]) ).

fof(c_0_828,plain,
    ! [X70,X71,X72,X73,X74,X75,X76,X77,X78,X79] :
      ( hAPP(hAPP(X75,hAPP(hAPP(X75,X77),X76)),hAPP(hAPP(X75,X71),X70)) = hAPP(hAPP(X75,X71),hAPP(hAPP(X75,hAPP(hAPP(X75,X77),X76)),X70))
      | ~ c_Groebner__Basis_Ogb__semiring(X78,X75,X74,X73,X72,X79) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_419])])]) ).

fof(c_0_829,plain,
    ! [X63,X64,X65,X66,X67,X68,X69,X70,X71,X72] :
      ( hAPP(hAPP(X70,hAPP(hAPP(X70,X71),X69)),hAPP(hAPP(X70,X68),X67)) = hAPP(hAPP(X70,hAPP(hAPP(X70,X71),X68)),hAPP(hAPP(X70,X69),X67))
      | ~ c_Groebner__Basis_Ogb__semiring(X70,X66,X65,X64,X63,X72) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_420])])]) ).

fof(c_0_830,plain,
    ! [X70,X71,X72,X73,X74,X75,X76,X77,X78,X79] :
      ( hAPP(hAPP(X75,hAPP(hAPP(X75,X77),X76)),hAPP(hAPP(X75,X71),X70)) = hAPP(hAPP(X75,X77),hAPP(hAPP(X75,X76),hAPP(hAPP(X75,X71),X70)))
      | ~ c_Groebner__Basis_Ogb__semiring(X78,X75,X74,X73,X72,X79) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_421])])]) ).

fof(c_0_831,plain,
    ! [X70,X71,X72,X73,X74,X75,X76,X77,X78,X79] :
      ( hAPP(hAPP(X75,hAPP(hAPP(X75,X77),X76)),hAPP(hAPP(X75,X71),X70)) = hAPP(hAPP(X75,hAPP(hAPP(X75,X77),X71)),hAPP(hAPP(X75,X76),X70))
      | ~ c_Groebner__Basis_Ogb__semiring(X78,X75,X74,X73,X72,X79) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_422])])]) ).

fof(c_0_832,plain,
    ! [X71,X72,X73,X74,X75,X76,X77,X78,X79] :
      ( hAPP(hAPP(X76,hAPP(hAPP(X77,X72),X71)),X75) = hAPP(hAPP(X77,hAPP(hAPP(X76,X72),X75)),hAPP(hAPP(X76,X71),X75))
      | ~ c_Groebner__Basis_Ogb__semiring(X78,X77,X76,X74,X73,X79) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_423])])]) ).

fof(c_0_833,plain,
    ! [X51,X52,X53,X54,X55,X56,X57,X58,X59] :
      ( hAPP(hAPP(X54,hAPP(hAPP(X57,X58),X56)),X55) = hAPP(hAPP(X57,hAPP(hAPP(X54,X58),X55)),hAPP(hAPP(X54,X56),X55))
      | ~ c_Groebner__Basis_Ogb__semiring(X57,X54,X53,X52,X51,X59) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_424])])]) ).

fof(c_0_834,plain,
    ! [X50,X51,X52,X53,X54,X55,X56,X57,X58] :
      ( hAPP(hAPP(X56,hAPP(hAPP(X53,X57),X54)),hAPP(hAPP(X53,X55),X54)) = hAPP(hAPP(X53,hAPP(hAPP(X56,X57),X55)),X54)
      | ~ c_Groebner__Basis_Ogb__semiring(X56,X53,X52,X51,X50,X58) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_425])])]) ).

fof(c_0_835,plain,
    ! [X72,X73,X74,X75,X76,X77,X78,X79,X80] :
      ( hAPP(hAPP(X78,hAPP(hAPP(X76,X72),X77)),hAPP(hAPP(X76,X72),X75)) = hAPP(hAPP(X76,X72),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X77),X75))
      | ~ c_Groebner__Basis_Ogb__semiring(X79,X78,X76,X74,X73,X80) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_426])])]) ).

fof(c_0_836,plain,
    ! [X65,X66,X67,X68,X69,X70,X71,X72,X73] :
      ( hAPP(hAPP(X71,X67),hAPP(hAPP(X72,X66),X65)) = hAPP(hAPP(X72,hAPP(hAPP(X71,X67),X66)),hAPP(hAPP(X71,X67),X65))
      | ~ c_Groebner__Basis_Ogb__semiring(X72,X71,X70,X69,X68,X73) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_427])])]) ).

fof(c_0_837,plain,
    ! [X51,X52,X53,X54,X55,X56,X57,X58,X59] :
      ( hAPP(hAPP(X57,hAPP(hAPP(X57,X58),X56)),X55) = hAPP(hAPP(X57,hAPP(hAPP(X57,X58),X55)),X56)
      | ~ c_Groebner__Basis_Ogb__semiring(X57,X54,X53,X52,X51,X59) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_428])])]) ).

fof(c_0_838,plain,
    ! [X70,X71,X72,X73,X74,X75,X76,X77,X78] :
      ( hAPP(hAPP(X74,hAPP(hAPP(X74,X76),X75)),X70) = hAPP(hAPP(X74,hAPP(hAPP(X74,X76),X70)),X75)
      | ~ c_Groebner__Basis_Ogb__semiring(X77,X74,X73,X72,X71,X78) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_429])])]) ).

fof(c_0_839,plain,
    ! [X49,X50,X51,X52,X53,X54,X55,X56] :
      ( hAPP(hAPP(X54,hAPP(hAPP(X52,X55),X53)),X53) = hAPP(hAPP(X52,hAPP(hAPP(X54,X55),X49)),X53)
      | ~ c_Groebner__Basis_Ogb__semiring(X54,X52,X51,X50,X49,X56) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_430])])]) ).

fof(c_0_840,plain,
    ! [X65,X66,X67,X68,X69,X70,X71,X72,X73] :
      ( hAPP(hAPP(X71,X67),hAPP(hAPP(X71,X66),X65)) = hAPP(hAPP(X71,hAPP(hAPP(X71,X67),X66)),X65)
      | ~ c_Groebner__Basis_Ogb__semiring(X72,X71,X70,X69,X68,X73) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_431])])]) ).

fof(c_0_841,plain,
    ! [X65,X66,X67,X68,X69,X70,X71,X72,X73] :
      ( hAPP(hAPP(X72,X67),hAPP(hAPP(X72,X66),X65)) = hAPP(hAPP(X72,hAPP(hAPP(X72,X67),X66)),X65)
      | ~ c_Groebner__Basis_Ogb__semiring(X72,X71,X70,X69,X68,X73) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_432])])]) ).

fof(c_0_842,plain,
    ! [X63,X64,X65,X66,X67,X68,X69,X70,X71] :
      ( hAPP(hAPP(X69,X70),hAPP(hAPP(X69,X68),X67)) = hAPP(hAPP(X69,hAPP(hAPP(X69,X70),X68)),X67)
      | ~ c_Groebner__Basis_Ogb__semiring(X69,X66,X65,X64,X63,X71) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_433])])]) ).

fof(c_0_843,plain,
    ! [X51,X52,X53,X54,X55,X56,X57,X58,X59] :
      ( hAPP(hAPP(X57,hAPP(hAPP(X57,X58),X56)),X55) = hAPP(hAPP(X57,X58),hAPP(hAPP(X57,X56),X55))
      | ~ c_Groebner__Basis_Ogb__semiring(X57,X54,X53,X52,X51,X59) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_434])])]) ).

fof(c_0_844,plain,
    ! [X70,X71,X72,X73,X74,X75,X76,X77,X78] :
      ( hAPP(hAPP(X75,X76),hAPP(hAPP(X75,X71),X70)) = hAPP(hAPP(X75,hAPP(hAPP(X75,X76),X71)),X70)
      | ~ c_Groebner__Basis_Ogb__semiring(X77,X75,X74,X73,X72,X78) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_435])])]) ).

fof(c_0_845,plain,
    ! [X70,X71,X72,X73,X74,X75,X76,X77,X78] :
      ( hAPP(hAPP(X74,hAPP(hAPP(X74,X76),X75)),X70) = hAPP(hAPP(X74,X76),hAPP(hAPP(X74,X75),X70))
      | ~ c_Groebner__Basis_Ogb__semiring(X77,X74,X73,X72,X71,X78) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_436])])]) ).

fof(c_0_846,plain,
    ! [X49,X50,X51,X52,X53,X54,X55,X56] :
      ( hAPP(hAPP(X54,X53),hAPP(hAPP(X52,X55),X53)) = hAPP(hAPP(X52,hAPP(hAPP(X54,X55),X49)),X53)
      | ~ c_Groebner__Basis_Ogb__semiring(X54,X52,X51,X50,X49,X56) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_437])])]) ).

fof(c_0_847,plain,
    ! [X63,X64,X65,X66,X67,X68,X69,X70,X71] :
      ( hAPP(hAPP(X69,X70),hAPP(hAPP(X69,X68),X67)) = hAPP(hAPP(X69,X68),hAPP(hAPP(X69,X70),X67))
      | ~ c_Groebner__Basis_Ogb__semiring(X69,X66,X65,X64,X63,X71) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_438])])]) ).

fof(c_0_848,plain,
    ! [X70,X71,X72,X73,X74,X75,X76,X77,X78] :
      ( hAPP(hAPP(X75,X76),hAPP(hAPP(X75,X71),X70)) = hAPP(hAPP(X75,X71),hAPP(hAPP(X75,X76),X70))
      | ~ c_Groebner__Basis_Ogb__semiring(X77,X75,X74,X73,X72,X78) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_439])])]) ).

fof(c_0_849,plain,
    ! [X49,X50,X51,X52,X53,X54,X55] :
      ( hAPP(hAPP(X54,X53),X53) = hAPP(hAPP(X52,hAPP(hAPP(X54,X49),X49)),X53)
      | ~ c_Groebner__Basis_Ogb__semiring(X54,X52,X51,X50,X49,X55) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_440])])]) ).

fof(c_0_850,plain,
    ! [X49,X50,X51,X52,X53,X54,X55,X56] :
      ( hAPP(hAPP(X54,X50),X49) = hAPP(hAPP(X54,X49),X50)
      | ~ c_Groebner__Basis_Ogb__semiring(X55,X54,X53,X52,X51,X56) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_441])])]) ).

fof(c_0_851,plain,
    ! [X49,X50,X51,X52,X53,X54,X55,X56] :
      ( hAPP(hAPP(X55,X50),X49) = hAPP(hAPP(X55,X49),X50)
      | ~ c_Groebner__Basis_Ogb__semiring(X55,X54,X53,X52,X51,X56) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_442])])]) ).

fof(c_0_852,plain,
    ! [X51,X52,X53,X54,X55,X56,X57,X58] :
      ( hAPP(hAPP(X56,X57),X55) = hAPP(hAPP(X56,X55),X57)
      | ~ c_Groebner__Basis_Ogb__semiring(X56,X54,X53,X52,X51,X58) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_443])])]) ).

fof(c_0_853,plain,
    ! [X50,X51,X52,X53,X54,X55,X56,X57] :
      ( hAPP(hAPP(X53,X55),X54) = hAPP(hAPP(X53,X54),X55)
      | ~ c_Groebner__Basis_Ogb__semiring(X56,X53,X52,X51,X50,X57) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_444])])]) ).

fof(c_0_854,plain,
    ! [X49,X50,X51,X52,X53,X54,X55] :
      ( hAPP(hAPP(X52,X49),c_HOL_Oone__class_Oone(tc_nat)) = X49
      | ~ c_Groebner__Basis_Ogb__semiring(X54,X53,X52,X51,X50,X55) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_445])])]) ).

fof(c_0_855,plain,
    ! [X49,X50,X51,X52,X53,X54,X55] :
      ( hAPP(hAPP(X52,X49),c_HOL_Ozero__class_Ozero(tc_nat)) = X50
      | ~ c_Groebner__Basis_Ogb__semiring(X54,X53,X52,X51,X50,X55) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_446])])]) ).

fof(c_0_856,plain,
    ! [X49,X50,X51,X52,X53,X54,X55] :
      ( hAPP(hAPP(X53,X50),X49) = X49
      | ~ c_Groebner__Basis_Ogb__semiring(X54,X53,X52,X51,X50,X55) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_447])])]) ).

fof(c_0_857,plain,
    ! [X49,X50,X51,X52,X53,X54,X55] :
      ( hAPP(hAPP(X53,X51),X49) = X51
      | ~ c_Groebner__Basis_Ogb__semiring(X54,X53,X52,X51,X50,X55) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_448])])]) ).

fof(c_0_858,plain,
    ! [X49,X50,X51,X52,X53,X54,X55] :
      ( hAPP(hAPP(X54,X51),X49) = X49
      | ~ c_Groebner__Basis_Ogb__semiring(X54,X53,X52,X51,X50,X55) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_449])])]) ).

fof(c_0_859,plain,
    ! [X49,X50,X51,X52,X53,X54,X55] :
      ( hAPP(hAPP(X52,X53),X49) = X53
      | ~ c_Groebner__Basis_Ogb__semiring(X54,X52,X51,X50,X49,X55) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_450])])]) ).

fof(c_0_860,plain,
    ! [X49,X50,X51,X52,X53,X54,X55] :
      ( hAPP(hAPP(X52,X49),X53) = X53
      | ~ c_Groebner__Basis_Ogb__semiring(X54,X52,X51,X50,X49,X55) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_451])])]) ).

fof(c_0_861,plain,
    ! [X49,X50,X51,X52,X53,X54,X55] :
      ( hAPP(hAPP(X52,X53),X50) = X50
      | ~ c_Groebner__Basis_Ogb__semiring(X54,X52,X51,X50,X49,X55) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_452])])]) ).

fof(c_0_862,plain,
    ! [X49,X50,X51,X52,X53,X54,X55] :
      ( hAPP(hAPP(X52,X50),X53) = X50
      | ~ c_Groebner__Basis_Ogb__semiring(X54,X52,X51,X50,X49,X55) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_453])])]) ).

fof(c_0_863,plain,
    ! [X49,X50,X51,X52,X53,X54,X55] :
      ( hAPP(hAPP(X53,X54),X50) = X54
      | ~ c_Groebner__Basis_Ogb__semiring(X53,X52,X51,X50,X49,X55) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_454])])]) ).

fof(c_0_864,plain,
    ! [X49,X50,X51,X52,X53,X54,X55] :
      ( hAPP(hAPP(X53,X50),X54) = X54
      | ~ c_Groebner__Basis_Ogb__semiring(X53,X52,X51,X50,X49,X55) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_455])])]) ).

fof(c_0_865,plain,
    ! [X43,X44,X45,X46,X47,X48] :
      ( ~ hBOOL(hAPP(X48,c_Lambda_OdB_OdB__case(X47,X46,X45,hAPP(hAPP(c_Lambda_OdB_OApp,X44),X43),t_a)))
      | hBOOL(hAPP(X48,hAPP(hAPP(X46,X44),X43))) ),
    inference(variable_rename,[status(thm)],[c_0_456]) ).

fof(c_0_866,plain,
    ! [X35,X36,X37,X38,X39,X40] :
      ( ~ hBOOL(hAPP(X40,c_Lambda_OdB_OdB__case(X37,X36,X35,hAPP(hAPP(c_Lambda_OdB_OApp,X39),X38),t_a)))
      | hBOOL(hAPP(X40,hAPP(hAPP(X36,X39),X38))) ),
    inference(variable_rename,[status(thm)],[c_0_457]) ).

fof(c_0_867,plain,
    ! [X35,X36] :
      ( hBOOL(hAPP(X36,c_ListApplication_Osko__ListApplication__Xlem__1__3(X36)))
      | ~ hBOOL(hAPP(X36,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_ListApplication_Osko__ListApplication__Xlem__1__1(X36)),c_ListApplication_Osko__ListApplication__Xlem__1__2(X36),tc_Lambda_OdB,tc_Lambda_OdB)))
      | hBOOL(hAPP(X36,X35)) ),
    inference(variable_rename,[status(thm)],[c_0_458]) ).

fof(c_0_868,plain,
    ! [X35,X36] :
      ( hBOOL(hAPP(X36,X35))
      | hBOOL(hAPP(X36,c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3(X36)))
      | ~ hBOOL(hAPP(X36,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1(X36)),c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2(X36),tc_Lambda_OdB,tc_Lambda_OdB))) ),
    inference(variable_rename,[status(thm)],[c_0_459]) ).

fof(c_0_869,plain,
    ! [X24,X25,X26,X27,X28] :
      ( X28 = X27
      | ~ c_Type_Otyping(X26,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X25),X24,tc_Lambda_OdB,tc_Lambda_OdB),X27)
      | ~ c_Type_Otyping(X26,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X25),X24,tc_Lambda_OdB,tc_Lambda_OdB),X28) ),
    inference(variable_rename,[status(thm)],[c_0_460]) ).

fof(c_0_870,plain,
    ! [X60,X61,X62,X63,X64] :
      ( ~ hBOOL(hAPP(X64,c_Lambda_OdB_OdB__case(X62,X61,X60,c_Lambda_OdB_OAbs(X63),t_a)))
      | hBOOL(hAPP(X64,hAPP(X60,X63))) ),
    inference(variable_rename,[status(thm)],[c_0_461]) ).

fof(c_0_871,plain,
    ! [X59,X60,X61,X62,X63] :
      ( ~ hBOOL(hAPP(X63,c_Lambda_OdB_OdB__case(X62,X61,X60,c_Lambda_OdB_OAbs(X59),t_a)))
      | hBOOL(hAPP(X63,hAPP(X60,X59))) ),
    inference(variable_rename,[status(thm)],[c_0_462]) ).

fof(c_0_872,plain,
    ! [X36,X37,X38,X39,X40] :
      ( ~ hBOOL(hAPP(X40,c_Lambda_OdB_OdB__case(X39,X38,X37,c_Lambda_OdB_OVar(X36),t_a)))
      | hBOOL(hAPP(X40,hAPP(X39,X36))) ),
    inference(variable_rename,[status(thm)],[c_0_463]) ).

fof(c_0_873,plain,
    ! [X35,X36,X37,X38,X39] :
      ( ~ hBOOL(hAPP(X39,c_Lambda_OdB_OdB__case(X38,X37,X36,c_Lambda_OdB_OVar(X35),t_a)))
      | hBOOL(hAPP(X39,hAPP(X38,X35))) ),
    inference(variable_rename,[status(thm)],[c_0_464]) ).

fof(c_0_874,plain,
    ! [X10,X11,X12] :
      ( ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X12),X11),c_HOL_Ozero__class_Ozero(tc_nat)),X10,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)
      | ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X11,tc_Lambda_OdB)
      | c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X12)),X11),X10,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB) ),
    inference(variable_rename,[status(thm)],[c_0_465]) ).

fof(c_0_875,plain,
    ! [X30] :
      ( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_sko__InductTermi__XIT__Xcases__4(X30)),v_sko__InductTermi__XIT__Xcases__5(X30)),c_HOL_Ozero__class_Ozero(tc_nat)),v_sko__InductTermi__XIT__Xcases__6(X30),tc_Lambda_OdB,tc_Lambda_OdB)))
      | hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X30)))
      | X30 = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X30)),v_sko__InductTermi__XIT__Xcases__1(X30),tc_Lambda_OdB,tc_Lambda_OdB)
      | ~ hBOOL(hAPP(c_InductTermi_OIT,X30)) ),
    inference(variable_rename,[status(thm)],[c_0_466]) ).

fof(c_0_876,plain,
    ! [X30] :
      ( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_sko__InductTermi__XIT__Xcases__4(X30)),v_sko__InductTermi__XIT__Xcases__5(X30)),c_HOL_Ozero__class_Ozero(tc_nat)),v_sko__InductTermi__XIT__Xcases__6(X30),tc_Lambda_OdB,tc_Lambda_OdB)))
      | X30 = c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X30))
      | X30 = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X30)),v_sko__InductTermi__XIT__Xcases__1(X30),tc_Lambda_OdB,tc_Lambda_OdB)
      | ~ hBOOL(hAPP(c_InductTermi_OIT,X30)) ),
    inference(variable_rename,[status(thm)],[c_0_467]) ).

fof(c_0_877,plain,
    ! [X30] :
      ( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_sko__InductTermi__XIT__Xcases__4(X30)),v_sko__InductTermi__XIT__Xcases__5(X30)),c_HOL_Ozero__class_Ozero(tc_nat)),v_sko__InductTermi__XIT__Xcases__6(X30),tc_Lambda_OdB,tc_Lambda_OdB)))
      | hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X30)))
      | c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X30),tc_Lambda_OdB)
      | ~ hBOOL(hAPP(c_InductTermi_OIT,X30)) ),
    inference(variable_rename,[status(thm)],[c_0_468]) ).

fof(c_0_878,plain,
    ! [X30] :
      ( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_sko__InductTermi__XIT__Xcases__4(X30)),v_sko__InductTermi__XIT__Xcases__5(X30)),c_HOL_Ozero__class_Ozero(tc_nat)),v_sko__InductTermi__XIT__Xcases__6(X30),tc_Lambda_OdB,tc_Lambda_OdB)))
      | X30 = c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X30))
      | c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X30),tc_Lambda_OdB)
      | ~ hBOOL(hAPP(c_InductTermi_OIT,X30)) ),
    inference(variable_rename,[status(thm)],[c_0_469]) ).

fof(c_0_879,plain,
    ! [X38,X39,X40,X41,X42] :
      ( c_Type_Otypings(c_Type_Oshift(X40,X39,X41,tc_Type_Otype),c_List_Omap(c_COMBC(c_Lambda_Olift,X39,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X38,tc_Lambda_OdB,tc_Lambda_OdB),X42)
      | ~ c_Type_Otypings(X40,X38,X42) ),
    inference(variable_rename,[status(thm)],[c_0_470]) ).

fof(c_0_880,plain,
    ! [X7] :
      ( c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X7,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)
      | ~ c_List_Olistsp(c_InductTermi_OIT,X7,tc_Lambda_OdB) ),
    inference(variable_rename,[status(thm)],[c_0_471]) ).

fof(c_0_881,plain,
    ! [X19,X20] :
      ( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X20),X19,tc_Lambda_OdB,tc_Lambda_OdB)))
      | ~ c_List_Olistsp(c_InductTermi_OIT,X19,tc_Lambda_OdB) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_472])])]) ).

fof(c_0_882,plain,
    ! [X24,X25,X26,X27] :
      ( c_Type_Otypings(X26,X24,c_Type_Osko__Type__Xvar__app__typesE__1__1(X27,X26,X25,X24))
      | ~ c_Type_Otyping(X26,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X25),X24,tc_Lambda_OdB,tc_Lambda_OdB),X27) ),
    inference(variable_rename,[status(thm)],[c_0_473]) ).

fof(c_0_883,plain,
    ! [X18,X19,X20,X21] :
      ( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X21),X20,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X19),X18,tc_Lambda_OdB,tc_Lambda_OdB)
      | X21 = X19 ),
    inference(variable_rename,[status(thm)],[c_0_474]) ).

fof(c_0_884,plain,
    ! [X18,X19,X20,X21] :
      ( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X21),X20,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X19),X18,tc_Lambda_OdB,tc_Lambda_OdB)
      | X20 = X18 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_475])])]) ).

fof(c_0_885,plain,
    ! [X19,X20,X21,X22] :
      ( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X22),X20,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X21),X19,tc_Lambda_OdB,tc_Lambda_OdB)
      | X22 = X21 ),
    inference(variable_rename,[status(thm)],[c_0_476]) ).

fof(c_0_886,plain,
    ! [X19,X20,X21,X22] :
      ( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X22),X20,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X21),X19,tc_Lambda_OdB,tc_Lambda_OdB)
      | X20 = X19 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_477])])]) ).

fof(c_0_887,plain,
    ! [X41,X42,X43,X44] :
      ( ~ class_OrderedGroup_Osemigroup__add(X44)
      | c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X44),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X44),X43),X42),X41,X44,X44) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X44),X43),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X44),X42,X41,X44,X44)) ),
    inference(variable_rename,[status(thm)],[c_0_478]) ).

fof(c_0_888,plain,
    ! [X9,X10,X11] :
      ( c_List_Ofoldl(c_Lambda_OdB_OApp,X11,X9,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,X10,X9,tc_Lambda_OdB,tc_Lambda_OdB)
      | X11 = X10 ),
    inference(variable_rename,[status(thm)],[c_0_479]) ).

fof(c_0_889,plain,
    ! [X41,X42,X43,X44,X45] :
      ( c_List_Ofoldl(X44,hAPP(hAPP(X44,X43),X42),X41,X45,X45) = hAPP(hAPP(X44,X43),c_List_Ofoldl(X44,X42,X41,X45,X45))
      | ~ c_OrderedGroup_Osemigroup__add(X44,X45) ),
    inference(variable_rename,[status(thm)],[c_0_480]) ).

fof(c_0_890,plain,
    ! [X40,X41,X42,X43,X44] :
      ( hAPP(hAPP(X43,X42),c_List_Ofoldl(X43,X41,X40,X44,X44)) = c_List_Ofoldl(X43,X42,X40,X44,X44)
      | ~ c_OrderedGroup_Omonoid__add(X41,X43,X44) ),
    inference(variable_rename,[status(thm)],[c_0_481]) ).

fof(c_0_891,plain,
    ! [X44,X45,X46] :
      ( ~ class_OrderedGroup_Omonoid__add(X46)
      | c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X46),X45,X44,X46,X46) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X46),X45),c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X46),X44,c_HOL_Ozero__class_Ozero(X46),X46,X46)) ),
    inference(variable_rename,[status(thm)],[c_0_482]) ).

fof(c_0_892,plain,
    ! [X29,X30,X31] :
      ( ~ class_OrderedGroup_Omonoid__add(X31)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X31),X30),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X31),c_HOL_Ozero__class_Ozero(X31),X29,X31,X31)) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X31),X30,X29,X31,X31) ),
    inference(variable_rename,[status(thm)],[c_0_483]) ).

fof(c_0_893,plain,
    ! [X28,X29,X30,X31] :
      ( hAPP(hAPP(c_Lambda_OdB_OApp,X31),X30) != c_List_Ofoldl(c_Lambda_OdB_OApp,X29,X28,tc_Lambda_OdB,tc_Lambda_OdB)
      | X31 = c_List_Ofoldl(c_Lambda_OdB_OApp,X29,c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1(X31,X30,X29,X28),tc_Lambda_OdB,tc_Lambda_OdB)
      | X28 = c_List_Olist_ONil(tc_Lambda_OdB) ),
    inference(variable_rename,[status(thm)],[c_0_484]) ).

fof(c_0_894,plain,
    ! [X30] :
      ( X30 = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__4(X30))),v_sko__InductTermi__XIT__Xcases__5(X30)),v_sko__InductTermi__XIT__Xcases__6(X30),tc_Lambda_OdB,tc_Lambda_OdB)
      | hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X30)))
      | X30 = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X30)),v_sko__InductTermi__XIT__Xcases__1(X30),tc_Lambda_OdB,tc_Lambda_OdB)
      | ~ hBOOL(hAPP(c_InductTermi_OIT,X30)) ),
    inference(variable_rename,[status(thm)],[c_0_485]) ).

fof(c_0_895,plain,
    ! [X30] :
      ( X30 = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__4(X30))),v_sko__InductTermi__XIT__Xcases__5(X30)),v_sko__InductTermi__XIT__Xcases__6(X30),tc_Lambda_OdB,tc_Lambda_OdB)
      | X30 = c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X30))
      | X30 = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X30)),v_sko__InductTermi__XIT__Xcases__1(X30),tc_Lambda_OdB,tc_Lambda_OdB)
      | ~ hBOOL(hAPP(c_InductTermi_OIT,X30)) ),
    inference(variable_rename,[status(thm)],[c_0_486]) ).

fof(c_0_896,plain,
    ! [X44,X45] :
      ( ~ class_OrderedGroup_Omonoid__add(X45)
      | c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X45),c_HOL_Ozero__class_Ozero(X45),X44,X45,X45) = c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X45),X44,c_HOL_Ozero__class_Ozero(X45),X45,X45) ),
    inference(variable_rename,[status(thm)],[c_0_487]) ).

fof(c_0_897,plain,
    ! [X44,X45,X46] :
      ( ~ class_OrderedGroup_Oab__semigroup__add(X46)
      | c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X46),X44,X45,X46,X46) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X46),X45,X44,X46,X46) ),
    inference(variable_rename,[status(thm)],[c_0_488]) ).

fof(c_0_898,plain,
    ! [X28,X29,X30] :
      ( hAPP(hAPP(c_Lambda_OdB_OApp,X30),X29) != c_List_Ofoldl(c_Lambda_OdB_OApp,X28,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)
      | hAPP(hAPP(c_Lambda_OdB_OApp,X30),X29) = X28 ),
    inference(variable_rename,[status(thm)],[c_0_489]) ).

fof(c_0_899,plain,
    ! [X10,X11,X12] :
      ( c_List_Ofoldl(c_Lambda_OdB_OApp,X11,X10,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X12)
      | X11 = c_Lambda_OdB_OAbs(X12) ),
    inference(variable_rename,[status(thm)],[c_0_490]) ).

fof(c_0_900,plain,
    ! [X10,X11,X12] :
      ( c_Lambda_OdB_OAbs(X12) != c_List_Ofoldl(c_Lambda_OdB_OApp,X11,X10,tc_Lambda_OdB,tc_Lambda_OdB)
      | c_Lambda_OdB_OAbs(X12) = X11 ),
    inference(variable_rename,[status(thm)],[c_0_491]) ).

fof(c_0_901,plain,
    ! [X11,X12,X13] :
      ( c_Lambda_OdB_OVar(X13) != c_List_Ofoldl(c_Lambda_OdB_OApp,X12,X11,tc_Lambda_OdB,tc_Lambda_OdB)
      | c_Lambda_OdB_OVar(X13) = X12 ),
    inference(variable_rename,[status(thm)],[c_0_492]) ).

fof(c_0_902,plain,
    ! [X28,X29,X30,X31] :
      ( hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(hAPP(c_Lambda_Osubst,X28),X29),X30)),X31) = hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,X28),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X31),c_HOL_Oone__class_Oone(tc_nat)))),hAPP(hAPP(c_Lambda_Olift,X29),X31)),X30)
      | ~ c_HOL_Oord__class_Oless(X30,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X31),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_493]) ).

fof(c_0_903,plain,
    ! [X10,X11,X12] :
      ( c_Lambda_OdB_OAbs(X12) != c_List_Ofoldl(c_Lambda_OdB_OApp,X11,X10,tc_Lambda_OdB,tc_Lambda_OdB)
      | X10 = c_List_Olist_ONil(tc_Lambda_OdB) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_494])])]) ).

fof(c_0_904,plain,
    ! [X10,X11,X12] :
      ( c_List_Ofoldl(c_Lambda_OdB_OApp,X11,X10,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X12)
      | X10 = c_List_Olist_ONil(tc_Lambda_OdB) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_495])])]) ).

fof(c_0_905,plain,
    ! [X11,X12,X13] :
      ( c_Lambda_OdB_OVar(X13) != c_List_Ofoldl(c_Lambda_OdB_OApp,X12,X11,tc_Lambda_OdB,tc_Lambda_OdB)
      | X11 = c_List_Olist_ONil(tc_Lambda_OdB) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_496])])]) ).

fof(c_0_906,plain,
    ! [X41,X42,X43,X44] :
      ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X43,X44),X41),X42))
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Predicate_Oconversep(X43,X44,X44),X44),X42),X41)) ),
    inference(variable_rename,[status(thm)],[c_0_497]) ).

fof(c_0_907,plain,
    ! [X52,X53,X54,X55,X56,X57] :
      ( hBOOL(hAPP(hAPP(X56,X53),X55))
      | c_ListOrder_Ostep1(X56,X52,X54,X57)
      | ~ c_ListOrder_Ostep1(X56,c_List_Oappend(X52,c_List_Olist_OCons(X53,c_List_Olist_ONil(X57),X57),X57),c_List_Oappend(X54,c_List_Olist_OCons(X55,c_List_Olist_ONil(X57),X57),X57),X57) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_498])])]) ).

fof(c_0_908,plain,
    ! [X52,X53,X54,X55,X56,X57] :
      ( X52 = X54
      | c_ListOrder_Ostep1(X56,X52,X54,X57)
      | ~ c_ListOrder_Ostep1(X56,c_List_Oappend(X52,c_List_Olist_OCons(X53,c_List_Olist_ONil(X57),X57),X57),c_List_Oappend(X54,c_List_Olist_OCons(X55,c_List_Olist_ONil(X57),X57),X57),X57) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_499])])]) ).

fof(c_0_909,plain,
    ! [X52,X53,X54,X55,X56,X57] :
      ( hBOOL(hAPP(hAPP(X56,X53),X55))
      | X53 = X55
      | ~ c_ListOrder_Ostep1(X56,c_List_Oappend(X52,c_List_Olist_OCons(X53,c_List_Olist_ONil(X57),X57),X57),c_List_Oappend(X54,c_List_Olist_OCons(X55,c_List_Olist_ONil(X57),X57),X57),X57) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_500])])]) ).

fof(c_0_910,plain,
    ! [X30] :
      ( X30 = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__4(X30))),v_sko__InductTermi__XIT__Xcases__5(X30)),v_sko__InductTermi__XIT__Xcases__6(X30),tc_Lambda_OdB,tc_Lambda_OdB)
      | hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X30)))
      | c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X30),tc_Lambda_OdB)
      | ~ hBOOL(hAPP(c_InductTermi_OIT,X30)) ),
    inference(variable_rename,[status(thm)],[c_0_501]) ).

fof(c_0_911,plain,
    ! [X52,X53,X54,X55,X56,X57] :
      ( X52 = X54
      | X53 = X55
      | ~ c_ListOrder_Ostep1(X56,c_List_Oappend(X52,c_List_Olist_OCons(X53,c_List_Olist_ONil(X57),X57),X57),c_List_Oappend(X54,c_List_Olist_OCons(X55,c_List_Olist_ONil(X57),X57),X57),X57) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_502])])]) ).

fof(c_0_912,plain,
    ! [X30] :
      ( X30 = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__4(X30))),v_sko__InductTermi__XIT__Xcases__5(X30)),v_sko__InductTermi__XIT__Xcases__6(X30),tc_Lambda_OdB,tc_Lambda_OdB)
      | X30 = c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X30))
      | c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X30),tc_Lambda_OdB)
      | ~ hBOOL(hAPP(c_InductTermi_OIT,X30)) ),
    inference(variable_rename,[status(thm)],[c_0_503]) ).

fof(c_0_913,plain,
    ! [X28,X29,X30,X31] :
      ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,X30),X28),X31)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X29),X28),X31)))
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X30),X29)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_504])])]) ).

fof(c_0_914,plain,
    ! [X28,X29,X30,X31] :
      ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,X28),X30),X31)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X28),X29),X31)))
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X30),X29)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_505])])]) ).

fof(c_0_915,plain,
    ! [X30] :
      ( hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__5(X30)))
      | hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X30)))
      | X30 = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X30)),v_sko__InductTermi__XIT__Xcases__1(X30),tc_Lambda_OdB,tc_Lambda_OdB)
      | ~ hBOOL(hAPP(c_InductTermi_OIT,X30)) ),
    inference(variable_rename,[status(thm)],[c_0_506]) ).

fof(c_0_916,plain,
    ! [X41,X42,X43,X44] :
      ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Predicate_Oconversep(X43,X44,X44),X44),X42),X41))
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X43,X44),X41),X42)) ),
    inference(variable_rename,[status(thm)],[c_0_507]) ).

fof(c_0_917,plain,
    ! [X30] :
      ( hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__5(X30)))
      | X30 = c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X30))
      | X30 = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X30)),v_sko__InductTermi__XIT__Xcases__1(X30),tc_Lambda_OdB,tc_Lambda_OdB)
      | ~ hBOOL(hAPP(c_InductTermi_OIT,X30)) ),
    inference(variable_rename,[status(thm)],[c_0_508]) ).

fof(c_0_918,plain,
    ! [X28,X29,X30,X31] :
      ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,X28),X30),X31)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X28),X29),X31)))
      | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X30),X29)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_509])])]) ).

fof(c_0_919,plain,
    ! [X44,X45] :
      ( ~ class_OrderedGroup_Omonoid__add(X45)
      | c_List_Olistsum(X44,X45) = c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X45),X44,c_HOL_Ozero__class_Ozero(X45),X45,X45) ),
    inference(variable_rename,[status(thm)],[c_0_510]) ).

fof(c_0_920,plain,
    ! [X44,X45] :
      ( ~ class_OrderedGroup_Omonoid__add(X45)
      | c_List_Olistsum(X44,X45) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X45),c_HOL_Ozero__class_Ozero(X45),X44,X45,X45) ),
    inference(variable_rename,[status(thm)],[c_0_511]) ).

fof(c_0_921,plain,
    ! [X28,X29,X30,X31] :
      ( hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(hAPP(c_Lambda_Osubst,X28),X29),X30)),X31) = hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,X28),X31)),hAPP(hAPP(c_Lambda_Olift,X29),X31)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X30),c_HOL_Oone__class_Oone(tc_nat)))
      | ~ c_HOL_Oord__class_Oless(X31,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X30),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_512]) ).

fof(c_0_922,plain,
    ! [X28,X29,X30,X31] :
      ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(hAPP(c_Lambda_Osubst,X30),X28),X31)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X29),X28),X31)))
      | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X30),X29)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_513])])]) ).

fof(c_0_923,plain,
    ! [X77,X78,X79,X80,X81,X82] :
      ( ~ c_Type_Otyping(X80,X77,X81)
      | ~ c_Type_Otyping(c_Type_Oshift(X80,X79,X81,tc_Type_Otype),X78,X82)
      | c_Type_Otyping(X80,hAPP(hAPP(hAPP(c_Lambda_Osubst,X78),X77),X79),X82) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_514])])]) ).

fof(c_0_924,plain,
    ! [X66,X67,X68,X69] :
      ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X69),X67)),hAPP(hAPP(c_Lambda_OdB_OApp,X68),X66)))
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X67),X66))
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X69),X68)) ),
    inference(variable_rename,[status(thm)],[c_0_515]) ).

fof(c_0_925,plain,
    ! [X52,X53,X54,X55,X56,X57] :
      ( c_ListOrder_Ostep1(X56,X52,X54,X57)
      | hBOOL(hAPP(hAPP(X56,X53),X55))
      | ~ c_ListOrder_Ostep1(X56,c_List_Olist_OCons(X53,X52,X57),c_List_Olist_OCons(X55,X54,X57),X57) ),
    inference(variable_rename,[status(thm)],[c_0_516]) ).

fof(c_0_926,plain,
    ! [X52,X53,X54,X55,X56,X57] :
      ( c_ListOrder_Ostep1(X56,X52,X54,X57)
      | X54 = X52
      | ~ c_ListOrder_Ostep1(X56,c_List_Olist_OCons(X53,X52,X57),c_List_Olist_OCons(X55,X54,X57),X57) ),
    inference(variable_rename,[status(thm)],[c_0_517]) ).

fof(c_0_927,plain,
    ! [X54,X55,X56,X57,X58] :
      ( hBOOL(hAPP(hAPP(X54,X55),X56))
      | ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X54,X58,X57),X56),X55)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_518])])]) ).

fof(c_0_928,plain,
    ! [X75,X76,X77,X78,X79] :
      ( hBOOL(hAPP(hAPP(X75,X76),X77))
      | ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X75,X79,X78),X77),X76)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_519])])]) ).

fof(c_0_929,plain,
    ! [X52,X53,X54,X55,X56] :
      ( ~ c_ListOrder_Ostep1(X55,X52,X53,X56)
      | c_ListOrder_Ostep1(X55,c_List_Oappend(X52,X54,X56),c_List_Oappend(X53,X54,X56),X56) ),
    inference(variable_rename,[status(thm)],[c_0_520]) ).

fof(c_0_930,plain,
    ! [X73,X74,X75,X76,X77] :
      ( c_ListOrder_Ostep1(X76,c_List_Oappend(X73,X74,X77),c_List_Oappend(X73,X75,X77),X77)
      | ~ c_ListOrder_Ostep1(X76,X74,X75,X77) ),
    inference(variable_rename,[status(thm)],[c_0_521]) ).

fof(c_0_931,plain,
    ! [X52,X53,X54,X55,X56] :
      ( c_ListOrder_Ostep1(X55,c_List_Olist_OCons(X54,X52,X56),c_List_Olist_OCons(X54,X53,X56),X56)
      | ~ c_ListOrder_Ostep1(X55,X52,X53,X56) ),
    inference(variable_rename,[status(thm)],[c_0_522]) ).

fof(c_0_932,plain,
    ! [X66,X67,X68] :
      ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X68),X66)),hAPP(hAPP(c_Lambda_OdB_OApp,X67),X66)))
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X68),X67)) ),
    inference(variable_rename,[status(thm)],[c_0_523]) ).

fof(c_0_933,plain,
    ! [X55,X56,X57] :
      ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X57),X56)),hAPP(hAPP(c_Lambda_OdB_OApp,X57),X55)))
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X56),X55)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_524])])]) ).

fof(c_0_934,plain,
    ! [X17,X18,X19] :
      ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_Olift,X18),X19)),hAPP(hAPP(c_Lambda_Olift,X17),X19)))
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X18),X17)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_525])])]) ).

fof(c_0_935,plain,
    ! [X52,X53,X54,X55,X56,X57] :
      ( X55 = X53
      | hBOOL(hAPP(hAPP(X56,X53),X55))
      | ~ c_ListOrder_Ostep1(X56,c_List_Olist_OCons(X53,X52,X57),c_List_Olist_OCons(X55,X54,X57),X57) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_526])])]) ).

fof(c_0_936,plain,
    ! [X65,X66,X67,X68,X69] :
      ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X68,X69),X67),X65))
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X68,X69),X66),X65))
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X68,X69),X67),X66)) ),
    inference(variable_rename,[status(thm)],[c_0_527]) ).

fof(c_0_937,plain,
    ! [X52,X53,X54,X55,X56,X57] :
      ( X55 = X53
      | X54 = X52
      | ~ c_ListOrder_Ostep1(X56,c_List_Olist_OCons(X53,X52,X57),c_List_Olist_OCons(X55,X54,X57),X57) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_528])])]) ).

fof(c_0_938,plain,
    ! [X63,X64,X65,X66,X67] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X67)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X67),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X67),X66),X65)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X67),X64),X63)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X67),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X67),X66),X64)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X67),X65),X63)) ),
    inference(variable_rename,[status(thm)],[c_0_529]) ).

fof(c_0_939,plain,
    ! [X28,X29,X30,X31,X32] :
      ( c_Type_Otyping(c_Type_Oshift(X30,X29,X31,tc_Type_Otype),hAPP(hAPP(c_Lambda_Olift,X28),X29),X32)
      | ~ c_Type_Otyping(X30,X28,X32) ),
    inference(variable_rename,[status(thm)],[c_0_530]) ).

fof(c_0_940,plain,
    ! [X54,X55,X56,X57,X58] :
      ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X54,X58,X57),X56),X55))
      | ~ hBOOL(hAPP(hAPP(X54,X55),X56)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_531])])]) ).

fof(c_0_941,plain,
    ! [X54,X55,X56,X57,X58] :
      ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X54,X58,X57),X55),X56))
      | ~ hBOOL(hAPP(hAPP(X54,X56),X55)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_532])])]) ).

fof(c_0_942,plain,
    ! [X17,X18,X19] :
      ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_Olift,X18),X19)),hAPP(hAPP(c_Lambda_Olift,X17),X19)))
      | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X18),X17)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_533])])]) ).

fof(c_0_943,plain,
    ! [X28,X29,X30] :
      ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,X28),X30)),hAPP(hAPP(c_Lambda_OdB_OApp,X28),X29)))
      | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X30),X29)) ),
    inference(variable_rename,[status(thm)],[c_0_534]) ).

fof(c_0_944,plain,
    ! [X28,X29,X30] :
      ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,X30),X28)),hAPP(hAPP(c_Lambda_OdB_OApp,X29),X28)))
      | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X30),X29)) ),
    inference(variable_rename,[status(thm)],[c_0_535]) ).

fof(c_0_945,plain,
    ! [X51,X52,X53,X54,X55] :
      ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X51,X55),X54),X52))
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X51,X55),X53),X52))
      | ~ hBOOL(hAPP(hAPP(X51,X54),X53)) ),
    inference(variable_rename,[status(thm)],[c_0_536]) ).

fof(c_0_946,plain,
    ! [X51,X52,X53,X54,X55] :
      ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X51,X55),X54),X52))
      | ~ hBOOL(hAPP(hAPP(X51,X53),X52))
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X51,X55),X54),X53)) ),
    inference(variable_rename,[status(thm)],[c_0_537]) ).

fof(c_0_947,plain,
    ! [X24,X25,X26,X27,X28] :
      ( hAPP(c_Type_Oshift(X26,X25,X27,X28),X24) = hAPP(X26,X24)
      | ~ c_HOL_Oord__class_Oless(X24,X25,tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_538])])]) ).

fof(c_0_948,plain,
    ! [X59,X60,X61,X62,X63] :
      ( ~ hBOOL(hAPP(hAPP(X62,X59),X60))
      | c_ListOrder_Ostep1(X62,c_List_Olist_OCons(X59,X61,X63),c_List_Olist_OCons(X60,X61,X63),X63) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_539])])]) ).

fof(c_0_949,plain,
    ! [X50,X51,X52,X53] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X53)
      | c_HOL_Oord__class_Oless(X52,X51,X53)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X53),X51,X53)
      | ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X52,X50,X53),c_Power_Opower__class_Opower(X51,X50,X53),X53) ),
    inference(variable_rename,[status(thm)],[c_0_540]) ).

fof(c_0_950,plain,
    ! [X30,X31,X32,X33] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X33)
      | c_HOL_Oord__class_Oless(X31,X30,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X32,X31,X33),c_Power_Opower__class_Opower(X32,X30,X33),X33)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X33),X32,X33) ),
    inference(variable_rename,[status(thm)],[c_0_541]) ).

fof(c_0_951,plain,
    ! [X50,X51,X52,X53] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X53)
      | c_HOL_Oord__class_Oless(X51,X50,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X52,X51,X53),c_Power_Opower__class_Opower(X52,X50,X53),X53)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X53),X52,X53) ),
    inference(variable_rename,[status(thm)],[c_0_542]) ).

fof(c_0_952,plain,
    ! [X76,X77,X78,X79] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X79)
      | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X77,X78,X79),c_Power_Opower__class_Opower(X77,X76,X79),X79)
      | ~ c_HOL_Oord__class_Oless(X77,c_HOL_Oone__class_Oone(X79),X79)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X79),X77,X79)
      | ~ c_HOL_Oord__class_Oless(X76,X78,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_543]) ).

fof(c_0_953,plain,
    ! [X52,X53,X54,X55,X56] :
      ( c_List_Oappend(X54,c_List_Olist_OCons(X55,c_List_Olist_ONil(X56),X56),X56) != c_List_Oappend(X52,c_List_Olist_OCons(X53,c_List_Olist_ONil(X56),X56),X56)
      | X54 = X52 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_544])])]) ).

fof(c_0_954,plain,
    ! [X52,X53,X54,X55,X56] :
      ( c_List_Oappend(X54,c_List_Olist_OCons(X55,c_List_Olist_ONil(X56),X56),X56) != c_List_Oappend(X52,c_List_Olist_OCons(X53,c_List_Olist_ONil(X56),X56),X56)
      | X55 = X53 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_545])])]) ).

fof(c_0_955,plain,
    ! [X50,X51,X52,X53] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X53)
      | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X52,X50,X53),c_Power_Opower__class_Opower(X51,X50,X53),X53)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X50,tc_nat)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X53),X52,X53)
      | ~ c_HOL_Oord__class_Oless(X52,X51,X53) ),
    inference(variable_rename,[status(thm)],[c_0_546]) ).

fof(c_0_956,plain,
    ! [X65,X66,X67,X68] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X68)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X68),c_Orderings_Oord__class_Omax(X67,X66,X68)),X65) = c_Orderings_Oord__class_Omax(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X68),X67),X65),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X68),X66),X65),X68) ),
    inference(variable_rename,[status(thm)],[c_0_547]) ).

fof(c_0_957,plain,
    ! [X51,X52,X53,X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X54)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X54),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X54),X53),X52)),X51) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X54),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X54),X53),X51)),X52) ),
    inference(variable_rename,[status(thm)],[c_0_548]) ).

fof(c_0_958,plain,
    ! [X63,X64,X65,X66,X67] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X67)
      | c_lessequals(X66,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X67),X65),X63),X67)
      | ~ c_lessequals(X64,X63,X67)
      | ~ c_lessequals(X66,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X67),X65),X64),X67) ),
    inference(variable_rename,[status(thm)],[c_0_549]) ).

fof(c_0_959,plain,
    ! [X51,X52,X53,X54] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X54)
      | c_lessequals(X53,X52,X54)
      | ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X54),X51),X53),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X54),X51),X52),X54) ),
    inference(variable_rename,[status(thm)],[c_0_550]) ).

fof(c_0_960,plain,
    ! [X51,X52,X53,X54] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X54)
      | c_lessequals(X53,X52,X54)
      | ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X54),X53),X51),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X54),X52),X51),X54) ),
    inference(variable_rename,[status(thm)],[c_0_551]) ).

fof(c_0_961,plain,
    ! [X51,X52,X53,X54] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X54)
      | c_HOL_Oord__class_Oless(X53,X52,X54)
      | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X54),X53),X51),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X54),X52),X51),X54) ),
    inference(variable_rename,[status(thm)],[c_0_552]) ).

fof(c_0_962,plain,
    ! [X51,X52,X53,X54] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X54)
      | c_HOL_Oord__class_Oless(X53,X52,X54)
      | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X54),X51),X53),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X54),X51),X52),X54) ),
    inference(variable_rename,[status(thm)],[c_0_553]) ).

fof(c_0_963,plain,
    ! [X50,X51,X52,X53] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X53)
      | c_Power_Opower__class_Opower(X52,X50,X53) != c_Power_Opower__class_Opower(X51,X50,X53)
      | X52 = X51
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X50,tc_nat)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X53),X51,X53)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X53),X52,X53) ),
    inference(variable_rename,[status(thm)],[c_0_554]) ).

fof(c_0_964,plain,
    ! [X17,X18,X19] :
      ( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,X17),c_Lambda_OdB_OVar(X19)),X18)))
      | ~ hBOOL(hAPP(c_InductTermi_OIT,X17)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_555])])]) ).

fof(c_0_965,plain,
    ! [X50,X51,X52,X53] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X53)
      | c_lessequals(c_Power_Opower__class_Opower(X52,X50,X53),c_Power_Opower__class_Opower(X51,X50,X53),X53)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X53),X52,X53)
      | ~ c_lessequals(X52,X51,X53) ),
    inference(variable_rename,[status(thm)],[c_0_556]) ).

fof(c_0_966,plain,
    ! [X76,X77,X78,X79] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X79)
      | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X77,X76,X79),c_Power_Opower__class_Opower(X77,X78,X79),X79)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X79),X77,X79)
      | ~ c_HOL_Oord__class_Oless(X76,X78,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_557]) ).

fof(c_0_967,plain,
    ! [X50,X51,X52,X53] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X53)
      | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X52,X51,X53),c_Power_Opower__class_Opower(X52,X50,X53),X53)
      | ~ c_HOL_Oord__class_Oless(X51,X50,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X53),X52,X53) ),
    inference(variable_rename,[status(thm)],[c_0_558]) ).

fof(c_0_968,plain,
    ! [X66,X67] :
      ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_OdB_OAbs(X67)),c_Lambda_OdB_OAbs(X66)))
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X67),X66)) ),
    inference(variable_rename,[status(thm)],[c_0_559]) ).

fof(c_0_969,plain,
    ! [X63,X64,X65,X66,X67] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X67)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X67),X66),X64),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X67),X65),X63),X67)
      | ~ c_HOL_Oord__class_Oless(X64,X63,X67)
      | ~ c_lessequals(X66,X65,X67) ),
    inference(variable_rename,[status(thm)],[c_0_560]) ).

fof(c_0_970,plain,
    ! [X63,X64,X65,X66,X67] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X67)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X67),X66),X64),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X67),X65),X63),X67)
      | ~ c_lessequals(X64,X63,X67)
      | ~ c_HOL_Oord__class_Oless(X66,X65,X67) ),
    inference(variable_rename,[status(thm)],[c_0_561]) ).

fof(c_0_971,plain,
    ! [X63,X64,X65,X66,X67] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X67)
      | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X67),X66),X64),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X67),X65),X63),X67)
      | ~ c_lessequals(X64,X63,X67)
      | ~ c_lessequals(X66,X65,X67) ),
    inference(variable_rename,[status(thm)],[c_0_562]) ).

fof(c_0_972,plain,
    ! [X63,X64,X65,X66,X67] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X67)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X67),X66),X64),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X67),X65),X63),X67)
      | ~ c_HOL_Oord__class_Oless(X64,X63,X67)
      | ~ c_HOL_Oord__class_Oless(X66,X65,X67) ),
    inference(variable_rename,[status(thm)],[c_0_563]) ).

fof(c_0_973,plain,
    ! [X50,X51,X52,X53] :
      ( c_Wellfounded_Oaccp(X50,X51,X53)
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X50,X53),X51),X52))
      | ~ c_Wellfounded_Oaccp(X50,X52,X53) ),
    inference(variable_rename,[status(thm)],[c_0_564]) ).

fof(c_0_974,plain,
    ! [X50,X51,X52,X53] :
      ( c_Wellfounded_Oaccp(X50,X51,X53)
      | ~ c_Wellfounded_Oaccp(X50,X52,X53)
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X50,X53),X51),X52)) ),
    inference(variable_rename,[status(thm)],[c_0_565]) ).

fof(c_0_975,plain,
    ! [X26,X27,X28] :
      ( c_HOL_Oord__class_Oless(X27,X26,tc_nat)
      | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X28),X27),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X28),X26),tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_566])])]) ).

fof(c_0_976,plain,
    ! [X51,X52,X53,X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X54)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X54),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X54),X53),X52)),X51) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X54),X53),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X54),X52),X51)) ),
    inference(variable_rename,[status(thm)],[c_0_567]) ).

fof(c_0_977,plain,
    ! [X63,X64,X65,X66] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X66)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X66),X65),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X66),X64),X63)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X66),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X66),X65),X64)),X63) ),
    inference(variable_rename,[status(thm)],[c_0_568]) ).

fof(c_0_978,plain,
    ! [X51,X52,X53,X54] :
      ( ~ class_OrderedGroup_Oab__semigroup__add(X54)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X54),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X54),X53),X52)),X51) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X54),X53),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X54),X52),X51)) ),
    inference(variable_rename,[status(thm)],[c_0_569]) ).

fof(c_0_979,plain,
    ! [X51,X52,X53,X54] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X54)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X54),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X54),X53),X52)),X51) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X54),X53),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X54),X52),X51)) ),
    inference(variable_rename,[status(thm)],[c_0_570]) ).

fof(c_0_980,plain,
    ! [X65,X66,X67,X68] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X68)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X68),X67),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X68),X66),X65)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X68),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X68),X67),X66)),X65) ),
    inference(variable_rename,[status(thm)],[c_0_571]) ).

fof(c_0_981,plain,
    ! [X62,X63,X64,X65] :
      ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X65),X63),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X64),X62),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X63,X62,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X65,X64,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_572]) ).

fof(c_0_982,plain,
    ! [X54,X55,X56,X57] :
      ( c_List_Olist_ONil(X57) != c_List_Omap(X55,X54,X56,X57)
      | X54 = c_List_Olist_ONil(X56) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_573])])]) ).

fof(c_0_983,plain,
    ! [X54,X55,X56,X57] :
      ( c_List_Omap(X55,X54,X56,X57) != c_List_Olist_ONil(X57)
      | X54 = c_List_Olist_ONil(X56) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_574])])]) ).

fof(c_0_984,plain,
    ! [X55,X56,X57,X58] :
      ( c_Type_Otyping(X57,X55,X58)
      | ~ c_Type_Otyping(X57,X56,X58)
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X56),X55)) ),
    inference(variable_rename,[status(thm)],[c_0_575]) ).

fof(c_0_985,plain,
    ! [X65,X66,X67,X68,X69] :
      ( ~ class_OrderedGroup_Oab__group__add(X69)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X69),X67),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X69),X66),X65)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X69),X66),X68)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X69),X67),X65) = X68 ),
    inference(variable_rename,[status(thm)],[c_0_576]) ).

fof(c_0_986,plain,
    ! [X65,X66,X67,X68] :
      ( ~ class_Orderings_Olinorder(X68)
      | c_lessequals(X65,X66,X68)
      | c_lessequals(X65,X67,X68)
      | ~ c_lessequals(X65,c_Orderings_Oord__class_Omax(X67,X66,X68),X68) ),
    inference(variable_rename,[status(thm)],[c_0_577]) ).

fof(c_0_987,plain,
    ! [X65,X66,X67,X68] :
      ( ~ class_Orderings_Olinorder(X68)
      | c_HOL_Oord__class_Oless(X65,X66,X68)
      | c_HOL_Oord__class_Oless(X65,X67,X68)
      | ~ c_HOL_Oord__class_Oless(X65,c_Orderings_Oord__class_Omax(X67,X66,X68),X68) ),
    inference(variable_rename,[status(thm)],[c_0_578]) ).

fof(c_0_988,plain,
    ! [X50,X51,X52] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X52)
      | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X52),X51),X50),c_HOL_Ozero__class_Ozero(X52),X52)
      | ~ c_lessequals(X50,c_HOL_Ozero__class_Ozero(X52),X52)
      | ~ c_lessequals(X51,c_HOL_Ozero__class_Ozero(X52),X52) ),
    inference(variable_rename,[status(thm)],[c_0_579]) ).

fof(c_0_989,plain,
    ! [X50,X51,X52] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X52)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X52),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X52),X51),X50),X52)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X52),X50,X52)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X52),X51,X52) ),
    inference(variable_rename,[status(thm)],[c_0_580]) ).

fof(c_0_990,plain,
    ! [X50,X51,X52] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X52)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X52),X51),X50),c_HOL_Ozero__class_Ozero(X52),X52)
      | ~ c_lessequals(X50,c_HOL_Ozero__class_Ozero(X52),X52)
      | ~ c_HOL_Oord__class_Oless(X51,c_HOL_Ozero__class_Ozero(X52),X52) ),
    inference(variable_rename,[status(thm)],[c_0_581]) ).

fof(c_0_991,plain,
    ! [X50,X51,X52] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X52)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X52),X51),X50),c_HOL_Ozero__class_Ozero(X52),X52)
      | ~ c_HOL_Oord__class_Oless(X50,c_HOL_Ozero__class_Ozero(X52),X52)
      | ~ c_lessequals(X51,c_HOL_Ozero__class_Ozero(X52),X52) ),
    inference(variable_rename,[status(thm)],[c_0_582]) ).

fof(c_0_992,plain,
    ! [X50,X51,X52] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X52)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X52),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X52),X51),X50),X52)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X52),X50,X52)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X52),X51,X52) ),
    inference(variable_rename,[status(thm)],[c_0_583]) ).

fof(c_0_993,plain,
    ! [X50,X51,X52] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X52)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X52),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X52),X51),X50),X52)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X52),X50,X52)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X52),X51,X52) ),
    inference(variable_rename,[status(thm)],[c_0_584]) ).

fof(c_0_994,plain,
    ! [X50,X51,X52] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X52)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X52),X51),X50),c_HOL_Ozero__class_Ozero(X52),X52)
      | ~ c_HOL_Oord__class_Oless(X50,c_HOL_Ozero__class_Ozero(X52),X52)
      | ~ c_HOL_Oord__class_Oless(X51,c_HOL_Ozero__class_Ozero(X52),X52) ),
    inference(variable_rename,[status(thm)],[c_0_585]) ).

fof(c_0_995,plain,
    ! [X50,X51,X52] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X52)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X52),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X52),X51),X50),X52)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X52),X50,X52)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X52),X51,X52) ),
    inference(variable_rename,[status(thm)],[c_0_586]) ).

fof(c_0_996,plain,
    ! [X30,X31,X32] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X32)
      | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X32),c_Power_Opower__class_Opower(X31,X30,X32),X32)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X30,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X32),X31,X32) ),
    inference(variable_rename,[status(thm)],[c_0_587]) ).

fof(c_0_997,plain,
    ! [X51,X52,X53,X54] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X54)
      | ~ class_OrderedGroup_Ocomm__monoid__add(X54)
      | c_lessequals(X52,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X54),X53),X51),X54)
      | ~ c_lessequals(X52,X53,X54)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X54),X51,X54) ),
    inference(variable_rename,[status(thm)],[c_0_588]) ).

fof(c_0_998,plain,
    ! [X51,X52,X53,X54] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X54)
      | ~ class_OrderedGroup_Ocomm__monoid__add(X54)
      | c_lessequals(X52,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X54),X53),X51),X54)
      | ~ c_lessequals(X52,X51,X54)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X54),X53,X54) ),
    inference(variable_rename,[status(thm)],[c_0_589]) ).

fof(c_0_999,plain,
    ! [X51,X52,X53,X54] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X54)
      | ~ class_OrderedGroup_Ocomm__monoid__add(X54)
      | c_HOL_Oord__class_Oless(X52,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X54),X53),X51),X54)
      | ~ c_lessequals(X52,X51,X54)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X54),X53,X54) ),
    inference(variable_rename,[status(thm)],[c_0_590]) ).

fof(c_0_1000,plain,
    ! [X51,X52,X53,X54] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X54)
      | ~ class_OrderedGroup_Ocomm__monoid__add(X54)
      | c_HOL_Oord__class_Oless(X52,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X54),X53),X51),X54)
      | ~ c_HOL_Oord__class_Oless(X52,X51,X54)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X54),X53,X54) ),
    inference(variable_rename,[status(thm)],[c_0_591]) ).

fof(c_0_1001,plain,
    ! [X51,X52,X53,X54] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X54)
      | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X54),X51),X53),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X54),X51),X52),X54)
      | ~ c_lessequals(X53,X52,X54) ),
    inference(variable_rename,[status(thm)],[c_0_592]) ).

fof(c_0_1002,plain,
    ! [X51,X52,X53,X54] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X54)
      | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X54),X53),X51),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X54),X52),X51),X54)
      | ~ c_lessequals(X53,X52,X54) ),
    inference(variable_rename,[status(thm)],[c_0_593]) ).

fof(c_0_1003,plain,
    ! [X51,X52,X53,X54] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X54)
      | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X54),X51),X53),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X54),X51),X52),X54)
      | ~ c_lessequals(X53,X52,X54) ),
    inference(variable_rename,[status(thm)],[c_0_594]) ).

fof(c_0_1004,plain,
    ! [X51,X52,X53,X54] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X54)
      | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X54),X53),X51),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X54),X52),X51),X54)
      | ~ c_lessequals(X53,X52,X54) ),
    inference(variable_rename,[status(thm)],[c_0_595]) ).

fof(c_0_1005,plain,
    ! [X51,X52,X53,X54] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X54)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X54),X53),X51),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X54),X52),X51),X54)
      | ~ c_HOL_Oord__class_Oless(X53,X52,X54) ),
    inference(variable_rename,[status(thm)],[c_0_596]) ).

fof(c_0_1006,plain,
    ! [X51,X52,X53,X54] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X54)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X54),X53),X51),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X54),X52),X51),X54)
      | ~ c_HOL_Oord__class_Oless(X53,X52,X54) ),
    inference(variable_rename,[status(thm)],[c_0_597]) ).

fof(c_0_1007,plain,
    ! [X51,X52,X53,X54] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X54)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X54),X51),X53),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X54),X51),X52),X54)
      | ~ c_HOL_Oord__class_Oless(X53,X52,X54) ),
    inference(variable_rename,[status(thm)],[c_0_598]) ).

fof(c_0_1008,plain,
    ! [X51,X52,X53,X54] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X54)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X54),X51),X53),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X54),X51),X52),X54)
      | ~ c_HOL_Oord__class_Oless(X53,X52,X54) ),
    inference(variable_rename,[status(thm)],[c_0_599]) ).

fof(c_0_1009,plain,
    ! [X51,X52,X53,X54] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X54)
      | c_HOL_Oord__class_Oless(X52,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X54),X53),X51),X54)
      | ~ c_HOL_Oord__class_Oless(X52,X51,X54)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X54),X53,X54) ),
    inference(variable_rename,[status(thm)],[c_0_600]) ).

fof(c_0_1010,plain,
    ! [X19,X20] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X19,tc_nat)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X20,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X20),X19),tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_601])])]) ).

fof(c_0_1011,plain,
    ! [X50,X51,X52,X53] :
      ( ~ class_Orderings_Olinorder(X53)
      | c_lessequals(c_Orderings_Oord__class_Omax(X52,X51,X53),X50,X53)
      | ~ c_lessequals(X51,X50,X53)
      | ~ c_lessequals(X52,X50,X53) ),
    inference(variable_rename,[status(thm)],[c_0_602]) ).

fof(c_0_1012,plain,
    ! [X65,X66,X67,X68] :
      ( ~ class_Orderings_Olinorder(X68)
      | c_lessequals(c_Orderings_Oord__class_Omax(X66,X65,X68),X67,X68)
      | ~ c_lessequals(X65,X67,X68)
      | ~ c_lessequals(X66,X67,X68) ),
    inference(variable_rename,[status(thm)],[c_0_603]) ).

fof(c_0_1013,plain,
    ! [X65,X66,X67,X68] :
      ( ~ class_Orderings_Olinorder(X68)
      | c_lessequals(c_Orderings_Oord__class_Omax(X67,X66,X68),X65,X68)
      | ~ c_lessequals(X66,X65,X68)
      | ~ c_lessequals(X67,X65,X68) ),
    inference(variable_rename,[status(thm)],[c_0_604]) ).

fof(c_0_1014,plain,
    ! [X65,X66,X67,X68] :
      ( ~ class_Orderings_Olinorder(X68)
      | c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X67,X66,X68),X65,X68)
      | ~ c_HOL_Oord__class_Oless(X66,X65,X68)
      | ~ c_HOL_Oord__class_Oless(X67,X65,X68) ),
    inference(variable_rename,[status(thm)],[c_0_605]) ).

fof(c_0_1015,plain,
    ! [X51,X52,X53,X54,X55] :
      ( hAPP(hAPP(X51,hAPP(hAPP(X51,X54),X53)),X52) = hAPP(hAPP(X51,X54),hAPP(hAPP(X51,X53),X52))
      | ~ c_OrderedGroup_Osemigroup__add(X51,X55) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_606])])]) ).

fof(c_0_1016,plain,
    ! [X61,X62,X63,X64] :
      ( c_List_Olistsp(X63,c_List_Oappend(X62,X61,X64),X64)
      | ~ c_List_Olistsp(X63,X61,X64)
      | ~ c_List_Olistsp(X63,X62,X64) ),
    inference(variable_rename,[status(thm)],[c_0_607]) ).

fof(c_0_1017,plain,
    ! [X65,X66,X67,X68] :
      ( ~ class_Orderings_Olinorder(X68)
      | c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omax(X67,X66,X68),X65,X68) = c_Orderings_Oord__class_Omax(X67,c_Orderings_Oord__class_Omax(X66,X65,X68),X68) ),
    inference(variable_rename,[status(thm)],[c_0_608]) ).

fof(c_0_1018,plain,
    ! [X65,X66,X67,X68] :
      ( ~ class_Orderings_Olinorder(X68)
      | c_Orderings_Oord__class_Omax(X67,c_Orderings_Oord__class_Omax(X66,X65,X68),X68) = c_Orderings_Oord__class_Omax(X66,c_Orderings_Oord__class_Omax(X67,X65,X68),X68) ),
    inference(variable_rename,[status(thm)],[c_0_609]) ).

fof(c_0_1019,plain,
    ! [X30,X31] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X31)
      | c_lessequals(X30,c_HOL_Ozero__class_Ozero(X31),X31)
      | ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X31),X30),X30),c_HOL_Ozero__class_Ozero(X31),X31) ),
    inference(variable_rename,[status(thm)],[c_0_610]) ).

fof(c_0_1020,plain,
    ! [X30,X31] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X31)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X31),X30,X31)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X31),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X31),X30),X30),X31) ),
    inference(variable_rename,[status(thm)],[c_0_611]) ).

fof(c_0_1021,plain,
    ! [X30,X31] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X31)
      | c_HOL_Oord__class_Oless(X30,c_HOL_Ozero__class_Ozero(X31),X31)
      | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X31),X30),X30),c_HOL_Ozero__class_Ozero(X31),X31) ),
    inference(variable_rename,[status(thm)],[c_0_612]) ).

fof(c_0_1022,plain,
    ! [X30,X31] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X31)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X31),X30,X31)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X31),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X31),X30),X30),X31) ),
    inference(variable_rename,[status(thm)],[c_0_613]) ).

fof(c_0_1023,plain,
    ! [X30,X31] :
      ( ~ class_Ring__and__Field_Oordered__idom(X31)
      | c_HOL_Oord__class_Oless(X30,c_HOL_Ozero__class_Ozero(X31),X31)
      | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X31),X30),X30),c_HOL_Ozero__class_Ozero(X31),X31) ),
    inference(variable_rename,[status(thm)],[c_0_614]) ).

fof(c_0_1024,plain,
    ! [X26,X27,X28] :
      ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X28),X26),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X27),X26),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X28,X27,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_615]) ).

fof(c_0_1025,plain,
    ! [X26,X27,X28] :
      ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X28),X27),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X28),X26),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X27,X26,tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_616])])]) ).

fof(c_0_1026,plain,
    ! [X50,X51,X52,X53] :
      ( ~ class_Orderings_Olinorder(X53)
      | c_lessequals(X52,X50,X53)
      | ~ c_lessequals(c_Orderings_Oord__class_Omax(X52,X51,X53),X50,X53) ),
    inference(variable_rename,[status(thm)],[c_0_617]) ).

fof(c_0_1027,plain,
    ! [X50,X51,X52,X53] :
      ( ~ class_Orderings_Olinorder(X53)
      | c_lessequals(X51,X50,X53)
      | ~ c_lessequals(c_Orderings_Oord__class_Omax(X52,X51,X53),X50,X53) ),
    inference(variable_rename,[status(thm)],[c_0_618]) ).

fof(c_0_1028,plain,
    ! [X65,X66,X67,X68] :
      ( ~ class_Orderings_Olinorder(X68)
      | c_lessequals(X67,X65,X68)
      | ~ c_lessequals(c_Orderings_Oord__class_Omax(X67,X66,X68),X65,X68) ),
    inference(variable_rename,[status(thm)],[c_0_619]) ).

fof(c_0_1029,plain,
    ! [X65,X66,X67,X68] :
      ( ~ class_Orderings_Olinorder(X68)
      | c_lessequals(X66,X65,X68)
      | ~ c_lessequals(c_Orderings_Oord__class_Omax(X67,X66,X68),X65,X68) ),
    inference(variable_rename,[status(thm)],[c_0_620]) ).

fof(c_0_1030,plain,
    ! [X65,X66,X67,X68] :
      ( ~ class_Orderings_Olinorder(X68)
      | c_HOL_Oord__class_Oless(X66,X65,X68)
      | ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X67,X66,X68),X65,X68) ),
    inference(variable_rename,[status(thm)],[c_0_621]) ).

fof(c_0_1031,plain,
    ! [X65,X66,X67,X68] :
      ( ~ class_Orderings_Olinorder(X68)
      | c_HOL_Oord__class_Oless(X67,X65,X68)
      | ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X67,X66,X68),X65,X68) ),
    inference(variable_rename,[status(thm)],[c_0_622]) ).

fof(c_0_1032,plain,
    ! [X63,X64,X65,X66] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X66)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X66),X65),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X66),X64),X63)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X66),X64),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X66),X65),X63)) ),
    inference(variable_rename,[status(thm)],[c_0_623]) ).

fof(c_0_1033,plain,
    ! [X51,X52,X53,X54] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X54)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X54),X53),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X54),X52),X51)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X54),X52),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X54),X53),X51)) ),
    inference(variable_rename,[status(thm)],[c_0_624]) ).

fof(c_0_1034,plain,
    ! [X65,X66,X67,X68] :
      ( ~ class_OrderedGroup_Oab__group__add(X68)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X68),X67),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X68),X66),X65)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X68),X66),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X68),X67),X65)) ),
    inference(variable_rename,[status(thm)],[c_0_625]) ).

fof(c_0_1035,plain,
    ! [X41,X42,X43,X44] :
      ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X43,X44),X42),X41))
      | ~ hBOOL(hAPP(hAPP(X43,X42),X41)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_626])])]) ).

fof(c_0_1036,plain,
    ! [X61,X62,X63,X64] :
      ( c_List_Olistsp(X63,X62,X64)
      | ~ c_List_Olistsp(X63,c_List_Oappend(X62,X61,X64),X64) ),
    inference(variable_rename,[status(thm)],[c_0_627]) ).

fof(c_0_1037,plain,
    ! [X61,X62,X63,X64] :
      ( c_List_Olistsp(X63,X61,X64)
      | ~ c_List_Olistsp(X63,c_List_Oappend(X62,X61,X64),X64) ),
    inference(variable_rename,[status(thm)],[c_0_628]) ).

fof(c_0_1038,plain,
    ! [X41,X42,X43] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X43)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X43),X42),X41) != c_HOL_Ozero__class_Ozero(X43)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X43),X41,X43)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X43),X42,X43)
      | X42 = c_HOL_Ozero__class_Ozero(X43) ),
    inference(variable_rename,[status(thm)],[c_0_629]) ).

fof(c_0_1039,plain,
    ! [X41,X42,X43] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X43)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X43),X42),X41) != c_HOL_Ozero__class_Ozero(X43)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X43),X41,X43)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X43),X42,X43)
      | X41 = c_HOL_Ozero__class_Ozero(X43) ),
    inference(variable_rename,[status(thm)],[c_0_630]) ).

fof(c_0_1040,plain,
    ! [X4] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X4)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_HOL_Ozero__class_Ozero(X4),X4)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_HOL_Ozero__class_Ozero(X4),X4)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),c_HOL_Ozero__class_Ozero(X4)),c_HOL_Ozero__class_Ozero(X4)) = c_HOL_Ozero__class_Ozero(X4) ),
    inference(variable_rename,[status(thm)],[c_0_631]) ).

fof(c_0_1041,plain,
    ! [X62,X63,X64,X65] :
      ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X63),X64) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X65),X62)
      | ~ c_HOL_Oord__class_Oless(X65,X64,tc_nat)
      | c_HOL_Oord__class_Oless(X63,X62,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_632]) ).

fof(c_0_1042,plain,
    ! [X26,X27,X28] :
      ( c_HOL_Oord__class_Oless(X28,X26,tc_nat)
      | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X28),X27),X26,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_633]) ).

fof(c_0_1043,plain,
    ! [X30,X31,X32,X33] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X33)
      | c_Power_Opower__class_Opower(X32,X31,X33) != c_Power_Opower__class_Opower(X32,X30,X33)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X33),X32,X33)
      | X31 = X30 ),
    inference(variable_rename,[status(thm)],[c_0_634]) ).

fof(c_0_1044,plain,
    ! [X30,X31,X32] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X32)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X32),c_Power_Opower__class_Opower(X31,X30,X32),X32)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X32),X31,X32) ),
    inference(variable_rename,[status(thm)],[c_0_635]) ).

fof(c_0_1045,plain,
    ! [X30,X31,X32] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X32)
      | c_lessequals(c_HOL_Oone__class_Oone(X32),c_Power_Opower__class_Opower(X31,X30,X32),X32)
      | ~ c_lessequals(c_HOL_Oone__class_Oone(X32),X31,X32) ),
    inference(variable_rename,[status(thm)],[c_0_636]) ).

fof(c_0_1046,plain,
    ! [X30,X31,X32] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X32)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X32),c_Power_Opower__class_Opower(X31,X30,X32),X32)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X32),X31,X32) ),
    inference(variable_rename,[status(thm)],[c_0_637]) ).

fof(c_0_1047,plain,
    ! [X41,X42,X43,X44] :
      ( c_Wellfounded_Oaccp(X42,X41,X44)
      | ~ hBOOL(hAPP(hAPP(X42,X41),X43))
      | ~ c_Wellfounded_Oaccp(X42,X43,X44) ),
    inference(variable_rename,[status(thm)],[c_0_638]) ).

fof(c_0_1048,plain,
    ! [X50,X51,X52,X53] :
      ( c_Wellfounded_Oaccp(X50,X52,X53)
      | ~ hBOOL(hAPP(hAPP(X50,X52),X51))
      | ~ c_Wellfounded_Oaccp(X50,X51,X53) ),
    inference(variable_rename,[status(thm)],[c_0_639]) ).

fof(c_0_1049,plain,
    ! [X30,X31] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X31)
      | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X31),X30),X30),c_HOL_Ozero__class_Ozero(X31),X31)
      | ~ c_lessequals(X30,c_HOL_Ozero__class_Ozero(X31),X31) ),
    inference(variable_rename,[status(thm)],[c_0_640]) ).

fof(c_0_1050,plain,
    ! [X30,X31] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X31)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X31),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X31),X30),X30),X31)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X31),X30,X31) ),
    inference(variable_rename,[status(thm)],[c_0_641]) ).

fof(c_0_1051,plain,
    ! [X30,X31] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X31)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X31),X30),X30),c_HOL_Ozero__class_Ozero(X31),X31)
      | ~ c_HOL_Oord__class_Oless(X30,c_HOL_Ozero__class_Ozero(X31),X31) ),
    inference(variable_rename,[status(thm)],[c_0_642]) ).

fof(c_0_1052,plain,
    ! [X30,X31] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X31)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X31),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X31),X30),X30),X31)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X31),X30,X31) ),
    inference(variable_rename,[status(thm)],[c_0_643]) ).

fof(c_0_1053,plain,
    ! [X30,X31] :
      ( ~ class_Ring__and__Field_Oordered__idom(X31)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X31),X30),X30),c_HOL_Ozero__class_Ozero(X31),X31)
      | ~ c_HOL_Oord__class_Oless(X30,c_HOL_Ozero__class_Ozero(X31),X31) ),
    inference(variable_rename,[status(thm)],[c_0_644]) ).

fof(c_0_1054,plain,
    ! [X9] :
      ( hBOOL(hAPP(c_InductTermi_OIT,X9))
      | ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X9,tc_Lambda_OdB) ),
    inference(variable_rename,[status(thm)],[c_0_645]) ).

fof(c_0_1055,plain,
    ! [X55,X56,X57,X58] :
      ( c_Type_Otyping(X57,X55,X58)
      | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X56),X55))
      | ~ c_Type_Otyping(X57,X56,X58) ),
    inference(variable_rename,[status(thm)],[c_0_646]) ).

fof(c_0_1056,plain,
    ! [X52,X53,X54] :
      ( ~ class_OrderedGroup_Omonoid__add(X54)
      | c_List_Olistsum(c_List_Oappend(X53,X52,X54),X54) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X54),c_List_Olistsum(X53,X54)),c_List_Olistsum(X52,X54)) ),
    inference(variable_rename,[status(thm)],[c_0_647]) ).

fof(c_0_1057,plain,
    ! [X50,X51,X52,X53] :
      ( ~ class_Orderings_Olinorder(X53)
      | c_lessequals(X50,c_Orderings_Oord__class_Omax(X52,X51,X53),X53)
      | ~ c_lessequals(X50,X52,X53) ),
    inference(variable_rename,[status(thm)],[c_0_648]) ).

fof(c_0_1058,plain,
    ! [X50,X51,X52,X53] :
      ( ~ class_Orderings_Olinorder(X53)
      | c_lessequals(X50,c_Orderings_Oord__class_Omax(X52,X51,X53),X53)
      | ~ c_lessequals(X50,X51,X53) ),
    inference(variable_rename,[status(thm)],[c_0_649]) ).

fof(c_0_1059,plain,
    ! [X65,X66,X67,X68] :
      ( ~ class_Orderings_Olinorder(X68)
      | c_lessequals(X65,c_Orderings_Oord__class_Omax(X67,X66,X68),X68)
      | ~ c_lessequals(X65,X67,X68) ),
    inference(variable_rename,[status(thm)],[c_0_650]) ).

fof(c_0_1060,plain,
    ! [X65,X66,X67,X68] :
      ( ~ class_Orderings_Olinorder(X68)
      | c_lessequals(X65,c_Orderings_Oord__class_Omax(X67,X66,X68),X68)
      | ~ c_lessequals(X65,X66,X68) ),
    inference(variable_rename,[status(thm)],[c_0_651]) ).

fof(c_0_1061,plain,
    ! [X65,X66,X67,X68] :
      ( ~ class_Orderings_Olinorder(X68)
      | c_HOL_Oord__class_Oless(X65,c_Orderings_Oord__class_Omax(X67,X66,X68),X68)
      | ~ c_HOL_Oord__class_Oless(X65,X66,X68) ),
    inference(variable_rename,[status(thm)],[c_0_652]) ).

fof(c_0_1062,plain,
    ! [X65,X66,X67,X68] :
      ( ~ class_Orderings_Olinorder(X68)
      | c_HOL_Oord__class_Oless(X65,c_Orderings_Oord__class_Omax(X67,X66,X68),X68)
      | ~ c_HOL_Oord__class_Oless(X65,X67,X68) ),
    inference(variable_rename,[status(thm)],[c_0_653]) ).

fof(c_0_1063,plain,
    ! [X50,X51,X52,X53] :
      ( ~ class_Orderings_Olinorder(X53)
      | c_HOL_Oord__class_Oless(X50,c_Orderings_Oord__class_Omax(X52,X51,X53),X53)
      | ~ c_HOL_Oord__class_Oless(X50,X51,X53) ),
    inference(variable_rename,[status(thm)],[c_0_654]) ).

fof(c_0_1064,plain,
    ! [X50,X51,X52,X53] :
      ( ~ class_Orderings_Olinorder(X53)
      | c_HOL_Oord__class_Oless(X50,c_Orderings_Oord__class_Omax(X52,X51,X53),X53)
      | ~ c_HOL_Oord__class_Oless(X50,X52,X53) ),
    inference(variable_rename,[status(thm)],[c_0_655]) ).

fof(c_0_1065,plain,
    ! [X19,X20,X21] :
      ( ~ class_Ring__and__Field_Osemiring__1(X21)
      | c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X20),X19),X21) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X21),c_Nat_Osemiring__1__class_Oof__nat(X20,X21)),c_Nat_Osemiring__1__class_Oof__nat(X19,X21)) ),
    inference(variable_rename,[status(thm)],[c_0_656]) ).

fof(c_0_1066,plain,
    ! [X19,X20] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X20),X19),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X19,tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_657])])]) ).

fof(c_0_1067,plain,
    ! [X19,X20] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X20),X19),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X20,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_658]) ).

fof(c_0_1068,plain,
    ! [X65,X66,X67,X68] :
      ( ~ class_Orderings_Opreorder(X68)
      | c_HOL_Oord__class_Oless(X67,X65,X68)
      | ~ c_lessequals(X66,X65,X68)
      | ~ c_HOL_Oord__class_Oless(X67,X66,X68) ),
    inference(variable_rename,[status(thm)],[c_0_659]) ).

fof(c_0_1069,plain,
    ! [X65,X66,X67,X68] :
      ( ~ class_Orderings_Opreorder(X68)
      | c_HOL_Oord__class_Oless(X67,X65,X68)
      | ~ c_HOL_Oord__class_Oless(X66,X65,X68)
      | ~ c_lessequals(X67,X66,X68) ),
    inference(variable_rename,[status(thm)],[c_0_660]) ).

fof(c_0_1070,plain,
    ! [X65,X66,X67,X68] :
      ( ~ class_Orderings_Opreorder(X68)
      | c_lessequals(X67,X65,X68)
      | ~ c_lessequals(X66,X65,X68)
      | ~ c_lessequals(X67,X66,X68) ),
    inference(variable_rename,[status(thm)],[c_0_661]) ).

fof(c_0_1071,plain,
    ! [X65,X66,X67,X68] :
      ( ~ class_Orderings_Oorder(X68)
      | c_HOL_Oord__class_Oless(X65,X67,X68)
      | ~ c_HOL_Oord__class_Oless(X65,X66,X68)
      | ~ c_lessequals(X66,X67,X68) ),
    inference(variable_rename,[status(thm)],[c_0_662]) ).

fof(c_0_1072,plain,
    ! [X65,X66,X67,X68] :
      ( ~ class_Orderings_Oorder(X68)
      | c_HOL_Oord__class_Oless(X65,X67,X68)
      | ~ c_lessequals(X65,X66,X68)
      | ~ c_HOL_Oord__class_Oless(X66,X67,X68) ),
    inference(variable_rename,[status(thm)],[c_0_663]) ).

fof(c_0_1073,plain,
    ! [X65,X66,X67,X68] :
      ( ~ class_Orderings_Oorder(X68)
      | c_lessequals(X65,X67,X68)
      | ~ c_lessequals(X65,X66,X68)
      | ~ c_lessequals(X66,X67,X68) ),
    inference(variable_rename,[status(thm)],[c_0_664]) ).

fof(c_0_1074,plain,
    ! [X65,X66,X67,X68] :
      ( ~ class_Orderings_Oorder(X68)
      | c_HOL_Oord__class_Oless(X65,X67,X68)
      | ~ c_HOL_Oord__class_Oless(X65,X66,X68)
      | ~ c_HOL_Oord__class_Oless(X66,X67,X68) ),
    inference(variable_rename,[status(thm)],[c_0_665]) ).

fof(c_0_1075,plain,
    ! [X65,X66,X67,X68] :
      ( ~ class_Orderings_Opreorder(X68)
      | c_HOL_Oord__class_Oless(X67,X65,X68)
      | ~ c_HOL_Oord__class_Oless(X66,X65,X68)
      | ~ c_HOL_Oord__class_Oless(X67,X66,X68) ),
    inference(variable_rename,[status(thm)],[c_0_666]) ).

fof(c_0_1076,plain,
    ! [X28,X29] :
      ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OAbs(X29)),c_Lambda_OdB_OAbs(X28)))
      | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X29),X28)) ),
    inference(variable_rename,[status(thm)],[c_0_667]) ).

fof(c_0_1077,plain,
    ! [X19,X20,X21] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X21)
      | c_HOL_Oord__class_Oless(X20,X19,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X20,X21),c_Nat_Osemiring__1__class_Oof__nat(X19,X21),X21) ),
    inference(variable_rename,[status(thm)],[c_0_668]) ).

fof(c_0_1078,plain,
    ! [X65,X66,X67] :
      ( c_HOL_Oord__class_Oless(X67,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X66),X65),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X67,X66,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_669]) ).

fof(c_0_1079,plain,
    ! [X65,X66,X67] :
      ( c_HOL_Oord__class_Oless(X67,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X66),X65),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X67,X65,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_670]) ).

fof(c_0_1080,plain,
    ! [X17,X18,X19] :
      ( c_HOL_Oord__class_Oless(X19,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X17),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X19,X18,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_671]) ).

fof(c_0_1081,plain,
    ! [X17,X18,X19] :
      ( c_HOL_Oord__class_Oless(X19,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X17),X18),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X19,X18,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_672]) ).

fof(c_0_1082,plain,
    ! [X41,X42,X43] :
      ( ~ class_Orderings_Olinorder(X43)
      | c_Orderings_Oord__class_Omax(X42,c_Orderings_Oord__class_Omax(X42,X41,X43),X43) = c_Orderings_Oord__class_Omax(X42,X41,X43) ),
    inference(variable_rename,[status(thm)],[c_0_673]) ).

fof(c_0_1083,plain,
    ! [X28,X29] :
      ( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_Olift,X28),X29)))
      | ~ hBOOL(hAPP(c_InductTermi_OIT,X28)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_674])])]) ).

fof(c_0_1084,plain,
    ! [X26,X27,X28] :
      ( c_Lambda_Oliftn(X26,c_Lambda_OdB_OVar(X28),X27) = c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X28),X26))
      | c_HOL_Oord__class_Oless(X28,X27,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_675]) ).

fof(c_0_1085,plain,
    ! [X4] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X4)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),c_HOL_Oone__class_Oone(X4)),c_HOL_Oone__class_Oone(X4)),X4) ),
    inference(variable_rename,[status(thm)],[c_0_676]) ).

fof(c_0_1086,plain,
    ! [X44,X45,X46] :
      ( ~ class_OrderedGroup_Omonoid__add(X46)
      | c_List_Olistsum(c_List_Olist_OCons(X45,X44,X46),X46) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X46),X45),c_List_Olistsum(X44,X46)) ),
    inference(variable_rename,[status(thm)],[c_0_677]) ).

fof(c_0_1087,plain,
    ! [X41,X42,X43] :
      ( ~ class_Orderings_Opreorder(X43)
      | c_HOL_Oord__class_Oless(X42,X41,X43)
      | c_lessequals(X41,X42,X43)
      | ~ c_lessequals(X42,X41,X43) ),
    inference(variable_rename,[status(thm)],[c_0_678]) ).

fof(c_0_1088,plain,
    ! [X26,X27] :
      ( hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(X27)),X26) = c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X27),c_HOL_Oone__class_Oone(tc_nat)))
      | c_HOL_Oord__class_Oless(X27,X26,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_679]) ).

fof(c_0_1089,plain,
    ! [X19,X20] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X20)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X19,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X20),c_Nat_Osemiring__1__class_Oof__nat(X19,X20),X20) ),
    inference(variable_rename,[status(thm)],[c_0_680]) ).

fof(c_0_1090,plain,
    ! [X27,X28,X29] :
      ( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X28)),X27),X29) = c_Lambda_OdB_OVar(X28)
      | ~ c_HOL_Oord__class_Oless(X28,X29,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_681]) ).

fof(c_0_1091,plain,
    ! [X19,X20,X21] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X21)
      | c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X20,X21),c_Nat_Osemiring__1__class_Oof__nat(X19,X21),X21)
      | ~ c_HOL_Oord__class_Oless(X20,X19,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_682]) ).

fof(c_0_1092,plain,
    ! [X28] :
      ( c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X28,tc_Lambda_OdB)
      | ~ hBOOL(hAPP(c_InductTermi_OIT,X28)) ),
    inference(variable_rename,[status(thm)],[c_0_683]) ).

fof(c_0_1093,plain,
    ! [X35,X36,X37] :
      ( hBOOL(hAPP(hAPP(X37,X35),X36))
      | c_HOL_Oord__class_Oless(X35,X36,tc_nat)
      | X36 = X35
      | c_HOL_Oord__class_Oless(X36,X35,tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_684])])]) ).

fof(c_0_1094,plain,
    ! [X19,X20] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X20)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X20),c_Nat_Osemiring__1__class_Oof__nat(X19,X20),X20)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X19,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_685]) ).

fof(c_0_1095,plain,
    ! [X41,X42,X43] :
      ( ~ class_Orderings_Oorder(X43)
      | X42 = X41
      | ~ c_lessequals(X42,X41,X43)
      | ~ c_lessequals(X41,X42,X43) ),
    inference(variable_rename,[status(thm)],[c_0_686]) ).

fof(c_0_1096,plain,
    ! [X41,X42,X43] :
      ( ~ class_Orderings_Oorder(X43)
      | X42 = X41
      | ~ c_lessequals(X41,X42,X43)
      | ~ c_lessequals(X42,X41,X43) ),
    inference(variable_rename,[status(thm)],[c_0_687]) ).

fof(c_0_1097,plain,
    ! [X41,X42,X43] :
      ( ~ class_Orderings_Oorder(X43)
      | X42 = X41
      | ~ c_lessequals(X41,X42,X43)
      | ~ c_lessequals(X42,X41,X43) ),
    inference(variable_rename,[status(thm)],[c_0_688]) ).

fof(c_0_1098,plain,
    ! [X65,X66,X67,X68] :
      ( ~ class_Ring__and__Field_Oidom(X68)
      | ~ class_Int_Onumber__ring(X68)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X68),X67),X66) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X68),X67),X65)
      | X66 = X65 ),
    inference(variable_rename,[status(thm)],[c_0_689]) ).

fof(c_0_1099,plain,
    ! [X30] :
      ( hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__5(X30)))
      | hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X30)))
      | c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X30),tc_Lambda_OdB)
      | ~ hBOOL(hAPP(c_InductTermi_OIT,X30)) ),
    inference(variable_rename,[status(thm)],[c_0_690]) ).

fof(c_0_1100,plain,
    ! [X25,X26] :
      ( ~ class_Orderings_Olinorder(X26)
      | ~ c_lessequals(X25,X25,X26)
      | ~ c_HOL_Oord__class_Oless(X25,X25,X26) ),
    inference(variable_rename,[status(thm)],[c_0_691]) ).

fof(c_0_1101,plain,
    ! [X41,X42,X43] :
      ( ~ class_Orderings_Olinorder(X43)
      | ~ c_HOL_Oord__class_Oless(X42,X41,X43)
      | ~ c_lessequals(X41,X42,X43) ),
    inference(variable_rename,[status(thm)],[c_0_692]) ).

fof(c_0_1102,plain,
    ! [X41,X42,X43] :
      ( ~ class_Orderings_Olinorder(X43)
      | ~ c_lessequals(X42,X41,X43)
      | ~ c_HOL_Oord__class_Oless(X41,X42,X43) ),
    inference(variable_rename,[status(thm)],[c_0_693]) ).

fof(c_0_1103,plain,
    ! [X41,X42,X43] :
      ( ~ class_Orderings_Opreorder(X43)
      | ~ c_lessequals(X41,X42,X43)
      | ~ c_HOL_Oord__class_Oless(X42,X41,X43) ),
    inference(variable_rename,[status(thm)],[c_0_694]) ).

fof(c_0_1104,plain,
    ! [X50,X51,X52] :
      ( ~ class_Orderings_Oorder(X52)
      | ~ c_HOL_Oord__class_Oless(X51,X50,X52)
      | ~ c_HOL_Oord__class_Oless(X50,X51,X52) ),
    inference(variable_rename,[status(thm)],[c_0_695]) ).

fof(c_0_1105,plain,
    ! [X41,X42,X43] :
      ( ~ class_Orderings_Olinorder(X43)
      | ~ c_HOL_Oord__class_Oless(X42,X41,X43)
      | ~ c_HOL_Oord__class_Oless(X41,X42,X43) ),
    inference(variable_rename,[status(thm)],[c_0_696]) ).

fof(c_0_1106,plain,
    ! [X41,X42,X43] :
      ( ~ class_Orderings_Opreorder(X43)
      | ~ c_HOL_Oord__class_Oless(X41,X42,X43)
      | ~ c_HOL_Oord__class_Oless(X42,X41,X43) ),
    inference(variable_rename,[status(thm)],[c_0_697]) ).

fof(c_0_1107,plain,
    ! [X50,X51,X52] :
      ( ~ class_Orderings_Opreorder(X52)
      | ~ c_HOL_Oord__class_Oless(X50,X51,X52)
      | ~ c_HOL_Oord__class_Oless(X51,X50,X52) ),
    inference(variable_rename,[status(thm)],[c_0_698]) ).

fof(c_0_1108,plain,
    ! [X41,X42,X43,X44,X45] :
      ( c_List_Oreplicate(X44,X42,X45) != c_List_Oreplicate(X43,X41,X45)
      | X42 = X41
      | X44 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_699])])]) ).

fof(c_0_1109,plain,
    ! [X30,X31] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X31)
      | c_HOL_Oord__class_Oless(X30,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X31),X30),c_HOL_Oone__class_Oone(X31)),X31) ),
    inference(variable_rename,[status(thm)],[c_0_700]) ).

fof(c_0_1110,plain,
    ! [X41,X42,X43,X44,X45] :
      ( c_List_Oreplicate(X44,X42,X45) != c_List_Oreplicate(X43,X41,X45)
      | X44 = X43 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_701])])]) ).

fof(c_0_1111,plain,
    ! [X52,X53,X54,X55] :
      ( c_List_Oappend(X53,X54,X55) != c_List_Oappend(X52,X54,X55)
      | X53 = X52 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_702])])]) ).

fof(c_0_1112,plain,
    ! [X52,X53,X54,X55] :
      ( c_List_Oappend(X54,X53,X55) != c_List_Oappend(X54,X52,X55)
      | X53 = X52 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_703])])]) ).

fof(c_0_1113,plain,
    ! [X51,X52,X53,X54] :
      ( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X54)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X54),X53),X52) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X54),X53),X51)
      | X52 = X51 ),
    inference(variable_rename,[status(thm)],[c_0_704]) ).

fof(c_0_1114,plain,
    ! [X51,X52,X53,X54] :
      ( ~ class_OrderedGroup_Ocancel__semigroup__add(X54)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X54),X53),X52) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X54),X53),X51)
      | X52 = X51 ),
    inference(variable_rename,[status(thm)],[c_0_705]) ).

fof(c_0_1115,plain,
    ! [X51,X52,X53,X54] :
      ( ~ class_OrderedGroup_Ocancel__semigroup__add(X54)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X54),X52),X53) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X54),X51),X53)
      | X52 = X51 ),
    inference(variable_rename,[status(thm)],[c_0_706]) ).

fof(c_0_1116,plain,
    ! [X58,X59,X60,X61,X62] :
      ( c_List_Olist_OCons(X61,X59,X62) != c_List_Olist_OCons(X60,X58,X62)
      | X61 = X60 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_707])])]) ).

fof(c_0_1117,plain,
    ! [X58,X59,X60,X61,X62] :
      ( c_List_Olist_OCons(X61,X59,X62) != c_List_Olist_OCons(X60,X58,X62)
      | X59 = X58 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_708])])]) ).

fof(c_0_1118,plain,
    ! [X25,X26] :
      ( c_HOL_Oord__class_Oless(X25,X25,tc_nat)
      | c_Lambda_Osubstn(c_Lambda_OdB_OVar(X25),X26,X25) = c_Lambda_Oliftn(X25,X26,c_HOL_Ozero__class_Ozero(tc_nat)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_709])])]) ).

fof(c_0_1119,plain,
    ! [X26,X27,X28] :
      ( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X28)),X26),X27) = c_Lambda_OdB_OVar(X28)
      | X28 = X27
      | c_HOL_Oord__class_Oless(X27,X28,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_710]) ).

fof(c_0_1120,plain,
    ! [X4,X5,X6] :
      ( X5 = X4
      | ~ hBOOL(hAPP(hAPP(c_fequal(X6),X5),X4)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_711])])]) ).

fof(c_0_1121,plain,
    ! [X41,X42,X43] :
      ( ~ class_Orderings_Olinorder(X43)
      | c_lessequals(X41,c_Orderings_Oord__class_Omax(X42,X41,X43),X43) ),
    inference(variable_rename,[status(thm)],[c_0_712]) ).

fof(c_0_1122,plain,
    ! [X41,X42,X43] :
      ( ~ class_Orderings_Olinorder(X43)
      | c_lessequals(X42,c_Orderings_Oord__class_Omax(X42,X41,X43),X43) ),
    inference(variable_rename,[status(thm)],[c_0_713]) ).

fof(c_0_1123,plain,
    ! [X25,X26] :
      ( c_HOL_Oord__class_Oless(X25,X25,tc_nat)
      | hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X25)),X26),X25) = X26 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_714])])]) ).

fof(c_0_1124,plain,
    ! [X30] :
      ( hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__5(X30)))
      | X30 = c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X30))
      | c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X30),tc_Lambda_OdB)
      | ~ hBOOL(hAPP(c_InductTermi_OIT,X30)) ),
    inference(variable_rename,[status(thm)],[c_0_715]) ).

fof(c_0_1125,plain,
    ! [X41,X42,X43] :
      ( ~ class_Orderings_Olinorder(X43)
      | X42 = X41
      | c_HOL_Oord__class_Oless(X42,X41,X43)
      | ~ c_lessequals(X42,X41,X43) ),
    inference(variable_rename,[status(thm)],[c_0_716]) ).

fof(c_0_1126,plain,
    ! [X41,X42,X43] :
      ( ~ class_Orderings_Olinorder(X43)
      | X42 = X41
      | ~ c_lessequals(X42,X41,X43)
      | c_HOL_Oord__class_Oless(X42,X41,X43) ),
    inference(variable_rename,[status(thm)],[c_0_717]) ).

fof(c_0_1127,plain,
    ! [X50,X51,X52] :
      ( ~ class_Orderings_Oorder(X52)
      | c_HOL_Oord__class_Oless(X51,X50,X52)
      | ~ c_lessequals(X51,X50,X52)
      | X51 = X50 ),
    inference(variable_rename,[status(thm)],[c_0_718]) ).

fof(c_0_1128,plain,
    ! [X50,X51,X52] :
      ( ~ class_Orderings_Oorder(X52)
      | c_HOL_Oord__class_Oless(X51,X50,X52)
      | X51 = X50
      | ~ c_lessequals(X51,X50,X52) ),
    inference(variable_rename,[status(thm)],[c_0_719]) ).

fof(c_0_1129,plain,
    ! [X41,X42,X43] :
      ( ~ class_Orderings_Oorder(X43)
      | c_HOL_Oord__class_Oless(X42,X41,X43)
      | X42 = X41
      | ~ c_lessequals(X42,X41,X43) ),
    inference(variable_rename,[status(thm)],[c_0_720]) ).

fof(c_0_1130,plain,
    ! [X41,X42,X43] :
      ( ~ class_Orderings_Oorder(X43)
      | X42 = X41
      | c_HOL_Oord__class_Oless(X42,X41,X43)
      | ~ c_lessequals(X42,X41,X43) ),
    inference(variable_rename,[status(thm)],[c_0_721]) ).

fof(c_0_1131,plain,
    ! [X50,X51,X52] :
      ( ~ class_Orderings_Oorder(X52)
      | c_HOL_Oord__class_Oless(X50,X51,X52)
      | ~ c_lessequals(X50,X51,X52)
      | X51 = X50 ),
    inference(variable_rename,[status(thm)],[c_0_722]) ).

fof(c_0_1132,plain,
    ! [X50,X51,X52] :
      ( ~ class_Orderings_Oorder(X52)
      | c_HOL_Oord__class_Oless(X50,X51,X52)
      | X51 = X50
      | ~ c_lessequals(X50,X51,X52) ),
    inference(variable_rename,[status(thm)],[c_0_723]) ).

fof(c_0_1133,plain,
    ! [X41,X42,X43] :
      ( ~ class_Orderings_Olinorder(X43)
      | c_Orderings_Oord__class_Omax(X42,X41,X43) != X41
      | c_lessequals(X42,X41,X43) ),
    inference(variable_rename,[status(thm)],[c_0_724]) ).

fof(c_0_1134,plain,
    ! [X41,X42,X43] :
      ( ~ class_Orderings_Olinorder(X43)
      | c_Orderings_Oord__class_Omax(X42,X41,X43) = X41
      | ~ c_lessequals(X42,X41,X43) ),
    inference(variable_rename,[status(thm)],[c_0_725]) ).

fof(c_0_1135,plain,
    ! [X41,X42,X43] :
      ( ~ class_Orderings_Olinorder(X43)
      | c_Orderings_Oord__class_Omax(X42,X41,X43) = X42
      | ~ c_lessequals(X41,X42,X43) ),
    inference(variable_rename,[status(thm)],[c_0_726]) ).

fof(c_0_1136,plain,
    ! [X26,X27,X28] :
      ( c_Lambda_Oliftn(X26,c_Lambda_OdB_OVar(X28),X27) = c_Lambda_OdB_OVar(X28)
      | ~ c_HOL_Oord__class_Oless(X28,X27,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_727]) ).

fof(c_0_1137,plain,
    ! [X41,X42,X43] :
      ( ~ class_Orderings_Opreorder(X43)
      | c_lessequals(X42,X41,X43)
      | ~ c_HOL_Oord__class_Oless(X42,X41,X43) ),
    inference(variable_rename,[status(thm)],[c_0_728]) ).

fof(c_0_1138,plain,
    ! [X41,X42,X43] :
      ( ~ class_Orderings_Oorder(X43)
      | c_lessequals(X42,X41,X43)
      | ~ c_HOL_Oord__class_Oless(X42,X41,X43) ),
    inference(variable_rename,[status(thm)],[c_0_729]) ).

fof(c_0_1139,plain,
    ! [X26,X27,X28] :
      ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X27),X28) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X26),X28)
      | X27 = X26 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_730])])]) ).

fof(c_0_1140,plain,
    ! [X65,X66,X67] :
      ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X67),X66) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X67),X65)
      | X66 = X65 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_731])])]) ).

fof(c_0_1141,plain,
    ! [X26,X27,X28] :
      ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X28),X27) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X28),X26)
      | X27 = X26 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_732])])]) ).

fof(c_0_1142,plain,
    ! [X11,X12] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X12)
      | ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X11,X12),c_HOL_Ozero__class_Ozero(X12),X12) ),
    inference(variable_rename,[status(thm)],[c_0_733]) ).

fof(c_0_1143,plain,
    ! [X26,X27] :
      ( hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(X27)),X26) = c_Lambda_OdB_OVar(X27)
      | ~ c_HOL_Oord__class_Oless(X27,X26,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_734]) ).

fof(c_0_1144,plain,
    ! [X40,X41,X42,X43] :
      ( hAPP(hAPP(X41,X42),X40) = X42
      | ~ c_OrderedGroup_Omonoid__add(X40,X41,X43) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_735])])]) ).

fof(c_0_1145,plain,
    ! [X40,X41,X42,X43] :
      ( hAPP(hAPP(X41,X40),X42) = X42
      | ~ c_OrderedGroup_Omonoid__add(X40,X41,X43) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_736])])]) ).

fof(c_0_1146,plain,
    ! [X30,X31,X32] :
      ( ~ class_Ring__and__Field_Ozero__neq__one(X32)
      | ~ class_Ring__and__Field_Ono__zero__divisors(X32)
      | ~ class_Ring__and__Field_Omult__zero(X32)
      | ~ class_Power_Opower(X32)
      | c_Power_Opower__class_Opower(X31,X30,X32) != c_HOL_Ozero__class_Ozero(X32)
      | X31 = c_HOL_Ozero__class_Ozero(X32) ),
    inference(variable_rename,[status(thm)],[c_0_737]) ).

fof(c_0_1147,plain,
    ! [X30,X31] :
      ( ~ class_Ring__and__Field_Ozero__neq__one(X31)
      | ~ class_Ring__and__Field_Ono__zero__divisors(X31)
      | ~ class_Ring__and__Field_Omult__zero(X31)
      | ~ class_Power_Opower(X31)
      | c_Power_Opower__class_Opower(X30,c_HOL_Ozero__class_Ozero(tc_nat),X31) != c_HOL_Ozero__class_Ozero(X31) ),
    inference(variable_rename,[status(thm)],[c_0_738]) ).

fof(c_0_1148,plain,
    ! [X26,X27,X28] :
      ( c_Lambda_Osubstn(c_Lambda_OdB_OVar(X28),X26,X27) = c_Lambda_OdB_OVar(X28)
      | X28 = X27
      | c_HOL_Oord__class_Oless(X27,X28,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_739]) ).

fof(c_0_1149,plain,
    ! [X41,X42,X43] :
      ( ~ class_Ring__and__Field_Oordered__idom(X43)
      | c_HOL_Oord__class_Oless(X41,X42,X43)
      | c_HOL_Oord__class_Oless(X42,X41,X43)
      | X42 = X41 ),
    inference(variable_rename,[status(thm)],[c_0_740]) ).

fof(c_0_1150,plain,
    ! [X41,X42,X43] :
      ( ~ class_Orderings_Olinorder(X43)
      | X42 = X41
      | c_HOL_Oord__class_Oless(X41,X42,X43)
      | c_HOL_Oord__class_Oless(X42,X41,X43) ),
    inference(variable_rename,[status(thm)],[c_0_741]) ).

fof(c_0_1151,plain,
    ! [X41,X42,X43] :
      ( ~ class_Orderings_Olinorder(X43)
      | c_HOL_Oord__class_Oless(X41,X42,X43)
      | c_HOL_Oord__class_Oless(X42,X41,X43)
      | X42 = X41 ),
    inference(variable_rename,[status(thm)],[c_0_742]) ).

fof(c_0_1152,plain,
    ! [X41,X42,X43] :
      ( ~ class_Orderings_Olinorder(X43)
      | c_HOL_Oord__class_Oless(X41,X42,X43)
      | X42 = X41
      | c_HOL_Oord__class_Oless(X42,X41,X43) ),
    inference(variable_rename,[status(thm)],[c_0_743]) ).

fof(c_0_1153,plain,
    ! [X41,X42,X43] :
      ( ~ class_Orderings_Olinorder(X43)
      | X42 = X41
      | c_HOL_Oord__class_Oless(X42,X41,X43)
      | c_HOL_Oord__class_Oless(X41,X42,X43) ),
    inference(variable_rename,[status(thm)],[c_0_744]) ).

fof(c_0_1154,plain,
    ! [X15,X16,X17,X18] :
      ( hAPP(hAPP(c_Lambda_OdB_OApp,X18),X16) != hAPP(hAPP(c_Lambda_OdB_OApp,X17),X15)
      | X18 = X17 ),
    inference(variable_rename,[status(thm)],[c_0_745]) ).

fof(c_0_1155,plain,
    ! [X15,X16,X17,X18] :
      ( hAPP(hAPP(c_Lambda_OdB_OApp,X18),X16) != hAPP(hAPP(c_Lambda_OdB_OApp,X17),X15)
      | X16 = X15 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_746])])]) ).

fof(c_0_1156,plain,
    ! [X41,X42,X43] :
      ( ~ class_Orderings_Olinorder(X43)
      | c_lessequals(X41,X42,X43)
      | c_lessequals(X42,X41,X43) ),
    inference(variable_rename,[status(thm)],[c_0_747]) ).

fof(c_0_1157,plain,
    ! [X41,X42,X43] :
      ( ~ class_Orderings_Olinorder(X43)
      | c_HOL_Oord__class_Oless(X42,X41,X43)
      | c_lessequals(X41,X42,X43) ),
    inference(variable_rename,[status(thm)],[c_0_748]) ).

fof(c_0_1158,plain,
    ! [X25,X26] :
      ( ~ class_Orderings_Olinorder(X26)
      | c_HOL_Oord__class_Oless(X25,X25,X26)
      | c_lessequals(X25,X25,X26) ),
    inference(variable_rename,[status(thm)],[c_0_749]) ).

fof(c_0_1159,plain,
    ! [X41,X42,X43] :
      ( ~ class_Orderings_Olinorder(X43)
      | c_lessequals(X41,X42,X43)
      | c_HOL_Oord__class_Oless(X42,X41,X43) ),
    inference(variable_rename,[status(thm)],[c_0_750]) ).

fof(c_0_1160,plain,
    ! [X41,X42,X43] :
      ( ~ class_Orderings_Olinorder(X43)
      | c_HOL_Oord__class_Oless(X41,X42,X43)
      | c_lessequals(X42,X41,X43) ),
    inference(variable_rename,[status(thm)],[c_0_751]) ).

fof(c_0_1161,plain,
    ! [X41,X42,X43] :
      ( ~ class_Orderings_Olinorder(X43)
      | c_Orderings_Oord__class_Omax(X42,X41,X43) = c_Orderings_Oord__class_Omax(X41,X42,X43) ),
    inference(variable_rename,[status(thm)],[c_0_752]) ).

fof(c_0_1162,plain,
    ! [X4] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X4)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
    inference(variable_rename,[status(thm)],[c_0_753]) ).

fof(c_0_1163,plain,
    ! [X4] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X4)
      | ~ c_lessequals(c_HOL_Oone__class_Oone(X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
    inference(variable_rename,[status(thm)],[c_0_754]) ).

fof(c_0_1164,plain,
    ! [X51,X52,X53] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X53)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X53),X52),X51) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X53),X51),X52) ),
    inference(variable_rename,[status(thm)],[c_0_755]) ).

fof(c_0_1165,plain,
    ! [X50,X51,X52] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X52)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X52),X51),X50) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X52),X50),X51) ),
    inference(variable_rename,[status(thm)],[c_0_756]) ).

fof(c_0_1166,plain,
    ! [X41,X42,X43] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X43)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X43),X42),X41) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X43),X41),X42) ),
    inference(variable_rename,[status(thm)],[c_0_757]) ).

fof(c_0_1167,plain,
    ! [X24,X25,X26] :
      ( hAPP(X25,X24) = X26
      | ~ c_Type_Otyping(X25,c_Lambda_OdB_OVar(X24),X26) ),
    inference(variable_rename,[status(thm)],[c_0_758]) ).

fof(c_0_1168,plain,
    ! [X19,X20] :
      ( c_HOL_Oord__class_Oless(X19,X20,tc_nat)
      | c_HOL_Oord__class_Oless(X20,X19,tc_nat)
      | X20 = X19 ),
    inference(variable_rename,[status(thm)],[c_0_759]) ).

fof(c_0_1169,plain,
    ! [X41,X42] :
      ( c_HOL_Oord__class_Oless(X41,X42,tc_nat)
      | c_HOL_Oord__class_Oless(X42,X41,tc_nat)
      | X42 = X41 ),
    inference(variable_rename,[status(thm)],[c_0_760]) ).

fof(c_0_1170,plain,
    ! [X30,X31,X32] :
      ( ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X32)
      | c_Power_Opower__class_Opower(X31,X30,X32) != c_HOL_Ozero__class_Ozero(X32)
      | X31 = c_HOL_Ozero__class_Ozero(X32) ),
    inference(variable_rename,[status(thm)],[c_0_761]) ).

fof(c_0_1171,plain,
    ! [X30,X31,X32] :
      ( ~ class_Ring__and__Field_Oidom(X32)
      | ~ class_Int_Onumber__ring(X32)
      | X30 != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X32),X30),X31)
      | X31 = c_HOL_Ozero__class_Ozero(X32) ),
    inference(variable_rename,[status(thm)],[c_0_762]) ).

fof(c_0_1172,plain,
    ! [X30,X31] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X31)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X31),X30),X30) != c_HOL_Ozero__class_Ozero(X31)
      | X30 = c_HOL_Ozero__class_Ozero(X31) ),
    inference(variable_rename,[status(thm)],[c_0_763]) ).

fof(c_0_1173,plain,
    ! [X52,X53,X54] :
      ( c_List_Olist_ONil(X54) != c_List_Oappend(X53,X52,X54)
      | X53 = c_List_Olist_ONil(X54) ),
    inference(variable_rename,[status(thm)],[c_0_764]) ).

fof(c_0_1174,plain,
    ! [X52,X53,X54] :
      ( c_List_Olist_ONil(X54) != c_List_Oappend(X53,X52,X54)
      | X52 = c_List_Olist_ONil(X54) ),
    inference(variable_rename,[status(thm)],[c_0_765]) ).

fof(c_0_1175,plain,
    ! [X52,X53,X54] :
      ( c_List_Oappend(X53,X52,X54) != c_List_Olist_ONil(X54)
      | X53 = c_List_Olist_ONil(X54) ),
    inference(variable_rename,[status(thm)],[c_0_766]) ).

fof(c_0_1176,plain,
    ! [X52,X53,X54] :
      ( c_List_Oappend(X53,X52,X54) != c_List_Olist_ONil(X54)
      | X52 = c_List_Olist_ONil(X54) ),
    inference(variable_rename,[status(thm)],[c_0_767]) ).

fof(c_0_1177,plain,
    ! [X19,X20] :
      ( ~ class_Ring__and__Field_Ozero__neq__one(X20)
      | ~ class_Ring__and__Field_Ono__zero__divisors(X20)
      | ~ class_Ring__and__Field_Omult__zero(X20)
      | ~ class_Power_Opower(X20)
      | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X20),X19,X20) = c_HOL_Ozero__class_Ozero(X20)
      | X19 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_768]) ).

fof(c_0_1178,plain,
    ! [X25,X26,X27] :
      ( c_List_Oreplicate(X26,X25,X27) != c_List_Olist_ONil(X27)
      | X26 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_769])])]) ).

fof(c_0_1179,plain,
    ! [X25,X26,X27] :
      ( c_List_Olist_ONil(X27) != c_List_Oreplicate(X26,X25,X27)
      | X26 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_770])])]) ).

fof(c_0_1180,plain,
    ! [X11,X12] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X12)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X12),c_Nat_Osemiring__1__class_Oof__nat(X11,X12),X12) ),
    inference(variable_rename,[status(thm)],[c_0_771]) ).

fof(c_0_1181,plain,
    ! [X19,X20] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X20)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X20),c_Nat_Osemiring__1__class_Oof__nat(X19,X20),X20) ),
    inference(variable_rename,[status(thm)],[c_0_772]) ).

fof(c_0_1182,plain,
    ! [X25,X26] :
      ( ~ class_Orderings_Oorder(X26)
      | ~ c_HOL_Oord__class_Oless(X25,X25,X26) ),
    inference(variable_rename,[status(thm)],[c_0_773]) ).

fof(c_0_1183,plain,
    ! [X25,X26] :
      ( ~ class_Orderings_Olinorder(X26)
      | ~ c_HOL_Oord__class_Oless(X25,X25,X26) ),
    inference(variable_rename,[status(thm)],[c_0_774]) ).

fof(c_0_1184,plain,
    ! [X25,X26] :
      ( ~ class_Orderings_Opreorder(X26)
      | ~ c_HOL_Oord__class_Oless(X25,X25,X26) ),
    inference(variable_rename,[status(thm)],[c_0_775]) ).

fof(c_0_1185,plain,
    ! [X52,X53,X54] :
      ( c_List_Oappend(X53,X52,X54) != X53
      | X52 = c_List_Olist_ONil(X54) ),
    inference(variable_rename,[status(thm)],[c_0_776]) ).

fof(c_0_1186,plain,
    ! [X52,X53,X54] :
      ( X53 != c_List_Oappend(X53,X52,X54)
      | X52 = c_List_Olist_ONil(X54) ),
    inference(variable_rename,[status(thm)],[c_0_777]) ).

fof(c_0_1187,plain,
    ! [X52,X53,X54] :
      ( c_List_Oappend(X53,X52,X54) != X52
      | X53 = c_List_Olist_ONil(X54) ),
    inference(variable_rename,[status(thm)],[c_0_778]) ).

fof(c_0_1188,plain,
    ! [X52,X53,X54] :
      ( X52 != c_List_Oappend(X53,X52,X54)
      | X53 = c_List_Olist_ONil(X54) ),
    inference(variable_rename,[status(thm)],[c_0_779]) ).

fof(c_0_1189,plain,
    ! [X19,X20] :
      ( ~ class_Ring__and__Field_Osemiring__0(X20)
      | ~ class_Power_Opower(X20)
      | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X20),X19,X20) = c_HOL_Ozero__class_Ozero(X20)
      | X19 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_780]) ).

fof(c_0_1190,plain,
    ! [X9] :
      ( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(X9)))
      | ~ hBOOL(hAPP(c_InductTermi_OIT,X9)) ),
    inference(variable_rename,[status(thm)],[c_0_781]) ).

fof(c_0_1191,plain,
    ! [X4] :
      ( ~ class_Ring__and__Field_Osemiring__0(X4)
      | ~ class_Power_Opower(X4)
      | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X4),c_HOL_Ozero__class_Ozero(tc_nat),X4) = c_HOL_Oone__class_Oone(X4) ),
    inference(variable_rename,[status(thm)],[c_0_782]) ).

fof(c_0_1192,plain,
    ! [X4] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X4)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),c_HOL_Ozero__class_Ozero(X4)),c_HOL_Ozero__class_Ozero(X4)) = c_HOL_Ozero__class_Ozero(X4) ),
    inference(variable_rename,[status(thm)],[c_0_783]) ).

fof(c_0_1193,plain,
    ! [X19,X20] :
      ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X20),X19) != c_HOL_Ozero__class_Ozero(tc_nat)
      | X19 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_784])])]) ).

fof(c_0_1194,plain,
    ! [X19,X20] :
      ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X20),X19) != c_HOL_Ozero__class_Ozero(tc_nat)
      | X20 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_785]) ).

fof(c_0_1195,plain,
    ! [X30,X31] :
      ( X30 != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X30),X31)
      | X31 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_786]) ).

fof(c_0_1196,plain,
    ! [X19,X20] :
      ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X20),X19) != X20
      | X19 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_787])])]) ).

fof(c_0_1197,plain,
    ! [X4] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X4)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oone__class_Oone(X4),X4) ),
    inference(variable_rename,[status(thm)],[c_0_788]) ).

fof(c_0_1198,plain,
    ! [X4] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X4)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oone__class_Oone(X4),X4) ),
    inference(variable_rename,[status(thm)],[c_0_789]) ).

fof(c_0_1199,plain,
    ! [X25,X26] :
      ( ~ class_Ring__and__Field_Oidom(X26)
      | ~ class_Int_Onumber__ring(X26)
      | X25 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X26),X25),c_HOL_Ozero__class_Ozero(X26)) ),
    inference(variable_rename,[status(thm)],[c_0_790]) ).

fof(c_0_1200,plain,
    ! [X25,X26] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X26)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X26),c_HOL_Ozero__class_Ozero(X26)),X25) = X25 ),
    inference(variable_rename,[status(thm)],[c_0_791]) ).

fof(c_0_1201,plain,
    ! [X30,X31] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X31)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X31),c_HOL_Ozero__class_Ozero(X31)),X30) = X30 ),
    inference(variable_rename,[status(thm)],[c_0_792]) ).

fof(c_0_1202,plain,
    ! [X30,X31] :
      ( ~ class_OrderedGroup_Omonoid__add(X31)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X31),c_HOL_Ozero__class_Ozero(X31)),X30) = X30 ),
    inference(variable_rename,[status(thm)],[c_0_793]) ).

fof(c_0_1203,plain,
    ! [X30,X31] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X31)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X31),c_HOL_Ozero__class_Ozero(X31)),X30) = X30 ),
    inference(variable_rename,[status(thm)],[c_0_794]) ).

fof(c_0_1204,plain,
    ! [X19,X20] :
      ( ~ class_OrderedGroup_Omonoid__mult(X20)
      | c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X20),X19,X20) = c_HOL_Oone__class_Oone(X20) ),
    inference(variable_rename,[status(thm)],[c_0_795]) ).

fof(c_0_1205,plain,
    ! [X30,X31] :
      ( ~ class_Power_Opower(X31)
      | c_Power_Opower__class_Opower(X30,c_HOL_Ozero__class_Ozero(tc_nat),X31) = c_HOL_Oone__class_Oone(X31) ),
    inference(variable_rename,[status(thm)],[c_0_796]) ).

fof(c_0_1206,plain,
    ! [X25,X26] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X26)
      | c_Power_Opower__class_Opower(X25,c_HOL_Ozero__class_Ozero(tc_nat),X26) = c_HOL_Oone__class_Oone(X26) ),
    inference(variable_rename,[status(thm)],[c_0_797]) ).

fof(c_0_1207,plain,
    ! [X30,X31] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X31)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X31),X30),c_HOL_Ozero__class_Ozero(X31)) = X30 ),
    inference(variable_rename,[status(thm)],[c_0_798]) ).

fof(c_0_1208,plain,
    ! [X30,X31] :
      ( ~ class_OrderedGroup_Omonoid__add(X31)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X31),X30),c_HOL_Ozero__class_Ozero(X31)) = X30 ),
    inference(variable_rename,[status(thm)],[c_0_799]) ).

fof(c_0_1209,plain,
    ! [X30,X31] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X31)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X31),X30),c_HOL_Ozero__class_Ozero(X31)) = X30 ),
    inference(variable_rename,[status(thm)],[c_0_800]) ).

fof(c_0_1210,plain,
    ! [X30,X31] :
      ( ~ class_OrderedGroup_Omonoid__mult(X31)
      | c_Power_Opower__class_Opower(X30,c_HOL_Oone__class_Oone(tc_nat),X31) = X30 ),
    inference(variable_rename,[status(thm)],[c_0_801]) ).

fof(c_0_1211,plain,
    ! [X25,X26] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X26)
      | c_Power_Opower__class_Opower(X25,c_HOL_Oone__class_Oone(tc_nat),X26) = X25 ),
    inference(variable_rename,[status(thm)],[c_0_802]) ).

fof(c_0_1212,plain,
    ! [X25,X26] :
      ( ~ class_Orderings_Olinorder(X26)
      | c_Orderings_Oord__class_Omax(X25,X25,X26) = X25 ),
    inference(variable_rename,[status(thm)],[c_0_803]) ).

fof(c_0_1213,plain,
    ! [X25,X26] :
      ( ~ class_Orderings_Opreorder(X26)
      | c_lessequals(X25,X25,X26) ),
    inference(variable_rename,[status(thm)],[c_0_804]) ).

fof(c_0_1214,plain,
    ! [X25,X26] :
      ( ~ class_Orderings_Oorder(X26)
      | c_lessequals(X25,X25,X26) ),
    inference(variable_rename,[status(thm)],[c_0_805]) ).

fof(c_0_1215,plain,
    ! [X19] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X19,tc_nat)
      | X19 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_806]) ).

fof(c_0_1216,plain,
    ! [X19,X20,X21] :
      ( ~ class_Nat_Osemiring__char__0(X21)
      | c_Nat_Osemiring__1__class_Oof__nat(X20,X21) != c_Nat_Osemiring__1__class_Oof__nat(X19,X21)
      | X20 = X19 ),
    inference(variable_rename,[status(thm)],[c_0_807]) ).

fof(c_0_1217,plain,
    ! [X6,X7] :
      ( class_Orderings_Opreorder(tc_fun(X6,X7))
      | ~ class_Orderings_Opreorder(X7) ),
    inference(variable_rename,[status(thm)],[c_0_808]) ).

fof(c_0_1218,plain,
    ! [X6,X7] :
      ( class_Orderings_Oorder(tc_fun(X6,X7))
      | ~ class_Orderings_Oorder(X7) ),
    inference(variable_rename,[status(thm)],[c_0_809]) ).

fof(c_0_1219,plain,
    ! [X4] :
      ( ~ class_OrderedGroup_Omonoid__add(X4)
      | c_List_Olistsum(c_List_Olist_ONil(X4),X4) = c_HOL_Ozero__class_Ozero(X4) ),
    inference(variable_rename,[status(thm)],[c_0_810]) ).

fof(c_0_1220,plain,
    ! [X4] :
      ( ~ class_Ring__and__Field_Osemiring__1(X4)
      | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),X4) = c_HOL_Oone__class_Oone(X4) ),
    inference(variable_rename,[status(thm)],[c_0_811]) ).

fof(c_0_1221,plain,
    ! [X4] :
      ( ~ class_Ring__and__Field_Osemiring__1(X4)
      | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X4) = c_HOL_Ozero__class_Ozero(X4) ),
    inference(variable_rename,[status(thm)],[c_0_812]) ).

fof(c_0_1222,plain,
    ! [X4] :
      ( ~ class_OrderedGroup_Osemigroup__add(X4)
      | c_OrderedGroup_Osemigroup__add(c_HOL_Oplus__class_Oplus(X4),X4) ),
    inference(variable_rename,[status(thm)],[c_0_813]) ).

fof(c_0_1223,plain,
    ! [X4] :
      ( ~ class_Ring__and__Field_Ozero__neq__one(X4)
      | c_HOL_Oone__class_Oone(X4) != c_HOL_Ozero__class_Ozero(X4) ),
    inference(variable_rename,[status(thm)],[c_0_814]) ).

fof(c_0_1224,plain,
    ! [X4] :
      ( ~ class_Ring__and__Field_Ozero__neq__one(X4)
      | c_HOL_Ozero__class_Ozero(X4) != c_HOL_Oone__class_Oone(X4) ),
    inference(variable_rename,[status(thm)],[c_0_815]) ).

fof(c_0_1225,plain,
    ! [X64,X65] :
      ( c_Lambda_OdB_OAbs(X65) != c_Lambda_OdB_OAbs(X64)
      | X65 = X64 ),
    inference(variable_rename,[status(thm)],[c_0_816]) ).

fof(c_0_1226,plain,
    ! [X21,X22] :
      ( c_Lambda_OdB_OVar(X22) != c_Lambda_OdB_OVar(X21)
      | X22 = X21 ),
    inference(variable_rename,[status(thm)],[c_0_817]) ).

cnf(c_0_1227,plain,
    ( X3 = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(X1,X2,X3),tc_Lambda_OdB,tc_Lambda_OdB)
    | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),X2,tc_Lambda_OdB,tc_Lambda_OdB)),X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_818]) ).

cnf(c_0_1228,plain,
    ( c_Type_Otypings(X1,c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,X2,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),X4,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X5,tc_Lambda_OdB,tc_Lambda_OdB),X6)
    | ~ c_Type_Otyping(X1,X2,X3)
    | ~ c_Type_Otypings(c_Type_Oshift(X1,X4,X3,tc_Type_Otype),X5,X6) ),
    inference(split_conjunct,[status(thm)],[c_0_819]) ).

cnf(c_0_1229,plain,
    ( c_Type_Otypings(X1,X4,c_Type_Osko__Type__Xvar__app__types__1__1(X5,X7,X1,X4))
    | ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X4,tc_Lambda_OdB,tc_Lambda_OdB),X5)
    | ~ c_Type_Otypings(X1,X3,X6)
    | ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X7) ),
    inference(split_conjunct,[status(thm)],[c_0_820]) ).

cnf(c_0_1230,plain,
    ( c_ListOrder_Ostep1(c_Lambda_Obeta,X2,c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(X1,X2,X3),tc_Lambda_OdB)
    | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),X2,tc_Lambda_OdB,tc_Lambda_OdB)),X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_821]) ).

cnf(c_0_1231,plain,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1(X1)),c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2(X1),tc_Lambda_OdB,tc_Lambda_OdB)))
    | ~ hBOOL(hAPP(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3(X1)),c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__4(X1),tc_Lambda_OdB,tc_Lambda_OdB))) ),
    inference(split_conjunct,[status(thm)],[c_0_822]) ).

cnf(c_0_1232,plain,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_ListApplication_Osko__ListApplication__Xlem__1__1(X1)),c_ListApplication_Osko__ListApplication__Xlem__1__2(X1),tc_Lambda_OdB,tc_Lambda_OdB)))
    | ~ hBOOL(hAPP(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(c_ListApplication_Osko__ListApplication__Xlem__1__3(X1)),c_ListApplication_Osko__ListApplication__Xlem__1__4(X1),tc_Lambda_OdB,tc_Lambda_OdB))) ),
    inference(split_conjunct,[status(thm)],[c_0_823]) ).

cnf(c_0_1233,plain,
    ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X1,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X2,tc_Lambda_OdB,tc_Lambda_OdB)))
    | ~ c_ListOrder_Ostep1(c_Lambda_Obeta,X1,X2,tc_Lambda_OdB) ),
    inference(split_conjunct,[status(thm)],[c_0_824]) ).

cnf(c_0_1234,plain,
    ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X3,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB)))
    | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_825]) ).

cnf(c_0_1235,plain,
    ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X3,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB)))
    | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_826]) ).

cnf(c_0_1236,plain,
    ( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1)),X2),X3,tc_Lambda_OdB,tc_Lambda_OdB)))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X2),c_HOL_Ozero__class_Ozero(tc_nat)),X3,tc_Lambda_OdB,tc_Lambda_OdB)))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_827]) ).

cnf(c_0_1237,plain,
    ( hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X8)),hAPP(hAPP(X2,X9),X10)) = hAPP(hAPP(X2,X9),hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X8)),X10))
    | ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
    inference(split_conjunct,[status(thm)],[c_0_828]) ).

cnf(c_0_1238,plain,
    ( hAPP(hAPP(X1,hAPP(hAPP(X1,X7),X8)),hAPP(hAPP(X1,X9),X10)) = hAPP(hAPP(X1,hAPP(hAPP(X1,X7),X9)),hAPP(hAPP(X1,X8),X10))
    | ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
    inference(split_conjunct,[status(thm)],[c_0_829]) ).

cnf(c_0_1239,plain,
    ( hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X8)),hAPP(hAPP(X2,X9),X10)) = hAPP(hAPP(X2,X7),hAPP(hAPP(X2,X8),hAPP(hAPP(X2,X9),X10)))
    | ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
    inference(split_conjunct,[status(thm)],[c_0_830]) ).

cnf(c_0_1240,plain,
    ( hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X8)),hAPP(hAPP(X2,X9),X10)) = hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X9)),hAPP(hAPP(X2,X8),X10))
    | ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
    inference(split_conjunct,[status(thm)],[c_0_831]) ).

cnf(c_0_1241,plain,
    ( hAPP(hAPP(X3,hAPP(hAPP(X2,X7),X8)),X9) = hAPP(hAPP(X2,hAPP(hAPP(X3,X7),X9)),hAPP(hAPP(X3,X8),X9))
    | ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
    inference(split_conjunct,[status(thm)],[c_0_832]) ).

cnf(c_0_1242,plain,
    ( hAPP(hAPP(X2,hAPP(hAPP(X1,X7),X8)),X9) = hAPP(hAPP(X1,hAPP(hAPP(X2,X7),X9)),hAPP(hAPP(X2,X8),X9))
    | ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
    inference(split_conjunct,[status(thm)],[c_0_833]) ).

cnf(c_0_1243,plain,
    ( hAPP(hAPP(X1,hAPP(hAPP(X2,X7),X8)),hAPP(hAPP(X2,X9),X8)) = hAPP(hAPP(X2,hAPP(hAPP(X1,X7),X9)),X8)
    | ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
    inference(split_conjunct,[status(thm)],[c_0_834]) ).

cnf(c_0_1244,plain,
    ( hAPP(hAPP(X2,hAPP(hAPP(X3,X7),X8)),hAPP(hAPP(X3,X7),X9)) = hAPP(hAPP(X3,X7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X8),X9))
    | ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
    inference(split_conjunct,[status(thm)],[c_0_835]) ).

cnf(c_0_1245,plain,
    ( hAPP(hAPP(X2,X7),hAPP(hAPP(X1,X8),X9)) = hAPP(hAPP(X1,hAPP(hAPP(X2,X7),X8)),hAPP(hAPP(X2,X7),X9))
    | ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
    inference(split_conjunct,[status(thm)],[c_0_836]) ).

cnf(c_0_1246,plain,
    ( hAPP(hAPP(X1,hAPP(hAPP(X1,X7),X8)),X9) = hAPP(hAPP(X1,hAPP(hAPP(X1,X7),X9)),X8)
    | ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
    inference(split_conjunct,[status(thm)],[c_0_837]) ).

cnf(c_0_1247,plain,
    ( hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X8)),X9) = hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X9)),X8)
    | ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
    inference(split_conjunct,[status(thm)],[c_0_838]) ).

cnf(c_0_1248,plain,
    ( hAPP(hAPP(X1,hAPP(hAPP(X2,X7),X8)),X8) = hAPP(hAPP(X2,hAPP(hAPP(X1,X7),X5)),X8)
    | ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
    inference(split_conjunct,[status(thm)],[c_0_839]) ).

cnf(c_0_1249,plain,
    ( hAPP(hAPP(X2,X7),hAPP(hAPP(X2,X8),X9)) = hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X8)),X9)
    | ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
    inference(split_conjunct,[status(thm)],[c_0_840]) ).

cnf(c_0_1250,plain,
    ( hAPP(hAPP(X1,X7),hAPP(hAPP(X1,X8),X9)) = hAPP(hAPP(X1,hAPP(hAPP(X1,X7),X8)),X9)
    | ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
    inference(split_conjunct,[status(thm)],[c_0_841]) ).

cnf(c_0_1251,plain,
    ( hAPP(hAPP(X1,X7),hAPP(hAPP(X1,X8),X9)) = hAPP(hAPP(X1,hAPP(hAPP(X1,X7),X8)),X9)
    | ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
    inference(split_conjunct,[status(thm)],[c_0_842]) ).

cnf(c_0_1252,plain,
    ( hAPP(hAPP(X1,hAPP(hAPP(X1,X7),X8)),X9) = hAPP(hAPP(X1,X7),hAPP(hAPP(X1,X8),X9))
    | ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
    inference(split_conjunct,[status(thm)],[c_0_843]) ).

cnf(c_0_1253,plain,
    ( hAPP(hAPP(X2,X7),hAPP(hAPP(X2,X8),X9)) = hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X8)),X9)
    | ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
    inference(split_conjunct,[status(thm)],[c_0_844]) ).

cnf(c_0_1254,plain,
    ( hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X8)),X9) = hAPP(hAPP(X2,X7),hAPP(hAPP(X2,X8),X9))
    | ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
    inference(split_conjunct,[status(thm)],[c_0_845]) ).

cnf(c_0_1255,plain,
    ( hAPP(hAPP(X1,X7),hAPP(hAPP(X2,X8),X7)) = hAPP(hAPP(X2,hAPP(hAPP(X1,X8),X5)),X7)
    | ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
    inference(split_conjunct,[status(thm)],[c_0_846]) ).

cnf(c_0_1256,plain,
    ( hAPP(hAPP(X1,X7),hAPP(hAPP(X1,X8),X9)) = hAPP(hAPP(X1,X8),hAPP(hAPP(X1,X7),X9))
    | ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
    inference(split_conjunct,[status(thm)],[c_0_847]) ).

cnf(c_0_1257,plain,
    ( hAPP(hAPP(X2,X7),hAPP(hAPP(X2,X8),X9)) = hAPP(hAPP(X2,X8),hAPP(hAPP(X2,X7),X9))
    | ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
    inference(split_conjunct,[status(thm)],[c_0_848]) ).

cnf(c_0_1258,plain,
    ( hAPP(hAPP(X1,X7),X7) = hAPP(hAPP(X2,hAPP(hAPP(X1,X5),X5)),X7)
    | ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
    inference(split_conjunct,[status(thm)],[c_0_849]) ).

cnf(c_0_1259,plain,
    ( hAPP(hAPP(X2,X7),X8) = hAPP(hAPP(X2,X8),X7)
    | ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
    inference(split_conjunct,[status(thm)],[c_0_850]) ).

cnf(c_0_1260,plain,
    ( hAPP(hAPP(X1,X7),X8) = hAPP(hAPP(X1,X8),X7)
    | ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
    inference(split_conjunct,[status(thm)],[c_0_851]) ).

cnf(c_0_1261,plain,
    ( hAPP(hAPP(X1,X7),X8) = hAPP(hAPP(X1,X8),X7)
    | ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
    inference(split_conjunct,[status(thm)],[c_0_852]) ).

cnf(c_0_1262,plain,
    ( hAPP(hAPP(X2,X7),X8) = hAPP(hAPP(X2,X8),X7)
    | ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
    inference(split_conjunct,[status(thm)],[c_0_853]) ).

cnf(c_0_1263,plain,
    ( hAPP(hAPP(X3,X7),c_HOL_Oone__class_Oone(tc_nat)) = X7
    | ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
    inference(split_conjunct,[status(thm)],[c_0_854]) ).

cnf(c_0_1264,plain,
    ( hAPP(hAPP(X3,X7),c_HOL_Ozero__class_Ozero(tc_nat)) = X5
    | ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
    inference(split_conjunct,[status(thm)],[c_0_855]) ).

cnf(c_0_1265,plain,
    ( hAPP(hAPP(X2,X5),X7) = X7
    | ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
    inference(split_conjunct,[status(thm)],[c_0_856]) ).

cnf(c_0_1266,plain,
    ( hAPP(hAPP(X2,X4),X7) = X4
    | ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
    inference(split_conjunct,[status(thm)],[c_0_857]) ).

cnf(c_0_1267,plain,
    ( hAPP(hAPP(X1,X4),X7) = X7
    | ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
    inference(split_conjunct,[status(thm)],[c_0_858]) ).

cnf(c_0_1268,plain,
    ( hAPP(hAPP(X2,X7),X5) = X7
    | ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
    inference(split_conjunct,[status(thm)],[c_0_859]) ).

cnf(c_0_1269,plain,
    ( hAPP(hAPP(X2,X5),X7) = X7
    | ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
    inference(split_conjunct,[status(thm)],[c_0_860]) ).

cnf(c_0_1270,plain,
    ( hAPP(hAPP(X2,X7),X4) = X4
    | ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
    inference(split_conjunct,[status(thm)],[c_0_861]) ).

cnf(c_0_1271,plain,
    ( hAPP(hAPP(X2,X4),X7) = X4
    | ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
    inference(split_conjunct,[status(thm)],[c_0_862]) ).

cnf(c_0_1272,plain,
    ( hAPP(hAPP(X1,X7),X4) = X7
    | ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
    inference(split_conjunct,[status(thm)],[c_0_863]) ).

cnf(c_0_1273,plain,
    ( hAPP(hAPP(X1,X4),X7) = X7
    | ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
    inference(split_conjunct,[status(thm)],[c_0_864]) ).

cnf(c_0_1274,plain,
    ( hBOOL(hAPP(X1,hAPP(hAPP(X2,X3),X4)))
    | ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X5,X2,X6,hAPP(hAPP(c_Lambda_OdB_OApp,X3),X4),t_a))) ),
    inference(split_conjunct,[status(thm)],[c_0_865]) ).

cnf(c_0_1275,plain,
    ( hBOOL(hAPP(X1,hAPP(hAPP(X2,X3),X4)))
    | ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X5,X2,X6,hAPP(hAPP(c_Lambda_OdB_OApp,X3),X4),t_a))) ),
    inference(split_conjunct,[status(thm)],[c_0_866]) ).

cnf(c_0_1276,plain,
    ( hBOOL(hAPP(X1,X2))
    | hBOOL(hAPP(X1,c_ListApplication_Osko__ListApplication__Xlem__1__3(X1)))
    | ~ hBOOL(hAPP(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_ListApplication_Osko__ListApplication__Xlem__1__1(X1)),c_ListApplication_Osko__ListApplication__Xlem__1__2(X1),tc_Lambda_OdB,tc_Lambda_OdB))) ),
    inference(split_conjunct,[status(thm)],[c_0_867]) ).

cnf(c_0_1277,plain,
    ( hBOOL(hAPP(X1,c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3(X1)))
    | hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1(X1)),c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2(X1),tc_Lambda_OdB,tc_Lambda_OdB))) ),
    inference(split_conjunct,[status(thm)],[c_0_868]) ).

cnf(c_0_1278,plain,
    ( X4 = X5
    | ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X4)
    | ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X5) ),
    inference(split_conjunct,[status(thm)],[c_0_869]) ).

cnf(c_0_1279,plain,
    ( hBOOL(hAPP(X1,hAPP(X2,X3)))
    | ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X4,X5,X2,c_Lambda_OdB_OAbs(X3),t_a))) ),
    inference(split_conjunct,[status(thm)],[c_0_870]) ).

cnf(c_0_1280,plain,
    ( hBOOL(hAPP(X1,hAPP(X2,X3)))
    | ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X4,X5,X2,c_Lambda_OdB_OAbs(X3),t_a))) ),
    inference(split_conjunct,[status(thm)],[c_0_871]) ).

cnf(c_0_1281,plain,
    ( hBOOL(hAPP(X1,hAPP(X2,X3)))
    | ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X2,X4,X5,c_Lambda_OdB_OVar(X3),t_a))) ),
    inference(split_conjunct,[status(thm)],[c_0_872]) ).

cnf(c_0_1282,plain,
    ( hBOOL(hAPP(X1,hAPP(X2,X3)))
    | ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X2,X4,X5,c_Lambda_OdB_OVar(X3),t_a))) ),
    inference(split_conjunct,[status(thm)],[c_0_873]) ).

cnf(c_0_1283,plain,
    ( c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1)),X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)
    | ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X2,tc_Lambda_OdB)
    | ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X2),c_HOL_Ozero__class_Ozero(tc_nat)),X3,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB) ),
    inference(split_conjunct,[status(thm)],[c_0_874]) ).

cnf(c_0_1284,plain,
    ( X1 = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X1)),v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB,tc_Lambda_OdB)
    | hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X1)))
    | hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_sko__InductTermi__XIT__Xcases__4(X1)),v_sko__InductTermi__XIT__Xcases__5(X1)),c_HOL_Ozero__class_Ozero(tc_nat)),v_sko__InductTermi__XIT__Xcases__6(X1),tc_Lambda_OdB,tc_Lambda_OdB)))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_875]) ).

cnf(c_0_1285,plain,
    ( X1 = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X1)),v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB,tc_Lambda_OdB)
    | X1 = c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X1))
    | hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_sko__InductTermi__XIT__Xcases__4(X1)),v_sko__InductTermi__XIT__Xcases__5(X1)),c_HOL_Ozero__class_Ozero(tc_nat)),v_sko__InductTermi__XIT__Xcases__6(X1),tc_Lambda_OdB,tc_Lambda_OdB)))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_876]) ).

cnf(c_0_1286,plain,
    ( c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB)
    | hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X1)))
    | hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_sko__InductTermi__XIT__Xcases__4(X1)),v_sko__InductTermi__XIT__Xcases__5(X1)),c_HOL_Ozero__class_Ozero(tc_nat)),v_sko__InductTermi__XIT__Xcases__6(X1),tc_Lambda_OdB,tc_Lambda_OdB)))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_877]) ).

cnf(c_0_1287,plain,
    ( c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB)
    | X1 = c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X1))
    | hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_sko__InductTermi__XIT__Xcases__4(X1)),v_sko__InductTermi__XIT__Xcases__5(X1)),c_HOL_Ozero__class_Ozero(tc_nat)),v_sko__InductTermi__XIT__Xcases__6(X1),tc_Lambda_OdB,tc_Lambda_OdB)))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_878]) ).

cnf(c_0_1288,plain,
    ( c_Type_Otypings(c_Type_Oshift(X1,X4,X5,tc_Type_Otype),c_List_Omap(c_COMBC(c_Lambda_Olift,X4,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X2,tc_Lambda_OdB,tc_Lambda_OdB),X3)
    | ~ c_Type_Otypings(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_879]) ).

cnf(c_0_1289,plain,
    ( c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X1,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)
    | ~ c_List_Olistsp(c_InductTermi_OIT,X1,tc_Lambda_OdB) ),
    inference(split_conjunct,[status(thm)],[c_0_880]) ).

cnf(c_0_1290,plain,
    ( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X1,tc_Lambda_OdB,tc_Lambda_OdB)))
    | ~ c_List_Olistsp(c_InductTermi_OIT,X1,tc_Lambda_OdB) ),
    inference(split_conjunct,[status(thm)],[c_0_881]) ).

cnf(c_0_1291,plain,
    ( c_Type_Otypings(X1,X3,c_Type_Osko__Type__Xvar__app__typesE__1__1(X4,X1,X2,X3))
    | ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X4) ),
    inference(split_conjunct,[status(thm)],[c_0_882]) ).

cnf(c_0_1292,plain,
    ( X1 = X2
    | c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1),X3,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X2),X4,tc_Lambda_OdB,tc_Lambda_OdB) ),
    inference(split_conjunct,[status(thm)],[c_0_883]) ).

cnf(c_0_1293,plain,
    ( X1 = X2
    | c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X3),X1,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X4),X2,tc_Lambda_OdB,tc_Lambda_OdB) ),
    inference(split_conjunct,[status(thm)],[c_0_884]) ).

cnf(c_0_1294,plain,
    ( X1 = X2
    | c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),X3,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X4,tc_Lambda_OdB,tc_Lambda_OdB) ),
    inference(split_conjunct,[status(thm)],[c_0_885]) ).

cnf(c_0_1295,plain,
    ( X1 = X2
    | c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X3),X1,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X4),X2,tc_Lambda_OdB,tc_Lambda_OdB) ),
    inference(split_conjunct,[status(thm)],[c_0_886]) ).

cnf(c_0_1296,plain,
    ( c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X4,X1,X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),X3,X4,X1,X1))
    | ~ class_OrderedGroup_Osemigroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_887]) ).

cnf(c_0_1297,plain,
    ( X1 = X2
    | c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X3,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB) ),
    inference(split_conjunct,[status(thm)],[c_0_888]) ).

cnf(c_0_1298,plain,
    ( c_List_Ofoldl(X1,hAPP(hAPP(X1,X3),X4),X5,X2,X2) = hAPP(hAPP(X1,X3),c_List_Ofoldl(X1,X4,X5,X2,X2))
    | ~ c_OrderedGroup_Osemigroup__add(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_889]) ).

cnf(c_0_1299,plain,
    ( hAPP(hAPP(X2,X4),c_List_Ofoldl(X2,X1,X5,X3,X3)) = c_List_Ofoldl(X2,X4,X5,X3,X3)
    | ~ c_OrderedGroup_Omonoid__add(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_890]) ).

cnf(c_0_1300,plain,
    ( c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),X2,X3,X1,X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X1),X3,c_HOL_Ozero__class_Ozero(X1),X1,X1))
    | ~ class_OrderedGroup_Omonoid__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_891]) ).

cnf(c_0_1301,plain,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1),X3,X1,X1)) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),X2,X3,X1,X1)
    | ~ class_OrderedGroup_Omonoid__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_892]) ).

cnf(c_0_1302,plain,
    ( X1 = c_List_Olist_ONil(tc_Lambda_OdB)
    | X2 = c_List_Ofoldl(c_Lambda_OdB_OApp,X3,c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1(X2,X4,X3,X1),tc_Lambda_OdB,tc_Lambda_OdB)
    | hAPP(hAPP(c_Lambda_OdB_OApp,X2),X4) != c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X1,tc_Lambda_OdB,tc_Lambda_OdB) ),
    inference(split_conjunct,[status(thm)],[c_0_893]) ).

cnf(c_0_1303,plain,
    ( X1 = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X1)),v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB,tc_Lambda_OdB)
    | hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X1)))
    | X1 = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__4(X1))),v_sko__InductTermi__XIT__Xcases__5(X1)),v_sko__InductTermi__XIT__Xcases__6(X1),tc_Lambda_OdB,tc_Lambda_OdB)
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_894]) ).

cnf(c_0_1304,plain,
    ( X1 = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X1)),v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB,tc_Lambda_OdB)
    | X1 = c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X1))
    | X1 = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__4(X1))),v_sko__InductTermi__XIT__Xcases__5(X1)),v_sko__InductTermi__XIT__Xcases__6(X1),tc_Lambda_OdB,tc_Lambda_OdB)
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_895]) ).

cnf(c_0_1305,plain,
    ( c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1),X2,X1,X1) = c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X1),X2,c_HOL_Ozero__class_Ozero(X1),X1,X1)
    | ~ class_OrderedGroup_Omonoid__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_896]) ).

cnf(c_0_1306,plain,
    ( c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X1),X2,X3,X1,X1) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),X3,X2,X1,X1)
    | ~ class_OrderedGroup_Oab__semigroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_897]) ).

cnf(c_0_1307,plain,
    ( hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) = X3
    | hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) != c_List_Ofoldl(c_Lambda_OdB_OApp,X3,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) ),
    inference(split_conjunct,[status(thm)],[c_0_898]) ).

cnf(c_0_1308,plain,
    ( X1 = c_Lambda_OdB_OAbs(X2)
    | c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X3,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_899]) ).

cnf(c_0_1309,plain,
    ( c_Lambda_OdB_OAbs(X1) = X2
    | c_Lambda_OdB_OAbs(X1) != c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB) ),
    inference(split_conjunct,[status(thm)],[c_0_900]) ).

cnf(c_0_1310,plain,
    ( c_Lambda_OdB_OVar(X1) = X2
    | c_Lambda_OdB_OVar(X1) != c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB) ),
    inference(split_conjunct,[status(thm)],[c_0_901]) ).

cnf(c_0_1311,plain,
    ( hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(hAPP(c_Lambda_Osubst,X3),X4),X1)),X2) = hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)))),hAPP(hAPP(c_Lambda_Olift,X4),X2)),X1)
    | ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_902]) ).

cnf(c_0_1312,plain,
    ( X1 = c_List_Olist_ONil(tc_Lambda_OdB)
    | c_Lambda_OdB_OAbs(X2) != c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X1,tc_Lambda_OdB,tc_Lambda_OdB) ),
    inference(split_conjunct,[status(thm)],[c_0_903]) ).

cnf(c_0_1313,plain,
    ( X1 = c_List_Olist_ONil(tc_Lambda_OdB)
    | c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X1,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_904]) ).

cnf(c_0_1314,plain,
    ( X1 = c_List_Olist_ONil(tc_Lambda_OdB)
    | c_Lambda_OdB_OVar(X2) != c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X1,tc_Lambda_OdB,tc_Lambda_OdB) ),
    inference(split_conjunct,[status(thm)],[c_0_905]) ).

cnf(c_0_1315,plain,
    ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X4),X3))
    | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Predicate_Oconversep(X1,X2,X2),X2),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[c_0_906]) ).

cnf(c_0_1316,plain,
    ( c_ListOrder_Ostep1(X1,X2,X5,X4)
    | hBOOL(hAPP(hAPP(X1,X3),X6))
    | ~ c_ListOrder_Ostep1(X1,c_List_Oappend(X2,c_List_Olist_OCons(X3,c_List_Olist_ONil(X4),X4),X4),c_List_Oappend(X5,c_List_Olist_OCons(X6,c_List_Olist_ONil(X4),X4),X4),X4) ),
    inference(split_conjunct,[status(thm)],[c_0_907]) ).

cnf(c_0_1317,plain,
    ( c_ListOrder_Ostep1(X1,X2,X5,X4)
    | X2 = X5
    | ~ c_ListOrder_Ostep1(X1,c_List_Oappend(X2,c_List_Olist_OCons(X3,c_List_Olist_ONil(X4),X4),X4),c_List_Oappend(X5,c_List_Olist_OCons(X6,c_List_Olist_ONil(X4),X4),X4),X4) ),
    inference(split_conjunct,[status(thm)],[c_0_908]) ).

cnf(c_0_1318,plain,
    ( X3 = X6
    | hBOOL(hAPP(hAPP(X1,X3),X6))
    | ~ c_ListOrder_Ostep1(X1,c_List_Oappend(X2,c_List_Olist_OCons(X3,c_List_Olist_ONil(X4),X4),X4),c_List_Oappend(X5,c_List_Olist_OCons(X6,c_List_Olist_ONil(X4),X4),X4),X4) ),
    inference(split_conjunct,[status(thm)],[c_0_909]) ).

cnf(c_0_1319,plain,
    ( c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB)
    | hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X1)))
    | X1 = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__4(X1))),v_sko__InductTermi__XIT__Xcases__5(X1)),v_sko__InductTermi__XIT__Xcases__6(X1),tc_Lambda_OdB,tc_Lambda_OdB)
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_910]) ).

cnf(c_0_1320,plain,
    ( X3 = X6
    | X2 = X5
    | ~ c_ListOrder_Ostep1(X1,c_List_Oappend(X2,c_List_Olist_OCons(X3,c_List_Olist_ONil(X4),X4),X4),c_List_Oappend(X5,c_List_Olist_OCons(X6,c_List_Olist_ONil(X4),X4),X4),X4) ),
    inference(split_conjunct,[status(thm)],[c_0_911]) ).

cnf(c_0_1321,plain,
    ( c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB)
    | X1 = c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X1))
    | X1 = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__4(X1))),v_sko__InductTermi__XIT__Xcases__5(X1)),v_sko__InductTermi__XIT__Xcases__6(X1),tc_Lambda_OdB,tc_Lambda_OdB)
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_912]) ).

cnf(c_0_1322,plain,
    ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X3),X4)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X2),X3),X4)))
    | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_913]) ).

cnf(c_0_1323,plain,
    ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,X3),X1),X4)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X3),X2),X4)))
    | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_914]) ).

cnf(c_0_1324,plain,
    ( X1 = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X1)),v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB,tc_Lambda_OdB)
    | hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X1)))
    | hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__5(X1)))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_915]) ).

cnf(c_0_1325,plain,
    ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Predicate_Oconversep(X1,X2,X2),X2),X4),X3))
    | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[c_0_916]) ).

cnf(c_0_1326,plain,
    ( X1 = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X1)),v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB,tc_Lambda_OdB)
    | X1 = c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X1))
    | hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__5(X1)))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_917]) ).

cnf(c_0_1327,plain,
    ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,X3),X1),X4)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X3),X2),X4)))
    | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_918]) ).

cnf(c_0_1328,plain,
    ( c_List_Olistsum(X1,X2) = c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X2),X1,c_HOL_Ozero__class_Ozero(X2),X2,X2)
    | ~ class_OrderedGroup_Omonoid__add(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_919]) ).

cnf(c_0_1329,plain,
    ( c_List_Olistsum(X1,X2) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X2),c_HOL_Ozero__class_Ozero(X2),X1,X2,X2)
    | ~ class_OrderedGroup_Omonoid__add(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_920]) ).

cnf(c_0_1330,plain,
    ( hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(hAPP(c_Lambda_Osubst,X3),X4),X2)),X1) = hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,X3),X1)),hAPP(hAPP(c_Lambda_Olift,X4),X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)))
    | ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_921]) ).

cnf(c_0_1331,plain,
    ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X3),X4)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X2),X3),X4)))
    | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_922]) ).

cnf(c_0_1332,plain,
    ( c_Type_Otyping(X1,hAPP(hAPP(hAPP(c_Lambda_Osubst,X2),X3),X4),X5)
    | ~ c_Type_Otyping(c_Type_Oshift(X1,X4,X6,tc_Type_Otype),X2,X5)
    | ~ c_Type_Otyping(X1,X3,X6) ),
    inference(split_conjunct,[status(thm)],[c_0_923]) ).

cnf(c_0_1333,plain,
    ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X1),X3)),hAPP(hAPP(c_Lambda_OdB_OApp,X2),X4)))
    | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[c_0_924]) ).

cnf(c_0_1334,plain,
    ( hBOOL(hAPP(hAPP(X1,X2),X5))
    | c_ListOrder_Ostep1(X1,X3,X6,X4)
    | ~ c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X2,X3,X4),c_List_Olist_OCons(X5,X6,X4),X4) ),
    inference(split_conjunct,[status(thm)],[c_0_925]) ).

cnf(c_0_1335,plain,
    ( X6 = X3
    | c_ListOrder_Ostep1(X1,X3,X6,X4)
    | ~ c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X2,X3,X4),c_List_Olist_OCons(X5,X6,X4),X4) ),
    inference(split_conjunct,[status(thm)],[c_0_926]) ).

cnf(c_0_1336,plain,
    ( hBOOL(hAPP(hAPP(X1,X5),X4))
    | ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X2,X3),X4),X5)) ),
    inference(split_conjunct,[status(thm)],[c_0_927]) ).

cnf(c_0_1337,plain,
    ( hBOOL(hAPP(hAPP(X1,X5),X4))
    | ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X2,X3),X4),X5)) ),
    inference(split_conjunct,[status(thm)],[c_0_928]) ).

cnf(c_0_1338,plain,
    ( c_ListOrder_Ostep1(X1,c_List_Oappend(X2,X3,X4),c_List_Oappend(X5,X3,X4),X4)
    | ~ c_ListOrder_Ostep1(X1,X2,X5,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_929]) ).

cnf(c_0_1339,plain,
    ( c_ListOrder_Ostep1(X1,c_List_Oappend(X5,X2,X4),c_List_Oappend(X5,X3,X4),X4)
    | ~ c_ListOrder_Ostep1(X1,X2,X3,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_930]) ).

cnf(c_0_1340,plain,
    ( c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X5,X2,X4),c_List_Olist_OCons(X5,X3,X4),X4)
    | ~ c_ListOrder_Ostep1(X1,X2,X3,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_931]) ).

cnf(c_0_1341,plain,
    ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X1),X3)),hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_932]) ).

cnf(c_0_1342,plain,
    ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X3),X1)),hAPP(hAPP(c_Lambda_OdB_OApp,X3),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_933]) ).

cnf(c_0_1343,plain,
    ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_Olift,X1),X3)),hAPP(hAPP(c_Lambda_Olift,X2),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_934]) ).

cnf(c_0_1344,plain,
    ( hBOOL(hAPP(hAPP(X1,X2),X5))
    | X5 = X2
    | ~ c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X2,X3,X4),c_List_Olist_OCons(X5,X6,X4),X4) ),
    inference(split_conjunct,[status(thm)],[c_0_935]) ).

cnf(c_0_1345,plain,
    ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X5))
    | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X4))
    | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X4),X5)) ),
    inference(split_conjunct,[status(thm)],[c_0_936]) ).

cnf(c_0_1346,plain,
    ( X6 = X3
    | X5 = X2
    | ~ c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X2,X3,X4),c_List_Olist_OCons(X5,X6,X4),X4) ),
    inference(split_conjunct,[status(thm)],[c_0_937]) ).

cnf(c_0_1347,plain,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X5)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X5))
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_938]) ).

cnf(c_0_1348,plain,
    ( c_Type_Otyping(c_Type_Oshift(X1,X4,X5,tc_Type_Otype),hAPP(hAPP(c_Lambda_Olift,X2),X4),X3)
    | ~ c_Type_Otyping(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_939]) ).

cnf(c_0_1349,plain,
    ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X4,X5),X3),X2))
    | ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_940]) ).

cnf(c_0_1350,plain,
    ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X4,X5),X3),X2))
    | ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_941]) ).

cnf(c_0_1351,plain,
    ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_Olift,X1),X3)),hAPP(hAPP(c_Lambda_Olift,X2),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_942]) ).

cnf(c_0_1352,plain,
    ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,X3),X1)),hAPP(hAPP(c_Lambda_OdB_OApp,X3),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_943]) ).

cnf(c_0_1353,plain,
    ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,X1),X3)),hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_944]) ).

cnf(c_0_1354,plain,
    ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X4),X2),X5))
    | ~ hBOOL(hAPP(hAPP(X1,X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X4),X3),X5)) ),
    inference(split_conjunct,[status(thm)],[c_0_945]) ).

cnf(c_0_1355,plain,
    ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X5))
    | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X4))
    | ~ hBOOL(hAPP(hAPP(X1,X4),X5)) ),
    inference(split_conjunct,[status(thm)],[c_0_946]) ).

cnf(c_0_1356,plain,
    ( hAPP(c_Type_Oshift(X3,X2,X4,X5),X1) = hAPP(X3,X1)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_947]) ).

cnf(c_0_1357,plain,
    ( c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X2,X3,X4),c_List_Olist_OCons(X5,X3,X4),X4)
    | ~ hBOOL(hAPP(hAPP(X1,X2),X5)) ),
    inference(split_conjunct,[status(thm)],[c_0_948]) ).

cnf(c_0_1358,plain,
    ( c_HOL_Oord__class_Oless(X1,X4,X3)
    | ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X4,X2,X3),X3)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
    | ~ class_Ring__and__Field_Oordered__semidom(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_949]) ).

cnf(c_0_1359,plain,
    ( c_HOL_Oord__class_Oless(X3,X4,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
    | ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_950]) ).

cnf(c_0_1360,plain,
    ( c_HOL_Oord__class_Oless(X3,X4,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
    | ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_951]) ).

cnf(c_0_1361,plain,
    ( c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X4,X2,X3),c_Power_Opower__class_Opower(X4,X1,X3),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
    | ~ c_HOL_Oord__class_Oless(X4,c_HOL_Oone__class_Oone(X3),X3)
    | ~ class_Ring__and__Field_Oordered__semidom(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_952]) ).

cnf(c_0_1362,plain,
    ( X1 = X2
    | c_List_Oappend(X1,c_List_Olist_OCons(X3,c_List_Olist_ONil(X4),X4),X4) != c_List_Oappend(X2,c_List_Olist_OCons(X5,c_List_Olist_ONil(X4),X4),X4) ),
    inference(split_conjunct,[status(thm)],[c_0_953]) ).

cnf(c_0_1363,plain,
    ( X1 = X2
    | c_List_Oappend(X3,c_List_Olist_OCons(X1,c_List_Olist_ONil(X4),X4),X4) != c_List_Oappend(X5,c_List_Olist_OCons(X2,c_List_Olist_ONil(X4),X4),X4) ),
    inference(split_conjunct,[status(thm)],[c_0_954]) ).

cnf(c_0_1364,plain,
    ( c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X4,X3),c_Power_Opower__class_Opower(X2,X4,X3),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
    | ~ class_Ring__and__Field_Oordered__semidom(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_955]) ).

cnf(c_0_1365,plain,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_Orderings_Oord__class_Omax(X2,X3,X1)),X4) = c_Orderings_Oord__class_Omax(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4),X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_956]) ).

cnf(c_0_1366,plain,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_957]) ).

cnf(c_0_1367,plain,
    ( c_lessequals(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),X5),X2)
    | ~ c_lessequals(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),X4),X2)
    | ~ c_lessequals(X4,X5,X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_958]) ).

cnf(c_0_1368,plain,
    ( c_lessequals(X3,X4,X1)
    | ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_959]) ).

cnf(c_0_1369,plain,
    ( c_lessequals(X2,X4,X1)
    | ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3),X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_960]) ).

cnf(c_0_1370,plain,
    ( c_HOL_Oord__class_Oless(X2,X4,X1)
    | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3),X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_961]) ).

cnf(c_0_1371,plain,
    ( c_HOL_Oord__class_Oless(X3,X4,X1)
    | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_962]) ).

cnf(c_0_1372,plain,
    ( X2 = X3
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
    | c_Power_Opower__class_Opower(X2,X4,X1) != c_Power_Opower__class_Opower(X3,X4,X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_963]) ).

cnf(c_0_1373,plain,
    ( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),c_Lambda_OdB_OVar(X2)),X3)))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_964]) ).

cnf(c_0_1374,plain,
    ( c_lessequals(c_Power_Opower__class_Opower(X1,X4,X3),c_Power_Opower__class_Opower(X2,X4,X3),X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
    | ~ class_Ring__and__Field_Oordered__semidom(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_965]) ).

cnf(c_0_1375,plain,
    ( c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X4,X1,X3),c_Power_Opower__class_Opower(X4,X2,X3),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X4,X3)
    | ~ class_Ring__and__Field_Oordered__semidom(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_966]) ).

cnf(c_0_1376,plain,
    ( c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
    | ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_967]) ).

cnf(c_0_1377,plain,
    ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_OdB_OAbs(X1)),c_Lambda_OdB_OAbs(X2)))
    | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_968]) ).

cnf(c_0_1378,plain,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X5),X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X4,X5,X3)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_969]) ).

cnf(c_0_1379,plain,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X5),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_lessequals(X4,X5,X3)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_970]) ).

cnf(c_0_1380,plain,
    ( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X5),X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_lessequals(X4,X5,X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_971]) ).

cnf(c_0_1381,plain,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X5),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X4,X5,X3)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_972]) ).

cnf(c_0_1382,plain,
    ( c_Wellfounded_Oaccp(X1,X4,X3)
    | ~ c_Wellfounded_Oaccp(X1,X2,X3)
    | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X3),X4),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_973]) ).

cnf(c_0_1383,plain,
    ( c_Wellfounded_Oaccp(X1,X3,X2)
    | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X4))
    | ~ c_Wellfounded_Oaccp(X1,X4,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_974]) ).

cnf(c_0_1384,plain,
    ( c_HOL_Oord__class_Oless(X2,X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_975]) ).

cnf(c_0_1385,plain,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_976]) ).

cnf(c_0_1386,plain,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_977]) ).

cnf(c_0_1387,plain,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
    | ~ class_OrderedGroup_Oab__semigroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_978]) ).

cnf(c_0_1388,plain,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_979]) ).

cnf(c_0_1389,plain,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_980]) ).

cnf(c_0_1390,plain,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X4),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_981]) ).

cnf(c_0_1391,plain,
    ( X1 = c_List_Olist_ONil(X2)
    | c_List_Olist_ONil(X3) != c_List_Omap(X4,X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_982]) ).

cnf(c_0_1392,plain,
    ( X1 = c_List_Olist_ONil(X2)
    | c_List_Omap(X3,X1,X2,X4) != c_List_Olist_ONil(X4) ),
    inference(split_conjunct,[status(thm)],[c_0_983]) ).

cnf(c_0_1393,plain,
    ( c_Type_Otyping(X3,X2,X4)
    | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2))
    | ~ c_Type_Otyping(X3,X1,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_984]) ).

cnf(c_0_1394,plain,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = X4
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X5),X3)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X5),X4)
    | ~ class_OrderedGroup_Oab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_985]) ).

cnf(c_0_1395,plain,
    ( c_lessequals(X1,X2,X4)
    | c_lessequals(X1,X3,X4)
    | ~ c_lessequals(X1,c_Orderings_Oord__class_Omax(X2,X3,X4),X4)
    | ~ class_Orderings_Olinorder(X4) ),
    inference(split_conjunct,[status(thm)],[c_0_986]) ).

cnf(c_0_1396,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,X4)
    | c_HOL_Oord__class_Oless(X1,X3,X4)
    | ~ c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X2,X3,X4),X4)
    | ~ class_Orderings_Olinorder(X4) ),
    inference(split_conjunct,[status(thm)],[c_0_987]) ).

cnf(c_0_1397,plain,
    ( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X3),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_988]) ).

cnf(c_0_1398,plain,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_989]) ).

cnf(c_0_1399,plain,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X3),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_990]) ).

cnf(c_0_1400,plain,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X3),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_991]) ).

cnf(c_0_1401,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_992]) ).

cnf(c_0_1402,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_993]) ).

cnf(c_0_1403,plain,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X3),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_994]) ).

cnf(c_0_1404,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_995]) ).

cnf(c_0_1405,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_996]) ).

cnf(c_0_1406,plain,
    ( c_lessequals(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X2),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_lessequals(X3,X4,X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_997]) ).

cnf(c_0_1407,plain,
    ( c_lessequals(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_lessequals(X3,X4,X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_998]) ).

cnf(c_0_1408,plain,
    ( c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_lessequals(X3,X4,X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_999]) ).

cnf(c_0_1409,plain,
    ( c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_HOL_Oord__class_Oless(X3,X4,X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1000]) ).

cnf(c_0_1410,plain,
    ( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2),X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1001]) ).

cnf(c_0_1411,plain,
    ( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4),X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1002]) ).

cnf(c_0_1412,plain,
    ( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2),X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1003]) ).

cnf(c_0_1413,plain,
    ( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4),X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1004]) ).

cnf(c_0_1414,plain,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1005]) ).

cnf(c_0_1415,plain,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1006]) ).

cnf(c_0_1416,plain,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1007]) ).

cnf(c_0_1417,plain,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1008]) ).

cnf(c_0_1418,plain,
    ( c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_HOL_Oord__class_Oless(X3,X4,X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1009]) ).

cnf(c_0_1419,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1010]) ).

cnf(c_0_1420,plain,
    ( c_lessequals(c_Orderings_Oord__class_Omax(X1,X4,X3),X2,X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_lessequals(X4,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1011]) ).

cnf(c_0_1421,plain,
    ( c_lessequals(c_Orderings_Oord__class_Omax(X1,X4,X3),X2,X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_lessequals(X4,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1012]) ).

cnf(c_0_1422,plain,
    ( c_lessequals(c_Orderings_Oord__class_Omax(X1,X4,X3),X2,X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_lessequals(X4,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1013]) ).

cnf(c_0_1423,plain,
    ( c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X1,X4,X3),X2,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X4,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1014]) ).

cnf(c_0_1424,plain,
    ( hAPP(hAPP(X1,hAPP(hAPP(X1,X3),X4)),X5) = hAPP(hAPP(X1,X3),hAPP(hAPP(X1,X4),X5))
    | ~ c_OrderedGroup_Osemigroup__add(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1015]) ).

cnf(c_0_1425,plain,
    ( c_List_Olistsp(X1,c_List_Oappend(X2,X4,X3),X3)
    | ~ c_List_Olistsp(X1,X2,X3)
    | ~ c_List_Olistsp(X1,X4,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1016]) ).

cnf(c_0_1426,plain,
    ( c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3) = c_Orderings_Oord__class_Omax(X1,c_Orderings_Oord__class_Omax(X2,X4,X3),X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1017]) ).

cnf(c_0_1427,plain,
    ( c_Orderings_Oord__class_Omax(X1,c_Orderings_Oord__class_Omax(X2,X3,X4),X4) = c_Orderings_Oord__class_Omax(X2,c_Orderings_Oord__class_Omax(X1,X3,X4),X4)
    | ~ class_Orderings_Olinorder(X4) ),
    inference(split_conjunct,[status(thm)],[c_0_1018]) ).

cnf(c_0_1428,plain,
    ( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1019]) ).

cnf(c_0_1429,plain,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1020]) ).

cnf(c_0_1430,plain,
    ( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1021]) ).

cnf(c_0_1431,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1022]) ).

cnf(c_0_1432,plain,
    ( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1023]) ).

cnf(c_0_1433,plain,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1024]) ).

cnf(c_0_1434,plain,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1025]) ).

cnf(c_0_1435,plain,
    ( c_lessequals(X1,X4,X3)
    | ~ c_lessequals(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1026]) ).

cnf(c_0_1436,plain,
    ( c_lessequals(X2,X4,X3)
    | ~ c_lessequals(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1027]) ).

cnf(c_0_1437,plain,
    ( c_lessequals(X1,X4,X3)
    | ~ c_lessequals(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1028]) ).

cnf(c_0_1438,plain,
    ( c_lessequals(X2,X4,X3)
    | ~ c_lessequals(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1029]) ).

cnf(c_0_1439,plain,
    ( c_HOL_Oord__class_Oless(X2,X4,X3)
    | ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1030]) ).

cnf(c_0_1440,plain,
    ( c_HOL_Oord__class_Oless(X1,X4,X3)
    | ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1031]) ).

cnf(c_0_1441,plain,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4))
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1032]) ).

cnf(c_0_1442,plain,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4))
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1033]) ).

cnf(c_0_1443,plain,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4))
    | ~ class_OrderedGroup_Oab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1034]) ).

cnf(c_0_1444,plain,
    ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X4),X2),X3))
    | ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_1035]) ).

cnf(c_0_1445,plain,
    ( c_List_Olistsp(X1,X2,X4)
    | ~ c_List_Olistsp(X1,c_List_Oappend(X2,X3,X4),X4) ),
    inference(split_conjunct,[status(thm)],[c_0_1036]) ).

cnf(c_0_1446,plain,
    ( c_List_Olistsp(X1,X3,X4)
    | ~ c_List_Olistsp(X1,c_List_Oappend(X2,X3,X4),X4) ),
    inference(split_conjunct,[status(thm)],[c_0_1037]) ).

cnf(c_0_1447,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(X2)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X1,X2)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X3) != c_HOL_Ozero__class_Ozero(X2)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1038]) ).

cnf(c_0_1448,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(X2)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X1,X2)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),X1) != c_HOL_Ozero__class_Ozero(X2)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1039]) ).

cnf(c_0_1449,plain,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1)) = c_HOL_Ozero__class_Ozero(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1040]) ).

cnf(c_0_1450,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X4) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1041]) ).

cnf(c_0_1451,plain,
    ( c_HOL_Oord__class_Oless(X1,X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X3,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1042]) ).

cnf(c_0_1452,plain,
    ( X1 = X2
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X4,X3)
    | c_Power_Opower__class_Opower(X4,X1,X3) != c_Power_Opower__class_Opower(X4,X2,X3)
    | ~ class_Ring__and__Field_Oordered__semidom(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1043]) ).

cnf(c_0_1453,plain,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1044]) ).

cnf(c_0_1454,plain,
    ( c_lessequals(c_HOL_Oone__class_Oone(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
    | ~ c_lessequals(c_HOL_Oone__class_Oone(X1),X2,X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1045]) ).

cnf(c_0_1455,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1046]) ).

cnf(c_0_1456,plain,
    ( c_Wellfounded_Oaccp(X1,X4,X3)
    | ~ c_Wellfounded_Oaccp(X1,X2,X3)
    | ~ hBOOL(hAPP(hAPP(X1,X4),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_1047]) ).

cnf(c_0_1457,plain,
    ( c_Wellfounded_Oaccp(X1,X4,X3)
    | ~ c_Wellfounded_Oaccp(X1,X2,X3)
    | ~ hBOOL(hAPP(hAPP(X1,X4),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_1048]) ).

cnf(c_0_1458,plain,
    ( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X1),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1049]) ).

cnf(c_0_1459,plain,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1050]) ).

cnf(c_0_1460,plain,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X1),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1051]) ).

cnf(c_0_1461,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1052]) ).

cnf(c_0_1462,plain,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X1),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1053]) ).

cnf(c_0_1463,plain,
    ( hBOOL(hAPP(c_InductTermi_OIT,X1))
    | ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X1,tc_Lambda_OdB) ),
    inference(split_conjunct,[status(thm)],[c_0_1054]) ).

cnf(c_0_1464,plain,
    ( c_Type_Otyping(X1,X4,X3)
    | ~ c_Type_Otyping(X1,X2,X3)
    | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X2),X4)) ),
    inference(split_conjunct,[status(thm)],[c_0_1055]) ).

cnf(c_0_1465,plain,
    ( c_List_Olistsum(c_List_Oappend(X1,X2,X3),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_List_Olistsum(X1,X3)),c_List_Olistsum(X2,X3))
    | ~ class_OrderedGroup_Omonoid__add(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1056]) ).

cnf(c_0_1466,plain,
    ( c_lessequals(X1,c_Orderings_Oord__class_Omax(X2,X4,X3),X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1057]) ).

cnf(c_0_1467,plain,
    ( c_lessequals(X1,c_Orderings_Oord__class_Omax(X4,X2,X3),X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1058]) ).

cnf(c_0_1468,plain,
    ( c_lessequals(X1,c_Orderings_Oord__class_Omax(X2,X4,X3),X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1059]) ).

cnf(c_0_1469,plain,
    ( c_lessequals(X1,c_Orderings_Oord__class_Omax(X4,X2,X3),X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1060]) ).

cnf(c_0_1470,plain,
    ( c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X4,X2,X3),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1061]) ).

cnf(c_0_1471,plain,
    ( c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X2,X4,X3),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1062]) ).

cnf(c_0_1472,plain,
    ( c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X4,X2,X3),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1063]) ).

cnf(c_0_1473,plain,
    ( c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X2,X4,X3),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1064]) ).

cnf(c_0_1474,plain,
    ( c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_Nat_Osemiring__1__class_Oof__nat(X1,X3)),c_Nat_Osemiring__1__class_Oof__nat(X2,X3))
    | ~ class_Ring__and__Field_Osemiring__1(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1065]) ).

cnf(c_0_1475,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1066]) ).

cnf(c_0_1476,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1067]) ).

cnf(c_0_1477,plain,
    ( c_HOL_Oord__class_Oless(X1,X4,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_lessequals(X2,X4,X3)
    | ~ class_Orderings_Opreorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1068]) ).

cnf(c_0_1478,plain,
    ( c_HOL_Oord__class_Oless(X1,X4,X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X2,X4,X3)
    | ~ class_Orderings_Opreorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1069]) ).

cnf(c_0_1479,plain,
    ( c_lessequals(X1,X4,X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_lessequals(X2,X4,X3)
    | ~ class_Orderings_Opreorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1070]) ).

cnf(c_0_1480,plain,
    ( c_HOL_Oord__class_Oless(X4,X2,X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X4,X1,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1071]) ).

cnf(c_0_1481,plain,
    ( c_HOL_Oord__class_Oless(X4,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_lessequals(X4,X1,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1072]) ).

cnf(c_0_1482,plain,
    ( c_lessequals(X4,X2,X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_lessequals(X4,X1,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1073]) ).

cnf(c_0_1483,plain,
    ( c_HOL_Oord__class_Oless(X4,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X4,X1,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1074]) ).

cnf(c_0_1484,plain,
    ( c_HOL_Oord__class_Oless(X1,X4,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X2,X4,X3)
    | ~ class_Orderings_Opreorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1075]) ).

cnf(c_0_1485,plain,
    ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OAbs(X1)),c_Lambda_OdB_OAbs(X2)))
    | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_1076]) ).

cnf(c_0_1486,plain,
    ( c_HOL_Oord__class_Oless(X1,X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_Nat_Osemiring__1__class_Oof__nat(X3,X2),X2)
    | ~ class_Ring__and__Field_Oordered__semidom(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1077]) ).

cnf(c_0_1487,plain,
    ( c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1078]) ).

cnf(c_0_1488,plain,
    ( c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1079]) ).

cnf(c_0_1489,plain,
    ( c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1080]) ).

cnf(c_0_1490,plain,
    ( c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1081]) ).

cnf(c_0_1491,plain,
    ( c_Orderings_Oord__class_Omax(X1,c_Orderings_Oord__class_Omax(X1,X2,X3),X3) = c_Orderings_Oord__class_Omax(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1082]) ).

cnf(c_0_1492,plain,
    ( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_Olift,X1),X2)))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_1083]) ).

cnf(c_0_1493,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_Lambda_Oliftn(X3,c_Lambda_OdB_OVar(X1),X2) = c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_1084]) ).

cnf(c_0_1494,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Oone__class_Oone(X1)),c_HOL_Oone__class_Oone(X1)),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1085]) ).

cnf(c_0_1495,plain,
    ( c_List_Olistsum(c_List_Olist_OCons(X1,X2,X3),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),c_List_Olistsum(X2,X3))
    | ~ class_OrderedGroup_Omonoid__add(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1086]) ).

cnf(c_0_1496,plain,
    ( c_lessequals(X2,X1,X3)
    | c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Opreorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1087]) ).

cnf(c_0_1497,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(X1)),X2) = c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat))) ),
    inference(split_conjunct,[status(thm)],[c_0_1088]) ).

cnf(c_0_1498,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1089]) ).

cnf(c_0_1499,plain,
    ( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X1)),X3),X2) = c_Lambda_OdB_OVar(X1)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1090]) ).

cnf(c_0_1500,plain,
    ( c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X3),c_Nat_Osemiring__1__class_Oof__nat(X2,X3),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ class_Ring__and__Field_Oordered__semidom(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1091]) ).

cnf(c_0_1501,plain,
    ( c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X1,tc_Lambda_OdB)
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_1092]) ).

cnf(c_0_1502,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | X1 = X2
    | c_HOL_Oord__class_Oless(X2,X1,tc_nat)
    | hBOOL(hAPP(hAPP(X3,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_1093]) ).

cnf(c_0_1503,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_Nat_Osemiring__1__class_Oof__nat(X1,X2),X2)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | ~ class_Ring__and__Field_Oordered__semidom(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1094]) ).

cnf(c_0_1504,plain,
    ( X2 = X1
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_lessequals(X2,X1,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1095]) ).

cnf(c_0_1505,plain,
    ( X1 = X2
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_lessequals(X2,X1,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1096]) ).

cnf(c_0_1506,plain,
    ( X1 = X2
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_lessequals(X2,X1,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1097]) ).

cnf(c_0_1507,plain,
    ( X1 = X2
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2)
    | ~ class_Int_Onumber__ring(X3)
    | ~ class_Ring__and__Field_Oidom(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1098]) ).

cnf(c_0_1508,plain,
    ( c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB)
    | hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X1)))
    | hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__5(X1)))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_1099]) ).

cnf(c_0_1509,plain,
    ( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
    | ~ c_lessequals(X1,X1,X2)
    | ~ class_Orderings_Olinorder(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1100]) ).

cnf(c_0_1510,plain,
    ( ~ c_lessequals(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X2,X1,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1101]) ).

cnf(c_0_1511,plain,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_lessequals(X2,X1,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1102]) ).

cnf(c_0_1512,plain,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_lessequals(X2,X1,X3)
    | ~ class_Orderings_Opreorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1103]) ).

cnf(c_0_1513,plain,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X2,X1,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1104]) ).

cnf(c_0_1514,plain,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X2,X1,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1105]) ).

cnf(c_0_1515,plain,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X2,X1,X3)
    | ~ class_Orderings_Opreorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1106]) ).

cnf(c_0_1516,plain,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X2,X1,X3)
    | ~ class_Orderings_Opreorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1107]) ).

cnf(c_0_1517,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X2 = X3
    | c_List_Oreplicate(X1,X2,X4) != c_List_Oreplicate(X5,X3,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_1108]) ).

cnf(c_0_1518,plain,
    ( c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),c_HOL_Oone__class_Oone(X2)),X2)
    | ~ class_Ring__and__Field_Oordered__semidom(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1109]) ).

cnf(c_0_1519,plain,
    ( X1 = X2
    | c_List_Oreplicate(X1,X3,X4) != c_List_Oreplicate(X2,X5,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_1110]) ).

cnf(c_0_1520,plain,
    ( X1 = X2
    | c_List_Oappend(X1,X3,X4) != c_List_Oappend(X2,X3,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_1111]) ).

cnf(c_0_1521,plain,
    ( X1 = X2
    | c_List_Oappend(X3,X1,X4) != c_List_Oappend(X3,X2,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_1112]) ).

cnf(c_0_1522,plain,
    ( X1 = X2
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2)
    | ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1113]) ).

cnf(c_0_1523,plain,
    ( X1 = X2
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2)
    | ~ class_OrderedGroup_Ocancel__semigroup__add(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1114]) ).

cnf(c_0_1524,plain,
    ( X1 = X2
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4)
    | ~ class_OrderedGroup_Ocancel__semigroup__add(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1115]) ).

cnf(c_0_1525,plain,
    ( X1 = X2
    | c_List_Olist_OCons(X1,X3,X4) != c_List_Olist_OCons(X2,X5,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_1116]) ).

cnf(c_0_1526,plain,
    ( X1 = X2
    | c_List_Olist_OCons(X3,X1,X4) != c_List_Olist_OCons(X5,X2,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_1117]) ).

cnf(c_0_1527,plain,
    ( c_Lambda_Osubstn(c_Lambda_OdB_OVar(X1),X2,X1) = c_Lambda_Oliftn(X1,X2,c_HOL_Ozero__class_Ozero(tc_nat))
    | c_HOL_Oord__class_Oless(X1,X1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1118]) ).

cnf(c_0_1528,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | X2 = X1
    | hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X2)),X3),X1) = c_Lambda_OdB_OVar(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1119]) ).

cnf(c_0_1529,plain,
    ( X2 = X3
    | ~ hBOOL(hAPP(hAPP(c_fequal(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_1120]) ).

cnf(c_0_1530,plain,
    ( c_lessequals(X1,c_Orderings_Oord__class_Omax(X2,X1,X3),X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1121]) ).

cnf(c_0_1531,plain,
    ( c_lessequals(X1,c_Orderings_Oord__class_Omax(X1,X2,X3),X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1122]) ).

cnf(c_0_1532,plain,
    ( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X1)),X2),X1) = X2
    | c_HOL_Oord__class_Oless(X1,X1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1123]) ).

cnf(c_0_1533,plain,
    ( c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB)
    | X1 = c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X1))
    | hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__5(X1)))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_1124]) ).

cnf(c_0_1534,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,X3)
    | X1 = X2
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1125]) ).

cnf(c_0_1535,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,X3)
    | X1 = X2
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1126]) ).

cnf(c_0_1536,plain,
    ( X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1127]) ).

cnf(c_0_1537,plain,
    ( X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1128]) ).

cnf(c_0_1538,plain,
    ( X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1129]) ).

cnf(c_0_1539,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,X3)
    | X1 = X2
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1130]) ).

cnf(c_0_1540,plain,
    ( X1 = X2
    | c_HOL_Oord__class_Oless(X2,X1,X3)
    | ~ c_lessequals(X2,X1,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1131]) ).

cnf(c_0_1541,plain,
    ( X2 = X1
    | c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1132]) ).

cnf(c_0_1542,plain,
    ( c_lessequals(X1,X2,X3)
    | c_Orderings_Oord__class_Omax(X1,X2,X3) != X2
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1133]) ).

cnf(c_0_1543,plain,
    ( c_Orderings_Oord__class_Omax(X1,X2,X3) = X2
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1134]) ).

cnf(c_0_1544,plain,
    ( c_Orderings_Oord__class_Omax(X2,X1,X3) = X2
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1135]) ).

cnf(c_0_1545,plain,
    ( c_Lambda_Oliftn(X3,c_Lambda_OdB_OVar(X1),X2) = c_Lambda_OdB_OVar(X1)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1136]) ).

cnf(c_0_1546,plain,
    ( c_lessequals(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ class_Orderings_Opreorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1137]) ).

cnf(c_0_1547,plain,
    ( c_lessequals(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1138]) ).

cnf(c_0_1548,plain,
    ( X1 = X2
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1139]) ).

cnf(c_0_1549,plain,
    ( X1 = X2
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1140]) ).

cnf(c_0_1550,plain,
    ( X1 = X2
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1141]) ).

cnf(c_0_1551,plain,
    ( ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_Ring__and__Field_Oordered__semidom(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1142]) ).

cnf(c_0_1552,plain,
    ( hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(X1)),X2) = c_Lambda_OdB_OVar(X1)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1143]) ).

cnf(c_0_1553,plain,
    ( hAPP(hAPP(X2,X4),X1) = X4
    | ~ c_OrderedGroup_Omonoid__add(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1144]) ).

cnf(c_0_1554,plain,
    ( hAPP(hAPP(X2,X1),X4) = X4
    | ~ c_OrderedGroup_Omonoid__add(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1145]) ).

cnf(c_0_1555,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(X2)
    | c_Power_Opower__class_Opower(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
    | ~ class_Power_Opower(X2)
    | ~ class_Ring__and__Field_Omult__zero(X2)
    | ~ class_Ring__and__Field_Ono__zero__divisors(X2)
    | ~ class_Ring__and__Field_Ozero__neq__one(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1146]) ).

cnf(c_0_1556,plain,
    ( c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X2) != c_HOL_Ozero__class_Ozero(X2)
    | ~ class_Power_Opower(X2)
    | ~ class_Ring__and__Field_Omult__zero(X2)
    | ~ class_Ring__and__Field_Ono__zero__divisors(X2)
    | ~ class_Ring__and__Field_Ozero__neq__one(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1147]) ).

cnf(c_0_1557,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | X2 = X1
    | c_Lambda_Osubstn(c_Lambda_OdB_OVar(X2),X3,X1) = c_Lambda_OdB_OVar(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1148]) ).

cnf(c_0_1558,plain,
    ( X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X2,X1,X3)
    | ~ class_Ring__and__Field_Oordered__idom(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1149]) ).

cnf(c_0_1559,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X2,X1,X3)
    | X1 = X2
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1150]) ).

cnf(c_0_1560,plain,
    ( X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X2,X1,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1151]) ).

cnf(c_0_1561,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,X3)
    | X1 = X2
    | c_HOL_Oord__class_Oless(X2,X1,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1152]) ).

cnf(c_0_1562,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X2,X1,X3)
    | X2 = X1
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1153]) ).

cnf(c_0_1563,plain,
    ( X1 = X2
    | hAPP(hAPP(c_Lambda_OdB_OApp,X1),X3) != hAPP(hAPP(c_Lambda_OdB_OApp,X2),X4) ),
    inference(split_conjunct,[status(thm)],[c_0_1154]) ).

cnf(c_0_1564,plain,
    ( X1 = X2
    | hAPP(hAPP(c_Lambda_OdB_OApp,X3),X1) != hAPP(hAPP(c_Lambda_OdB_OApp,X4),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1155]) ).

cnf(c_0_1565,plain,
    ( c_lessequals(X1,X2,X3)
    | c_lessequals(X2,X1,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1156]) ).

cnf(c_0_1566,plain,
    ( c_lessequals(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X2,X1,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1157]) ).

cnf(c_0_1567,plain,
    ( c_lessequals(X1,X1,X2)
    | c_HOL_Oord__class_Oless(X1,X1,X2)
    | ~ class_Orderings_Olinorder(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1158]) ).

cnf(c_0_1568,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_lessequals(X2,X1,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1159]) ).

cnf(c_0_1569,plain,
    ( c_lessequals(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X2,X1,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1160]) ).

cnf(c_0_1570,plain,
    ( c_Orderings_Oord__class_Omax(X1,X2,X3) = c_Orderings_Oord__class_Omax(X2,X1,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1161]) ).

cnf(c_0_1571,plain,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1162]) ).

cnf(c_0_1572,plain,
    ( ~ c_lessequals(c_HOL_Oone__class_Oone(X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1163]) ).

cnf(c_0_1573,plain,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X2)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1164]) ).

cnf(c_0_1574,plain,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X2)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1165]) ).

cnf(c_0_1575,plain,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X2)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1166]) ).

cnf(c_0_1576,plain,
    ( hAPP(X1,X2) = X3
    | ~ c_Type_Otyping(X1,c_Lambda_OdB_OVar(X2),X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1167]) ).

cnf(c_0_1577,plain,
    ( X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1168]) ).

cnf(c_0_1578,plain,
    ( X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1169]) ).

cnf(c_0_1579,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(X2)
    | c_Power_Opower__class_Opower(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
    | ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1170]) ).

cnf(c_0_1580,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(X2)
    | X3 != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),X1)
    | ~ class_Int_Onumber__ring(X2)
    | ~ class_Ring__and__Field_Oidom(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1171]) ).

cnf(c_0_1581,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(X2)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X1) != c_HOL_Ozero__class_Ozero(X2)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1172]) ).

cnf(c_0_1582,plain,
    ( X1 = c_List_Olist_ONil(X2)
    | c_List_Olist_ONil(X2) != c_List_Oappend(X1,X3,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1173]) ).

cnf(c_0_1583,plain,
    ( X1 = c_List_Olist_ONil(X2)
    | c_List_Olist_ONil(X2) != c_List_Oappend(X3,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1174]) ).

cnf(c_0_1584,plain,
    ( X1 = c_List_Olist_ONil(X2)
    | c_List_Oappend(X1,X3,X2) != c_List_Olist_ONil(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1175]) ).

cnf(c_0_1585,plain,
    ( X1 = c_List_Olist_ONil(X2)
    | c_List_Oappend(X3,X1,X2) != c_List_Olist_ONil(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1176]) ).

cnf(c_0_1586,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X2),X1,X2) = c_HOL_Ozero__class_Ozero(X2)
    | ~ class_Power_Opower(X2)
    | ~ class_Ring__and__Field_Omult__zero(X2)
    | ~ class_Ring__and__Field_Ono__zero__divisors(X2)
    | ~ class_Ring__and__Field_Ozero__neq__one(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1177]) ).

cnf(c_0_1587,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_List_Oreplicate(X1,X2,X3) != c_List_Olist_ONil(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1178]) ).

cnf(c_0_1588,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_List_Olist_ONil(X2) != c_List_Oreplicate(X1,X3,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1179]) ).

cnf(c_0_1589,plain,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1180]) ).

cnf(c_0_1590,plain,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1181]) ).

cnf(c_0_1591,plain,
    ( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
    | ~ class_Orderings_Oorder(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1182]) ).

cnf(c_0_1592,plain,
    ( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
    | ~ class_Orderings_Olinorder(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1183]) ).

cnf(c_0_1593,plain,
    ( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
    | ~ class_Orderings_Opreorder(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1184]) ).

cnf(c_0_1594,plain,
    ( X1 = c_List_Olist_ONil(X2)
    | c_List_Oappend(X3,X1,X2) != X3 ),
    inference(split_conjunct,[status(thm)],[c_0_1185]) ).

cnf(c_0_1595,plain,
    ( X1 = c_List_Olist_ONil(X2)
    | X3 != c_List_Oappend(X3,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1186]) ).

cnf(c_0_1596,plain,
    ( X1 = c_List_Olist_ONil(X2)
    | c_List_Oappend(X1,X3,X2) != X3 ),
    inference(split_conjunct,[status(thm)],[c_0_1187]) ).

cnf(c_0_1597,plain,
    ( X1 = c_List_Olist_ONil(X2)
    | X3 != c_List_Oappend(X1,X3,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1188]) ).

cnf(c_0_1598,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X2),X1,X2) = c_HOL_Ozero__class_Ozero(X2)
    | ~ class_Power_Opower(X2)
    | ~ class_Ring__and__Field_Osemiring__0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1189]) ).

cnf(c_0_1599,plain,
    ( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(X1)))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_1190]) ).

cnf(c_0_1600,plain,
    ( c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(tc_nat),X1) = c_HOL_Oone__class_Oone(X1)
    | ~ class_Power_Opower(X1)
    | ~ class_Ring__and__Field_Osemiring__0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1191]) ).

cnf(c_0_1601,plain,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1)) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1192]) ).

cnf(c_0_1602,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1193]) ).

cnf(c_0_1603,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1194]) ).

cnf(c_0_1604,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X2 != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1195]) ).

cnf(c_0_1605,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != X2 ),
    inference(split_conjunct,[status(thm)],[c_0_1196]) ).

cnf(c_0_1606,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oone__class_Oone(X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1197]) ).

cnf(c_0_1607,plain,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oone__class_Oone(X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1198]) ).

cnf(c_0_1608,plain,
    ( X1 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),c_HOL_Ozero__class_Ozero(X2))
    | ~ class_Int_Onumber__ring(X2)
    | ~ class_Ring__and__Field_Oidom(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1199]) ).

cnf(c_0_1609,plain,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1200]) ).

cnf(c_0_1610,plain,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1201]) ).

cnf(c_0_1611,plain,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
    | ~ class_OrderedGroup_Omonoid__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1202]) ).

cnf(c_0_1612,plain,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1203]) ).

cnf(c_0_1613,plain,
    ( c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X1),X2,X1) = c_HOL_Oone__class_Oone(X1)
    | ~ class_OrderedGroup_Omonoid__mult(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1204]) ).

cnf(c_0_1614,plain,
    ( c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X2) = c_HOL_Oone__class_Oone(X2)
    | ~ class_Power_Opower(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1205]) ).

cnf(c_0_1615,plain,
    ( c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X2) = c_HOL_Oone__class_Oone(X2)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1206]) ).

cnf(c_0_1616,plain,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = X2
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1207]) ).

cnf(c_0_1617,plain,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = X2
    | ~ class_OrderedGroup_Omonoid__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1208]) ).

cnf(c_0_1618,plain,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = X2
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1209]) ).

cnf(c_0_1619,plain,
    ( c_Power_Opower__class_Opower(X1,c_HOL_Oone__class_Oone(tc_nat),X2) = X1
    | ~ class_OrderedGroup_Omonoid__mult(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1210]) ).

cnf(c_0_1620,plain,
    ( c_Power_Opower__class_Opower(X1,c_HOL_Oone__class_Oone(tc_nat),X2) = X1
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1211]) ).

cnf(c_0_1621,plain,
    ( c_Orderings_Oord__class_Omax(X1,X1,X2) = X1
    | ~ class_Orderings_Olinorder(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1212]) ).

cnf(c_0_1622,plain,
    ( c_lessequals(X1,X1,X2)
    | ~ class_Orderings_Opreorder(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1213]) ).

cnf(c_0_1623,plain,
    ( c_lessequals(X1,X1,X2)
    | ~ class_Orderings_Oorder(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1214]) ).

cnf(c_0_1624,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1215]) ).

cnf(c_0_1625,plain,
    ( X1 = X2
    | c_Nat_Osemiring__1__class_Oof__nat(X1,X3) != c_Nat_Osemiring__1__class_Oof__nat(X2,X3)
    | ~ class_Nat_Osemiring__char__0(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1216]) ).

cnf(c_0_1626,plain,
    ( class_Orderings_Opreorder(tc_fun(X2,X1))
    | ~ class_Orderings_Opreorder(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1217]) ).

cnf(c_0_1627,plain,
    ( class_Orderings_Oorder(tc_fun(X2,X1))
    | ~ class_Orderings_Oorder(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1218]) ).

cnf(c_0_1628,plain,
    ( c_List_Olistsum(c_List_Olist_ONil(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_OrderedGroup_Omonoid__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1219]) ).

cnf(c_0_1629,plain,
    ( c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),X1) = c_HOL_Oone__class_Oone(X1)
    | ~ class_Ring__and__Field_Osemiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1220]) ).

cnf(c_0_1630,plain,
    ( c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Osemiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1221]) ).

cnf(c_0_1631,plain,
    ( c_OrderedGroup_Osemigroup__add(c_HOL_Oplus__class_Oplus(X1),X1)
    | ~ class_OrderedGroup_Osemigroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1222]) ).

cnf(c_0_1632,plain,
    ( c_HOL_Oone__class_Oone(X1) != c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Ozero__neq__one(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1223]) ).

cnf(c_0_1633,plain,
    ( c_HOL_Ozero__class_Ozero(X1) != c_HOL_Oone__class_Oone(X1)
    | ~ class_Ring__and__Field_Ozero__neq__one(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1224]) ).

cnf(c_0_1634,plain,
    ( X1 = X2
    | c_Lambda_OdB_OAbs(X1) != c_Lambda_OdB_OAbs(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1225]) ).

cnf(c_0_1635,plain,
    ( X1 = X2
    | c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OVar(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1226]) ).

cnf(c_0_1636,plain,
    ( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(X1,X2,X3),tc_Lambda_OdB,tc_Lambda_OdB) = X3
    | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),X2,tc_Lambda_OdB,tc_Lambda_OdB)),X3)) ),
    c_0_1227,
    [final] ).

cnf(c_0_1637,plain,
    ( c_Type_Otypings(X1,c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,X2,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),X4,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X5,tc_Lambda_OdB,tc_Lambda_OdB),X6)
    | ~ c_Type_Otyping(X1,X2,X3)
    | ~ c_Type_Otypings(c_Type_Oshift(X1,X4,X3,tc_Type_Otype),X5,X6) ),
    c_0_1228,
    [final] ).

cnf(c_0_1638,plain,
    ( c_Type_Otypings(X1,X4,c_Type_Osko__Type__Xvar__app__types__1__1(X5,X7,X1,X4))
    | ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X4,tc_Lambda_OdB,tc_Lambda_OdB),X5)
    | ~ c_Type_Otypings(X1,X3,X6)
    | ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X7) ),
    c_0_1229,
    [final] ).

cnf(c_0_1639,plain,
    ( c_ListOrder_Ostep1(c_Lambda_Obeta,X2,c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(X1,X2,X3),tc_Lambda_OdB)
    | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),X2,tc_Lambda_OdB,tc_Lambda_OdB)),X3)) ),
    c_0_1230,
    [final] ).

cnf(c_0_1640,plain,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1(X1)),c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2(X1),tc_Lambda_OdB,tc_Lambda_OdB)))
    | ~ hBOOL(hAPP(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3(X1)),c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__4(X1),tc_Lambda_OdB,tc_Lambda_OdB))) ),
    c_0_1231,
    [final] ).

cnf(c_0_1641,plain,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_ListApplication_Osko__ListApplication__Xlem__1__1(X1)),c_ListApplication_Osko__ListApplication__Xlem__1__2(X1),tc_Lambda_OdB,tc_Lambda_OdB)))
    | ~ hBOOL(hAPP(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(c_ListApplication_Osko__ListApplication__Xlem__1__3(X1)),c_ListApplication_Osko__ListApplication__Xlem__1__4(X1),tc_Lambda_OdB,tc_Lambda_OdB))) ),
    c_0_1232,
    [final] ).

cnf(c_0_1642,plain,
    ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X1,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X2,tc_Lambda_OdB,tc_Lambda_OdB)))
    | ~ c_ListOrder_Ostep1(c_Lambda_Obeta,X1,X2,tc_Lambda_OdB) ),
    c_0_1233,
    [final] ).

cnf(c_0_1643,plain,
    ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X3,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB)))
    | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2)) ),
    c_0_1234,
    [final] ).

cnf(c_0_1644,plain,
    ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X3,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB)))
    | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2)) ),
    c_0_1235,
    [final] ).

cnf(c_0_1645,plain,
    ( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1)),X2),X3,tc_Lambda_OdB,tc_Lambda_OdB)))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X2),c_HOL_Ozero__class_Ozero(tc_nat)),X3,tc_Lambda_OdB,tc_Lambda_OdB)))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X2)) ),
    c_0_1236,
    [final] ).

cnf(c_0_1646,plain,
    ( hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X8)),hAPP(hAPP(X2,X9),X10)) = hAPP(hAPP(X2,X9),hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X8)),X10))
    | ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
    c_0_1237,
    [final] ).

cnf(c_0_1647,plain,
    ( hAPP(hAPP(X1,hAPP(hAPP(X1,X7),X8)),hAPP(hAPP(X1,X9),X10)) = hAPP(hAPP(X1,hAPP(hAPP(X1,X7),X9)),hAPP(hAPP(X1,X8),X10))
    | ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
    c_0_1238,
    [final] ).

cnf(c_0_1648,plain,
    ( hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X8)),hAPP(hAPP(X2,X9),X10)) = hAPP(hAPP(X2,X7),hAPP(hAPP(X2,X8),hAPP(hAPP(X2,X9),X10)))
    | ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
    c_0_1239,
    [final] ).

cnf(c_0_1649,plain,
    ( hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X8)),hAPP(hAPP(X2,X9),X10)) = hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X9)),hAPP(hAPP(X2,X8),X10))
    | ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
    c_0_1240,
    [final] ).

cnf(c_0_1650,plain,
    ( hAPP(hAPP(X2,hAPP(hAPP(X3,X7),X9)),hAPP(hAPP(X3,X8),X9)) = hAPP(hAPP(X3,hAPP(hAPP(X2,X7),X8)),X9)
    | ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
    c_0_1241,
    [final] ).

cnf(c_0_1651,plain,
    ( hAPP(hAPP(X1,hAPP(hAPP(X2,X7),X9)),hAPP(hAPP(X2,X8),X9)) = hAPP(hAPP(X2,hAPP(hAPP(X1,X7),X8)),X9)
    | ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
    c_0_1242,
    [final] ).

cnf(c_0_1652,plain,
    ( hAPP(hAPP(X1,hAPP(hAPP(X2,X7),X8)),hAPP(hAPP(X2,X9),X8)) = hAPP(hAPP(X2,hAPP(hAPP(X1,X7),X9)),X8)
    | ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
    c_0_1243,
    [final] ).

cnf(c_0_1653,plain,
    ( hAPP(hAPP(X2,hAPP(hAPP(X3,X7),X8)),hAPP(hAPP(X3,X7),X9)) = hAPP(hAPP(X3,X7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X8),X9))
    | ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
    c_0_1244,
    [final] ).

cnf(c_0_1654,plain,
    ( hAPP(hAPP(X1,hAPP(hAPP(X2,X7),X8)),hAPP(hAPP(X2,X7),X9)) = hAPP(hAPP(X2,X7),hAPP(hAPP(X1,X8),X9))
    | ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
    c_0_1245,
    [final] ).

cnf(c_0_1655,plain,
    ( hAPP(hAPP(X1,hAPP(hAPP(X1,X7),X8)),X9) = hAPP(hAPP(X1,hAPP(hAPP(X1,X7),X9)),X8)
    | ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
    c_0_1246,
    [final] ).

cnf(c_0_1656,plain,
    ( hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X8)),X9) = hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X9)),X8)
    | ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
    c_0_1247,
    [final] ).

cnf(c_0_1657,plain,
    ( hAPP(hAPP(X1,hAPP(hAPP(X2,X7),X8)),X8) = hAPP(hAPP(X2,hAPP(hAPP(X1,X7),X5)),X8)
    | ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
    c_0_1248,
    [final] ).

cnf(c_0_1658,plain,
    ( hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X8)),X9) = hAPP(hAPP(X2,X7),hAPP(hAPP(X2,X8),X9))
    | ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
    c_0_1249,
    [final] ).

cnf(c_0_1659,plain,
    ( hAPP(hAPP(X1,hAPP(hAPP(X1,X7),X8)),X9) = hAPP(hAPP(X1,X7),hAPP(hAPP(X1,X8),X9))
    | ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
    c_0_1250,
    [final] ).

cnf(c_0_1660,plain,
    ( hAPP(hAPP(X1,hAPP(hAPP(X1,X7),X8)),X9) = hAPP(hAPP(X1,X7),hAPP(hAPP(X1,X8),X9))
    | ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
    c_0_1251,
    [final] ).

cnf(c_0_1661,plain,
    ( hAPP(hAPP(X1,hAPP(hAPP(X1,X7),X8)),X9) = hAPP(hAPP(X1,X7),hAPP(hAPP(X1,X8),X9))
    | ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
    c_0_1252,
    [final] ).

cnf(c_0_1662,plain,
    ( hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X8)),X9) = hAPP(hAPP(X2,X7),hAPP(hAPP(X2,X8),X9))
    | ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
    c_0_1253,
    [final] ).

cnf(c_0_1663,plain,
    ( hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X8)),X9) = hAPP(hAPP(X2,X7),hAPP(hAPP(X2,X8),X9))
    | ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
    c_0_1254,
    [final] ).

cnf(c_0_1664,plain,
    ( hAPP(hAPP(X1,X7),hAPP(hAPP(X2,X8),X7)) = hAPP(hAPP(X2,hAPP(hAPP(X1,X8),X5)),X7)
    | ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
    c_0_1255,
    [final] ).

cnf(c_0_1665,plain,
    ( hAPP(hAPP(X1,X7),hAPP(hAPP(X1,X8),X9)) = hAPP(hAPP(X1,X8),hAPP(hAPP(X1,X7),X9))
    | ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
    c_0_1256,
    [final] ).

cnf(c_0_1666,plain,
    ( hAPP(hAPP(X2,X7),hAPP(hAPP(X2,X8),X9)) = hAPP(hAPP(X2,X8),hAPP(hAPP(X2,X7),X9))
    | ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
    c_0_1257,
    [final] ).

cnf(c_0_1667,plain,
    ( hAPP(hAPP(X1,X7),X7) = hAPP(hAPP(X2,hAPP(hAPP(X1,X5),X5)),X7)
    | ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
    c_0_1258,
    [final] ).

cnf(c_0_1668,plain,
    ( hAPP(hAPP(X2,X7),X8) = hAPP(hAPP(X2,X8),X7)
    | ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
    c_0_1259,
    [final] ).

cnf(c_0_1669,plain,
    ( hAPP(hAPP(X1,X7),X8) = hAPP(hAPP(X1,X8),X7)
    | ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
    c_0_1260,
    [final] ).

cnf(c_0_1670,plain,
    ( hAPP(hAPP(X1,X7),X8) = hAPP(hAPP(X1,X8),X7)
    | ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
    c_0_1261,
    [final] ).

cnf(c_0_1671,plain,
    ( hAPP(hAPP(X2,X7),X8) = hAPP(hAPP(X2,X8),X7)
    | ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
    c_0_1262,
    [final] ).

cnf(c_0_1672,plain,
    ( hAPP(hAPP(X3,X7),c_HOL_Oone__class_Oone(tc_nat)) = X7
    | ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
    c_0_1263,
    [final] ).

cnf(c_0_1673,plain,
    ( hAPP(hAPP(X3,X7),c_HOL_Ozero__class_Ozero(tc_nat)) = X5
    | ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
    c_0_1264,
    [final] ).

cnf(c_0_1674,plain,
    ( hAPP(hAPP(X2,X5),X7) = X7
    | ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
    c_0_1265,
    [final] ).

cnf(c_0_1675,plain,
    ( hAPP(hAPP(X2,X4),X7) = X4
    | ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
    c_0_1266,
    [final] ).

cnf(c_0_1676,plain,
    ( hAPP(hAPP(X1,X4),X7) = X7
    | ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
    c_0_1267,
    [final] ).

cnf(c_0_1677,plain,
    ( hAPP(hAPP(X2,X7),X5) = X7
    | ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
    c_0_1268,
    [final] ).

cnf(c_0_1678,plain,
    ( hAPP(hAPP(X2,X5),X7) = X7
    | ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
    c_0_1269,
    [final] ).

cnf(c_0_1679,plain,
    ( hAPP(hAPP(X2,X7),X4) = X4
    | ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
    c_0_1270,
    [final] ).

cnf(c_0_1680,plain,
    ( hAPP(hAPP(X2,X4),X7) = X4
    | ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
    c_0_1271,
    [final] ).

cnf(c_0_1681,plain,
    ( hAPP(hAPP(X1,X7),X4) = X7
    | ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
    c_0_1272,
    [final] ).

cnf(c_0_1682,plain,
    ( hAPP(hAPP(X1,X4),X7) = X7
    | ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
    c_0_1273,
    [final] ).

cnf(c_0_1683,plain,
    ( hBOOL(hAPP(X1,hAPP(hAPP(X2,X3),X4)))
    | ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X5,X2,X6,hAPP(hAPP(c_Lambda_OdB_OApp,X3),X4),t_a))) ),
    c_0_1274,
    [final] ).

cnf(c_0_1684,plain,
    ( hBOOL(hAPP(X1,hAPP(hAPP(X2,X3),X4)))
    | ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X5,X2,X6,hAPP(hAPP(c_Lambda_OdB_OApp,X3),X4),t_a))) ),
    c_0_1275,
    [final] ).

cnf(c_0_1685,plain,
    ( hBOOL(hAPP(X1,X2))
    | hBOOL(hAPP(X1,c_ListApplication_Osko__ListApplication__Xlem__1__3(X1)))
    | ~ hBOOL(hAPP(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_ListApplication_Osko__ListApplication__Xlem__1__1(X1)),c_ListApplication_Osko__ListApplication__Xlem__1__2(X1),tc_Lambda_OdB,tc_Lambda_OdB))) ),
    c_0_1276,
    [final] ).

cnf(c_0_1686,plain,
    ( hBOOL(hAPP(X1,c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3(X1)))
    | hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1(X1)),c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2(X1),tc_Lambda_OdB,tc_Lambda_OdB))) ),
    c_0_1277,
    [final] ).

cnf(c_0_1687,plain,
    ( X4 = X5
    | ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X4)
    | ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X5) ),
    c_0_1278,
    [final] ).

cnf(c_0_1688,plain,
    ( hBOOL(hAPP(X1,hAPP(X2,X3)))
    | ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X4,X5,X2,c_Lambda_OdB_OAbs(X3),t_a))) ),
    c_0_1279,
    [final] ).

cnf(c_0_1689,plain,
    ( hBOOL(hAPP(X1,hAPP(X2,X3)))
    | ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X4,X5,X2,c_Lambda_OdB_OAbs(X3),t_a))) ),
    c_0_1280,
    [final] ).

cnf(c_0_1690,plain,
    ( hBOOL(hAPP(X1,hAPP(X2,X3)))
    | ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X2,X4,X5,c_Lambda_OdB_OVar(X3),t_a))) ),
    c_0_1281,
    [final] ).

cnf(c_0_1691,plain,
    ( hBOOL(hAPP(X1,hAPP(X2,X3)))
    | ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X2,X4,X5,c_Lambda_OdB_OVar(X3),t_a))) ),
    c_0_1282,
    [final] ).

cnf(c_0_1692,plain,
    ( c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1)),X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)
    | ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X2,tc_Lambda_OdB)
    | ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X2),c_HOL_Ozero__class_Ozero(tc_nat)),X3,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB) ),
    c_0_1283,
    [final] ).

cnf(c_0_1693,plain,
    ( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X1)),v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB,tc_Lambda_OdB) = X1
    | hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X1)))
    | hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_sko__InductTermi__XIT__Xcases__4(X1)),v_sko__InductTermi__XIT__Xcases__5(X1)),c_HOL_Ozero__class_Ozero(tc_nat)),v_sko__InductTermi__XIT__Xcases__6(X1),tc_Lambda_OdB,tc_Lambda_OdB)))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
    c_0_1284,
    [final] ).

cnf(c_0_1694,plain,
    ( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X1)),v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB,tc_Lambda_OdB) = X1
    | c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X1)) = X1
    | hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_sko__InductTermi__XIT__Xcases__4(X1)),v_sko__InductTermi__XIT__Xcases__5(X1)),c_HOL_Ozero__class_Ozero(tc_nat)),v_sko__InductTermi__XIT__Xcases__6(X1),tc_Lambda_OdB,tc_Lambda_OdB)))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
    c_0_1285,
    [final] ).

cnf(c_0_1695,plain,
    ( c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB)
    | hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X1)))
    | hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_sko__InductTermi__XIT__Xcases__4(X1)),v_sko__InductTermi__XIT__Xcases__5(X1)),c_HOL_Ozero__class_Ozero(tc_nat)),v_sko__InductTermi__XIT__Xcases__6(X1),tc_Lambda_OdB,tc_Lambda_OdB)))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
    c_0_1286,
    [final] ).

cnf(c_0_1696,plain,
    ( c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB)
    | c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X1)) = X1
    | hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_sko__InductTermi__XIT__Xcases__4(X1)),v_sko__InductTermi__XIT__Xcases__5(X1)),c_HOL_Ozero__class_Ozero(tc_nat)),v_sko__InductTermi__XIT__Xcases__6(X1),tc_Lambda_OdB,tc_Lambda_OdB)))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
    c_0_1287,
    [final] ).

cnf(c_0_1697,plain,
    ( c_Type_Otypings(c_Type_Oshift(X1,X4,X5,tc_Type_Otype),c_List_Omap(c_COMBC(c_Lambda_Olift,X4,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X2,tc_Lambda_OdB,tc_Lambda_OdB),X3)
    | ~ c_Type_Otypings(X1,X2,X3) ),
    c_0_1288,
    [final] ).

cnf(c_0_1698,plain,
    ( c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X1,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)
    | ~ c_List_Olistsp(c_InductTermi_OIT,X1,tc_Lambda_OdB) ),
    c_0_1289,
    [final] ).

cnf(c_0_1699,plain,
    ( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X1,tc_Lambda_OdB,tc_Lambda_OdB)))
    | ~ c_List_Olistsp(c_InductTermi_OIT,X1,tc_Lambda_OdB) ),
    c_0_1290,
    [final] ).

cnf(c_0_1700,plain,
    ( c_Type_Otypings(X1,X3,c_Type_Osko__Type__Xvar__app__typesE__1__1(X4,X1,X2,X3))
    | ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X4) ),
    c_0_1291,
    [final] ).

cnf(c_0_1701,plain,
    ( X1 = X2
    | c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1),X3,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X2),X4,tc_Lambda_OdB,tc_Lambda_OdB) ),
    c_0_1292,
    [final] ).

cnf(c_0_1702,plain,
    ( X1 = X2
    | c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X3),X1,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X4),X2,tc_Lambda_OdB,tc_Lambda_OdB) ),
    c_0_1293,
    [final] ).

cnf(c_0_1703,plain,
    ( X1 = X2
    | c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),X3,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X4,tc_Lambda_OdB,tc_Lambda_OdB) ),
    c_0_1294,
    [final] ).

cnf(c_0_1704,plain,
    ( X1 = X2
    | c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X3),X1,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X4),X2,tc_Lambda_OdB,tc_Lambda_OdB) ),
    c_0_1295,
    [final] ).

cnf(c_0_1705,plain,
    ( c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X4,X1,X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),X3,X4,X1,X1))
    | ~ class_OrderedGroup_Osemigroup__add(X1) ),
    c_0_1296,
    [final] ).

cnf(c_0_1706,plain,
    ( X1 = X2
    | c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X3,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB) ),
    c_0_1297,
    [final] ).

cnf(c_0_1707,plain,
    ( c_List_Ofoldl(X1,hAPP(hAPP(X1,X3),X4),X5,X2,X2) = hAPP(hAPP(X1,X3),c_List_Ofoldl(X1,X4,X5,X2,X2))
    | ~ c_OrderedGroup_Osemigroup__add(X1,X2) ),
    c_0_1298,
    [final] ).

cnf(c_0_1708,plain,
    ( hAPP(hAPP(X2,X4),c_List_Ofoldl(X2,X1,X5,X3,X3)) = c_List_Ofoldl(X2,X4,X5,X3,X3)
    | ~ c_OrderedGroup_Omonoid__add(X1,X2,X3) ),
    c_0_1299,
    [final] ).

cnf(c_0_1709,plain,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X1),X3,c_HOL_Ozero__class_Ozero(X1),X1,X1)) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),X2,X3,X1,X1)
    | ~ class_OrderedGroup_Omonoid__add(X1) ),
    c_0_1300,
    [final] ).

cnf(c_0_1710,plain,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1),X3,X1,X1)) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),X2,X3,X1,X1)
    | ~ class_OrderedGroup_Omonoid__add(X1) ),
    c_0_1301,
    [final] ).

cnf(c_0_1711,plain,
    ( X1 = c_List_Olist_ONil(tc_Lambda_OdB)
    | c_List_Ofoldl(c_Lambda_OdB_OApp,X3,c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1(X2,X4,X3,X1),tc_Lambda_OdB,tc_Lambda_OdB) = X2
    | hAPP(hAPP(c_Lambda_OdB_OApp,X2),X4) != c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X1,tc_Lambda_OdB,tc_Lambda_OdB) ),
    c_0_1302,
    [final] ).

cnf(c_0_1712,plain,
    ( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X1)),v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB,tc_Lambda_OdB) = X1
    | hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X1)))
    | c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__4(X1))),v_sko__InductTermi__XIT__Xcases__5(X1)),v_sko__InductTermi__XIT__Xcases__6(X1),tc_Lambda_OdB,tc_Lambda_OdB) = X1
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
    c_0_1303,
    [final] ).

cnf(c_0_1713,plain,
    ( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X1)),v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB,tc_Lambda_OdB) = X1
    | c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X1)) = X1
    | c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__4(X1))),v_sko__InductTermi__XIT__Xcases__5(X1)),v_sko__InductTermi__XIT__Xcases__6(X1),tc_Lambda_OdB,tc_Lambda_OdB) = X1
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
    c_0_1304,
    [final] ).

cnf(c_0_1714,plain,
    ( c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X1),X2,c_HOL_Ozero__class_Ozero(X1),X1,X1) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1),X2,X1,X1)
    | ~ class_OrderedGroup_Omonoid__add(X1) ),
    c_0_1305,
    [final] ).

cnf(c_0_1715,plain,
    ( c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X1),X2,X3,X1,X1) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),X3,X2,X1,X1)
    | ~ class_OrderedGroup_Oab__semigroup__add(X1) ),
    c_0_1306,
    [final] ).

cnf(c_0_1716,plain,
    ( hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) = X3
    | hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) != c_List_Ofoldl(c_Lambda_OdB_OApp,X3,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) ),
    c_0_1307,
    [final] ).

cnf(c_0_1717,plain,
    ( X1 = c_Lambda_OdB_OAbs(X2)
    | c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X3,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X2) ),
    c_0_1308,
    [final] ).

cnf(c_0_1718,plain,
    ( c_Lambda_OdB_OAbs(X1) = X2
    | c_Lambda_OdB_OAbs(X1) != c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB) ),
    c_0_1309,
    [final] ).

cnf(c_0_1719,plain,
    ( c_Lambda_OdB_OVar(X1) = X2
    | c_Lambda_OdB_OVar(X1) != c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB) ),
    c_0_1310,
    [final] ).

cnf(c_0_1720,plain,
    ( hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)))),hAPP(hAPP(c_Lambda_Olift,X4),X2)),X1) = hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(hAPP(c_Lambda_Osubst,X3),X4),X1)),X2)
    | ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
    c_0_1311,
    [final] ).

cnf(c_0_1721,plain,
    ( X1 = c_List_Olist_ONil(tc_Lambda_OdB)
    | c_Lambda_OdB_OAbs(X2) != c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X1,tc_Lambda_OdB,tc_Lambda_OdB) ),
    c_0_1312,
    [final] ).

cnf(c_0_1722,plain,
    ( X1 = c_List_Olist_ONil(tc_Lambda_OdB)
    | c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X1,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X3) ),
    c_0_1313,
    [final] ).

cnf(c_0_1723,plain,
    ( X1 = c_List_Olist_ONil(tc_Lambda_OdB)
    | c_Lambda_OdB_OVar(X2) != c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X1,tc_Lambda_OdB,tc_Lambda_OdB) ),
    c_0_1314,
    [final] ).

cnf(c_0_1724,plain,
    ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X4),X3))
    | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Predicate_Oconversep(X1,X2,X2),X2),X3),X4)) ),
    c_0_1315,
    [final] ).

cnf(c_0_1725,plain,
    ( c_ListOrder_Ostep1(X1,X2,X5,X4)
    | hBOOL(hAPP(hAPP(X1,X3),X6))
    | ~ c_ListOrder_Ostep1(X1,c_List_Oappend(X2,c_List_Olist_OCons(X3,c_List_Olist_ONil(X4),X4),X4),c_List_Oappend(X5,c_List_Olist_OCons(X6,c_List_Olist_ONil(X4),X4),X4),X4) ),
    c_0_1316,
    [final] ).

cnf(c_0_1726,plain,
    ( c_ListOrder_Ostep1(X1,X2,X5,X4)
    | X2 = X5
    | ~ c_ListOrder_Ostep1(X1,c_List_Oappend(X2,c_List_Olist_OCons(X3,c_List_Olist_ONil(X4),X4),X4),c_List_Oappend(X5,c_List_Olist_OCons(X6,c_List_Olist_ONil(X4),X4),X4),X4) ),
    c_0_1317,
    [final] ).

cnf(c_0_1727,plain,
    ( X3 = X6
    | hBOOL(hAPP(hAPP(X1,X3),X6))
    | ~ c_ListOrder_Ostep1(X1,c_List_Oappend(X2,c_List_Olist_OCons(X3,c_List_Olist_ONil(X4),X4),X4),c_List_Oappend(X5,c_List_Olist_OCons(X6,c_List_Olist_ONil(X4),X4),X4),X4) ),
    c_0_1318,
    [final] ).

cnf(c_0_1728,plain,
    ( c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB)
    | hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X1)))
    | c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__4(X1))),v_sko__InductTermi__XIT__Xcases__5(X1)),v_sko__InductTermi__XIT__Xcases__6(X1),tc_Lambda_OdB,tc_Lambda_OdB) = X1
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
    c_0_1319,
    [final] ).

cnf(c_0_1729,plain,
    ( X3 = X6
    | X2 = X5
    | ~ c_ListOrder_Ostep1(X1,c_List_Oappend(X2,c_List_Olist_OCons(X3,c_List_Olist_ONil(X4),X4),X4),c_List_Oappend(X5,c_List_Olist_OCons(X6,c_List_Olist_ONil(X4),X4),X4),X4) ),
    c_0_1320,
    [final] ).

cnf(c_0_1730,plain,
    ( c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB)
    | c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X1)) = X1
    | c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__4(X1))),v_sko__InductTermi__XIT__Xcases__5(X1)),v_sko__InductTermi__XIT__Xcases__6(X1),tc_Lambda_OdB,tc_Lambda_OdB) = X1
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
    c_0_1321,
    [final] ).

cnf(c_0_1731,plain,
    ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X3),X4)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X2),X3),X4)))
    | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2)) ),
    c_0_1322,
    [final] ).

cnf(c_0_1732,plain,
    ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,X3),X1),X4)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X3),X2),X4)))
    | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2)) ),
    c_0_1323,
    [final] ).

cnf(c_0_1733,plain,
    ( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X1)),v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB,tc_Lambda_OdB) = X1
    | hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X1)))
    | hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__5(X1)))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
    c_0_1324,
    [final] ).

cnf(c_0_1734,plain,
    ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Predicate_Oconversep(X1,X2,X2),X2),X4),X3))
    | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X4)) ),
    c_0_1325,
    [final] ).

cnf(c_0_1735,plain,
    ( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X1)),v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB,tc_Lambda_OdB) = X1
    | c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X1)) = X1
    | hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__5(X1)))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
    c_0_1326,
    [final] ).

cnf(c_0_1736,plain,
    ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,X3),X1),X4)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X3),X2),X4)))
    | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2)) ),
    c_0_1327,
    [final] ).

cnf(c_0_1737,plain,
    ( c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X2),X1,c_HOL_Ozero__class_Ozero(X2),X2,X2) = c_List_Olistsum(X1,X2)
    | ~ class_OrderedGroup_Omonoid__add(X2) ),
    c_0_1328,
    [final] ).

cnf(c_0_1738,plain,
    ( c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X2),c_HOL_Ozero__class_Ozero(X2),X1,X2,X2) = c_List_Olistsum(X1,X2)
    | ~ class_OrderedGroup_Omonoid__add(X2) ),
    c_0_1329,
    [final] ).

cnf(c_0_1739,plain,
    ( hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,X3),X1)),hAPP(hAPP(c_Lambda_Olift,X4),X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat))) = hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(hAPP(c_Lambda_Osubst,X3),X4),X2)),X1)
    | ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
    c_0_1330,
    [final] ).

cnf(c_0_1740,plain,
    ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X3),X4)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X2),X3),X4)))
    | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2)) ),
    c_0_1331,
    [final] ).

cnf(c_0_1741,plain,
    ( c_Type_Otyping(X1,hAPP(hAPP(hAPP(c_Lambda_Osubst,X2),X3),X4),X5)
    | ~ c_Type_Otyping(c_Type_Oshift(X1,X4,X6,tc_Type_Otype),X2,X5)
    | ~ c_Type_Otyping(X1,X3,X6) ),
    c_0_1332,
    [final] ).

cnf(c_0_1742,plain,
    ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X1),X3)),hAPP(hAPP(c_Lambda_OdB_OApp,X2),X4)))
    | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X3),X4)) ),
    c_0_1333,
    [final] ).

cnf(c_0_1743,plain,
    ( hBOOL(hAPP(hAPP(X1,X2),X5))
    | c_ListOrder_Ostep1(X1,X3,X6,X4)
    | ~ c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X2,X3,X4),c_List_Olist_OCons(X5,X6,X4),X4) ),
    c_0_1334,
    [final] ).

cnf(c_0_1744,plain,
    ( X6 = X3
    | c_ListOrder_Ostep1(X1,X3,X6,X4)
    | ~ c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X2,X3,X4),c_List_Olist_OCons(X5,X6,X4),X4) ),
    c_0_1335,
    [final] ).

cnf(c_0_1745,plain,
    ( hBOOL(hAPP(hAPP(X1,X5),X4))
    | ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X2,X3),X4),X5)) ),
    c_0_1336,
    [final] ).

cnf(c_0_1746,plain,
    ( hBOOL(hAPP(hAPP(X1,X5),X4))
    | ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X2,X3),X4),X5)) ),
    c_0_1337,
    [final] ).

cnf(c_0_1747,plain,
    ( c_ListOrder_Ostep1(X1,c_List_Oappend(X2,X3,X4),c_List_Oappend(X5,X3,X4),X4)
    | ~ c_ListOrder_Ostep1(X1,X2,X5,X4) ),
    c_0_1338,
    [final] ).

cnf(c_0_1748,plain,
    ( c_ListOrder_Ostep1(X1,c_List_Oappend(X5,X2,X4),c_List_Oappend(X5,X3,X4),X4)
    | ~ c_ListOrder_Ostep1(X1,X2,X3,X4) ),
    c_0_1339,
    [final] ).

cnf(c_0_1749,plain,
    ( c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X5,X2,X4),c_List_Olist_OCons(X5,X3,X4),X4)
    | ~ c_ListOrder_Ostep1(X1,X2,X3,X4) ),
    c_0_1340,
    [final] ).

cnf(c_0_1750,plain,
    ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X1),X3)),hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2)) ),
    c_0_1341,
    [final] ).

cnf(c_0_1751,plain,
    ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X3),X1)),hAPP(hAPP(c_Lambda_OdB_OApp,X3),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2)) ),
    c_0_1342,
    [final] ).

cnf(c_0_1752,plain,
    ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_Olift,X1),X3)),hAPP(hAPP(c_Lambda_Olift,X2),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2)) ),
    c_0_1343,
    [final] ).

cnf(c_0_1753,plain,
    ( hBOOL(hAPP(hAPP(X1,X2),X5))
    | X5 = X2
    | ~ c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X2,X3,X4),c_List_Olist_OCons(X5,X6,X4),X4) ),
    c_0_1344,
    [final] ).

cnf(c_0_1754,plain,
    ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X5))
    | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X4))
    | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X4),X5)) ),
    c_0_1345,
    [final] ).

cnf(c_0_1755,plain,
    ( X6 = X3
    | X5 = X2
    | ~ c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X2,X3,X4),c_List_Olist_OCons(X5,X6,X4),X4) ),
    c_0_1346,
    [final] ).

cnf(c_0_1756,plain,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X5)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X5))
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    c_0_1347,
    [final] ).

cnf(c_0_1757,plain,
    ( c_Type_Otyping(c_Type_Oshift(X1,X4,X5,tc_Type_Otype),hAPP(hAPP(c_Lambda_Olift,X2),X4),X3)
    | ~ c_Type_Otyping(X1,X2,X3) ),
    c_0_1348,
    [final] ).

cnf(c_0_1758,plain,
    ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X4,X5),X3),X2))
    | ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
    c_0_1349,
    [final] ).

cnf(c_0_1759,plain,
    ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X4,X5),X3),X2))
    | ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
    c_0_1350,
    [final] ).

cnf(c_0_1760,plain,
    ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_Olift,X1),X3)),hAPP(hAPP(c_Lambda_Olift,X2),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2)) ),
    c_0_1351,
    [final] ).

cnf(c_0_1761,plain,
    ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,X3),X1)),hAPP(hAPP(c_Lambda_OdB_OApp,X3),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2)) ),
    c_0_1352,
    [final] ).

cnf(c_0_1762,plain,
    ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,X1),X3)),hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2)) ),
    c_0_1353,
    [final] ).

cnf(c_0_1763,plain,
    ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X4),X2),X5))
    | ~ hBOOL(hAPP(hAPP(X1,X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X4),X3),X5)) ),
    c_0_1354,
    [final] ).

cnf(c_0_1764,plain,
    ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X5))
    | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X4))
    | ~ hBOOL(hAPP(hAPP(X1,X4),X5)) ),
    c_0_1355,
    [final] ).

cnf(c_0_1765,plain,
    ( hAPP(c_Type_Oshift(X3,X2,X4,X5),X1) = hAPP(X3,X1)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    c_0_1356,
    [final] ).

cnf(c_0_1766,plain,
    ( c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X2,X3,X4),c_List_Olist_OCons(X5,X3,X4),X4)
    | ~ hBOOL(hAPP(hAPP(X1,X2),X5)) ),
    c_0_1357,
    [final] ).

cnf(c_0_1767,plain,
    ( c_HOL_Oord__class_Oless(X1,X4,X3)
    | ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X4,X2,X3),X3)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
    | ~ class_Ring__and__Field_Oordered__semidom(X3) ),
    c_0_1358,
    [final] ).

cnf(c_0_1768,plain,
    ( c_HOL_Oord__class_Oless(X3,X4,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
    | ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_1359,
    [final] ).

cnf(c_0_1769,plain,
    ( c_HOL_Oord__class_Oless(X3,X4,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
    | ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_1360,
    [final] ).

cnf(c_0_1770,plain,
    ( c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X4,X2,X3),c_Power_Opower__class_Opower(X4,X1,X3),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
    | ~ c_HOL_Oord__class_Oless(X4,c_HOL_Oone__class_Oone(X3),X3)
    | ~ class_Ring__and__Field_Oordered__semidom(X3) ),
    c_0_1361,
    [final] ).

cnf(c_0_1771,plain,
    ( X1 = X2
    | c_List_Oappend(X1,c_List_Olist_OCons(X3,c_List_Olist_ONil(X4),X4),X4) != c_List_Oappend(X2,c_List_Olist_OCons(X5,c_List_Olist_ONil(X4),X4),X4) ),
    c_0_1362,
    [final] ).

cnf(c_0_1772,plain,
    ( X1 = X2
    | c_List_Oappend(X3,c_List_Olist_OCons(X1,c_List_Olist_ONil(X4),X4),X4) != c_List_Oappend(X5,c_List_Olist_OCons(X2,c_List_Olist_ONil(X4),X4),X4) ),
    c_0_1363,
    [final] ).

cnf(c_0_1773,plain,
    ( c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X4,X3),c_Power_Opower__class_Opower(X2,X4,X3),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
    | ~ class_Ring__and__Field_Oordered__semidom(X3) ),
    c_0_1364,
    [final] ).

cnf(c_0_1774,plain,
    ( c_Orderings_Oord__class_Omax(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4),X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_Orderings_Oord__class_Omax(X2,X3,X1)),X4)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    c_0_1365,
    [final] ).

cnf(c_0_1775,plain,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    c_0_1366,
    [final] ).

cnf(c_0_1776,plain,
    ( c_lessequals(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),X5),X2)
    | ~ c_lessequals(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),X4),X2)
    | ~ c_lessequals(X4,X5,X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
    c_0_1367,
    [final] ).

cnf(c_0_1777,plain,
    ( c_lessequals(X3,X4,X1)
    | ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    c_0_1368,
    [final] ).

cnf(c_0_1778,plain,
    ( c_lessequals(X2,X4,X1)
    | ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3),X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    c_0_1369,
    [final] ).

cnf(c_0_1779,plain,
    ( c_HOL_Oord__class_Oless(X2,X4,X1)
    | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3),X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    c_0_1370,
    [final] ).

cnf(c_0_1780,plain,
    ( c_HOL_Oord__class_Oless(X3,X4,X1)
    | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    c_0_1371,
    [final] ).

cnf(c_0_1781,plain,
    ( X2 = X3
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
    | c_Power_Opower__class_Opower(X2,X4,X1) != c_Power_Opower__class_Opower(X3,X4,X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_1372,
    [final] ).

cnf(c_0_1782,plain,
    ( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),c_Lambda_OdB_OVar(X2)),X3)))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
    c_0_1373,
    [final] ).

cnf(c_0_1783,plain,
    ( c_lessequals(c_Power_Opower__class_Opower(X1,X4,X3),c_Power_Opower__class_Opower(X2,X4,X3),X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
    | ~ class_Ring__and__Field_Oordered__semidom(X3) ),
    c_0_1374,
    [final] ).

cnf(c_0_1784,plain,
    ( c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X4,X1,X3),c_Power_Opower__class_Opower(X4,X2,X3),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X4,X3)
    | ~ class_Ring__and__Field_Oordered__semidom(X3) ),
    c_0_1375,
    [final] ).

cnf(c_0_1785,plain,
    ( c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
    | ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_1376,
    [final] ).

cnf(c_0_1786,plain,
    ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_OdB_OAbs(X1)),c_Lambda_OdB_OAbs(X2)))
    | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2)) ),
    c_0_1377,
    [final] ).

cnf(c_0_1787,plain,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X5),X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X4,X5,X3)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
    c_0_1378,
    [final] ).

cnf(c_0_1788,plain,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X5),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_lessequals(X4,X5,X3)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
    c_0_1379,
    [final] ).

cnf(c_0_1789,plain,
    ( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X5),X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_lessequals(X4,X5,X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3) ),
    c_0_1380,
    [final] ).

cnf(c_0_1790,plain,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X5),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X4,X5,X3)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
    c_0_1381,
    [final] ).

cnf(c_0_1791,plain,
    ( c_Wellfounded_Oaccp(X1,X4,X3)
    | ~ c_Wellfounded_Oaccp(X1,X2,X3)
    | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X3),X4),X2)) ),
    c_0_1382,
    [final] ).

cnf(c_0_1792,plain,
    ( c_Wellfounded_Oaccp(X1,X3,X2)
    | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X4))
    | ~ c_Wellfounded_Oaccp(X1,X4,X2) ),
    c_0_1383,
    [final] ).

cnf(c_0_1793,plain,
    ( c_HOL_Oord__class_Oless(X2,X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),tc_nat) ),
    c_0_1384,
    [final] ).

cnf(c_0_1794,plain,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    c_0_1385,
    [final] ).

cnf(c_0_1795,plain,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    c_0_1386,
    [final] ).

cnf(c_0_1796,plain,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
    | ~ class_OrderedGroup_Oab__semigroup__add(X1) ),
    c_0_1387,
    [final] ).

cnf(c_0_1797,plain,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
    c_0_1388,
    [final] ).

cnf(c_0_1798,plain,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    c_0_1389,
    [final] ).

cnf(c_0_1799,plain,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X4),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat) ),
    c_0_1390,
    [final] ).

cnf(c_0_1800,plain,
    ( X1 = c_List_Olist_ONil(X2)
    | c_List_Omap(X4,X1,X2,X3) != c_List_Olist_ONil(X3) ),
    c_0_1391,
    [final] ).

cnf(c_0_1801,plain,
    ( X1 = c_List_Olist_ONil(X2)
    | c_List_Omap(X3,X1,X2,X4) != c_List_Olist_ONil(X4) ),
    c_0_1392,
    [final] ).

cnf(c_0_1802,plain,
    ( c_Type_Otyping(X3,X2,X4)
    | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2))
    | ~ c_Type_Otyping(X3,X1,X4) ),
    c_0_1393,
    [final] ).

cnf(c_0_1803,plain,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = X4
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X5),X3)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X5),X4)
    | ~ class_OrderedGroup_Oab__group__add(X1) ),
    c_0_1394,
    [final] ).

cnf(c_0_1804,plain,
    ( c_lessequals(X1,X2,X4)
    | c_lessequals(X1,X3,X4)
    | ~ c_lessequals(X1,c_Orderings_Oord__class_Omax(X2,X3,X4),X4)
    | ~ class_Orderings_Olinorder(X4) ),
    c_0_1395,
    [final] ).

cnf(c_0_1805,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,X4)
    | c_HOL_Oord__class_Oless(X1,X3,X4)
    | ~ c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X2,X3,X4),X4)
    | ~ class_Orderings_Olinorder(X4) ),
    c_0_1396,
    [final] ).

cnf(c_0_1806,plain,
    ( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X3),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
    c_0_1397,
    [final] ).

cnf(c_0_1807,plain,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
    c_0_1398,
    [final] ).

cnf(c_0_1808,plain,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X3),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
    c_0_1399,
    [final] ).

cnf(c_0_1809,plain,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X3),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
    c_0_1400,
    [final] ).

cnf(c_0_1810,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
    c_0_1401,
    [final] ).

cnf(c_0_1811,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
    c_0_1402,
    [final] ).

cnf(c_0_1812,plain,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X3),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
    c_0_1403,
    [final] ).

cnf(c_0_1813,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
    c_0_1404,
    [final] ).

cnf(c_0_1814,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_1405,
    [final] ).

cnf(c_0_1815,plain,
    ( c_lessequals(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X2),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_lessequals(X3,X4,X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    c_0_1406,
    [final] ).

cnf(c_0_1816,plain,
    ( c_lessequals(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_lessequals(X3,X4,X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    c_0_1407,
    [final] ).

cnf(c_0_1817,plain,
    ( c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_lessequals(X3,X4,X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    c_0_1408,
    [final] ).

cnf(c_0_1818,plain,
    ( c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_HOL_Oord__class_Oless(X3,X4,X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    c_0_1409,
    [final] ).

cnf(c_0_1819,plain,
    ( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2),X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3) ),
    c_0_1410,
    [final] ).

cnf(c_0_1820,plain,
    ( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4),X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3) ),
    c_0_1411,
    [final] ).

cnf(c_0_1821,plain,
    ( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2),X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
    c_0_1412,
    [final] ).

cnf(c_0_1822,plain,
    ( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4),X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
    c_0_1413,
    [final] ).

cnf(c_0_1823,plain,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
    c_0_1414,
    [final] ).

cnf(c_0_1824,plain,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
    c_0_1415,
    [final] ).

cnf(c_0_1825,plain,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
    c_0_1416,
    [final] ).

cnf(c_0_1826,plain,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
    c_0_1417,
    [final] ).

cnf(c_0_1827,plain,
    ( c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_HOL_Oord__class_Oless(X3,X4,X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_1418,
    [final] ).

cnf(c_0_1828,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),tc_nat) ),
    c_0_1419,
    [final] ).

cnf(c_0_1829,plain,
    ( c_lessequals(c_Orderings_Oord__class_Omax(X1,X4,X3),X2,X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_lessequals(X4,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_1420,
    [final] ).

cnf(c_0_1830,plain,
    ( c_lessequals(c_Orderings_Oord__class_Omax(X1,X4,X3),X2,X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_lessequals(X4,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_1421,
    [final] ).

cnf(c_0_1831,plain,
    ( c_lessequals(c_Orderings_Oord__class_Omax(X1,X4,X3),X2,X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_lessequals(X4,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_1422,
    [final] ).

cnf(c_0_1832,plain,
    ( c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X1,X4,X3),X2,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X4,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_1423,
    [final] ).

cnf(c_0_1833,plain,
    ( hAPP(hAPP(X1,hAPP(hAPP(X1,X3),X4)),X5) = hAPP(hAPP(X1,X3),hAPP(hAPP(X1,X4),X5))
    | ~ c_OrderedGroup_Osemigroup__add(X1,X2) ),
    c_0_1424,
    [final] ).

cnf(c_0_1834,plain,
    ( c_List_Olistsp(X1,c_List_Oappend(X2,X4,X3),X3)
    | ~ c_List_Olistsp(X1,X2,X3)
    | ~ c_List_Olistsp(X1,X4,X3) ),
    c_0_1425,
    [final] ).

cnf(c_0_1835,plain,
    ( c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3) = c_Orderings_Oord__class_Omax(X1,c_Orderings_Oord__class_Omax(X2,X4,X3),X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_1426,
    [final] ).

cnf(c_0_1836,plain,
    ( c_Orderings_Oord__class_Omax(X1,c_Orderings_Oord__class_Omax(X2,X3,X4),X4) = c_Orderings_Oord__class_Omax(X2,c_Orderings_Oord__class_Omax(X1,X3,X4),X4)
    | ~ class_Orderings_Olinorder(X4) ),
    c_0_1427,
    [final] ).

cnf(c_0_1837,plain,
    ( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
    c_0_1428,
    [final] ).

cnf(c_0_1838,plain,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
    c_0_1429,
    [final] ).

cnf(c_0_1839,plain,
    ( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
    c_0_1430,
    [final] ).

cnf(c_0_1840,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
    c_0_1431,
    [final] ).

cnf(c_0_1841,plain,
    ( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_1432,
    [final] ).

cnf(c_0_1842,plain,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    c_0_1433,
    [final] ).

cnf(c_0_1843,plain,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    c_0_1434,
    [final] ).

cnf(c_0_1844,plain,
    ( c_lessequals(X1,X4,X3)
    | ~ c_lessequals(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_1435,
    [final] ).

cnf(c_0_1845,plain,
    ( c_lessequals(X2,X4,X3)
    | ~ c_lessequals(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_1436,
    [final] ).

cnf(c_0_1846,plain,
    ( c_lessequals(X1,X4,X3)
    | ~ c_lessequals(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_1437,
    [final] ).

cnf(c_0_1847,plain,
    ( c_lessequals(X2,X4,X3)
    | ~ c_lessequals(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_1438,
    [final] ).

cnf(c_0_1848,plain,
    ( c_HOL_Oord__class_Oless(X2,X4,X3)
    | ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_1439,
    [final] ).

cnf(c_0_1849,plain,
    ( c_HOL_Oord__class_Oless(X1,X4,X3)
    | ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_1440,
    [final] ).

cnf(c_0_1850,plain,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4))
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    c_0_1441,
    [final] ).

cnf(c_0_1851,plain,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4))
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
    c_0_1442,
    [final] ).

cnf(c_0_1852,plain,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4))
    | ~ class_OrderedGroup_Oab__group__add(X1) ),
    c_0_1443,
    [final] ).

cnf(c_0_1853,plain,
    ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X4),X2),X3))
    | ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
    c_0_1444,
    [final] ).

cnf(c_0_1854,plain,
    ( c_List_Olistsp(X1,X2,X4)
    | ~ c_List_Olistsp(X1,c_List_Oappend(X2,X3,X4),X4) ),
    c_0_1445,
    [final] ).

cnf(c_0_1855,plain,
    ( c_List_Olistsp(X1,X3,X4)
    | ~ c_List_Olistsp(X1,c_List_Oappend(X2,X3,X4),X4) ),
    c_0_1446,
    [final] ).

cnf(c_0_1856,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(X2)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X1,X2)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X3) != c_HOL_Ozero__class_Ozero(X2)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
    c_0_1447,
    [final] ).

cnf(c_0_1857,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(X2)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X1,X2)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),X1) != c_HOL_Ozero__class_Ozero(X2)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
    c_0_1448,
    [final] ).

cnf(c_0_1858,plain,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1)) = c_HOL_Ozero__class_Ozero(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
    c_0_1449,
    [final] ).

cnf(c_0_1859,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X4) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2) ),
    c_0_1450,
    [final] ).

cnf(c_0_1860,plain,
    ( c_HOL_Oord__class_Oless(X1,X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X3,tc_nat) ),
    c_0_1451,
    [final] ).

cnf(c_0_1861,plain,
    ( X1 = X2
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X4,X3)
    | c_Power_Opower__class_Opower(X4,X1,X3) != c_Power_Opower__class_Opower(X4,X2,X3)
    | ~ class_Ring__and__Field_Oordered__semidom(X3) ),
    c_0_1452,
    [final] ).

cnf(c_0_1862,plain,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_1453,
    [final] ).

cnf(c_0_1863,plain,
    ( c_lessequals(c_HOL_Oone__class_Oone(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
    | ~ c_lessequals(c_HOL_Oone__class_Oone(X1),X2,X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_1454,
    [final] ).

cnf(c_0_1864,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_1455,
    [final] ).

cnf(c_0_1865,plain,
    ( c_Wellfounded_Oaccp(X1,X4,X3)
    | ~ c_Wellfounded_Oaccp(X1,X2,X3)
    | ~ hBOOL(hAPP(hAPP(X1,X4),X2)) ),
    c_0_1456,
    [final] ).

cnf(c_0_1866,plain,
    ( c_Wellfounded_Oaccp(X1,X4,X3)
    | ~ c_Wellfounded_Oaccp(X1,X2,X3)
    | ~ hBOOL(hAPP(hAPP(X1,X4),X2)) ),
    c_0_1457,
    [final] ).

cnf(c_0_1867,plain,
    ( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X1),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
    c_0_1458,
    [final] ).

cnf(c_0_1868,plain,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
    c_0_1459,
    [final] ).

cnf(c_0_1869,plain,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X1),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
    c_0_1460,
    [final] ).

cnf(c_0_1870,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
    c_0_1461,
    [final] ).

cnf(c_0_1871,plain,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X1),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2) ),
    c_0_1462,
    [final] ).

cnf(c_0_1872,plain,
    ( hBOOL(hAPP(c_InductTermi_OIT,X1))
    | ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X1,tc_Lambda_OdB) ),
    c_0_1463,
    [final] ).

cnf(c_0_1873,plain,
    ( c_Type_Otyping(X1,X4,X3)
    | ~ c_Type_Otyping(X1,X2,X3)
    | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X2),X4)) ),
    c_0_1464,
    [final] ).

cnf(c_0_1874,plain,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_List_Olistsum(X1,X3)),c_List_Olistsum(X2,X3)) = c_List_Olistsum(c_List_Oappend(X1,X2,X3),X3)
    | ~ class_OrderedGroup_Omonoid__add(X3) ),
    c_0_1465,
    [final] ).

cnf(c_0_1875,plain,
    ( c_lessequals(X1,c_Orderings_Oord__class_Omax(X2,X4,X3),X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_1466,
    [final] ).

cnf(c_0_1876,plain,
    ( c_lessequals(X1,c_Orderings_Oord__class_Omax(X4,X2,X3),X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_1467,
    [final] ).

cnf(c_0_1877,plain,
    ( c_lessequals(X1,c_Orderings_Oord__class_Omax(X2,X4,X3),X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_1468,
    [final] ).

cnf(c_0_1878,plain,
    ( c_lessequals(X1,c_Orderings_Oord__class_Omax(X4,X2,X3),X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_1469,
    [final] ).

cnf(c_0_1879,plain,
    ( c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X4,X2,X3),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_1470,
    [final] ).

cnf(c_0_1880,plain,
    ( c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X2,X4,X3),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_1471,
    [final] ).

cnf(c_0_1881,plain,
    ( c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X4,X2,X3),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_1472,
    [final] ).

cnf(c_0_1882,plain,
    ( c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X2,X4,X3),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_1473,
    [final] ).

cnf(c_0_1883,plain,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_Nat_Osemiring__1__class_Oof__nat(X1,X3)),c_Nat_Osemiring__1__class_Oof__nat(X2,X3)) = c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X3)
    | ~ class_Ring__and__Field_Osemiring__1(X3) ),
    c_0_1474,
    [final] ).

cnf(c_0_1884,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    c_0_1475,
    [final] ).

cnf(c_0_1885,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    c_0_1476,
    [final] ).

cnf(c_0_1886,plain,
    ( c_HOL_Oord__class_Oless(X1,X4,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_lessequals(X2,X4,X3)
    | ~ class_Orderings_Opreorder(X3) ),
    c_0_1477,
    [final] ).

cnf(c_0_1887,plain,
    ( c_HOL_Oord__class_Oless(X1,X4,X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X2,X4,X3)
    | ~ class_Orderings_Opreorder(X3) ),
    c_0_1478,
    [final] ).

cnf(c_0_1888,plain,
    ( c_lessequals(X1,X4,X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_lessequals(X2,X4,X3)
    | ~ class_Orderings_Opreorder(X3) ),
    c_0_1479,
    [final] ).

cnf(c_0_1889,plain,
    ( c_HOL_Oord__class_Oless(X4,X2,X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X4,X1,X3)
    | ~ class_Orderings_Oorder(X3) ),
    c_0_1480,
    [final] ).

cnf(c_0_1890,plain,
    ( c_HOL_Oord__class_Oless(X4,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_lessequals(X4,X1,X3)
    | ~ class_Orderings_Oorder(X3) ),
    c_0_1481,
    [final] ).

cnf(c_0_1891,plain,
    ( c_lessequals(X4,X2,X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_lessequals(X4,X1,X3)
    | ~ class_Orderings_Oorder(X3) ),
    c_0_1482,
    [final] ).

cnf(c_0_1892,plain,
    ( c_HOL_Oord__class_Oless(X4,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X4,X1,X3)
    | ~ class_Orderings_Oorder(X3) ),
    c_0_1483,
    [final] ).

cnf(c_0_1893,plain,
    ( c_HOL_Oord__class_Oless(X1,X4,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X2,X4,X3)
    | ~ class_Orderings_Opreorder(X3) ),
    c_0_1484,
    [final] ).

cnf(c_0_1894,plain,
    ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OAbs(X1)),c_Lambda_OdB_OAbs(X2)))
    | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2)) ),
    c_0_1485,
    [final] ).

cnf(c_0_1895,plain,
    ( c_HOL_Oord__class_Oless(X1,X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_Nat_Osemiring__1__class_Oof__nat(X3,X2),X2)
    | ~ class_Ring__and__Field_Oordered__semidom(X2) ),
    c_0_1486,
    [final] ).

cnf(c_0_1896,plain,
    ( c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    c_0_1487,
    [final] ).

cnf(c_0_1897,plain,
    ( c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    c_0_1488,
    [final] ).

cnf(c_0_1898,plain,
    ( c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    c_0_1489,
    [final] ).

cnf(c_0_1899,plain,
    ( c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    c_0_1490,
    [final] ).

cnf(c_0_1900,plain,
    ( c_Orderings_Oord__class_Omax(X1,c_Orderings_Oord__class_Omax(X1,X2,X3),X3) = c_Orderings_Oord__class_Omax(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_1491,
    [final] ).

cnf(c_0_1901,plain,
    ( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_Olift,X1),X2)))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
    c_0_1492,
    [final] ).

cnf(c_0_1902,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_Lambda_Oliftn(X3,c_Lambda_OdB_OVar(X1),X2) = c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3)) ),
    c_0_1493,
    [final] ).

cnf(c_0_1903,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Oone__class_Oone(X1)),c_HOL_Oone__class_Oone(X1)),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_1494,
    [final] ).

cnf(c_0_1904,plain,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),c_List_Olistsum(X2,X3)) = c_List_Olistsum(c_List_Olist_OCons(X1,X2,X3),X3)
    | ~ class_OrderedGroup_Omonoid__add(X3) ),
    c_0_1495,
    [final] ).

cnf(c_0_1905,plain,
    ( c_lessequals(X2,X1,X3)
    | c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Opreorder(X3) ),
    c_0_1496,
    [final] ).

cnf(c_0_1906,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(X1)),X2) = c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat))) ),
    c_0_1497,
    [final] ).

cnf(c_0_1907,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_1498,
    [final] ).

cnf(c_0_1908,plain,
    ( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X1)),X3),X2) = c_Lambda_OdB_OVar(X1)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    c_0_1499,
    [final] ).

cnf(c_0_1909,plain,
    ( c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X3),c_Nat_Osemiring__1__class_Oof__nat(X2,X3),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ class_Ring__and__Field_Oordered__semidom(X3) ),
    c_0_1500,
    [final] ).

cnf(c_0_1910,plain,
    ( c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X1,tc_Lambda_OdB)
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
    c_0_1501,
    [final] ).

cnf(c_0_1911,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | X1 = X2
    | c_HOL_Oord__class_Oless(X2,X1,tc_nat)
    | hBOOL(hAPP(hAPP(X3,X2),X1)) ),
    c_0_1502,
    [final] ).

cnf(c_0_1912,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_Nat_Osemiring__1__class_Oof__nat(X1,X2),X2)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | ~ class_Ring__and__Field_Oordered__semidom(X2) ),
    c_0_1503,
    [final] ).

cnf(c_0_1913,plain,
    ( X2 = X1
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_lessequals(X2,X1,X3)
    | ~ class_Orderings_Oorder(X3) ),
    c_0_1504,
    [final] ).

cnf(c_0_1914,plain,
    ( X1 = X2
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_lessequals(X2,X1,X3)
    | ~ class_Orderings_Oorder(X3) ),
    c_0_1505,
    [final] ).

cnf(c_0_1915,plain,
    ( X1 = X2
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_lessequals(X2,X1,X3)
    | ~ class_Orderings_Oorder(X3) ),
    c_0_1506,
    [final] ).

cnf(c_0_1916,plain,
    ( X1 = X2
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2)
    | ~ class_Int_Onumber__ring(X3)
    | ~ class_Ring__and__Field_Oidom(X3) ),
    c_0_1507,
    [final] ).

cnf(c_0_1917,plain,
    ( c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB)
    | hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X1)))
    | hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__5(X1)))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
    c_0_1508,
    [final] ).

cnf(c_0_1918,plain,
    ( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
    | ~ c_lessequals(X1,X1,X2)
    | ~ class_Orderings_Olinorder(X2) ),
    c_0_1509,
    [final] ).

cnf(c_0_1919,plain,
    ( ~ c_lessequals(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X2,X1,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_1510,
    [final] ).

cnf(c_0_1920,plain,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_lessequals(X2,X1,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_1511,
    [final] ).

cnf(c_0_1921,plain,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_lessequals(X2,X1,X3)
    | ~ class_Orderings_Opreorder(X3) ),
    c_0_1512,
    [final] ).

cnf(c_0_1922,plain,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X2,X1,X3)
    | ~ class_Orderings_Oorder(X3) ),
    c_0_1513,
    [final] ).

cnf(c_0_1923,plain,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X2,X1,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_1514,
    [final] ).

cnf(c_0_1924,plain,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X2,X1,X3)
    | ~ class_Orderings_Opreorder(X3) ),
    c_0_1515,
    [final] ).

cnf(c_0_1925,plain,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X2,X1,X3)
    | ~ class_Orderings_Opreorder(X3) ),
    c_0_1516,
    [final] ).

cnf(c_0_1926,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X2 = X3
    | c_List_Oreplicate(X1,X2,X4) != c_List_Oreplicate(X5,X3,X4) ),
    c_0_1517,
    [final] ).

cnf(c_0_1927,plain,
    ( c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),c_HOL_Oone__class_Oone(X2)),X2)
    | ~ class_Ring__and__Field_Oordered__semidom(X2) ),
    c_0_1518,
    [final] ).

cnf(c_0_1928,plain,
    ( X1 = X2
    | c_List_Oreplicate(X1,X3,X4) != c_List_Oreplicate(X2,X5,X4) ),
    c_0_1519,
    [final] ).

cnf(c_0_1929,plain,
    ( X1 = X2
    | c_List_Oappend(X1,X3,X4) != c_List_Oappend(X2,X3,X4) ),
    c_0_1520,
    [final] ).

cnf(c_0_1930,plain,
    ( X1 = X2
    | c_List_Oappend(X3,X1,X4) != c_List_Oappend(X3,X2,X4) ),
    c_0_1521,
    [final] ).

cnf(c_0_1931,plain,
    ( X1 = X2
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2)
    | ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X3) ),
    c_0_1522,
    [final] ).

cnf(c_0_1932,plain,
    ( X1 = X2
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2)
    | ~ class_OrderedGroup_Ocancel__semigroup__add(X3) ),
    c_0_1523,
    [final] ).

cnf(c_0_1933,plain,
    ( X1 = X2
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4)
    | ~ class_OrderedGroup_Ocancel__semigroup__add(X3) ),
    c_0_1524,
    [final] ).

cnf(c_0_1934,plain,
    ( X1 = X2
    | c_List_Olist_OCons(X1,X3,X4) != c_List_Olist_OCons(X2,X5,X4) ),
    c_0_1525,
    [final] ).

cnf(c_0_1935,plain,
    ( X1 = X2
    | c_List_Olist_OCons(X3,X1,X4) != c_List_Olist_OCons(X5,X2,X4) ),
    c_0_1526,
    [final] ).

cnf(c_0_1936,plain,
    ( c_Lambda_Osubstn(c_Lambda_OdB_OVar(X1),X2,X1) = c_Lambda_Oliftn(X1,X2,c_HOL_Ozero__class_Ozero(tc_nat))
    | c_HOL_Oord__class_Oless(X1,X1,tc_nat) ),
    c_0_1527,
    [final] ).

cnf(c_0_1937,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | X2 = X1
    | hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X2)),X3),X1) = c_Lambda_OdB_OVar(X2) ),
    c_0_1528,
    [final] ).

cnf(c_0_1938,plain,
    ( X2 = X3
    | ~ hBOOL(hAPP(hAPP(c_fequal(X1),X2),X3)) ),
    c_0_1529,
    [final] ).

cnf(c_0_1939,plain,
    ( c_lessequals(X1,c_Orderings_Oord__class_Omax(X2,X1,X3),X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_1530,
    [final] ).

cnf(c_0_1940,plain,
    ( c_lessequals(X1,c_Orderings_Oord__class_Omax(X1,X2,X3),X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_1531,
    [final] ).

cnf(c_0_1941,plain,
    ( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X1)),X2),X1) = X2
    | c_HOL_Oord__class_Oless(X1,X1,tc_nat) ),
    c_0_1532,
    [final] ).

cnf(c_0_1942,plain,
    ( c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB)
    | c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X1)) = X1
    | hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__5(X1)))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
    c_0_1533,
    [final] ).

cnf(c_0_1943,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,X3)
    | X1 = X2
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_1534,
    [final] ).

cnf(c_0_1944,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,X3)
    | X1 = X2
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_1535,
    [final] ).

cnf(c_0_1945,plain,
    ( X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Oorder(X3) ),
    c_0_1536,
    [final] ).

cnf(c_0_1946,plain,
    ( X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Oorder(X3) ),
    c_0_1537,
    [final] ).

cnf(c_0_1947,plain,
    ( X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Oorder(X3) ),
    c_0_1538,
    [final] ).

cnf(c_0_1948,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,X3)
    | X1 = X2
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Oorder(X3) ),
    c_0_1539,
    [final] ).

cnf(c_0_1949,plain,
    ( X1 = X2
    | c_HOL_Oord__class_Oless(X2,X1,X3)
    | ~ c_lessequals(X2,X1,X3)
    | ~ class_Orderings_Oorder(X3) ),
    c_0_1540,
    [final] ).

cnf(c_0_1950,plain,
    ( X2 = X1
    | c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Oorder(X3) ),
    c_0_1541,
    [final] ).

cnf(c_0_1951,plain,
    ( c_lessequals(X1,X2,X3)
    | c_Orderings_Oord__class_Omax(X1,X2,X3) != X2
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_1542,
    [final] ).

cnf(c_0_1952,plain,
    ( c_Orderings_Oord__class_Omax(X1,X2,X3) = X2
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_1543,
    [final] ).

cnf(c_0_1953,plain,
    ( c_Orderings_Oord__class_Omax(X2,X1,X3) = X2
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_1544,
    [final] ).

cnf(c_0_1954,plain,
    ( c_Lambda_Oliftn(X3,c_Lambda_OdB_OVar(X1),X2) = c_Lambda_OdB_OVar(X1)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    c_0_1545,
    [final] ).

cnf(c_0_1955,plain,
    ( c_lessequals(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ class_Orderings_Opreorder(X3) ),
    c_0_1546,
    [final] ).

cnf(c_0_1956,plain,
    ( c_lessequals(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ class_Orderings_Oorder(X3) ),
    c_0_1547,
    [final] ).

cnf(c_0_1957,plain,
    ( X1 = X2
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3) ),
    c_0_1548,
    [final] ).

cnf(c_0_1958,plain,
    ( X1 = X2
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2) ),
    c_0_1549,
    [final] ).

cnf(c_0_1959,plain,
    ( X1 = X2
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2) ),
    c_0_1550,
    [final] ).

cnf(c_0_1960,plain,
    ( ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_Ring__and__Field_Oordered__semidom(X2) ),
    c_0_1551,
    [final] ).

cnf(c_0_1961,plain,
    ( hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(X1)),X2) = c_Lambda_OdB_OVar(X1)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    c_0_1552,
    [final] ).

cnf(c_0_1962,plain,
    ( hAPP(hAPP(X2,X4),X1) = X4
    | ~ c_OrderedGroup_Omonoid__add(X1,X2,X3) ),
    c_0_1553,
    [final] ).

cnf(c_0_1963,plain,
    ( hAPP(hAPP(X2,X1),X4) = X4
    | ~ c_OrderedGroup_Omonoid__add(X1,X2,X3) ),
    c_0_1554,
    [final] ).

cnf(c_0_1964,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(X2)
    | c_Power_Opower__class_Opower(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
    | ~ class_Power_Opower(X2)
    | ~ class_Ring__and__Field_Omult__zero(X2)
    | ~ class_Ring__and__Field_Ono__zero__divisors(X2)
    | ~ class_Ring__and__Field_Ozero__neq__one(X2) ),
    c_0_1555,
    [final] ).

cnf(c_0_1965,plain,
    ( c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X2) != c_HOL_Ozero__class_Ozero(X2)
    | ~ class_Power_Opower(X2)
    | ~ class_Ring__and__Field_Omult__zero(X2)
    | ~ class_Ring__and__Field_Ono__zero__divisors(X2)
    | ~ class_Ring__and__Field_Ozero__neq__one(X2) ),
    c_0_1556,
    [final] ).

cnf(c_0_1966,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | X2 = X1
    | c_Lambda_Osubstn(c_Lambda_OdB_OVar(X2),X3,X1) = c_Lambda_OdB_OVar(X2) ),
    c_0_1557,
    [final] ).

cnf(c_0_1967,plain,
    ( X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X2,X1,X3)
    | ~ class_Ring__and__Field_Oordered__idom(X3) ),
    c_0_1558,
    [final] ).

cnf(c_0_1968,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X2,X1,X3)
    | X1 = X2
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_1559,
    [final] ).

cnf(c_0_1969,plain,
    ( X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X2,X1,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_1560,
    [final] ).

cnf(c_0_1970,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,X3)
    | X1 = X2
    | c_HOL_Oord__class_Oless(X2,X1,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_1561,
    [final] ).

cnf(c_0_1971,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X2,X1,X3)
    | X2 = X1
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_1562,
    [final] ).

cnf(c_0_1972,plain,
    ( X1 = X2
    | hAPP(hAPP(c_Lambda_OdB_OApp,X1),X3) != hAPP(hAPP(c_Lambda_OdB_OApp,X2),X4) ),
    c_0_1563,
    [final] ).

cnf(c_0_1973,plain,
    ( X1 = X2
    | hAPP(hAPP(c_Lambda_OdB_OApp,X3),X1) != hAPP(hAPP(c_Lambda_OdB_OApp,X4),X2) ),
    c_0_1564,
    [final] ).

cnf(c_0_1974,plain,
    ( c_lessequals(X1,X2,X3)
    | c_lessequals(X2,X1,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_1565,
    [final] ).

cnf(c_0_1975,plain,
    ( c_lessequals(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X2,X1,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_1566,
    [final] ).

cnf(c_0_1976,plain,
    ( c_lessequals(X1,X1,X2)
    | c_HOL_Oord__class_Oless(X1,X1,X2)
    | ~ class_Orderings_Olinorder(X2) ),
    c_0_1567,
    [final] ).

cnf(c_0_1977,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_lessequals(X2,X1,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_1568,
    [final] ).

cnf(c_0_1978,plain,
    ( c_lessequals(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X2,X1,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_1569,
    [final] ).

cnf(c_0_1979,plain,
    ( c_Orderings_Oord__class_Omax(X1,X2,X3) = c_Orderings_Oord__class_Omax(X2,X1,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_1570,
    [final] ).

cnf(c_0_1980,plain,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_1571,
    [final] ).

cnf(c_0_1981,plain,
    ( ~ c_lessequals(c_HOL_Oone__class_Oone(X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_1572,
    [final] ).

cnf(c_0_1982,plain,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X2)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    c_0_1573,
    [final] ).

cnf(c_0_1983,plain,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X2)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
    c_0_1574,
    [final] ).

cnf(c_0_1984,plain,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X2)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    c_0_1575,
    [final] ).

cnf(c_0_1985,plain,
    ( hAPP(X1,X2) = X3
    | ~ c_Type_Otyping(X1,c_Lambda_OdB_OVar(X2),X3) ),
    c_0_1576,
    [final] ).

cnf(c_0_1986,plain,
    ( X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
    c_0_1577,
    [final] ).

cnf(c_0_1987,plain,
    ( X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
    c_0_1578,
    [final] ).

cnf(c_0_1988,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(X2)
    | c_Power_Opower__class_Opower(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
    | ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X2) ),
    c_0_1579,
    [final] ).

cnf(c_0_1989,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(X2)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),X1) != X3
    | ~ class_Int_Onumber__ring(X2)
    | ~ class_Ring__and__Field_Oidom(X2) ),
    c_0_1580,
    [final] ).

cnf(c_0_1990,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(X2)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X1) != c_HOL_Ozero__class_Ozero(X2)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
    c_0_1581,
    [final] ).

cnf(c_0_1991,plain,
    ( X1 = c_List_Olist_ONil(X2)
    | c_List_Oappend(X1,X3,X2) != c_List_Olist_ONil(X2) ),
    c_0_1582,
    [final] ).

cnf(c_0_1992,plain,
    ( X1 = c_List_Olist_ONil(X2)
    | c_List_Oappend(X3,X1,X2) != c_List_Olist_ONil(X2) ),
    c_0_1583,
    [final] ).

cnf(c_0_1993,plain,
    ( X1 = c_List_Olist_ONil(X2)
    | c_List_Oappend(X1,X3,X2) != c_List_Olist_ONil(X2) ),
    c_0_1584,
    [final] ).

cnf(c_0_1994,plain,
    ( X1 = c_List_Olist_ONil(X2)
    | c_List_Oappend(X3,X1,X2) != c_List_Olist_ONil(X2) ),
    c_0_1585,
    [final] ).

cnf(c_0_1995,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X2),X1,X2) = c_HOL_Ozero__class_Ozero(X2)
    | ~ class_Power_Opower(X2)
    | ~ class_Ring__and__Field_Omult__zero(X2)
    | ~ class_Ring__and__Field_Ono__zero__divisors(X2)
    | ~ class_Ring__and__Field_Ozero__neq__one(X2) ),
    c_0_1586,
    [final] ).

cnf(c_0_1996,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_List_Oreplicate(X1,X2,X3) != c_List_Olist_ONil(X3) ),
    c_0_1587,
    [final] ).

cnf(c_0_1997,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_List_Oreplicate(X1,X3,X2) != c_List_Olist_ONil(X2) ),
    c_0_1588,
    [final] ).

cnf(c_0_1998,plain,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_1589,
    [final] ).

cnf(c_0_1999,plain,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_1590,
    [final] ).

cnf(c_0_2000,plain,
    ( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
    | ~ class_Orderings_Oorder(X2) ),
    c_0_1591,
    [final] ).

cnf(c_0_2001,plain,
    ( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
    | ~ class_Orderings_Olinorder(X2) ),
    c_0_1592,
    [final] ).

cnf(c_0_2002,plain,
    ( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
    | ~ class_Orderings_Opreorder(X2) ),
    c_0_1593,
    [final] ).

cnf(c_0_2003,plain,
    ( X1 = c_List_Olist_ONil(X2)
    | c_List_Oappend(X3,X1,X2) != X3 ),
    c_0_1594,
    [final] ).

cnf(c_0_2004,plain,
    ( X1 = c_List_Olist_ONil(X2)
    | c_List_Oappend(X3,X1,X2) != X3 ),
    c_0_1595,
    [final] ).

cnf(c_0_2005,plain,
    ( X1 = c_List_Olist_ONil(X2)
    | c_List_Oappend(X1,X3,X2) != X3 ),
    c_0_1596,
    [final] ).

cnf(c_0_2006,plain,
    ( X1 = c_List_Olist_ONil(X2)
    | c_List_Oappend(X1,X3,X2) != X3 ),
    c_0_1597,
    [final] ).

cnf(c_0_2007,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X2),X1,X2) = c_HOL_Ozero__class_Ozero(X2)
    | ~ class_Power_Opower(X2)
    | ~ class_Ring__and__Field_Osemiring__0(X2) ),
    c_0_1598,
    [final] ).

cnf(c_0_2008,plain,
    ( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(X1)))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
    c_0_1599,
    [final] ).

cnf(c_0_2009,plain,
    ( c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(tc_nat),X1) = c_HOL_Oone__class_Oone(X1)
    | ~ class_Power_Opower(X1)
    | ~ class_Ring__and__Field_Osemiring__0(X1) ),
    c_0_1600,
    [final] ).

cnf(c_0_2010,plain,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1)) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
    c_0_1601,
    [final] ).

cnf(c_0_2011,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != c_HOL_Ozero__class_Ozero(tc_nat) ),
    c_0_1602,
    [final] ).

cnf(c_0_2012,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_HOL_Ozero__class_Ozero(tc_nat) ),
    c_0_1603,
    [final] ).

cnf(c_0_2013,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != X2 ),
    c_0_1604,
    [final] ).

cnf(c_0_2014,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != X2 ),
    c_0_1605,
    [final] ).

cnf(c_0_2015,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oone__class_Oone(X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_1606,
    [final] ).

cnf(c_0_2016,plain,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oone__class_Oone(X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_1607,
    [final] ).

cnf(c_0_2017,plain,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),c_HOL_Ozero__class_Ozero(X2)) = X1
    | ~ class_Int_Onumber__ring(X2)
    | ~ class_Ring__and__Field_Oidom(X2) ),
    c_0_1608,
    [final] ).

cnf(c_0_2018,plain,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    c_0_1609,
    [final] ).

cnf(c_0_2019,plain,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
    c_0_1610,
    [final] ).

cnf(c_0_2020,plain,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
    | ~ class_OrderedGroup_Omonoid__add(X1) ),
    c_0_1611,
    [final] ).

cnf(c_0_2021,plain,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    c_0_1612,
    [final] ).

cnf(c_0_2022,plain,
    ( c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X1),X2,X1) = c_HOL_Oone__class_Oone(X1)
    | ~ class_OrderedGroup_Omonoid__mult(X1) ),
    c_0_1613,
    [final] ).

cnf(c_0_2023,plain,
    ( c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X2) = c_HOL_Oone__class_Oone(X2)
    | ~ class_Power_Opower(X2) ),
    c_0_1614,
    [final] ).

cnf(c_0_2024,plain,
    ( c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X2) = c_HOL_Oone__class_Oone(X2)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ),
    c_0_1615,
    [final] ).

cnf(c_0_2025,plain,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = X2
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
    c_0_1616,
    [final] ).

cnf(c_0_2026,plain,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = X2
    | ~ class_OrderedGroup_Omonoid__add(X1) ),
    c_0_1617,
    [final] ).

cnf(c_0_2027,plain,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = X2
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    c_0_1618,
    [final] ).

cnf(c_0_2028,plain,
    ( c_Power_Opower__class_Opower(X1,c_HOL_Oone__class_Oone(tc_nat),X2) = X1
    | ~ class_OrderedGroup_Omonoid__mult(X2) ),
    c_0_1619,
    [final] ).

cnf(c_0_2029,plain,
    ( c_Power_Opower__class_Opower(X1,c_HOL_Oone__class_Oone(tc_nat),X2) = X1
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ),
    c_0_1620,
    [final] ).

cnf(c_0_2030,plain,
    ( c_Orderings_Oord__class_Omax(X1,X1,X2) = X1
    | ~ class_Orderings_Olinorder(X2) ),
    c_0_1621,
    [final] ).

cnf(c_0_2031,plain,
    ( c_lessequals(X1,X1,X2)
    | ~ class_Orderings_Opreorder(X2) ),
    c_0_1622,
    [final] ).

cnf(c_0_2032,plain,
    ( c_lessequals(X1,X1,X2)
    | ~ class_Orderings_Oorder(X2) ),
    c_0_1623,
    [final] ).

cnf(c_0_2033,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    c_0_1624,
    [final] ).

cnf(c_0_2034,plain,
    ( X1 = X2
    | c_Nat_Osemiring__1__class_Oof__nat(X1,X3) != c_Nat_Osemiring__1__class_Oof__nat(X2,X3)
    | ~ class_Nat_Osemiring__char__0(X3) ),
    c_0_1625,
    [final] ).

cnf(c_0_2035,plain,
    ( class_Orderings_Opreorder(tc_fun(X2,X1))
    | ~ class_Orderings_Opreorder(X1) ),
    c_0_1626,
    [final] ).

cnf(c_0_2036,plain,
    ( class_Orderings_Oorder(tc_fun(X2,X1))
    | ~ class_Orderings_Oorder(X1) ),
    c_0_1627,
    [final] ).

cnf(c_0_2037,plain,
    ( c_List_Olistsum(c_List_Olist_ONil(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_OrderedGroup_Omonoid__add(X1) ),
    c_0_1628,
    [final] ).

cnf(c_0_2038,plain,
    ( c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),X1) = c_HOL_Oone__class_Oone(X1)
    | ~ class_Ring__and__Field_Osemiring__1(X1) ),
    c_0_1629,
    [final] ).

cnf(c_0_2039,plain,
    ( c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Osemiring__1(X1) ),
    c_0_1630,
    [final] ).

cnf(c_0_2040,plain,
    ( c_OrderedGroup_Osemigroup__add(c_HOL_Oplus__class_Oplus(X1),X1)
    | ~ class_OrderedGroup_Osemigroup__add(X1) ),
    c_0_1631,
    [final] ).

cnf(c_0_2041,plain,
    ( c_HOL_Oone__class_Oone(X1) != c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Ozero__neq__one(X1) ),
    c_0_1632,
    [final] ).

cnf(c_0_2042,plain,
    ( c_HOL_Oone__class_Oone(X1) != c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Ozero__neq__one(X1) ),
    c_0_1633,
    [final] ).

cnf(c_0_2043,plain,
    ( X1 = X2
    | c_Lambda_OdB_OAbs(X1) != c_Lambda_OdB_OAbs(X2) ),
    c_0_1634,
    [final] ).

cnf(c_0_2044,plain,
    ( X1 = X2
    | c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OVar(X2) ),
    c_0_1635,
    [final] ).

% End CNF derivation
% Generating one_way clauses for all literals in the CNF.
cnf(c_0_1636_0,axiom,
    ( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(X1,X2,X3),tc_Lambda_OdB,tc_Lambda_OdB) = X3
    | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),X2,tc_Lambda_OdB,tc_Lambda_OdB)),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_1636]) ).

cnf(c_0_1636_1,axiom,
    ( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),X2,tc_Lambda_OdB,tc_Lambda_OdB)),X3))
    | c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(X1,X2,X3),tc_Lambda_OdB,tc_Lambda_OdB) = X3 ),
    inference(literals_permutation,[status(thm)],[c_0_1636]) ).

cnf(c_0_1637_0,axiom,
    ( c_Type_Otypings(X1,c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,X2,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),X4,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X5,tc_Lambda_OdB,tc_Lambda_OdB),X6)
    | ~ c_Type_Otyping(X1,X2,X3)
    | ~ c_Type_Otypings(c_Type_Oshift(X1,X4,X3,tc_Type_Otype),X5,X6) ),
    inference(literals_permutation,[status(thm)],[c_0_1637]) ).

cnf(c_0_1637_1,axiom,
    ( ~ c_Type_Otyping(X1,X2,X3)
    | c_Type_Otypings(X1,c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,X2,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),X4,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X5,tc_Lambda_OdB,tc_Lambda_OdB),X6)
    | ~ c_Type_Otypings(c_Type_Oshift(X1,X4,X3,tc_Type_Otype),X5,X6) ),
    inference(literals_permutation,[status(thm)],[c_0_1637]) ).

cnf(c_0_1637_2,axiom,
    ( ~ c_Type_Otypings(c_Type_Oshift(X1,X4,X3,tc_Type_Otype),X5,X6)
    | ~ c_Type_Otyping(X1,X2,X3)
    | c_Type_Otypings(X1,c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,X2,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),X4,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X5,tc_Lambda_OdB,tc_Lambda_OdB),X6) ),
    inference(literals_permutation,[status(thm)],[c_0_1637]) ).

cnf(c_0_1638_0,axiom,
    ( c_Type_Otypings(X1,X4,c_Type_Osko__Type__Xvar__app__types__1__1(X5,X7,X1,X4))
    | ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X4,tc_Lambda_OdB,tc_Lambda_OdB),X5)
    | ~ c_Type_Otypings(X1,X3,X6)
    | ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X7) ),
    inference(literals_permutation,[status(thm)],[c_0_1638]) ).

cnf(c_0_1638_1,axiom,
    ( ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X4,tc_Lambda_OdB,tc_Lambda_OdB),X5)
    | c_Type_Otypings(X1,X4,c_Type_Osko__Type__Xvar__app__types__1__1(X5,X7,X1,X4))
    | ~ c_Type_Otypings(X1,X3,X6)
    | ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X7) ),
    inference(literals_permutation,[status(thm)],[c_0_1638]) ).

cnf(c_0_1638_2,axiom,
    ( ~ c_Type_Otypings(X1,X3,X6)
    | ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X4,tc_Lambda_OdB,tc_Lambda_OdB),X5)
    | c_Type_Otypings(X1,X4,c_Type_Osko__Type__Xvar__app__types__1__1(X5,X7,X1,X4))
    | ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X7) ),
    inference(literals_permutation,[status(thm)],[c_0_1638]) ).

cnf(c_0_1638_3,axiom,
    ( ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X7)
    | ~ c_Type_Otypings(X1,X3,X6)
    | ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X4,tc_Lambda_OdB,tc_Lambda_OdB),X5)
    | c_Type_Otypings(X1,X4,c_Type_Osko__Type__Xvar__app__types__1__1(X5,X7,X1,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_1638]) ).

cnf(c_0_1639_0,axiom,
    ( c_ListOrder_Ostep1(c_Lambda_Obeta,X2,c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(X1,X2,X3),tc_Lambda_OdB)
    | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),X2,tc_Lambda_OdB,tc_Lambda_OdB)),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_1639]) ).

cnf(c_0_1639_1,axiom,
    ( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),X2,tc_Lambda_OdB,tc_Lambda_OdB)),X3))
    | c_ListOrder_Ostep1(c_Lambda_Obeta,X2,c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(X1,X2,X3),tc_Lambda_OdB) ),
    inference(literals_permutation,[status(thm)],[c_0_1639]) ).

cnf(c_0_1640_0,axiom,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1(X1)),c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2(X1),tc_Lambda_OdB,tc_Lambda_OdB)))
    | ~ hBOOL(hAPP(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3(X1)),c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__4(X1),tc_Lambda_OdB,tc_Lambda_OdB))) ),
    inference(literals_permutation,[status(thm)],[c_0_1640]) ).

cnf(c_0_1640_1,axiom,
    ( ~ hBOOL(hAPP(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1(X1)),c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2(X1),tc_Lambda_OdB,tc_Lambda_OdB)))
    | hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3(X1)),c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__4(X1),tc_Lambda_OdB,tc_Lambda_OdB))) ),
    inference(literals_permutation,[status(thm)],[c_0_1640]) ).

cnf(c_0_1640_2,axiom,
    ( ~ hBOOL(hAPP(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3(X1)),c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__4(X1),tc_Lambda_OdB,tc_Lambda_OdB)))
    | ~ hBOOL(hAPP(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1(X1)),c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2(X1),tc_Lambda_OdB,tc_Lambda_OdB)))
    | hBOOL(hAPP(X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_1640]) ).

cnf(c_0_1641_0,axiom,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_ListApplication_Osko__ListApplication__Xlem__1__1(X1)),c_ListApplication_Osko__ListApplication__Xlem__1__2(X1),tc_Lambda_OdB,tc_Lambda_OdB)))
    | ~ hBOOL(hAPP(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(c_ListApplication_Osko__ListApplication__Xlem__1__3(X1)),c_ListApplication_Osko__ListApplication__Xlem__1__4(X1),tc_Lambda_OdB,tc_Lambda_OdB))) ),
    inference(literals_permutation,[status(thm)],[c_0_1641]) ).

cnf(c_0_1641_1,axiom,
    ( ~ hBOOL(hAPP(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_ListApplication_Osko__ListApplication__Xlem__1__1(X1)),c_ListApplication_Osko__ListApplication__Xlem__1__2(X1),tc_Lambda_OdB,tc_Lambda_OdB)))
    | hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(c_ListApplication_Osko__ListApplication__Xlem__1__3(X1)),c_ListApplication_Osko__ListApplication__Xlem__1__4(X1),tc_Lambda_OdB,tc_Lambda_OdB))) ),
    inference(literals_permutation,[status(thm)],[c_0_1641]) ).

cnf(c_0_1641_2,axiom,
    ( ~ hBOOL(hAPP(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(c_ListApplication_Osko__ListApplication__Xlem__1__3(X1)),c_ListApplication_Osko__ListApplication__Xlem__1__4(X1),tc_Lambda_OdB,tc_Lambda_OdB)))
    | ~ hBOOL(hAPP(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_ListApplication_Osko__ListApplication__Xlem__1__1(X1)),c_ListApplication_Osko__ListApplication__Xlem__1__2(X1),tc_Lambda_OdB,tc_Lambda_OdB)))
    | hBOOL(hAPP(X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_1641]) ).

cnf(c_0_1642_0,axiom,
    ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X1,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X2,tc_Lambda_OdB,tc_Lambda_OdB)))
    | ~ c_ListOrder_Ostep1(c_Lambda_Obeta,X1,X2,tc_Lambda_OdB) ),
    inference(literals_permutation,[status(thm)],[c_0_1642]) ).

cnf(c_0_1642_1,axiom,
    ( ~ c_ListOrder_Ostep1(c_Lambda_Obeta,X1,X2,tc_Lambda_OdB)
    | hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X1,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X2,tc_Lambda_OdB,tc_Lambda_OdB))) ),
    inference(literals_permutation,[status(thm)],[c_0_1642]) ).

cnf(c_0_1643_0,axiom,
    ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X3,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB)))
    | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_1643]) ).

cnf(c_0_1643_1,axiom,
    ( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2))
    | hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X3,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB))) ),
    inference(literals_permutation,[status(thm)],[c_0_1643]) ).

cnf(c_0_1644_0,axiom,
    ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X3,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB)))
    | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_1644]) ).

cnf(c_0_1644_1,axiom,
    ( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2))
    | hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X3,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB))) ),
    inference(literals_permutation,[status(thm)],[c_0_1644]) ).

cnf(c_0_1645_0,axiom,
    ( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1)),X2),X3,tc_Lambda_OdB,tc_Lambda_OdB)))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X2),c_HOL_Ozero__class_Ozero(tc_nat)),X3,tc_Lambda_OdB,tc_Lambda_OdB)))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_1645]) ).

cnf(c_0_1645_1,axiom,
    ( ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X2),c_HOL_Ozero__class_Ozero(tc_nat)),X3,tc_Lambda_OdB,tc_Lambda_OdB)))
    | hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1)),X2),X3,tc_Lambda_OdB,tc_Lambda_OdB)))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_1645]) ).

cnf(c_0_1645_2,axiom,
    ( ~ hBOOL(hAPP(c_InductTermi_OIT,X2))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X2),c_HOL_Ozero__class_Ozero(tc_nat)),X3,tc_Lambda_OdB,tc_Lambda_OdB)))
    | hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1)),X2),X3,tc_Lambda_OdB,tc_Lambda_OdB))) ),
    inference(literals_permutation,[status(thm)],[c_0_1645]) ).

cnf(c_0_1646_0,axiom,
    ( hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X8)),hAPP(hAPP(X2,X9),X10)) = hAPP(hAPP(X2,X9),hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X8)),X10))
    | ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
    inference(literals_permutation,[status(thm)],[c_0_1646]) ).

cnf(c_0_1646_1,axiom,
    ( ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6)
    | hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X8)),hAPP(hAPP(X2,X9),X10)) = hAPP(hAPP(X2,X9),hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X8)),X10)) ),
    inference(literals_permutation,[status(thm)],[c_0_1646]) ).

cnf(c_0_1647_0,axiom,
    ( hAPP(hAPP(X1,hAPP(hAPP(X1,X7),X8)),hAPP(hAPP(X1,X9),X10)) = hAPP(hAPP(X1,hAPP(hAPP(X1,X7),X9)),hAPP(hAPP(X1,X8),X10))
    | ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
    inference(literals_permutation,[status(thm)],[c_0_1647]) ).

cnf(c_0_1647_1,axiom,
    ( ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6)
    | hAPP(hAPP(X1,hAPP(hAPP(X1,X7),X8)),hAPP(hAPP(X1,X9),X10)) = hAPP(hAPP(X1,hAPP(hAPP(X1,X7),X9)),hAPP(hAPP(X1,X8),X10)) ),
    inference(literals_permutation,[status(thm)],[c_0_1647]) ).

cnf(c_0_1648_0,axiom,
    ( hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X8)),hAPP(hAPP(X2,X9),X10)) = hAPP(hAPP(X2,X7),hAPP(hAPP(X2,X8),hAPP(hAPP(X2,X9),X10)))
    | ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
    inference(literals_permutation,[status(thm)],[c_0_1648]) ).

cnf(c_0_1648_1,axiom,
    ( ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6)
    | hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X8)),hAPP(hAPP(X2,X9),X10)) = hAPP(hAPP(X2,X7),hAPP(hAPP(X2,X8),hAPP(hAPP(X2,X9),X10))) ),
    inference(literals_permutation,[status(thm)],[c_0_1648]) ).

cnf(c_0_1649_0,axiom,
    ( hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X8)),hAPP(hAPP(X2,X9),X10)) = hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X9)),hAPP(hAPP(X2,X8),X10))
    | ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
    inference(literals_permutation,[status(thm)],[c_0_1649]) ).

cnf(c_0_1649_1,axiom,
    ( ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6)
    | hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X8)),hAPP(hAPP(X2,X9),X10)) = hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X9)),hAPP(hAPP(X2,X8),X10)) ),
    inference(literals_permutation,[status(thm)],[c_0_1649]) ).

cnf(c_0_1650_0,axiom,
    ( hAPP(hAPP(X2,hAPP(hAPP(X3,X7),X9)),hAPP(hAPP(X3,X8),X9)) = hAPP(hAPP(X3,hAPP(hAPP(X2,X7),X8)),X9)
    | ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
    inference(literals_permutation,[status(thm)],[c_0_1650]) ).

cnf(c_0_1650_1,axiom,
    ( ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6)
    | hAPP(hAPP(X2,hAPP(hAPP(X3,X7),X9)),hAPP(hAPP(X3,X8),X9)) = hAPP(hAPP(X3,hAPP(hAPP(X2,X7),X8)),X9) ),
    inference(literals_permutation,[status(thm)],[c_0_1650]) ).

cnf(c_0_1651_0,axiom,
    ( hAPP(hAPP(X1,hAPP(hAPP(X2,X7),X9)),hAPP(hAPP(X2,X8),X9)) = hAPP(hAPP(X2,hAPP(hAPP(X1,X7),X8)),X9)
    | ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
    inference(literals_permutation,[status(thm)],[c_0_1651]) ).

cnf(c_0_1651_1,axiom,
    ( ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6)
    | hAPP(hAPP(X1,hAPP(hAPP(X2,X7),X9)),hAPP(hAPP(X2,X8),X9)) = hAPP(hAPP(X2,hAPP(hAPP(X1,X7),X8)),X9) ),
    inference(literals_permutation,[status(thm)],[c_0_1651]) ).

cnf(c_0_1652_0,axiom,
    ( hAPP(hAPP(X1,hAPP(hAPP(X2,X7),X8)),hAPP(hAPP(X2,X9),X8)) = hAPP(hAPP(X2,hAPP(hAPP(X1,X7),X9)),X8)
    | ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
    inference(literals_permutation,[status(thm)],[c_0_1652]) ).

cnf(c_0_1652_1,axiom,
    ( ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6)
    | hAPP(hAPP(X1,hAPP(hAPP(X2,X7),X8)),hAPP(hAPP(X2,X9),X8)) = hAPP(hAPP(X2,hAPP(hAPP(X1,X7),X9)),X8) ),
    inference(literals_permutation,[status(thm)],[c_0_1652]) ).

cnf(c_0_1653_0,axiom,
    ( hAPP(hAPP(X2,hAPP(hAPP(X3,X7),X8)),hAPP(hAPP(X3,X7),X9)) = hAPP(hAPP(X3,X7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X8),X9))
    | ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
    inference(literals_permutation,[status(thm)],[c_0_1653]) ).

cnf(c_0_1653_1,axiom,
    ( ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6)
    | hAPP(hAPP(X2,hAPP(hAPP(X3,X7),X8)),hAPP(hAPP(X3,X7),X9)) = hAPP(hAPP(X3,X7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X8),X9)) ),
    inference(literals_permutation,[status(thm)],[c_0_1653]) ).

cnf(c_0_1654_0,axiom,
    ( hAPP(hAPP(X1,hAPP(hAPP(X2,X7),X8)),hAPP(hAPP(X2,X7),X9)) = hAPP(hAPP(X2,X7),hAPP(hAPP(X1,X8),X9))
    | ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
    inference(literals_permutation,[status(thm)],[c_0_1654]) ).

cnf(c_0_1654_1,axiom,
    ( ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6)
    | hAPP(hAPP(X1,hAPP(hAPP(X2,X7),X8)),hAPP(hAPP(X2,X7),X9)) = hAPP(hAPP(X2,X7),hAPP(hAPP(X1,X8),X9)) ),
    inference(literals_permutation,[status(thm)],[c_0_1654]) ).

cnf(c_0_1655_0,axiom,
    ( hAPP(hAPP(X1,hAPP(hAPP(X1,X7),X8)),X9) = hAPP(hAPP(X1,hAPP(hAPP(X1,X7),X9)),X8)
    | ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
    inference(literals_permutation,[status(thm)],[c_0_1655]) ).

cnf(c_0_1655_1,axiom,
    ( ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6)
    | hAPP(hAPP(X1,hAPP(hAPP(X1,X7),X8)),X9) = hAPP(hAPP(X1,hAPP(hAPP(X1,X7),X9)),X8) ),
    inference(literals_permutation,[status(thm)],[c_0_1655]) ).

cnf(c_0_1656_0,axiom,
    ( hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X8)),X9) = hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X9)),X8)
    | ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
    inference(literals_permutation,[status(thm)],[c_0_1656]) ).

cnf(c_0_1656_1,axiom,
    ( ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6)
    | hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X8)),X9) = hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X9)),X8) ),
    inference(literals_permutation,[status(thm)],[c_0_1656]) ).

cnf(c_0_1657_0,axiom,
    ( hAPP(hAPP(X1,hAPP(hAPP(X2,X7),X8)),X8) = hAPP(hAPP(X2,hAPP(hAPP(X1,X7),X5)),X8)
    | ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
    inference(literals_permutation,[status(thm)],[c_0_1657]) ).

cnf(c_0_1657_1,axiom,
    ( ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6)
    | hAPP(hAPP(X1,hAPP(hAPP(X2,X7),X8)),X8) = hAPP(hAPP(X2,hAPP(hAPP(X1,X7),X5)),X8) ),
    inference(literals_permutation,[status(thm)],[c_0_1657]) ).

cnf(c_0_1658_0,axiom,
    ( hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X8)),X9) = hAPP(hAPP(X2,X7),hAPP(hAPP(X2,X8),X9))
    | ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
    inference(literals_permutation,[status(thm)],[c_0_1658]) ).

cnf(c_0_1658_1,axiom,
    ( ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6)
    | hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X8)),X9) = hAPP(hAPP(X2,X7),hAPP(hAPP(X2,X8),X9)) ),
    inference(literals_permutation,[status(thm)],[c_0_1658]) ).

cnf(c_0_1659_0,axiom,
    ( hAPP(hAPP(X1,hAPP(hAPP(X1,X7),X8)),X9) = hAPP(hAPP(X1,X7),hAPP(hAPP(X1,X8),X9))
    | ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
    inference(literals_permutation,[status(thm)],[c_0_1659]) ).

cnf(c_0_1659_1,axiom,
    ( ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6)
    | hAPP(hAPP(X1,hAPP(hAPP(X1,X7),X8)),X9) = hAPP(hAPP(X1,X7),hAPP(hAPP(X1,X8),X9)) ),
    inference(literals_permutation,[status(thm)],[c_0_1659]) ).

cnf(c_0_1660_0,axiom,
    ( hAPP(hAPP(X1,hAPP(hAPP(X1,X7),X8)),X9) = hAPP(hAPP(X1,X7),hAPP(hAPP(X1,X8),X9))
    | ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
    inference(literals_permutation,[status(thm)],[c_0_1660]) ).

cnf(c_0_1660_1,axiom,
    ( ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6)
    | hAPP(hAPP(X1,hAPP(hAPP(X1,X7),X8)),X9) = hAPP(hAPP(X1,X7),hAPP(hAPP(X1,X8),X9)) ),
    inference(literals_permutation,[status(thm)],[c_0_1660]) ).

cnf(c_0_1661_0,axiom,
    ( hAPP(hAPP(X1,hAPP(hAPP(X1,X7),X8)),X9) = hAPP(hAPP(X1,X7),hAPP(hAPP(X1,X8),X9))
    | ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
    inference(literals_permutation,[status(thm)],[c_0_1661]) ).

cnf(c_0_1661_1,axiom,
    ( ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6)
    | hAPP(hAPP(X1,hAPP(hAPP(X1,X7),X8)),X9) = hAPP(hAPP(X1,X7),hAPP(hAPP(X1,X8),X9)) ),
    inference(literals_permutation,[status(thm)],[c_0_1661]) ).

cnf(c_0_1662_0,axiom,
    ( hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X8)),X9) = hAPP(hAPP(X2,X7),hAPP(hAPP(X2,X8),X9))
    | ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
    inference(literals_permutation,[status(thm)],[c_0_1662]) ).

cnf(c_0_1662_1,axiom,
    ( ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6)
    | hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X8)),X9) = hAPP(hAPP(X2,X7),hAPP(hAPP(X2,X8),X9)) ),
    inference(literals_permutation,[status(thm)],[c_0_1662]) ).

cnf(c_0_1663_0,axiom,
    ( hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X8)),X9) = hAPP(hAPP(X2,X7),hAPP(hAPP(X2,X8),X9))
    | ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
    inference(literals_permutation,[status(thm)],[c_0_1663]) ).

cnf(c_0_1663_1,axiom,
    ( ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6)
    | hAPP(hAPP(X2,hAPP(hAPP(X2,X7),X8)),X9) = hAPP(hAPP(X2,X7),hAPP(hAPP(X2,X8),X9)) ),
    inference(literals_permutation,[status(thm)],[c_0_1663]) ).

cnf(c_0_1664_0,axiom,
    ( hAPP(hAPP(X1,X7),hAPP(hAPP(X2,X8),X7)) = hAPP(hAPP(X2,hAPP(hAPP(X1,X8),X5)),X7)
    | ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
    inference(literals_permutation,[status(thm)],[c_0_1664]) ).

cnf(c_0_1664_1,axiom,
    ( ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6)
    | hAPP(hAPP(X1,X7),hAPP(hAPP(X2,X8),X7)) = hAPP(hAPP(X2,hAPP(hAPP(X1,X8),X5)),X7) ),
    inference(literals_permutation,[status(thm)],[c_0_1664]) ).

cnf(c_0_1665_0,axiom,
    ( hAPP(hAPP(X1,X7),hAPP(hAPP(X1,X8),X9)) = hAPP(hAPP(X1,X8),hAPP(hAPP(X1,X7),X9))
    | ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
    inference(literals_permutation,[status(thm)],[c_0_1665]) ).

cnf(c_0_1665_1,axiom,
    ( ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6)
    | hAPP(hAPP(X1,X7),hAPP(hAPP(X1,X8),X9)) = hAPP(hAPP(X1,X8),hAPP(hAPP(X1,X7),X9)) ),
    inference(literals_permutation,[status(thm)],[c_0_1665]) ).

cnf(c_0_1666_0,axiom,
    ( hAPP(hAPP(X2,X7),hAPP(hAPP(X2,X8),X9)) = hAPP(hAPP(X2,X8),hAPP(hAPP(X2,X7),X9))
    | ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
    inference(literals_permutation,[status(thm)],[c_0_1666]) ).

cnf(c_0_1666_1,axiom,
    ( ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6)
    | hAPP(hAPP(X2,X7),hAPP(hAPP(X2,X8),X9)) = hAPP(hAPP(X2,X8),hAPP(hAPP(X2,X7),X9)) ),
    inference(literals_permutation,[status(thm)],[c_0_1666]) ).

cnf(c_0_1667_0,axiom,
    ( hAPP(hAPP(X1,X7),X7) = hAPP(hAPP(X2,hAPP(hAPP(X1,X5),X5)),X7)
    | ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
    inference(literals_permutation,[status(thm)],[c_0_1667]) ).

cnf(c_0_1667_1,axiom,
    ( ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6)
    | hAPP(hAPP(X1,X7),X7) = hAPP(hAPP(X2,hAPP(hAPP(X1,X5),X5)),X7) ),
    inference(literals_permutation,[status(thm)],[c_0_1667]) ).

cnf(c_0_1668_0,axiom,
    ( hAPP(hAPP(X2,X7),X8) = hAPP(hAPP(X2,X8),X7)
    | ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
    inference(literals_permutation,[status(thm)],[c_0_1668]) ).

cnf(c_0_1668_1,axiom,
    ( ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6)
    | hAPP(hAPP(X2,X7),X8) = hAPP(hAPP(X2,X8),X7) ),
    inference(literals_permutation,[status(thm)],[c_0_1668]) ).

cnf(c_0_1669_0,axiom,
    ( hAPP(hAPP(X1,X7),X8) = hAPP(hAPP(X1,X8),X7)
    | ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
    inference(literals_permutation,[status(thm)],[c_0_1669]) ).

cnf(c_0_1669_1,axiom,
    ( ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6)
    | hAPP(hAPP(X1,X7),X8) = hAPP(hAPP(X1,X8),X7) ),
    inference(literals_permutation,[status(thm)],[c_0_1669]) ).

cnf(c_0_1670_0,axiom,
    ( hAPP(hAPP(X1,X7),X8) = hAPP(hAPP(X1,X8),X7)
    | ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
    inference(literals_permutation,[status(thm)],[c_0_1670]) ).

cnf(c_0_1670_1,axiom,
    ( ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6)
    | hAPP(hAPP(X1,X7),X8) = hAPP(hAPP(X1,X8),X7) ),
    inference(literals_permutation,[status(thm)],[c_0_1670]) ).

cnf(c_0_1671_0,axiom,
    ( hAPP(hAPP(X2,X7),X8) = hAPP(hAPP(X2,X8),X7)
    | ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
    inference(literals_permutation,[status(thm)],[c_0_1671]) ).

cnf(c_0_1671_1,axiom,
    ( ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6)
    | hAPP(hAPP(X2,X7),X8) = hAPP(hAPP(X2,X8),X7) ),
    inference(literals_permutation,[status(thm)],[c_0_1671]) ).

cnf(c_0_1672_0,axiom,
    ( hAPP(hAPP(X3,X7),c_HOL_Oone__class_Oone(tc_nat)) = X7
    | ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
    inference(literals_permutation,[status(thm)],[c_0_1672]) ).

cnf(c_0_1672_1,axiom,
    ( ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6)
    | hAPP(hAPP(X3,X7),c_HOL_Oone__class_Oone(tc_nat)) = X7 ),
    inference(literals_permutation,[status(thm)],[c_0_1672]) ).

cnf(c_0_1673_0,axiom,
    ( hAPP(hAPP(X3,X7),c_HOL_Ozero__class_Ozero(tc_nat)) = X5
    | ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
    inference(literals_permutation,[status(thm)],[c_0_1673]) ).

cnf(c_0_1673_1,axiom,
    ( ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6)
    | hAPP(hAPP(X3,X7),c_HOL_Ozero__class_Ozero(tc_nat)) = X5 ),
    inference(literals_permutation,[status(thm)],[c_0_1673]) ).

cnf(c_0_1674_0,axiom,
    ( hAPP(hAPP(X2,X5),X7) = X7
    | ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
    inference(literals_permutation,[status(thm)],[c_0_1674]) ).

cnf(c_0_1674_1,axiom,
    ( ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6)
    | hAPP(hAPP(X2,X5),X7) = X7 ),
    inference(literals_permutation,[status(thm)],[c_0_1674]) ).

cnf(c_0_1675_0,axiom,
    ( hAPP(hAPP(X2,X4),X7) = X4
    | ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
    inference(literals_permutation,[status(thm)],[c_0_1675]) ).

cnf(c_0_1675_1,axiom,
    ( ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6)
    | hAPP(hAPP(X2,X4),X7) = X4 ),
    inference(literals_permutation,[status(thm)],[c_0_1675]) ).

cnf(c_0_1676_0,axiom,
    ( hAPP(hAPP(X1,X4),X7) = X7
    | ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
    inference(literals_permutation,[status(thm)],[c_0_1676]) ).

cnf(c_0_1676_1,axiom,
    ( ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6)
    | hAPP(hAPP(X1,X4),X7) = X7 ),
    inference(literals_permutation,[status(thm)],[c_0_1676]) ).

cnf(c_0_1677_0,axiom,
    ( hAPP(hAPP(X2,X7),X5) = X7
    | ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
    inference(literals_permutation,[status(thm)],[c_0_1677]) ).

cnf(c_0_1677_1,axiom,
    ( ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6)
    | hAPP(hAPP(X2,X7),X5) = X7 ),
    inference(literals_permutation,[status(thm)],[c_0_1677]) ).

cnf(c_0_1678_0,axiom,
    ( hAPP(hAPP(X2,X5),X7) = X7
    | ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
    inference(literals_permutation,[status(thm)],[c_0_1678]) ).

cnf(c_0_1678_1,axiom,
    ( ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6)
    | hAPP(hAPP(X2,X5),X7) = X7 ),
    inference(literals_permutation,[status(thm)],[c_0_1678]) ).

cnf(c_0_1679_0,axiom,
    ( hAPP(hAPP(X2,X7),X4) = X4
    | ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
    inference(literals_permutation,[status(thm)],[c_0_1679]) ).

cnf(c_0_1679_1,axiom,
    ( ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6)
    | hAPP(hAPP(X2,X7),X4) = X4 ),
    inference(literals_permutation,[status(thm)],[c_0_1679]) ).

cnf(c_0_1680_0,axiom,
    ( hAPP(hAPP(X2,X4),X7) = X4
    | ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
    inference(literals_permutation,[status(thm)],[c_0_1680]) ).

cnf(c_0_1680_1,axiom,
    ( ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6)
    | hAPP(hAPP(X2,X4),X7) = X4 ),
    inference(literals_permutation,[status(thm)],[c_0_1680]) ).

cnf(c_0_1681_0,axiom,
    ( hAPP(hAPP(X1,X7),X4) = X7
    | ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
    inference(literals_permutation,[status(thm)],[c_0_1681]) ).

cnf(c_0_1681_1,axiom,
    ( ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6)
    | hAPP(hAPP(X1,X7),X4) = X7 ),
    inference(literals_permutation,[status(thm)],[c_0_1681]) ).

cnf(c_0_1682_0,axiom,
    ( hAPP(hAPP(X1,X4),X7) = X7
    | ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6) ),
    inference(literals_permutation,[status(thm)],[c_0_1682]) ).

cnf(c_0_1682_1,axiom,
    ( ~ c_Groebner__Basis_Ogb__semiring(X1,X2,X3,X4,X5,X6)
    | hAPP(hAPP(X1,X4),X7) = X7 ),
    inference(literals_permutation,[status(thm)],[c_0_1682]) ).

cnf(c_0_1683_0,axiom,
    ( hBOOL(hAPP(X1,hAPP(hAPP(X2,X3),X4)))
    | ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X5,X2,X6,hAPP(hAPP(c_Lambda_OdB_OApp,X3),X4),t_a))) ),
    inference(literals_permutation,[status(thm)],[c_0_1683]) ).

cnf(c_0_1683_1,axiom,
    ( ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X5,X2,X6,hAPP(hAPP(c_Lambda_OdB_OApp,X3),X4),t_a)))
    | hBOOL(hAPP(X1,hAPP(hAPP(X2,X3),X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_1683]) ).

cnf(c_0_1684_0,axiom,
    ( hBOOL(hAPP(X1,hAPP(hAPP(X2,X3),X4)))
    | ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X5,X2,X6,hAPP(hAPP(c_Lambda_OdB_OApp,X3),X4),t_a))) ),
    inference(literals_permutation,[status(thm)],[c_0_1684]) ).

cnf(c_0_1684_1,axiom,
    ( ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X5,X2,X6,hAPP(hAPP(c_Lambda_OdB_OApp,X3),X4),t_a)))
    | hBOOL(hAPP(X1,hAPP(hAPP(X2,X3),X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_1684]) ).

cnf(c_0_1685_0,axiom,
    ( hBOOL(hAPP(X1,X2))
    | hBOOL(hAPP(X1,c_ListApplication_Osko__ListApplication__Xlem__1__3(X1)))
    | ~ hBOOL(hAPP(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_ListApplication_Osko__ListApplication__Xlem__1__1(X1)),c_ListApplication_Osko__ListApplication__Xlem__1__2(X1),tc_Lambda_OdB,tc_Lambda_OdB))) ),
    inference(literals_permutation,[status(thm)],[c_0_1685]) ).

cnf(c_0_1685_1,axiom,
    ( hBOOL(hAPP(X1,c_ListApplication_Osko__ListApplication__Xlem__1__3(X1)))
    | hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_ListApplication_Osko__ListApplication__Xlem__1__1(X1)),c_ListApplication_Osko__ListApplication__Xlem__1__2(X1),tc_Lambda_OdB,tc_Lambda_OdB))) ),
    inference(literals_permutation,[status(thm)],[c_0_1685]) ).

cnf(c_0_1685_2,axiom,
    ( ~ hBOOL(hAPP(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_ListApplication_Osko__ListApplication__Xlem__1__1(X1)),c_ListApplication_Osko__ListApplication__Xlem__1__2(X1),tc_Lambda_OdB,tc_Lambda_OdB)))
    | hBOOL(hAPP(X1,c_ListApplication_Osko__ListApplication__Xlem__1__3(X1)))
    | hBOOL(hAPP(X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_1685]) ).

cnf(c_0_1686_0,axiom,
    ( hBOOL(hAPP(X1,c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3(X1)))
    | hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1(X1)),c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2(X1),tc_Lambda_OdB,tc_Lambda_OdB))) ),
    inference(literals_permutation,[status(thm)],[c_0_1686]) ).

cnf(c_0_1686_1,axiom,
    ( hBOOL(hAPP(X1,X2))
    | hBOOL(hAPP(X1,c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3(X1)))
    | ~ hBOOL(hAPP(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1(X1)),c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2(X1),tc_Lambda_OdB,tc_Lambda_OdB))) ),
    inference(literals_permutation,[status(thm)],[c_0_1686]) ).

cnf(c_0_1686_2,axiom,
    ( ~ hBOOL(hAPP(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1(X1)),c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2(X1),tc_Lambda_OdB,tc_Lambda_OdB)))
    | hBOOL(hAPP(X1,X2))
    | hBOOL(hAPP(X1,c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3(X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_1686]) ).

cnf(c_0_1687_0,axiom,
    ( X4 = X5
    | ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X4)
    | ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X5) ),
    inference(literals_permutation,[status(thm)],[c_0_1687]) ).

cnf(c_0_1687_1,axiom,
    ( ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X4)
    | X4 = X5
    | ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X5) ),
    inference(literals_permutation,[status(thm)],[c_0_1687]) ).

cnf(c_0_1687_2,axiom,
    ( ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X5)
    | ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X4)
    | X4 = X5 ),
    inference(literals_permutation,[status(thm)],[c_0_1687]) ).

cnf(c_0_1688_0,axiom,
    ( hBOOL(hAPP(X1,hAPP(X2,X3)))
    | ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X4,X5,X2,c_Lambda_OdB_OAbs(X3),t_a))) ),
    inference(literals_permutation,[status(thm)],[c_0_1688]) ).

cnf(c_0_1688_1,axiom,
    ( ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X4,X5,X2,c_Lambda_OdB_OAbs(X3),t_a)))
    | hBOOL(hAPP(X1,hAPP(X2,X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_1688]) ).

cnf(c_0_1689_0,axiom,
    ( hBOOL(hAPP(X1,hAPP(X2,X3)))
    | ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X4,X5,X2,c_Lambda_OdB_OAbs(X3),t_a))) ),
    inference(literals_permutation,[status(thm)],[c_0_1689]) ).

cnf(c_0_1689_1,axiom,
    ( ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X4,X5,X2,c_Lambda_OdB_OAbs(X3),t_a)))
    | hBOOL(hAPP(X1,hAPP(X2,X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_1689]) ).

cnf(c_0_1690_0,axiom,
    ( hBOOL(hAPP(X1,hAPP(X2,X3)))
    | ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X2,X4,X5,c_Lambda_OdB_OVar(X3),t_a))) ),
    inference(literals_permutation,[status(thm)],[c_0_1690]) ).

cnf(c_0_1690_1,axiom,
    ( ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X2,X4,X5,c_Lambda_OdB_OVar(X3),t_a)))
    | hBOOL(hAPP(X1,hAPP(X2,X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_1690]) ).

cnf(c_0_1691_0,axiom,
    ( hBOOL(hAPP(X1,hAPP(X2,X3)))
    | ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X2,X4,X5,c_Lambda_OdB_OVar(X3),t_a))) ),
    inference(literals_permutation,[status(thm)],[c_0_1691]) ).

cnf(c_0_1691_1,axiom,
    ( ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X2,X4,X5,c_Lambda_OdB_OVar(X3),t_a)))
    | hBOOL(hAPP(X1,hAPP(X2,X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_1691]) ).

cnf(c_0_1692_0,axiom,
    ( c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1)),X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)
    | ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X2,tc_Lambda_OdB)
    | ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X2),c_HOL_Ozero__class_Ozero(tc_nat)),X3,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB) ),
    inference(literals_permutation,[status(thm)],[c_0_1692]) ).

cnf(c_0_1692_1,axiom,
    ( ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X2,tc_Lambda_OdB)
    | c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1)),X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)
    | ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X2),c_HOL_Ozero__class_Ozero(tc_nat)),X3,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB) ),
    inference(literals_permutation,[status(thm)],[c_0_1692]) ).

cnf(c_0_1692_2,axiom,
    ( ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X2),c_HOL_Ozero__class_Ozero(tc_nat)),X3,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)
    | ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X2,tc_Lambda_OdB)
    | c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1)),X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB) ),
    inference(literals_permutation,[status(thm)],[c_0_1692]) ).

cnf(c_0_1693_0,axiom,
    ( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X1)),v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB,tc_Lambda_OdB) = X1
    | hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X1)))
    | hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_sko__InductTermi__XIT__Xcases__4(X1)),v_sko__InductTermi__XIT__Xcases__5(X1)),c_HOL_Ozero__class_Ozero(tc_nat)),v_sko__InductTermi__XIT__Xcases__6(X1),tc_Lambda_OdB,tc_Lambda_OdB)))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_1693]) ).

cnf(c_0_1693_1,axiom,
    ( hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X1)))
    | c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X1)),v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB,tc_Lambda_OdB) = X1
    | hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_sko__InductTermi__XIT__Xcases__4(X1)),v_sko__InductTermi__XIT__Xcases__5(X1)),c_HOL_Ozero__class_Ozero(tc_nat)),v_sko__InductTermi__XIT__Xcases__6(X1),tc_Lambda_OdB,tc_Lambda_OdB)))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_1693]) ).

cnf(c_0_1693_2,axiom,
    ( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_sko__InductTermi__XIT__Xcases__4(X1)),v_sko__InductTermi__XIT__Xcases__5(X1)),c_HOL_Ozero__class_Ozero(tc_nat)),v_sko__InductTermi__XIT__Xcases__6(X1),tc_Lambda_OdB,tc_Lambda_OdB)))
    | hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X1)))
    | c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X1)),v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB,tc_Lambda_OdB) = X1
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_1693]) ).

cnf(c_0_1693_3,axiom,
    ( ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
    | hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_sko__InductTermi__XIT__Xcases__4(X1)),v_sko__InductTermi__XIT__Xcases__5(X1)),c_HOL_Ozero__class_Ozero(tc_nat)),v_sko__InductTermi__XIT__Xcases__6(X1),tc_Lambda_OdB,tc_Lambda_OdB)))
    | hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X1)))
    | c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X1)),v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB,tc_Lambda_OdB) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_1693]) ).

cnf(c_0_1694_0,axiom,
    ( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X1)),v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB,tc_Lambda_OdB) = X1
    | c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X1)) = X1
    | hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_sko__InductTermi__XIT__Xcases__4(X1)),v_sko__InductTermi__XIT__Xcases__5(X1)),c_HOL_Ozero__class_Ozero(tc_nat)),v_sko__InductTermi__XIT__Xcases__6(X1),tc_Lambda_OdB,tc_Lambda_OdB)))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_1694]) ).

cnf(c_0_1694_1,axiom,
    ( c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X1)) = X1
    | c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X1)),v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB,tc_Lambda_OdB) = X1
    | hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_sko__InductTermi__XIT__Xcases__4(X1)),v_sko__InductTermi__XIT__Xcases__5(X1)),c_HOL_Ozero__class_Ozero(tc_nat)),v_sko__InductTermi__XIT__Xcases__6(X1),tc_Lambda_OdB,tc_Lambda_OdB)))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_1694]) ).

cnf(c_0_1694_2,axiom,
    ( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_sko__InductTermi__XIT__Xcases__4(X1)),v_sko__InductTermi__XIT__Xcases__5(X1)),c_HOL_Ozero__class_Ozero(tc_nat)),v_sko__InductTermi__XIT__Xcases__6(X1),tc_Lambda_OdB,tc_Lambda_OdB)))
    | c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X1)) = X1
    | c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X1)),v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB,tc_Lambda_OdB) = X1
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_1694]) ).

cnf(c_0_1694_3,axiom,
    ( ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
    | hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_sko__InductTermi__XIT__Xcases__4(X1)),v_sko__InductTermi__XIT__Xcases__5(X1)),c_HOL_Ozero__class_Ozero(tc_nat)),v_sko__InductTermi__XIT__Xcases__6(X1),tc_Lambda_OdB,tc_Lambda_OdB)))
    | c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X1)) = X1
    | c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X1)),v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB,tc_Lambda_OdB) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_1694]) ).

cnf(c_0_1695_0,axiom,
    ( c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB)
    | hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X1)))
    | hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_sko__InductTermi__XIT__Xcases__4(X1)),v_sko__InductTermi__XIT__Xcases__5(X1)),c_HOL_Ozero__class_Ozero(tc_nat)),v_sko__InductTermi__XIT__Xcases__6(X1),tc_Lambda_OdB,tc_Lambda_OdB)))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_1695]) ).

cnf(c_0_1695_1,axiom,
    ( hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X1)))
    | c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB)
    | hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_sko__InductTermi__XIT__Xcases__4(X1)),v_sko__InductTermi__XIT__Xcases__5(X1)),c_HOL_Ozero__class_Ozero(tc_nat)),v_sko__InductTermi__XIT__Xcases__6(X1),tc_Lambda_OdB,tc_Lambda_OdB)))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_1695]) ).

cnf(c_0_1695_2,axiom,
    ( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_sko__InductTermi__XIT__Xcases__4(X1)),v_sko__InductTermi__XIT__Xcases__5(X1)),c_HOL_Ozero__class_Ozero(tc_nat)),v_sko__InductTermi__XIT__Xcases__6(X1),tc_Lambda_OdB,tc_Lambda_OdB)))
    | hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X1)))
    | c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB)
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_1695]) ).

cnf(c_0_1695_3,axiom,
    ( ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
    | hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_sko__InductTermi__XIT__Xcases__4(X1)),v_sko__InductTermi__XIT__Xcases__5(X1)),c_HOL_Ozero__class_Ozero(tc_nat)),v_sko__InductTermi__XIT__Xcases__6(X1),tc_Lambda_OdB,tc_Lambda_OdB)))
    | hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X1)))
    | c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB) ),
    inference(literals_permutation,[status(thm)],[c_0_1695]) ).

cnf(c_0_1696_0,axiom,
    ( c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB)
    | c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X1)) = X1
    | hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_sko__InductTermi__XIT__Xcases__4(X1)),v_sko__InductTermi__XIT__Xcases__5(X1)),c_HOL_Ozero__class_Ozero(tc_nat)),v_sko__InductTermi__XIT__Xcases__6(X1),tc_Lambda_OdB,tc_Lambda_OdB)))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_1696]) ).

cnf(c_0_1696_1,axiom,
    ( c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X1)) = X1
    | c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB)
    | hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_sko__InductTermi__XIT__Xcases__4(X1)),v_sko__InductTermi__XIT__Xcases__5(X1)),c_HOL_Ozero__class_Ozero(tc_nat)),v_sko__InductTermi__XIT__Xcases__6(X1),tc_Lambda_OdB,tc_Lambda_OdB)))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_1696]) ).

cnf(c_0_1696_2,axiom,
    ( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_sko__InductTermi__XIT__Xcases__4(X1)),v_sko__InductTermi__XIT__Xcases__5(X1)),c_HOL_Ozero__class_Ozero(tc_nat)),v_sko__InductTermi__XIT__Xcases__6(X1),tc_Lambda_OdB,tc_Lambda_OdB)))
    | c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X1)) = X1
    | c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB)
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_1696]) ).

cnf(c_0_1696_3,axiom,
    ( ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
    | hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_sko__InductTermi__XIT__Xcases__4(X1)),v_sko__InductTermi__XIT__Xcases__5(X1)),c_HOL_Ozero__class_Ozero(tc_nat)),v_sko__InductTermi__XIT__Xcases__6(X1),tc_Lambda_OdB,tc_Lambda_OdB)))
    | c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X1)) = X1
    | c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB) ),
    inference(literals_permutation,[status(thm)],[c_0_1696]) ).

cnf(c_0_1697_0,axiom,
    ( c_Type_Otypings(c_Type_Oshift(X1,X4,X5,tc_Type_Otype),c_List_Omap(c_COMBC(c_Lambda_Olift,X4,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X2,tc_Lambda_OdB,tc_Lambda_OdB),X3)
    | ~ c_Type_Otypings(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1697]) ).

cnf(c_0_1697_1,axiom,
    ( ~ c_Type_Otypings(X1,X2,X3)
    | c_Type_Otypings(c_Type_Oshift(X1,X4,X5,tc_Type_Otype),c_List_Omap(c_COMBC(c_Lambda_Olift,X4,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X2,tc_Lambda_OdB,tc_Lambda_OdB),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1697]) ).

cnf(c_0_1698_0,axiom,
    ( c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X1,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)
    | ~ c_List_Olistsp(c_InductTermi_OIT,X1,tc_Lambda_OdB) ),
    inference(literals_permutation,[status(thm)],[c_0_1698]) ).

cnf(c_0_1698_1,axiom,
    ( ~ c_List_Olistsp(c_InductTermi_OIT,X1,tc_Lambda_OdB)
    | c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X1,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB) ),
    inference(literals_permutation,[status(thm)],[c_0_1698]) ).

cnf(c_0_1699_0,axiom,
    ( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X1,tc_Lambda_OdB,tc_Lambda_OdB)))
    | ~ c_List_Olistsp(c_InductTermi_OIT,X1,tc_Lambda_OdB) ),
    inference(literals_permutation,[status(thm)],[c_0_1699]) ).

cnf(c_0_1699_1,axiom,
    ( ~ c_List_Olistsp(c_InductTermi_OIT,X1,tc_Lambda_OdB)
    | hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X1,tc_Lambda_OdB,tc_Lambda_OdB))) ),
    inference(literals_permutation,[status(thm)],[c_0_1699]) ).

cnf(c_0_1700_0,axiom,
    ( c_Type_Otypings(X1,X3,c_Type_Osko__Type__Xvar__app__typesE__1__1(X4,X1,X2,X3))
    | ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_1700]) ).

cnf(c_0_1700_1,axiom,
    ( ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X4)
    | c_Type_Otypings(X1,X3,c_Type_Osko__Type__Xvar__app__typesE__1__1(X4,X1,X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_1700]) ).

cnf(c_0_1701_0,axiom,
    ( X1 = X2
    | c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1),X3,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X2),X4,tc_Lambda_OdB,tc_Lambda_OdB) ),
    inference(literals_permutation,[status(thm)],[c_0_1701]) ).

cnf(c_0_1701_1,axiom,
    ( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1),X3,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X2),X4,tc_Lambda_OdB,tc_Lambda_OdB)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_1701]) ).

cnf(c_0_1702_0,axiom,
    ( X1 = X2
    | c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X3),X1,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X4),X2,tc_Lambda_OdB,tc_Lambda_OdB) ),
    inference(literals_permutation,[status(thm)],[c_0_1702]) ).

cnf(c_0_1702_1,axiom,
    ( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X3),X1,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X4),X2,tc_Lambda_OdB,tc_Lambda_OdB)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_1702]) ).

cnf(c_0_1703_0,axiom,
    ( X1 = X2
    | c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),X3,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X4,tc_Lambda_OdB,tc_Lambda_OdB) ),
    inference(literals_permutation,[status(thm)],[c_0_1703]) ).

cnf(c_0_1703_1,axiom,
    ( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),X3,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X4,tc_Lambda_OdB,tc_Lambda_OdB)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_1703]) ).

cnf(c_0_1704_0,axiom,
    ( X1 = X2
    | c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X3),X1,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X4),X2,tc_Lambda_OdB,tc_Lambda_OdB) ),
    inference(literals_permutation,[status(thm)],[c_0_1704]) ).

cnf(c_0_1704_1,axiom,
    ( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X3),X1,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X4),X2,tc_Lambda_OdB,tc_Lambda_OdB)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_1704]) ).

cnf(c_0_1705_0,axiom,
    ( c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X4,X1,X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),X3,X4,X1,X1))
    | ~ class_OrderedGroup_Osemigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1705]) ).

cnf(c_0_1705_1,axiom,
    ( ~ class_OrderedGroup_Osemigroup__add(X1)
    | c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X4,X1,X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),X3,X4,X1,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_1705]) ).

cnf(c_0_1706_0,axiom,
    ( X1 = X2
    | c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X3,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB) ),
    inference(literals_permutation,[status(thm)],[c_0_1706]) ).

cnf(c_0_1706_1,axiom,
    ( c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X3,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_1706]) ).

cnf(c_0_1707_0,axiom,
    ( c_List_Ofoldl(X1,hAPP(hAPP(X1,X3),X4),X5,X2,X2) = hAPP(hAPP(X1,X3),c_List_Ofoldl(X1,X4,X5,X2,X2))
    | ~ c_OrderedGroup_Osemigroup__add(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1707]) ).

cnf(c_0_1707_1,axiom,
    ( ~ c_OrderedGroup_Osemigroup__add(X1,X2)
    | c_List_Ofoldl(X1,hAPP(hAPP(X1,X3),X4),X5,X2,X2) = hAPP(hAPP(X1,X3),c_List_Ofoldl(X1,X4,X5,X2,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_1707]) ).

cnf(c_0_1708_0,axiom,
    ( hAPP(hAPP(X2,X4),c_List_Ofoldl(X2,X1,X5,X3,X3)) = c_List_Ofoldl(X2,X4,X5,X3,X3)
    | ~ c_OrderedGroup_Omonoid__add(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1708]) ).

cnf(c_0_1708_1,axiom,
    ( ~ c_OrderedGroup_Omonoid__add(X1,X2,X3)
    | hAPP(hAPP(X2,X4),c_List_Ofoldl(X2,X1,X5,X3,X3)) = c_List_Ofoldl(X2,X4,X5,X3,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1708]) ).

cnf(c_0_1709_0,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X1),X3,c_HOL_Ozero__class_Ozero(X1),X1,X1)) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),X2,X3,X1,X1)
    | ~ class_OrderedGroup_Omonoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1709]) ).

cnf(c_0_1709_1,axiom,
    ( ~ class_OrderedGroup_Omonoid__add(X1)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X1),X3,c_HOL_Ozero__class_Ozero(X1),X1,X1)) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),X2,X3,X1,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1709]) ).

cnf(c_0_1710_0,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1),X3,X1,X1)) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),X2,X3,X1,X1)
    | ~ class_OrderedGroup_Omonoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1710]) ).

cnf(c_0_1710_1,axiom,
    ( ~ class_OrderedGroup_Omonoid__add(X1)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1),X3,X1,X1)) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),X2,X3,X1,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1710]) ).

cnf(c_0_1711_0,axiom,
    ( X1 = c_List_Olist_ONil(tc_Lambda_OdB)
    | c_List_Ofoldl(c_Lambda_OdB_OApp,X3,c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1(X2,X4,X3,X1),tc_Lambda_OdB,tc_Lambda_OdB) = X2
    | hAPP(hAPP(c_Lambda_OdB_OApp,X2),X4) != c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X1,tc_Lambda_OdB,tc_Lambda_OdB) ),
    inference(literals_permutation,[status(thm)],[c_0_1711]) ).

cnf(c_0_1711_1,axiom,
    ( c_List_Ofoldl(c_Lambda_OdB_OApp,X3,c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1(X2,X4,X3,X1),tc_Lambda_OdB,tc_Lambda_OdB) = X2
    | X1 = c_List_Olist_ONil(tc_Lambda_OdB)
    | hAPP(hAPP(c_Lambda_OdB_OApp,X2),X4) != c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X1,tc_Lambda_OdB,tc_Lambda_OdB) ),
    inference(literals_permutation,[status(thm)],[c_0_1711]) ).

cnf(c_0_1711_2,axiom,
    ( hAPP(hAPP(c_Lambda_OdB_OApp,X2),X4) != c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X1,tc_Lambda_OdB,tc_Lambda_OdB)
    | c_List_Ofoldl(c_Lambda_OdB_OApp,X3,c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1(X2,X4,X3,X1),tc_Lambda_OdB,tc_Lambda_OdB) = X2
    | X1 = c_List_Olist_ONil(tc_Lambda_OdB) ),
    inference(literals_permutation,[status(thm)],[c_0_1711]) ).

cnf(c_0_1712_0,axiom,
    ( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X1)),v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB,tc_Lambda_OdB) = X1
    | hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X1)))
    | c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__4(X1))),v_sko__InductTermi__XIT__Xcases__5(X1)),v_sko__InductTermi__XIT__Xcases__6(X1),tc_Lambda_OdB,tc_Lambda_OdB) = X1
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_1712]) ).

cnf(c_0_1712_1,axiom,
    ( hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X1)))
    | c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X1)),v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB,tc_Lambda_OdB) = X1
    | c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__4(X1))),v_sko__InductTermi__XIT__Xcases__5(X1)),v_sko__InductTermi__XIT__Xcases__6(X1),tc_Lambda_OdB,tc_Lambda_OdB) = X1
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_1712]) ).

cnf(c_0_1712_2,axiom,
    ( c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__4(X1))),v_sko__InductTermi__XIT__Xcases__5(X1)),v_sko__InductTermi__XIT__Xcases__6(X1),tc_Lambda_OdB,tc_Lambda_OdB) = X1
    | hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X1)))
    | c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X1)),v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB,tc_Lambda_OdB) = X1
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_1712]) ).

cnf(c_0_1712_3,axiom,
    ( ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
    | c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__4(X1))),v_sko__InductTermi__XIT__Xcases__5(X1)),v_sko__InductTermi__XIT__Xcases__6(X1),tc_Lambda_OdB,tc_Lambda_OdB) = X1
    | hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X1)))
    | c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X1)),v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB,tc_Lambda_OdB) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_1712]) ).

cnf(c_0_1713_0,axiom,
    ( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X1)),v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB,tc_Lambda_OdB) = X1
    | c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X1)) = X1
    | c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__4(X1))),v_sko__InductTermi__XIT__Xcases__5(X1)),v_sko__InductTermi__XIT__Xcases__6(X1),tc_Lambda_OdB,tc_Lambda_OdB) = X1
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_1713]) ).

cnf(c_0_1713_1,axiom,
    ( c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X1)) = X1
    | c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X1)),v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB,tc_Lambda_OdB) = X1
    | c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__4(X1))),v_sko__InductTermi__XIT__Xcases__5(X1)),v_sko__InductTermi__XIT__Xcases__6(X1),tc_Lambda_OdB,tc_Lambda_OdB) = X1
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_1713]) ).

cnf(c_0_1713_2,axiom,
    ( c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__4(X1))),v_sko__InductTermi__XIT__Xcases__5(X1)),v_sko__InductTermi__XIT__Xcases__6(X1),tc_Lambda_OdB,tc_Lambda_OdB) = X1
    | c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X1)) = X1
    | c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X1)),v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB,tc_Lambda_OdB) = X1
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_1713]) ).

cnf(c_0_1713_3,axiom,
    ( ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
    | c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__4(X1))),v_sko__InductTermi__XIT__Xcases__5(X1)),v_sko__InductTermi__XIT__Xcases__6(X1),tc_Lambda_OdB,tc_Lambda_OdB) = X1
    | c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X1)) = X1
    | c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X1)),v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB,tc_Lambda_OdB) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_1713]) ).

cnf(c_0_1714_0,axiom,
    ( c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X1),X2,c_HOL_Ozero__class_Ozero(X1),X1,X1) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1),X2,X1,X1)
    | ~ class_OrderedGroup_Omonoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1714]) ).

cnf(c_0_1714_1,axiom,
    ( ~ class_OrderedGroup_Omonoid__add(X1)
    | c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X1),X2,c_HOL_Ozero__class_Ozero(X1),X1,X1) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1),X2,X1,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1714]) ).

cnf(c_0_1715_0,axiom,
    ( c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X1),X2,X3,X1,X1) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),X3,X2,X1,X1)
    | ~ class_OrderedGroup_Oab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1715]) ).

cnf(c_0_1715_1,axiom,
    ( ~ class_OrderedGroup_Oab__semigroup__add(X1)
    | c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X1),X2,X3,X1,X1) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),X3,X2,X1,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1715]) ).

cnf(c_0_1716_0,axiom,
    ( hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) = X3
    | hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) != c_List_Ofoldl(c_Lambda_OdB_OApp,X3,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) ),
    inference(literals_permutation,[status(thm)],[c_0_1716]) ).

cnf(c_0_1716_1,axiom,
    ( hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) != c_List_Ofoldl(c_Lambda_OdB_OApp,X3,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)
    | hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) = X3 ),
    inference(literals_permutation,[status(thm)],[c_0_1716]) ).

cnf(c_0_1717_0,axiom,
    ( X1 = c_Lambda_OdB_OAbs(X2)
    | c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X3,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1717]) ).

cnf(c_0_1717_1,axiom,
    ( c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X3,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X2)
    | X1 = c_Lambda_OdB_OAbs(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1717]) ).

cnf(c_0_1718_0,axiom,
    ( c_Lambda_OdB_OAbs(X1) = X2
    | c_Lambda_OdB_OAbs(X1) != c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB) ),
    inference(literals_permutation,[status(thm)],[c_0_1718]) ).

cnf(c_0_1718_1,axiom,
    ( c_Lambda_OdB_OAbs(X1) != c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB)
    | c_Lambda_OdB_OAbs(X1) = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_1718]) ).

cnf(c_0_1719_0,axiom,
    ( c_Lambda_OdB_OVar(X1) = X2
    | c_Lambda_OdB_OVar(X1) != c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB) ),
    inference(literals_permutation,[status(thm)],[c_0_1719]) ).

cnf(c_0_1719_1,axiom,
    ( c_Lambda_OdB_OVar(X1) != c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB)
    | c_Lambda_OdB_OVar(X1) = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_1719]) ).

cnf(c_0_1720_0,axiom,
    ( hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)))),hAPP(hAPP(c_Lambda_Olift,X4),X2)),X1) = hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(hAPP(c_Lambda_Osubst,X3),X4),X1)),X2)
    | ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_1720]) ).

cnf(c_0_1720_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),tc_nat)
    | hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)))),hAPP(hAPP(c_Lambda_Olift,X4),X2)),X1) = hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(hAPP(c_Lambda_Osubst,X3),X4),X1)),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1720]) ).

cnf(c_0_1721_0,axiom,
    ( X1 = c_List_Olist_ONil(tc_Lambda_OdB)
    | c_Lambda_OdB_OAbs(X2) != c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X1,tc_Lambda_OdB,tc_Lambda_OdB) ),
    inference(literals_permutation,[status(thm)],[c_0_1721]) ).

cnf(c_0_1721_1,axiom,
    ( c_Lambda_OdB_OAbs(X2) != c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X1,tc_Lambda_OdB,tc_Lambda_OdB)
    | X1 = c_List_Olist_ONil(tc_Lambda_OdB) ),
    inference(literals_permutation,[status(thm)],[c_0_1721]) ).

cnf(c_0_1722_0,axiom,
    ( X1 = c_List_Olist_ONil(tc_Lambda_OdB)
    | c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X1,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1722]) ).

cnf(c_0_1722_1,axiom,
    ( c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X1,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X3)
    | X1 = c_List_Olist_ONil(tc_Lambda_OdB) ),
    inference(literals_permutation,[status(thm)],[c_0_1722]) ).

cnf(c_0_1723_0,axiom,
    ( X1 = c_List_Olist_ONil(tc_Lambda_OdB)
    | c_Lambda_OdB_OVar(X2) != c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X1,tc_Lambda_OdB,tc_Lambda_OdB) ),
    inference(literals_permutation,[status(thm)],[c_0_1723]) ).

cnf(c_0_1723_1,axiom,
    ( c_Lambda_OdB_OVar(X2) != c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X1,tc_Lambda_OdB,tc_Lambda_OdB)
    | X1 = c_List_Olist_ONil(tc_Lambda_OdB) ),
    inference(literals_permutation,[status(thm)],[c_0_1723]) ).

cnf(c_0_1724_0,axiom,
    ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X4),X3))
    | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Predicate_Oconversep(X1,X2,X2),X2),X3),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_1724]) ).

cnf(c_0_1724_1,axiom,
    ( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Predicate_Oconversep(X1,X2,X2),X2),X3),X4))
    | hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X4),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_1724]) ).

cnf(c_0_1725_0,axiom,
    ( c_ListOrder_Ostep1(X1,X2,X5,X4)
    | hBOOL(hAPP(hAPP(X1,X3),X6))
    | ~ c_ListOrder_Ostep1(X1,c_List_Oappend(X2,c_List_Olist_OCons(X3,c_List_Olist_ONil(X4),X4),X4),c_List_Oappend(X5,c_List_Olist_OCons(X6,c_List_Olist_ONil(X4),X4),X4),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_1725]) ).

cnf(c_0_1725_1,axiom,
    ( hBOOL(hAPP(hAPP(X1,X3),X6))
    | c_ListOrder_Ostep1(X1,X2,X5,X4)
    | ~ c_ListOrder_Ostep1(X1,c_List_Oappend(X2,c_List_Olist_OCons(X3,c_List_Olist_ONil(X4),X4),X4),c_List_Oappend(X5,c_List_Olist_OCons(X6,c_List_Olist_ONil(X4),X4),X4),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_1725]) ).

cnf(c_0_1725_2,axiom,
    ( ~ c_ListOrder_Ostep1(X1,c_List_Oappend(X2,c_List_Olist_OCons(X3,c_List_Olist_ONil(X4),X4),X4),c_List_Oappend(X5,c_List_Olist_OCons(X6,c_List_Olist_ONil(X4),X4),X4),X4)
    | hBOOL(hAPP(hAPP(X1,X3),X6))
    | c_ListOrder_Ostep1(X1,X2,X5,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_1725]) ).

cnf(c_0_1726_0,axiom,
    ( c_ListOrder_Ostep1(X1,X2,X5,X4)
    | X2 = X5
    | ~ c_ListOrder_Ostep1(X1,c_List_Oappend(X2,c_List_Olist_OCons(X3,c_List_Olist_ONil(X4),X4),X4),c_List_Oappend(X5,c_List_Olist_OCons(X6,c_List_Olist_ONil(X4),X4),X4),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_1726]) ).

cnf(c_0_1726_1,axiom,
    ( X2 = X5
    | c_ListOrder_Ostep1(X1,X2,X5,X4)
    | ~ c_ListOrder_Ostep1(X1,c_List_Oappend(X2,c_List_Olist_OCons(X3,c_List_Olist_ONil(X4),X4),X4),c_List_Oappend(X5,c_List_Olist_OCons(X6,c_List_Olist_ONil(X4),X4),X4),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_1726]) ).

cnf(c_0_1726_2,axiom,
    ( ~ c_ListOrder_Ostep1(X1,c_List_Oappend(X2,c_List_Olist_OCons(X3,c_List_Olist_ONil(X4),X4),X4),c_List_Oappend(X5,c_List_Olist_OCons(X6,c_List_Olist_ONil(X4),X4),X4),X4)
    | X2 = X5
    | c_ListOrder_Ostep1(X1,X2,X5,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_1726]) ).

cnf(c_0_1727_0,axiom,
    ( X3 = X6
    | hBOOL(hAPP(hAPP(X1,X3),X6))
    | ~ c_ListOrder_Ostep1(X1,c_List_Oappend(X2,c_List_Olist_OCons(X3,c_List_Olist_ONil(X4),X4),X4),c_List_Oappend(X5,c_List_Olist_OCons(X6,c_List_Olist_ONil(X4),X4),X4),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_1727]) ).

cnf(c_0_1727_1,axiom,
    ( hBOOL(hAPP(hAPP(X1,X3),X6))
    | X3 = X6
    | ~ c_ListOrder_Ostep1(X1,c_List_Oappend(X2,c_List_Olist_OCons(X3,c_List_Olist_ONil(X4),X4),X4),c_List_Oappend(X5,c_List_Olist_OCons(X6,c_List_Olist_ONil(X4),X4),X4),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_1727]) ).

cnf(c_0_1727_2,axiom,
    ( ~ c_ListOrder_Ostep1(X1,c_List_Oappend(X2,c_List_Olist_OCons(X3,c_List_Olist_ONil(X4),X4),X4),c_List_Oappend(X5,c_List_Olist_OCons(X6,c_List_Olist_ONil(X4),X4),X4),X4)
    | hBOOL(hAPP(hAPP(X1,X3),X6))
    | X3 = X6 ),
    inference(literals_permutation,[status(thm)],[c_0_1727]) ).

cnf(c_0_1728_0,axiom,
    ( c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB)
    | hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X1)))
    | c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__4(X1))),v_sko__InductTermi__XIT__Xcases__5(X1)),v_sko__InductTermi__XIT__Xcases__6(X1),tc_Lambda_OdB,tc_Lambda_OdB) = X1
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_1728]) ).

cnf(c_0_1728_1,axiom,
    ( hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X1)))
    | c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB)
    | c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__4(X1))),v_sko__InductTermi__XIT__Xcases__5(X1)),v_sko__InductTermi__XIT__Xcases__6(X1),tc_Lambda_OdB,tc_Lambda_OdB) = X1
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_1728]) ).

cnf(c_0_1728_2,axiom,
    ( c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__4(X1))),v_sko__InductTermi__XIT__Xcases__5(X1)),v_sko__InductTermi__XIT__Xcases__6(X1),tc_Lambda_OdB,tc_Lambda_OdB) = X1
    | hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X1)))
    | c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB)
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_1728]) ).

cnf(c_0_1728_3,axiom,
    ( ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
    | c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__4(X1))),v_sko__InductTermi__XIT__Xcases__5(X1)),v_sko__InductTermi__XIT__Xcases__6(X1),tc_Lambda_OdB,tc_Lambda_OdB) = X1
    | hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X1)))
    | c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB) ),
    inference(literals_permutation,[status(thm)],[c_0_1728]) ).

cnf(c_0_1729_0,axiom,
    ( X3 = X6
    | X2 = X5
    | ~ c_ListOrder_Ostep1(X1,c_List_Oappend(X2,c_List_Olist_OCons(X3,c_List_Olist_ONil(X4),X4),X4),c_List_Oappend(X5,c_List_Olist_OCons(X6,c_List_Olist_ONil(X4),X4),X4),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_1729]) ).

cnf(c_0_1729_1,axiom,
    ( X2 = X5
    | X3 = X6
    | ~ c_ListOrder_Ostep1(X1,c_List_Oappend(X2,c_List_Olist_OCons(X3,c_List_Olist_ONil(X4),X4),X4),c_List_Oappend(X5,c_List_Olist_OCons(X6,c_List_Olist_ONil(X4),X4),X4),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_1729]) ).

cnf(c_0_1729_2,axiom,
    ( ~ c_ListOrder_Ostep1(X1,c_List_Oappend(X2,c_List_Olist_OCons(X3,c_List_Olist_ONil(X4),X4),X4),c_List_Oappend(X5,c_List_Olist_OCons(X6,c_List_Olist_ONil(X4),X4),X4),X4)
    | X2 = X5
    | X3 = X6 ),
    inference(literals_permutation,[status(thm)],[c_0_1729]) ).

cnf(c_0_1730_0,axiom,
    ( c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB)
    | c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X1)) = X1
    | c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__4(X1))),v_sko__InductTermi__XIT__Xcases__5(X1)),v_sko__InductTermi__XIT__Xcases__6(X1),tc_Lambda_OdB,tc_Lambda_OdB) = X1
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_1730]) ).

cnf(c_0_1730_1,axiom,
    ( c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X1)) = X1
    | c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB)
    | c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__4(X1))),v_sko__InductTermi__XIT__Xcases__5(X1)),v_sko__InductTermi__XIT__Xcases__6(X1),tc_Lambda_OdB,tc_Lambda_OdB) = X1
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_1730]) ).

cnf(c_0_1730_2,axiom,
    ( c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__4(X1))),v_sko__InductTermi__XIT__Xcases__5(X1)),v_sko__InductTermi__XIT__Xcases__6(X1),tc_Lambda_OdB,tc_Lambda_OdB) = X1
    | c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X1)) = X1
    | c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB)
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_1730]) ).

cnf(c_0_1730_3,axiom,
    ( ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
    | c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__4(X1))),v_sko__InductTermi__XIT__Xcases__5(X1)),v_sko__InductTermi__XIT__Xcases__6(X1),tc_Lambda_OdB,tc_Lambda_OdB) = X1
    | c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X1)) = X1
    | c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB) ),
    inference(literals_permutation,[status(thm)],[c_0_1730]) ).

cnf(c_0_1731_0,axiom,
    ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X3),X4)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X2),X3),X4)))
    | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_1731]) ).

cnf(c_0_1731_1,axiom,
    ( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2))
    | hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X3),X4)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X2),X3),X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_1731]) ).

cnf(c_0_1732_0,axiom,
    ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,X3),X1),X4)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X3),X2),X4)))
    | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_1732]) ).

cnf(c_0_1732_1,axiom,
    ( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2))
    | hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,X3),X1),X4)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X3),X2),X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_1732]) ).

cnf(c_0_1733_0,axiom,
    ( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X1)),v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB,tc_Lambda_OdB) = X1
    | hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X1)))
    | hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__5(X1)))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_1733]) ).

cnf(c_0_1733_1,axiom,
    ( hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X1)))
    | c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X1)),v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB,tc_Lambda_OdB) = X1
    | hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__5(X1)))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_1733]) ).

cnf(c_0_1733_2,axiom,
    ( hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__5(X1)))
    | hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X1)))
    | c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X1)),v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB,tc_Lambda_OdB) = X1
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_1733]) ).

cnf(c_0_1733_3,axiom,
    ( ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
    | hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__5(X1)))
    | hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X1)))
    | c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X1)),v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB,tc_Lambda_OdB) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_1733]) ).

cnf(c_0_1734_0,axiom,
    ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Predicate_Oconversep(X1,X2,X2),X2),X4),X3))
    | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_1734]) ).

cnf(c_0_1734_1,axiom,
    ( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X4))
    | hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Predicate_Oconversep(X1,X2,X2),X2),X4),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_1734]) ).

cnf(c_0_1735_0,axiom,
    ( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X1)),v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB,tc_Lambda_OdB) = X1
    | c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X1)) = X1
    | hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__5(X1)))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_1735]) ).

cnf(c_0_1735_1,axiom,
    ( c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X1)) = X1
    | c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X1)),v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB,tc_Lambda_OdB) = X1
    | hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__5(X1)))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_1735]) ).

cnf(c_0_1735_2,axiom,
    ( hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__5(X1)))
    | c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X1)) = X1
    | c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X1)),v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB,tc_Lambda_OdB) = X1
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_1735]) ).

cnf(c_0_1735_3,axiom,
    ( ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
    | hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__5(X1)))
    | c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X1)) = X1
    | c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X1)),v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB,tc_Lambda_OdB) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_1735]) ).

cnf(c_0_1736_0,axiom,
    ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,X3),X1),X4)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X3),X2),X4)))
    | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_1736]) ).

cnf(c_0_1736_1,axiom,
    ( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2))
    | hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,X3),X1),X4)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X3),X2),X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_1736]) ).

cnf(c_0_1737_0,axiom,
    ( c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X2),X1,c_HOL_Ozero__class_Ozero(X2),X2,X2) = c_List_Olistsum(X1,X2)
    | ~ class_OrderedGroup_Omonoid__add(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1737]) ).

cnf(c_0_1737_1,axiom,
    ( ~ class_OrderedGroup_Omonoid__add(X2)
    | c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X2),X1,c_HOL_Ozero__class_Ozero(X2),X2,X2) = c_List_Olistsum(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1737]) ).

cnf(c_0_1738_0,axiom,
    ( c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X2),c_HOL_Ozero__class_Ozero(X2),X1,X2,X2) = c_List_Olistsum(X1,X2)
    | ~ class_OrderedGroup_Omonoid__add(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1738]) ).

cnf(c_0_1738_1,axiom,
    ( ~ class_OrderedGroup_Omonoid__add(X2)
    | c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X2),c_HOL_Ozero__class_Ozero(X2),X1,X2,X2) = c_List_Olistsum(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1738]) ).

cnf(c_0_1739_0,axiom,
    ( hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,X3),X1)),hAPP(hAPP(c_Lambda_Olift,X4),X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat))) = hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(hAPP(c_Lambda_Osubst,X3),X4),X2)),X1)
    | ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_1739]) ).

cnf(c_0_1739_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),tc_nat)
    | hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,X3),X1)),hAPP(hAPP(c_Lambda_Olift,X4),X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat))) = hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(hAPP(c_Lambda_Osubst,X3),X4),X2)),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1739]) ).

cnf(c_0_1740_0,axiom,
    ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X3),X4)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X2),X3),X4)))
    | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_1740]) ).

cnf(c_0_1740_1,axiom,
    ( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2))
    | hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X3),X4)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X2),X3),X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_1740]) ).

cnf(c_0_1741_0,axiom,
    ( c_Type_Otyping(X1,hAPP(hAPP(hAPP(c_Lambda_Osubst,X2),X3),X4),X5)
    | ~ c_Type_Otyping(c_Type_Oshift(X1,X4,X6,tc_Type_Otype),X2,X5)
    | ~ c_Type_Otyping(X1,X3,X6) ),
    inference(literals_permutation,[status(thm)],[c_0_1741]) ).

cnf(c_0_1741_1,axiom,
    ( ~ c_Type_Otyping(c_Type_Oshift(X1,X4,X6,tc_Type_Otype),X2,X5)
    | c_Type_Otyping(X1,hAPP(hAPP(hAPP(c_Lambda_Osubst,X2),X3),X4),X5)
    | ~ c_Type_Otyping(X1,X3,X6) ),
    inference(literals_permutation,[status(thm)],[c_0_1741]) ).

cnf(c_0_1741_2,axiom,
    ( ~ c_Type_Otyping(X1,X3,X6)
    | ~ c_Type_Otyping(c_Type_Oshift(X1,X4,X6,tc_Type_Otype),X2,X5)
    | c_Type_Otyping(X1,hAPP(hAPP(hAPP(c_Lambda_Osubst,X2),X3),X4),X5) ),
    inference(literals_permutation,[status(thm)],[c_0_1741]) ).

cnf(c_0_1742_0,axiom,
    ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X1),X3)),hAPP(hAPP(c_Lambda_OdB_OApp,X2),X4)))
    | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X3),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_1742]) ).

cnf(c_0_1742_1,axiom,
    ( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2))
    | hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X1),X3)),hAPP(hAPP(c_Lambda_OdB_OApp,X2),X4)))
    | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X3),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_1742]) ).

cnf(c_0_1742_2,axiom,
    ( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X3),X4))
    | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2))
    | hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X1),X3)),hAPP(hAPP(c_Lambda_OdB_OApp,X2),X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_1742]) ).

cnf(c_0_1743_0,axiom,
    ( hBOOL(hAPP(hAPP(X1,X2),X5))
    | c_ListOrder_Ostep1(X1,X3,X6,X4)
    | ~ c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X2,X3,X4),c_List_Olist_OCons(X5,X6,X4),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_1743]) ).

cnf(c_0_1743_1,axiom,
    ( c_ListOrder_Ostep1(X1,X3,X6,X4)
    | hBOOL(hAPP(hAPP(X1,X2),X5))
    | ~ c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X2,X3,X4),c_List_Olist_OCons(X5,X6,X4),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_1743]) ).

cnf(c_0_1743_2,axiom,
    ( ~ c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X2,X3,X4),c_List_Olist_OCons(X5,X6,X4),X4)
    | c_ListOrder_Ostep1(X1,X3,X6,X4)
    | hBOOL(hAPP(hAPP(X1,X2),X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_1743]) ).

cnf(c_0_1744_0,axiom,
    ( X6 = X3
    | c_ListOrder_Ostep1(X1,X3,X6,X4)
    | ~ c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X2,X3,X4),c_List_Olist_OCons(X5,X6,X4),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_1744]) ).

cnf(c_0_1744_1,axiom,
    ( c_ListOrder_Ostep1(X1,X3,X6,X4)
    | X6 = X3
    | ~ c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X2,X3,X4),c_List_Olist_OCons(X5,X6,X4),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_1744]) ).

cnf(c_0_1744_2,axiom,
    ( ~ c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X2,X3,X4),c_List_Olist_OCons(X5,X6,X4),X4)
    | c_ListOrder_Ostep1(X1,X3,X6,X4)
    | X6 = X3 ),
    inference(literals_permutation,[status(thm)],[c_0_1744]) ).

cnf(c_0_1745_0,axiom,
    ( hBOOL(hAPP(hAPP(X1,X5),X4))
    | ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X2,X3),X4),X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_1745]) ).

cnf(c_0_1745_1,axiom,
    ( ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X2,X3),X4),X5))
    | hBOOL(hAPP(hAPP(X1,X5),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_1745]) ).

cnf(c_0_1746_0,axiom,
    ( hBOOL(hAPP(hAPP(X1,X5),X4))
    | ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X2,X3),X4),X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_1746]) ).

cnf(c_0_1746_1,axiom,
    ( ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X2,X3),X4),X5))
    | hBOOL(hAPP(hAPP(X1,X5),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_1746]) ).

cnf(c_0_1747_0,axiom,
    ( c_ListOrder_Ostep1(X1,c_List_Oappend(X2,X3,X4),c_List_Oappend(X5,X3,X4),X4)
    | ~ c_ListOrder_Ostep1(X1,X2,X5,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_1747]) ).

cnf(c_0_1747_1,axiom,
    ( ~ c_ListOrder_Ostep1(X1,X2,X5,X4)
    | c_ListOrder_Ostep1(X1,c_List_Oappend(X2,X3,X4),c_List_Oappend(X5,X3,X4),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_1747]) ).

cnf(c_0_1748_0,axiom,
    ( c_ListOrder_Ostep1(X1,c_List_Oappend(X5,X2,X4),c_List_Oappend(X5,X3,X4),X4)
    | ~ c_ListOrder_Ostep1(X1,X2,X3,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_1748]) ).

cnf(c_0_1748_1,axiom,
    ( ~ c_ListOrder_Ostep1(X1,X2,X3,X4)
    | c_ListOrder_Ostep1(X1,c_List_Oappend(X5,X2,X4),c_List_Oappend(X5,X3,X4),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_1748]) ).

cnf(c_0_1749_0,axiom,
    ( c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X5,X2,X4),c_List_Olist_OCons(X5,X3,X4),X4)
    | ~ c_ListOrder_Ostep1(X1,X2,X3,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_1749]) ).

cnf(c_0_1749_1,axiom,
    ( ~ c_ListOrder_Ostep1(X1,X2,X3,X4)
    | c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X5,X2,X4),c_List_Olist_OCons(X5,X3,X4),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_1749]) ).

cnf(c_0_1750_0,axiom,
    ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X1),X3)),hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_1750]) ).

cnf(c_0_1750_1,axiom,
    ( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2))
    | hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X1),X3)),hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_1750]) ).

cnf(c_0_1751_0,axiom,
    ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X3),X1)),hAPP(hAPP(c_Lambda_OdB_OApp,X3),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_1751]) ).

cnf(c_0_1751_1,axiom,
    ( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2))
    | hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X3),X1)),hAPP(hAPP(c_Lambda_OdB_OApp,X3),X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_1751]) ).

cnf(c_0_1752_0,axiom,
    ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_Olift,X1),X3)),hAPP(hAPP(c_Lambda_Olift,X2),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_1752]) ).

cnf(c_0_1752_1,axiom,
    ( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2))
    | hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_Olift,X1),X3)),hAPP(hAPP(c_Lambda_Olift,X2),X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_1752]) ).

cnf(c_0_1753_0,axiom,
    ( hBOOL(hAPP(hAPP(X1,X2),X5))
    | X5 = X2
    | ~ c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X2,X3,X4),c_List_Olist_OCons(X5,X6,X4),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_1753]) ).

cnf(c_0_1753_1,axiom,
    ( X5 = X2
    | hBOOL(hAPP(hAPP(X1,X2),X5))
    | ~ c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X2,X3,X4),c_List_Olist_OCons(X5,X6,X4),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_1753]) ).

cnf(c_0_1753_2,axiom,
    ( ~ c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X2,X3,X4),c_List_Olist_OCons(X5,X6,X4),X4)
    | X5 = X2
    | hBOOL(hAPP(hAPP(X1,X2),X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_1753]) ).

cnf(c_0_1754_0,axiom,
    ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X5))
    | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X4))
    | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X4),X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_1754]) ).

cnf(c_0_1754_1,axiom,
    ( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X4))
    | hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X5))
    | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X4),X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_1754]) ).

cnf(c_0_1754_2,axiom,
    ( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X4),X5))
    | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X4))
    | hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_1754]) ).

cnf(c_0_1755_0,axiom,
    ( X6 = X3
    | X5 = X2
    | ~ c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X2,X3,X4),c_List_Olist_OCons(X5,X6,X4),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_1755]) ).

cnf(c_0_1755_1,axiom,
    ( X5 = X2
    | X6 = X3
    | ~ c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X2,X3,X4),c_List_Olist_OCons(X5,X6,X4),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_1755]) ).

cnf(c_0_1755_2,axiom,
    ( ~ c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X2,X3,X4),c_List_Olist_OCons(X5,X6,X4),X4)
    | X5 = X2
    | X6 = X3 ),
    inference(literals_permutation,[status(thm)],[c_0_1755]) ).

cnf(c_0_1756_0,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X5)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X5))
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1756]) ).

cnf(c_0_1756_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X5)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_1756]) ).

cnf(c_0_1757_0,axiom,
    ( c_Type_Otyping(c_Type_Oshift(X1,X4,X5,tc_Type_Otype),hAPP(hAPP(c_Lambda_Olift,X2),X4),X3)
    | ~ c_Type_Otyping(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1757]) ).

cnf(c_0_1757_1,axiom,
    ( ~ c_Type_Otyping(X1,X2,X3)
    | c_Type_Otyping(c_Type_Oshift(X1,X4,X5,tc_Type_Otype),hAPP(hAPP(c_Lambda_Olift,X2),X4),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1757]) ).

cnf(c_0_1758_0,axiom,
    ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X4,X5),X3),X2))
    | ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_1758]) ).

cnf(c_0_1758_1,axiom,
    ( ~ hBOOL(hAPP(hAPP(X1,X2),X3))
    | hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X4,X5),X3),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_1758]) ).

cnf(c_0_1759_0,axiom,
    ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X4,X5),X3),X2))
    | ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_1759]) ).

cnf(c_0_1759_1,axiom,
    ( ~ hBOOL(hAPP(hAPP(X1,X2),X3))
    | hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X4,X5),X3),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_1759]) ).

cnf(c_0_1760_0,axiom,
    ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_Olift,X1),X3)),hAPP(hAPP(c_Lambda_Olift,X2),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_1760]) ).

cnf(c_0_1760_1,axiom,
    ( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2))
    | hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_Olift,X1),X3)),hAPP(hAPP(c_Lambda_Olift,X2),X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_1760]) ).

cnf(c_0_1761_0,axiom,
    ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,X3),X1)),hAPP(hAPP(c_Lambda_OdB_OApp,X3),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_1761]) ).

cnf(c_0_1761_1,axiom,
    ( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2))
    | hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,X3),X1)),hAPP(hAPP(c_Lambda_OdB_OApp,X3),X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_1761]) ).

cnf(c_0_1762_0,axiom,
    ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,X1),X3)),hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_1762]) ).

cnf(c_0_1762_1,axiom,
    ( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2))
    | hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,X1),X3)),hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_1762]) ).

cnf(c_0_1763_0,axiom,
    ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X4),X2),X5))
    | ~ hBOOL(hAPP(hAPP(X1,X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X4),X3),X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_1763]) ).

cnf(c_0_1763_1,axiom,
    ( ~ hBOOL(hAPP(hAPP(X1,X2),X3))
    | hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X4),X2),X5))
    | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X4),X3),X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_1763]) ).

cnf(c_0_1763_2,axiom,
    ( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X4),X3),X5))
    | ~ hBOOL(hAPP(hAPP(X1,X2),X3))
    | hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X4),X2),X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_1763]) ).

cnf(c_0_1764_0,axiom,
    ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X5))
    | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X4))
    | ~ hBOOL(hAPP(hAPP(X1,X4),X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_1764]) ).

cnf(c_0_1764_1,axiom,
    ( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X4))
    | hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X5))
    | ~ hBOOL(hAPP(hAPP(X1,X4),X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_1764]) ).

cnf(c_0_1764_2,axiom,
    ( ~ hBOOL(hAPP(hAPP(X1,X4),X5))
    | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X4))
    | hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_1764]) ).

cnf(c_0_1765_0,axiom,
    ( hAPP(c_Type_Oshift(X3,X2,X4,X5),X1) = hAPP(X3,X1)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_1765]) ).

cnf(c_0_1765_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | hAPP(c_Type_Oshift(X3,X2,X4,X5),X1) = hAPP(X3,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1765]) ).

cnf(c_0_1766_0,axiom,
    ( c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X2,X3,X4),c_List_Olist_OCons(X5,X3,X4),X4)
    | ~ hBOOL(hAPP(hAPP(X1,X2),X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_1766]) ).

cnf(c_0_1766_1,axiom,
    ( ~ hBOOL(hAPP(hAPP(X1,X2),X5))
    | c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X2,X3,X4),c_List_Olist_OCons(X5,X3,X4),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_1766]) ).

cnf(c_0_1767_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,X4,X3)
    | ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X4,X2,X3),X3)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
    | ~ class_Ring__and__Field_Oordered__semidom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1767]) ).

cnf(c_0_1767_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X4,X2,X3),X3)
    | c_HOL_Oord__class_Oless(X1,X4,X3)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
    | ~ class_Ring__and__Field_Oordered__semidom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1767]) ).

cnf(c_0_1767_2,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
    | ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X4,X2,X3),X3)
    | c_HOL_Oord__class_Oless(X1,X4,X3)
    | ~ class_Ring__and__Field_Oordered__semidom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1767]) ).

cnf(c_0_1767_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X3)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
    | ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X4,X2,X3),X3)
    | c_HOL_Oord__class_Oless(X1,X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1767]) ).

cnf(c_0_1768_0,axiom,
    ( c_HOL_Oord__class_Oless(X3,X4,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
    | ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1768]) ).

cnf(c_0_1768_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
    | c_HOL_Oord__class_Oless(X3,X4,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1768]) ).

cnf(c_0_1768_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
    | c_HOL_Oord__class_Oless(X3,X4,tc_nat)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1768]) ).

cnf(c_0_1768_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
    | c_HOL_Oord__class_Oless(X3,X4,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_1768]) ).

cnf(c_0_1769_0,axiom,
    ( c_HOL_Oord__class_Oless(X3,X4,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
    | ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1769]) ).

cnf(c_0_1769_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
    | c_HOL_Oord__class_Oless(X3,X4,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1769]) ).

cnf(c_0_1769_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
    | c_HOL_Oord__class_Oless(X3,X4,tc_nat)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1769]) ).

cnf(c_0_1769_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
    | c_HOL_Oord__class_Oless(X3,X4,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_1769]) ).

cnf(c_0_1770_0,axiom,
    ( c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X4,X2,X3),c_Power_Opower__class_Opower(X4,X1,X3),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
    | ~ c_HOL_Oord__class_Oless(X4,c_HOL_Oone__class_Oone(X3),X3)
    | ~ class_Ring__and__Field_Oordered__semidom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1770]) ).

cnf(c_0_1770_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X4,X2,X3),c_Power_Opower__class_Opower(X4,X1,X3),X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
    | ~ c_HOL_Oord__class_Oless(X4,c_HOL_Oone__class_Oone(X3),X3)
    | ~ class_Ring__and__Field_Oordered__semidom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1770]) ).

cnf(c_0_1770_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X4,X2,X3),c_Power_Opower__class_Opower(X4,X1,X3),X3)
    | ~ c_HOL_Oord__class_Oless(X4,c_HOL_Oone__class_Oone(X3),X3)
    | ~ class_Ring__and__Field_Oordered__semidom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1770]) ).

cnf(c_0_1770_3,axiom,
    ( ~ c_HOL_Oord__class_Oless(X4,c_HOL_Oone__class_Oone(X3),X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X4,X2,X3),c_Power_Opower__class_Opower(X4,X1,X3),X3)
    | ~ class_Ring__and__Field_Oordered__semidom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1770]) ).

cnf(c_0_1770_4,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X3)
    | ~ c_HOL_Oord__class_Oless(X4,c_HOL_Oone__class_Oone(X3),X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X4,X2,X3),c_Power_Opower__class_Opower(X4,X1,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1770]) ).

cnf(c_0_1771_0,axiom,
    ( X1 = X2
    | c_List_Oappend(X1,c_List_Olist_OCons(X3,c_List_Olist_ONil(X4),X4),X4) != c_List_Oappend(X2,c_List_Olist_OCons(X5,c_List_Olist_ONil(X4),X4),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_1771]) ).

cnf(c_0_1771_1,axiom,
    ( c_List_Oappend(X1,c_List_Olist_OCons(X3,c_List_Olist_ONil(X4),X4),X4) != c_List_Oappend(X2,c_List_Olist_OCons(X5,c_List_Olist_ONil(X4),X4),X4)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_1771]) ).

cnf(c_0_1772_0,axiom,
    ( X1 = X2
    | c_List_Oappend(X3,c_List_Olist_OCons(X1,c_List_Olist_ONil(X4),X4),X4) != c_List_Oappend(X5,c_List_Olist_OCons(X2,c_List_Olist_ONil(X4),X4),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_1772]) ).

cnf(c_0_1772_1,axiom,
    ( c_List_Oappend(X3,c_List_Olist_OCons(X1,c_List_Olist_ONil(X4),X4),X4) != c_List_Oappend(X5,c_List_Olist_OCons(X2,c_List_Olist_ONil(X4),X4),X4)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_1772]) ).

cnf(c_0_1773_0,axiom,
    ( c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X4,X3),c_Power_Opower__class_Opower(X2,X4,X3),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
    | ~ class_Ring__and__Field_Oordered__semidom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1773]) ).

cnf(c_0_1773_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X4,X3),c_Power_Opower__class_Opower(X2,X4,X3),X3)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
    | ~ class_Ring__and__Field_Oordered__semidom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1773]) ).

cnf(c_0_1773_2,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X4,X3),c_Power_Opower__class_Opower(X2,X4,X3),X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
    | ~ class_Ring__and__Field_Oordered__semidom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1773]) ).

cnf(c_0_1773_3,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X4,X3),c_Power_Opower__class_Opower(X2,X4,X3),X3)
    | ~ class_Ring__and__Field_Oordered__semidom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1773]) ).

cnf(c_0_1773_4,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X4,X3),c_Power_Opower__class_Opower(X2,X4,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1773]) ).

cnf(c_0_1774_0,axiom,
    ( c_Orderings_Oord__class_Omax(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4),X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_Orderings_Oord__class_Omax(X2,X3,X1)),X4)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1774]) ).

cnf(c_0_1774_1,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | c_Orderings_Oord__class_Omax(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4),X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_Orderings_Oord__class_Omax(X2,X3,X1)),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_1774]) ).

cnf(c_0_1775_0,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1775]) ).

cnf(c_0_1775_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1775]) ).

cnf(c_0_1776_0,axiom,
    ( c_lessequals(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),X5),X2)
    | ~ c_lessequals(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),X4),X2)
    | ~ c_lessequals(X4,X5,X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1776]) ).

cnf(c_0_1776_1,axiom,
    ( ~ c_lessequals(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),X4),X2)
    | c_lessequals(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),X5),X2)
    | ~ c_lessequals(X4,X5,X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1776]) ).

cnf(c_0_1776_2,axiom,
    ( ~ c_lessequals(X4,X5,X2)
    | ~ c_lessequals(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),X4),X2)
    | c_lessequals(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),X5),X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1776]) ).

cnf(c_0_1776_3,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
    | ~ c_lessequals(X4,X5,X2)
    | ~ c_lessequals(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),X4),X2)
    | c_lessequals(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),X5),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1776]) ).

cnf(c_0_1777_0,axiom,
    ( c_lessequals(X3,X4,X1)
    | ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1777]) ).

cnf(c_0_1777_1,axiom,
    ( ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
    | c_lessequals(X3,X4,X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1777]) ).

cnf(c_0_1777_2,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
    | c_lessequals(X3,X4,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1777]) ).

cnf(c_0_1778_0,axiom,
    ( c_lessequals(X2,X4,X1)
    | ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3),X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1778]) ).

cnf(c_0_1778_1,axiom,
    ( ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3),X1)
    | c_lessequals(X2,X4,X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1778]) ).

cnf(c_0_1778_2,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3),X1)
    | c_lessequals(X2,X4,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1778]) ).

cnf(c_0_1779_0,axiom,
    ( c_HOL_Oord__class_Oless(X2,X4,X1)
    | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3),X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1779]) ).

cnf(c_0_1779_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3),X1)
    | c_HOL_Oord__class_Oless(X2,X4,X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1779]) ).

cnf(c_0_1779_2,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3),X1)
    | c_HOL_Oord__class_Oless(X2,X4,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1779]) ).

cnf(c_0_1780_0,axiom,
    ( c_HOL_Oord__class_Oless(X3,X4,X1)
    | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1780]) ).

cnf(c_0_1780_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
    | c_HOL_Oord__class_Oless(X3,X4,X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1780]) ).

cnf(c_0_1780_2,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
    | c_HOL_Oord__class_Oless(X3,X4,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1780]) ).

cnf(c_0_1781_0,axiom,
    ( X2 = X3
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
    | c_Power_Opower__class_Opower(X2,X4,X1) != c_Power_Opower__class_Opower(X3,X4,X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1781]) ).

cnf(c_0_1781_1,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | X2 = X3
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
    | c_Power_Opower__class_Opower(X2,X4,X1) != c_Power_Opower__class_Opower(X3,X4,X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1781]) ).

cnf(c_0_1781_2,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | X2 = X3
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
    | c_Power_Opower__class_Opower(X2,X4,X1) != c_Power_Opower__class_Opower(X3,X4,X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1781]) ).

cnf(c_0_1781_3,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | X2 = X3
    | c_Power_Opower__class_Opower(X2,X4,X1) != c_Power_Opower__class_Opower(X3,X4,X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1781]) ).

cnf(c_0_1781_4,axiom,
    ( c_Power_Opower__class_Opower(X2,X4,X1) != c_Power_Opower__class_Opower(X3,X4,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | X2 = X3
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1781]) ).

cnf(c_0_1781_5,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | c_Power_Opower__class_Opower(X2,X4,X1) != c_Power_Opower__class_Opower(X3,X4,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | X2 = X3 ),
    inference(literals_permutation,[status(thm)],[c_0_1781]) ).

cnf(c_0_1782_0,axiom,
    ( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),c_Lambda_OdB_OVar(X2)),X3)))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_1782]) ).

cnf(c_0_1782_1,axiom,
    ( ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
    | hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),c_Lambda_OdB_OVar(X2)),X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_1782]) ).

cnf(c_0_1783_0,axiom,
    ( c_lessequals(c_Power_Opower__class_Opower(X1,X4,X3),c_Power_Opower__class_Opower(X2,X4,X3),X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
    | ~ class_Ring__and__Field_Oordered__semidom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1783]) ).

cnf(c_0_1783_1,axiom,
    ( ~ c_lessequals(X1,X2,X3)
    | c_lessequals(c_Power_Opower__class_Opower(X1,X4,X3),c_Power_Opower__class_Opower(X2,X4,X3),X3)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
    | ~ class_Ring__and__Field_Oordered__semidom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1783]) ).

cnf(c_0_1783_2,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_lessequals(c_Power_Opower__class_Opower(X1,X4,X3),c_Power_Opower__class_Opower(X2,X4,X3),X3)
    | ~ class_Ring__and__Field_Oordered__semidom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1783]) ).

cnf(c_0_1783_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X3)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_lessequals(c_Power_Opower__class_Opower(X1,X4,X3),c_Power_Opower__class_Opower(X2,X4,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1783]) ).

cnf(c_0_1784_0,axiom,
    ( c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X4,X1,X3),c_Power_Opower__class_Opower(X4,X2,X3),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X4,X3)
    | ~ class_Ring__and__Field_Oordered__semidom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1784]) ).

cnf(c_0_1784_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X4,X1,X3),c_Power_Opower__class_Opower(X4,X2,X3),X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X4,X3)
    | ~ class_Ring__and__Field_Oordered__semidom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1784]) ).

cnf(c_0_1784_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X4,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X4,X1,X3),c_Power_Opower__class_Opower(X4,X2,X3),X3)
    | ~ class_Ring__and__Field_Oordered__semidom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1784]) ).

cnf(c_0_1784_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X4,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X4,X1,X3),c_Power_Opower__class_Opower(X4,X2,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1784]) ).

cnf(c_0_1785_0,axiom,
    ( c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
    | ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1785]) ).

cnf(c_0_1785_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
    | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1)
    | ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1785]) ).

cnf(c_0_1785_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
    | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1785]) ).

cnf(c_0_1785_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
    | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1785]) ).

cnf(c_0_1786_0,axiom,
    ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_OdB_OAbs(X1)),c_Lambda_OdB_OAbs(X2)))
    | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_1786]) ).

cnf(c_0_1786_1,axiom,
    ( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2))
    | hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_OdB_OAbs(X1)),c_Lambda_OdB_OAbs(X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_1786]) ).

cnf(c_0_1787_0,axiom,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X5),X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X4,X5,X3)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1787]) ).

cnf(c_0_1787_1,axiom,
    ( ~ c_lessequals(X1,X2,X3)
    | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X5),X3)
    | ~ c_HOL_Oord__class_Oless(X4,X5,X3)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1787]) ).

cnf(c_0_1787_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(X4,X5,X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X5),X3)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1787]) ).

cnf(c_0_1787_3,axiom,
    ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
    | ~ c_HOL_Oord__class_Oless(X4,X5,X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X5),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1787]) ).

cnf(c_0_1788_0,axiom,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X5),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_lessequals(X4,X5,X3)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1788]) ).

cnf(c_0_1788_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X5),X3)
    | ~ c_lessequals(X4,X5,X3)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1788]) ).

cnf(c_0_1788_2,axiom,
    ( ~ c_lessequals(X4,X5,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X5),X3)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1788]) ).

cnf(c_0_1788_3,axiom,
    ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
    | ~ c_lessequals(X4,X5,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X5),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1788]) ).

cnf(c_0_1789_0,axiom,
    ( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X5),X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_lessequals(X4,X5,X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1789]) ).

cnf(c_0_1789_1,axiom,
    ( ~ c_lessequals(X1,X2,X3)
    | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X5),X3)
    | ~ c_lessequals(X4,X5,X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1789]) ).

cnf(c_0_1789_2,axiom,
    ( ~ c_lessequals(X4,X5,X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X5),X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1789]) ).

cnf(c_0_1789_3,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3)
    | ~ c_lessequals(X4,X5,X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X5),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1789]) ).

cnf(c_0_1790_0,axiom,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X5),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X4,X5,X3)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1790]) ).

cnf(c_0_1790_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X5),X3)
    | ~ c_HOL_Oord__class_Oless(X4,X5,X3)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1790]) ).

cnf(c_0_1790_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(X4,X5,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X5),X3)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1790]) ).

cnf(c_0_1790_3,axiom,
    ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
    | ~ c_HOL_Oord__class_Oless(X4,X5,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X5),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1790]) ).

cnf(c_0_1791_0,axiom,
    ( c_Wellfounded_Oaccp(X1,X4,X3)
    | ~ c_Wellfounded_Oaccp(X1,X2,X3)
    | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X3),X4),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_1791]) ).

cnf(c_0_1791_1,axiom,
    ( ~ c_Wellfounded_Oaccp(X1,X2,X3)
    | c_Wellfounded_Oaccp(X1,X4,X3)
    | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X3),X4),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_1791]) ).

cnf(c_0_1791_2,axiom,
    ( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X3),X4),X2))
    | ~ c_Wellfounded_Oaccp(X1,X2,X3)
    | c_Wellfounded_Oaccp(X1,X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1791]) ).

cnf(c_0_1792_0,axiom,
    ( c_Wellfounded_Oaccp(X1,X3,X2)
    | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X4))
    | ~ c_Wellfounded_Oaccp(X1,X4,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1792]) ).

cnf(c_0_1792_1,axiom,
    ( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X4))
    | c_Wellfounded_Oaccp(X1,X3,X2)
    | ~ c_Wellfounded_Oaccp(X1,X4,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1792]) ).

cnf(c_0_1792_2,axiom,
    ( ~ c_Wellfounded_Oaccp(X1,X4,X2)
    | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X4))
    | c_Wellfounded_Oaccp(X1,X3,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1792]) ).

cnf(c_0_1793_0,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_1793]) ).

cnf(c_0_1793_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),tc_nat)
    | c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_1793]) ).

cnf(c_0_1794_0,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1794]) ).

cnf(c_0_1794_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_1794]) ).

cnf(c_0_1795_0,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1795]) ).

cnf(c_0_1795_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_1795]) ).

cnf(c_0_1796_0,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
    | ~ class_OrderedGroup_Oab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1796]) ).

cnf(c_0_1796_1,axiom,
    ( ~ class_OrderedGroup_Oab__semigroup__add(X1)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_1796]) ).

cnf(c_0_1797_0,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1797]) ).

cnf(c_0_1797_1,axiom,
    ( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_1797]) ).

cnf(c_0_1798_0,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1798]) ).

cnf(c_0_1798_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_1798]) ).

cnf(c_0_1799_0,axiom,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X4),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_1799]) ).

cnf(c_0_1799_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X4),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_1799]) ).

cnf(c_0_1799_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X4),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_1799]) ).

cnf(c_0_1800_0,axiom,
    ( X1 = c_List_Olist_ONil(X2)
    | c_List_Omap(X4,X1,X2,X3) != c_List_Olist_ONil(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1800]) ).

cnf(c_0_1800_1,axiom,
    ( c_List_Omap(X4,X1,X2,X3) != c_List_Olist_ONil(X3)
    | X1 = c_List_Olist_ONil(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1800]) ).

cnf(c_0_1801_0,axiom,
    ( X1 = c_List_Olist_ONil(X2)
    | c_List_Omap(X3,X1,X2,X4) != c_List_Olist_ONil(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_1801]) ).

cnf(c_0_1801_1,axiom,
    ( c_List_Omap(X3,X1,X2,X4) != c_List_Olist_ONil(X4)
    | X1 = c_List_Olist_ONil(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1801]) ).

cnf(c_0_1802_0,axiom,
    ( c_Type_Otyping(X3,X2,X4)
    | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2))
    | ~ c_Type_Otyping(X3,X1,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_1802]) ).

cnf(c_0_1802_1,axiom,
    ( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2))
    | c_Type_Otyping(X3,X2,X4)
    | ~ c_Type_Otyping(X3,X1,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_1802]) ).

cnf(c_0_1802_2,axiom,
    ( ~ c_Type_Otyping(X3,X1,X4)
    | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2))
    | c_Type_Otyping(X3,X2,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_1802]) ).

cnf(c_0_1803_0,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = X4
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X5),X3)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X5),X4)
    | ~ class_OrderedGroup_Oab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1803]) ).

cnf(c_0_1803_1,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X5),X3)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X5),X4)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = X4
    | ~ class_OrderedGroup_Oab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1803]) ).

cnf(c_0_1803_2,axiom,
    ( ~ class_OrderedGroup_Oab__group__add(X1)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X5),X3)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X5),X4)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = X4 ),
    inference(literals_permutation,[status(thm)],[c_0_1803]) ).

cnf(c_0_1804_0,axiom,
    ( c_lessequals(X1,X2,X4)
    | c_lessequals(X1,X3,X4)
    | ~ c_lessequals(X1,c_Orderings_Oord__class_Omax(X2,X3,X4),X4)
    | ~ class_Orderings_Olinorder(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_1804]) ).

cnf(c_0_1804_1,axiom,
    ( c_lessequals(X1,X3,X4)
    | c_lessequals(X1,X2,X4)
    | ~ c_lessequals(X1,c_Orderings_Oord__class_Omax(X2,X3,X4),X4)
    | ~ class_Orderings_Olinorder(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_1804]) ).

cnf(c_0_1804_2,axiom,
    ( ~ c_lessequals(X1,c_Orderings_Oord__class_Omax(X2,X3,X4),X4)
    | c_lessequals(X1,X3,X4)
    | c_lessequals(X1,X2,X4)
    | ~ class_Orderings_Olinorder(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_1804]) ).

cnf(c_0_1804_3,axiom,
    ( ~ class_Orderings_Olinorder(X4)
    | ~ c_lessequals(X1,c_Orderings_Oord__class_Omax(X2,X3,X4),X4)
    | c_lessequals(X1,X3,X4)
    | c_lessequals(X1,X2,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_1804]) ).

cnf(c_0_1805_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,X4)
    | c_HOL_Oord__class_Oless(X1,X3,X4)
    | ~ c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X2,X3,X4),X4)
    | ~ class_Orderings_Olinorder(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_1805]) ).

cnf(c_0_1805_1,axiom,
    ( c_HOL_Oord__class_Oless(X1,X3,X4)
    | c_HOL_Oord__class_Oless(X1,X2,X4)
    | ~ c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X2,X3,X4),X4)
    | ~ class_Orderings_Olinorder(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_1805]) ).

cnf(c_0_1805_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X2,X3,X4),X4)
    | c_HOL_Oord__class_Oless(X1,X3,X4)
    | c_HOL_Oord__class_Oless(X1,X2,X4)
    | ~ class_Orderings_Olinorder(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_1805]) ).

cnf(c_0_1805_3,axiom,
    ( ~ class_Orderings_Olinorder(X4)
    | ~ c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X2,X3,X4),X4)
    | c_HOL_Oord__class_Oless(X1,X3,X4)
    | c_HOL_Oord__class_Oless(X1,X2,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_1805]) ).

cnf(c_0_1806_0,axiom,
    ( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X3),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1806]) ).

cnf(c_0_1806_1,axiom,
    ( ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X3),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1806]) ).

cnf(c_0_1806_2,axiom,
    ( ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X3),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1806]) ).

cnf(c_0_1806_3,axiom,
    ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X2)
    | ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X3),c_HOL_Ozero__class_Ozero(X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1806]) ).

cnf(c_0_1807_0,axiom,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1807]) ).

cnf(c_0_1807_1,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1807]) ).

cnf(c_0_1807_2,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X1)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1807]) ).

cnf(c_0_1807_3,axiom,
    ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1807]) ).

cnf(c_0_1808_0,axiom,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X3),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1808]) ).

cnf(c_0_1808_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X3),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1808]) ).

cnf(c_0_1808_2,axiom,
    ( ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X3),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1808]) ).

cnf(c_0_1808_3,axiom,
    ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X2)
    | ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X3),c_HOL_Ozero__class_Ozero(X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1808]) ).

cnf(c_0_1809_0,axiom,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X3),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1809]) ).

cnf(c_0_1809_1,axiom,
    ( ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X3),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1809]) ).

cnf(c_0_1809_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X3),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1809]) ).

cnf(c_0_1809_3,axiom,
    ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X2)
    | ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X3),c_HOL_Ozero__class_Ozero(X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1809]) ).

cnf(c_0_1810_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1810]) ).

cnf(c_0_1810_1,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1810]) ).

cnf(c_0_1810_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X1)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1810]) ).

cnf(c_0_1810_3,axiom,
    ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1810]) ).

cnf(c_0_1811_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1811]) ).

cnf(c_0_1811_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1811]) ).

cnf(c_0_1811_2,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X1)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1811]) ).

cnf(c_0_1811_3,axiom,
    ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1811]) ).

cnf(c_0_1812_0,axiom,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X3),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1812]) ).

cnf(c_0_1812_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X3),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1812]) ).

cnf(c_0_1812_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X3),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1812]) ).

cnf(c_0_1812_3,axiom,
    ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X2)
    | ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X3),c_HOL_Ozero__class_Ozero(X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1812]) ).

cnf(c_0_1813_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1813]) ).

cnf(c_0_1813_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1813]) ).

cnf(c_0_1813_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X1)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1813]) ).

cnf(c_0_1813_3,axiom,
    ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1813]) ).

cnf(c_0_1814_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1814]) ).

cnf(c_0_1814_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
    | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1814]) ).

cnf(c_0_1814_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
    | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1814]) ).

cnf(c_0_1814_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
    | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1814]) ).

cnf(c_0_1815_0,axiom,
    ( c_lessequals(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X2),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_lessequals(X3,X4,X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1815]) ).

cnf(c_0_1815_1,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_lessequals(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X2),X1)
    | ~ c_lessequals(X3,X4,X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1815]) ).

cnf(c_0_1815_2,axiom,
    ( ~ c_lessequals(X3,X4,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_lessequals(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X2),X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1815]) ).

cnf(c_0_1815_3,axiom,
    ( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ c_lessequals(X3,X4,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_lessequals(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X2),X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1815]) ).

cnf(c_0_1815_4,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ c_lessequals(X3,X4,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_lessequals(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X2),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1815]) ).

cnf(c_0_1816_0,axiom,
    ( c_lessequals(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_lessequals(X3,X4,X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1816]) ).

cnf(c_0_1816_1,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_lessequals(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
    | ~ c_lessequals(X3,X4,X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1816]) ).

cnf(c_0_1816_2,axiom,
    ( ~ c_lessequals(X3,X4,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_lessequals(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1816]) ).

cnf(c_0_1816_3,axiom,
    ( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ c_lessequals(X3,X4,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_lessequals(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1816]) ).

cnf(c_0_1816_4,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ c_lessequals(X3,X4,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_lessequals(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1816]) ).

cnf(c_0_1817_0,axiom,
    ( c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_lessequals(X3,X4,X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1817]) ).

cnf(c_0_1817_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
    | ~ c_lessequals(X3,X4,X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1817]) ).

cnf(c_0_1817_2,axiom,
    ( ~ c_lessequals(X3,X4,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1817]) ).

cnf(c_0_1817_3,axiom,
    ( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ c_lessequals(X3,X4,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1817]) ).

cnf(c_0_1817_4,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ c_lessequals(X3,X4,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1817]) ).

cnf(c_0_1818_0,axiom,
    ( c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_HOL_Oord__class_Oless(X3,X4,X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1818]) ).

cnf(c_0_1818_1,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
    | ~ c_HOL_Oord__class_Oless(X3,X4,X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1818]) ).

cnf(c_0_1818_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(X3,X4,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1818]) ).

cnf(c_0_1818_3,axiom,
    ( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ c_HOL_Oord__class_Oless(X3,X4,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1818]) ).

cnf(c_0_1818_4,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ c_HOL_Oord__class_Oless(X3,X4,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1818]) ).

cnf(c_0_1819_0,axiom,
    ( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2),X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1819]) ).

cnf(c_0_1819_1,axiom,
    ( ~ c_lessequals(X1,X2,X3)
    | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2),X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1819]) ).

cnf(c_0_1819_2,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1819]) ).

cnf(c_0_1820_0,axiom,
    ( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4),X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1820]) ).

cnf(c_0_1820_1,axiom,
    ( ~ c_lessequals(X1,X2,X3)
    | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4),X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1820]) ).

cnf(c_0_1820_2,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1820]) ).

cnf(c_0_1821_0,axiom,
    ( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2),X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1821]) ).

cnf(c_0_1821_1,axiom,
    ( ~ c_lessequals(X1,X2,X3)
    | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2),X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1821]) ).

cnf(c_0_1821_2,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1821]) ).

cnf(c_0_1822_0,axiom,
    ( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4),X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1822]) ).

cnf(c_0_1822_1,axiom,
    ( ~ c_lessequals(X1,X2,X3)
    | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4),X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1822]) ).

cnf(c_0_1822_2,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1822]) ).

cnf(c_0_1823_0,axiom,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1823]) ).

cnf(c_0_1823_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4),X3)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1823]) ).

cnf(c_0_1823_2,axiom,
    ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1823]) ).

cnf(c_0_1824_0,axiom,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1824]) ).

cnf(c_0_1824_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4),X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1824]) ).

cnf(c_0_1824_2,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1824]) ).

cnf(c_0_1825_0,axiom,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1825]) ).

cnf(c_0_1825_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2),X3)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1825]) ).

cnf(c_0_1825_2,axiom,
    ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1825]) ).

cnf(c_0_1826_0,axiom,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1826]) ).

cnf(c_0_1826_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2),X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1826]) ).

cnf(c_0_1826_2,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1826]) ).

cnf(c_0_1827_0,axiom,
    ( c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_HOL_Oord__class_Oless(X3,X4,X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1827]) ).

cnf(c_0_1827_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
    | ~ c_HOL_Oord__class_Oless(X3,X4,X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1827]) ).

cnf(c_0_1827_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(X3,X4,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1827]) ).

cnf(c_0_1827_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | ~ c_HOL_Oord__class_Oless(X3,X4,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1827]) ).

cnf(c_0_1828_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_1828]) ).

cnf(c_0_1828_1,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_1828]) ).

cnf(c_0_1828_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),tc_nat)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_1828]) ).

cnf(c_0_1829_0,axiom,
    ( c_lessequals(c_Orderings_Oord__class_Omax(X1,X4,X3),X2,X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_lessequals(X4,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1829]) ).

cnf(c_0_1829_1,axiom,
    ( ~ c_lessequals(X1,X2,X3)
    | c_lessequals(c_Orderings_Oord__class_Omax(X1,X4,X3),X2,X3)
    | ~ c_lessequals(X4,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1829]) ).

cnf(c_0_1829_2,axiom,
    ( ~ c_lessequals(X4,X2,X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_lessequals(c_Orderings_Oord__class_Omax(X1,X4,X3),X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1829]) ).

cnf(c_0_1829_3,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | ~ c_lessequals(X4,X2,X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_lessequals(c_Orderings_Oord__class_Omax(X1,X4,X3),X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1829]) ).

cnf(c_0_1830_0,axiom,
    ( c_lessequals(c_Orderings_Oord__class_Omax(X1,X4,X3),X2,X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_lessequals(X4,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1830]) ).

cnf(c_0_1830_1,axiom,
    ( ~ c_lessequals(X1,X2,X3)
    | c_lessequals(c_Orderings_Oord__class_Omax(X1,X4,X3),X2,X3)
    | ~ c_lessequals(X4,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1830]) ).

cnf(c_0_1830_2,axiom,
    ( ~ c_lessequals(X4,X2,X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_lessequals(c_Orderings_Oord__class_Omax(X1,X4,X3),X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1830]) ).

cnf(c_0_1830_3,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | ~ c_lessequals(X4,X2,X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_lessequals(c_Orderings_Oord__class_Omax(X1,X4,X3),X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1830]) ).

cnf(c_0_1831_0,axiom,
    ( c_lessequals(c_Orderings_Oord__class_Omax(X1,X4,X3),X2,X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_lessequals(X4,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1831]) ).

cnf(c_0_1831_1,axiom,
    ( ~ c_lessequals(X1,X2,X3)
    | c_lessequals(c_Orderings_Oord__class_Omax(X1,X4,X3),X2,X3)
    | ~ c_lessequals(X4,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1831]) ).

cnf(c_0_1831_2,axiom,
    ( ~ c_lessequals(X4,X2,X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_lessequals(c_Orderings_Oord__class_Omax(X1,X4,X3),X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1831]) ).

cnf(c_0_1831_3,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | ~ c_lessequals(X4,X2,X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_lessequals(c_Orderings_Oord__class_Omax(X1,X4,X3),X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1831]) ).

cnf(c_0_1832_0,axiom,
    ( c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X1,X4,X3),X2,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X4,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1832]) ).

cnf(c_0_1832_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X1,X4,X3),X2,X3)
    | ~ c_HOL_Oord__class_Oless(X4,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1832]) ).

cnf(c_0_1832_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(X4,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X1,X4,X3),X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1832]) ).

cnf(c_0_1832_3,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | ~ c_HOL_Oord__class_Oless(X4,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X1,X4,X3),X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1832]) ).

cnf(c_0_1833_0,axiom,
    ( hAPP(hAPP(X1,hAPP(hAPP(X1,X3),X4)),X5) = hAPP(hAPP(X1,X3),hAPP(hAPP(X1,X4),X5))
    | ~ c_OrderedGroup_Osemigroup__add(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1833]) ).

cnf(c_0_1833_1,axiom,
    ( ~ c_OrderedGroup_Osemigroup__add(X1,X2)
    | hAPP(hAPP(X1,hAPP(hAPP(X1,X3),X4)),X5) = hAPP(hAPP(X1,X3),hAPP(hAPP(X1,X4),X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_1833]) ).

cnf(c_0_1834_0,axiom,
    ( c_List_Olistsp(X1,c_List_Oappend(X2,X4,X3),X3)
    | ~ c_List_Olistsp(X1,X2,X3)
    | ~ c_List_Olistsp(X1,X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1834]) ).

cnf(c_0_1834_1,axiom,
    ( ~ c_List_Olistsp(X1,X2,X3)
    | c_List_Olistsp(X1,c_List_Oappend(X2,X4,X3),X3)
    | ~ c_List_Olistsp(X1,X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1834]) ).

cnf(c_0_1834_2,axiom,
    ( ~ c_List_Olistsp(X1,X4,X3)
    | ~ c_List_Olistsp(X1,X2,X3)
    | c_List_Olistsp(X1,c_List_Oappend(X2,X4,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1834]) ).

cnf(c_0_1835_0,axiom,
    ( c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3) = c_Orderings_Oord__class_Omax(X1,c_Orderings_Oord__class_Omax(X2,X4,X3),X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1835]) ).

cnf(c_0_1835_1,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3) = c_Orderings_Oord__class_Omax(X1,c_Orderings_Oord__class_Omax(X2,X4,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1835]) ).

cnf(c_0_1836_0,axiom,
    ( c_Orderings_Oord__class_Omax(X1,c_Orderings_Oord__class_Omax(X2,X3,X4),X4) = c_Orderings_Oord__class_Omax(X2,c_Orderings_Oord__class_Omax(X1,X3,X4),X4)
    | ~ class_Orderings_Olinorder(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_1836]) ).

cnf(c_0_1836_1,axiom,
    ( ~ class_Orderings_Olinorder(X4)
    | c_Orderings_Oord__class_Omax(X1,c_Orderings_Oord__class_Omax(X2,X3,X4),X4) = c_Orderings_Oord__class_Omax(X2,c_Orderings_Oord__class_Omax(X1,X3,X4),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_1836]) ).

cnf(c_0_1837_0,axiom,
    ( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1837]) ).

cnf(c_0_1837_1,axiom,
    ( ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),c_HOL_Ozero__class_Ozero(X1),X1)
    | c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1837]) ).

cnf(c_0_1837_2,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__add(X1)
    | ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),c_HOL_Ozero__class_Ozero(X1),X1)
    | c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1837]) ).

cnf(c_0_1838_0,axiom,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1838]) ).

cnf(c_0_1838_1,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),X1)
    | c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1838]) ).

cnf(c_0_1838_2,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__add(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),X1)
    | c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1838]) ).

cnf(c_0_1839_0,axiom,
    ( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1839]) ).

cnf(c_0_1839_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),c_HOL_Ozero__class_Ozero(X1),X1)
    | c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1839]) ).

cnf(c_0_1839_2,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__add(X1)
    | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),c_HOL_Ozero__class_Ozero(X1),X1)
    | c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1839]) ).

cnf(c_0_1840_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1840]) ).

cnf(c_0_1840_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),X1)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1840]) ).

cnf(c_0_1840_2,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__add(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),X1)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1840]) ).

cnf(c_0_1841_0,axiom,
    ( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1841]) ).

cnf(c_0_1841_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),c_HOL_Ozero__class_Ozero(X1),X1)
    | c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1841]) ).

cnf(c_0_1841_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),c_HOL_Ozero__class_Ozero(X1),X1)
    | c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1841]) ).

cnf(c_0_1842_0,axiom,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_1842]) ).

cnf(c_0_1842_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_1842]) ).

cnf(c_0_1843_0,axiom,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_1843]) ).

cnf(c_0_1843_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_1843]) ).

cnf(c_0_1844_0,axiom,
    ( c_lessequals(X1,X4,X3)
    | ~ c_lessequals(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1844]) ).

cnf(c_0_1844_1,axiom,
    ( ~ c_lessequals(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3)
    | c_lessequals(X1,X4,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1844]) ).

cnf(c_0_1844_2,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | ~ c_lessequals(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3)
    | c_lessequals(X1,X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1844]) ).

cnf(c_0_1845_0,axiom,
    ( c_lessequals(X2,X4,X3)
    | ~ c_lessequals(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1845]) ).

cnf(c_0_1845_1,axiom,
    ( ~ c_lessequals(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3)
    | c_lessequals(X2,X4,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1845]) ).

cnf(c_0_1845_2,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | ~ c_lessequals(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3)
    | c_lessequals(X2,X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1845]) ).

cnf(c_0_1846_0,axiom,
    ( c_lessequals(X1,X4,X3)
    | ~ c_lessequals(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1846]) ).

cnf(c_0_1846_1,axiom,
    ( ~ c_lessequals(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3)
    | c_lessequals(X1,X4,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1846]) ).

cnf(c_0_1846_2,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | ~ c_lessequals(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3)
    | c_lessequals(X1,X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1846]) ).

cnf(c_0_1847_0,axiom,
    ( c_lessequals(X2,X4,X3)
    | ~ c_lessequals(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1847]) ).

cnf(c_0_1847_1,axiom,
    ( ~ c_lessequals(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3)
    | c_lessequals(X2,X4,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1847]) ).

cnf(c_0_1847_2,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | ~ c_lessequals(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3)
    | c_lessequals(X2,X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1847]) ).

cnf(c_0_1848_0,axiom,
    ( c_HOL_Oord__class_Oless(X2,X4,X3)
    | ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1848]) ).

cnf(c_0_1848_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3)
    | c_HOL_Oord__class_Oless(X2,X4,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1848]) ).

cnf(c_0_1848_2,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3)
    | c_HOL_Oord__class_Oless(X2,X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1848]) ).

cnf(c_0_1849_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,X4,X3)
    | ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1849]) ).

cnf(c_0_1849_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3)
    | c_HOL_Oord__class_Oless(X1,X4,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1849]) ).

cnf(c_0_1849_2,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3)
    | c_HOL_Oord__class_Oless(X1,X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1849]) ).

cnf(c_0_1850_0,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4))
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1850]) ).

cnf(c_0_1850_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_1850]) ).

cnf(c_0_1851_0,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4))
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1851]) ).

cnf(c_0_1851_1,axiom,
    ( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_1851]) ).

cnf(c_0_1852_0,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4))
    | ~ class_OrderedGroup_Oab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1852]) ).

cnf(c_0_1852_1,axiom,
    ( ~ class_OrderedGroup_Oab__group__add(X1)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_1852]) ).

cnf(c_0_1853_0,axiom,
    ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X4),X2),X3))
    | ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_1853]) ).

cnf(c_0_1853_1,axiom,
    ( ~ hBOOL(hAPP(hAPP(X1,X2),X3))
    | hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X4),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_1853]) ).

cnf(c_0_1854_0,axiom,
    ( c_List_Olistsp(X1,X2,X4)
    | ~ c_List_Olistsp(X1,c_List_Oappend(X2,X3,X4),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_1854]) ).

cnf(c_0_1854_1,axiom,
    ( ~ c_List_Olistsp(X1,c_List_Oappend(X2,X3,X4),X4)
    | c_List_Olistsp(X1,X2,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_1854]) ).

cnf(c_0_1855_0,axiom,
    ( c_List_Olistsp(X1,X3,X4)
    | ~ c_List_Olistsp(X1,c_List_Oappend(X2,X3,X4),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_1855]) ).

cnf(c_0_1855_1,axiom,
    ( ~ c_List_Olistsp(X1,c_List_Oappend(X2,X3,X4),X4)
    | c_List_Olistsp(X1,X3,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_1855]) ).

cnf(c_0_1856_0,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(X2)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X1,X2)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X3) != c_HOL_Ozero__class_Ozero(X2)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1856]) ).

cnf(c_0_1856_1,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X1,X2)
    | X1 = c_HOL_Ozero__class_Ozero(X2)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X3) != c_HOL_Ozero__class_Ozero(X2)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1856]) ).

cnf(c_0_1856_2,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X1,X2)
    | X1 = c_HOL_Ozero__class_Ozero(X2)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X3) != c_HOL_Ozero__class_Ozero(X2)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1856]) ).

cnf(c_0_1856_3,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X3) != c_HOL_Ozero__class_Ozero(X2)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X1,X2)
    | X1 = c_HOL_Ozero__class_Ozero(X2)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1856]) ).

cnf(c_0_1856_4,axiom,
    ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X2)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X3) != c_HOL_Ozero__class_Ozero(X2)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X1,X2)
    | X1 = c_HOL_Ozero__class_Ozero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1856]) ).

cnf(c_0_1857_0,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(X2)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X1,X2)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),X1) != c_HOL_Ozero__class_Ozero(X2)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1857]) ).

cnf(c_0_1857_1,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
    | X1 = c_HOL_Ozero__class_Ozero(X2)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X1,X2)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),X1) != c_HOL_Ozero__class_Ozero(X2)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1857]) ).

cnf(c_0_1857_2,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X1,X2)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
    | X1 = c_HOL_Ozero__class_Ozero(X2)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),X1) != c_HOL_Ozero__class_Ozero(X2)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1857]) ).

cnf(c_0_1857_3,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),X1) != c_HOL_Ozero__class_Ozero(X2)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X1,X2)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
    | X1 = c_HOL_Ozero__class_Ozero(X2)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1857]) ).

cnf(c_0_1857_4,axiom,
    ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X2)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),X1) != c_HOL_Ozero__class_Ozero(X2)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X1,X2)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
    | X1 = c_HOL_Ozero__class_Ozero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1857]) ).

cnf(c_0_1858_0,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1)) = c_HOL_Ozero__class_Ozero(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1858]) ).

cnf(c_0_1858_1,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1)) = c_HOL_Ozero__class_Ozero(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1858]) ).

cnf(c_0_1858_2,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1)) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1858]) ).

cnf(c_0_1858_3,axiom,
    ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1)) = c_HOL_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1858]) ).

cnf(c_0_1859_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X4) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1859]) ).

cnf(c_0_1859_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
    | c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X4) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1859]) ).

cnf(c_0_1859_2,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X4) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2)
    | ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
    | c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_1859]) ).

cnf(c_0_1860_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_1860]) ).

cnf(c_0_1860_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X3,tc_nat)
    | c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_1860]) ).

cnf(c_0_1861_0,axiom,
    ( X1 = X2
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X4,X3)
    | c_Power_Opower__class_Opower(X4,X1,X3) != c_Power_Opower__class_Opower(X4,X2,X3)
    | ~ class_Ring__and__Field_Oordered__semidom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1861]) ).

cnf(c_0_1861_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X4,X3)
    | X1 = X2
    | c_Power_Opower__class_Opower(X4,X1,X3) != c_Power_Opower__class_Opower(X4,X2,X3)
    | ~ class_Ring__and__Field_Oordered__semidom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1861]) ).

cnf(c_0_1861_2,axiom,
    ( c_Power_Opower__class_Opower(X4,X1,X3) != c_Power_Opower__class_Opower(X4,X2,X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X4,X3)
    | X1 = X2
    | ~ class_Ring__and__Field_Oordered__semidom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1861]) ).

cnf(c_0_1861_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X3)
    | c_Power_Opower__class_Opower(X4,X1,X3) != c_Power_Opower__class_Opower(X4,X2,X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X4,X3)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_1861]) ).

cnf(c_0_1862_0,axiom,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1862]) ).

cnf(c_0_1862_1,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1862]) ).

cnf(c_0_1862_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1862]) ).

cnf(c_0_1863_0,axiom,
    ( c_lessequals(c_HOL_Oone__class_Oone(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
    | ~ c_lessequals(c_HOL_Oone__class_Oone(X1),X2,X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1863]) ).

cnf(c_0_1863_1,axiom,
    ( ~ c_lessequals(c_HOL_Oone__class_Oone(X1),X2,X1)
    | c_lessequals(c_HOL_Oone__class_Oone(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1863]) ).

cnf(c_0_1863_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | ~ c_lessequals(c_HOL_Oone__class_Oone(X1),X2,X1)
    | c_lessequals(c_HOL_Oone__class_Oone(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1863]) ).

cnf(c_0_1864_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1864]) ).

cnf(c_0_1864_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1864]) ).

cnf(c_0_1864_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1864]) ).

cnf(c_0_1865_0,axiom,
    ( c_Wellfounded_Oaccp(X1,X4,X3)
    | ~ c_Wellfounded_Oaccp(X1,X2,X3)
    | ~ hBOOL(hAPP(hAPP(X1,X4),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_1865]) ).

cnf(c_0_1865_1,axiom,
    ( ~ c_Wellfounded_Oaccp(X1,X2,X3)
    | c_Wellfounded_Oaccp(X1,X4,X3)
    | ~ hBOOL(hAPP(hAPP(X1,X4),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_1865]) ).

cnf(c_0_1865_2,axiom,
    ( ~ hBOOL(hAPP(hAPP(X1,X4),X2))
    | ~ c_Wellfounded_Oaccp(X1,X2,X3)
    | c_Wellfounded_Oaccp(X1,X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1865]) ).

cnf(c_0_1866_0,axiom,
    ( c_Wellfounded_Oaccp(X1,X4,X3)
    | ~ c_Wellfounded_Oaccp(X1,X2,X3)
    | ~ hBOOL(hAPP(hAPP(X1,X4),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_1866]) ).

cnf(c_0_1866_1,axiom,
    ( ~ c_Wellfounded_Oaccp(X1,X2,X3)
    | c_Wellfounded_Oaccp(X1,X4,X3)
    | ~ hBOOL(hAPP(hAPP(X1,X4),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_1866]) ).

cnf(c_0_1866_2,axiom,
    ( ~ hBOOL(hAPP(hAPP(X1,X4),X2))
    | ~ c_Wellfounded_Oaccp(X1,X2,X3)
    | c_Wellfounded_Oaccp(X1,X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1866]) ).

cnf(c_0_1867_0,axiom,
    ( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X1),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1867]) ).

cnf(c_0_1867_1,axiom,
    ( ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X1),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1867]) ).

cnf(c_0_1867_2,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__add(X2)
    | ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X1),c_HOL_Ozero__class_Ozero(X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1867]) ).

cnf(c_0_1868_0,axiom,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1868]) ).

cnf(c_0_1868_1,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1868]) ).

cnf(c_0_1868_2,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__add(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1868]) ).

cnf(c_0_1869_0,axiom,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X1),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1869]) ).

cnf(c_0_1869_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X1),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1869]) ).

cnf(c_0_1869_2,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__add(X2)
    | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X1),c_HOL_Ozero__class_Ozero(X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1869]) ).

cnf(c_0_1870_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1870]) ).

cnf(c_0_1870_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1870]) ).

cnf(c_0_1870_2,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__add(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1870]) ).

cnf(c_0_1871_0,axiom,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X1),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1871]) ).

cnf(c_0_1871_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X1),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1871]) ).

cnf(c_0_1871_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X1),c_HOL_Ozero__class_Ozero(X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1871]) ).

cnf(c_0_1872_0,axiom,
    ( hBOOL(hAPP(c_InductTermi_OIT,X1))
    | ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X1,tc_Lambda_OdB) ),
    inference(literals_permutation,[status(thm)],[c_0_1872]) ).

cnf(c_0_1872_1,axiom,
    ( ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X1,tc_Lambda_OdB)
    | hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_1872]) ).

cnf(c_0_1873_0,axiom,
    ( c_Type_Otyping(X1,X4,X3)
    | ~ c_Type_Otyping(X1,X2,X3)
    | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X2),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_1873]) ).

cnf(c_0_1873_1,axiom,
    ( ~ c_Type_Otyping(X1,X2,X3)
    | c_Type_Otyping(X1,X4,X3)
    | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X2),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_1873]) ).

cnf(c_0_1873_2,axiom,
    ( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X2),X4))
    | ~ c_Type_Otyping(X1,X2,X3)
    | c_Type_Otyping(X1,X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1873]) ).

cnf(c_0_1874_0,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_List_Olistsum(X1,X3)),c_List_Olistsum(X2,X3)) = c_List_Olistsum(c_List_Oappend(X1,X2,X3),X3)
    | ~ class_OrderedGroup_Omonoid__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1874]) ).

cnf(c_0_1874_1,axiom,
    ( ~ class_OrderedGroup_Omonoid__add(X3)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_List_Olistsum(X1,X3)),c_List_Olistsum(X2,X3)) = c_List_Olistsum(c_List_Oappend(X1,X2,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1874]) ).

cnf(c_0_1875_0,axiom,
    ( c_lessequals(X1,c_Orderings_Oord__class_Omax(X2,X4,X3),X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1875]) ).

cnf(c_0_1875_1,axiom,
    ( ~ c_lessequals(X1,X2,X3)
    | c_lessequals(X1,c_Orderings_Oord__class_Omax(X2,X4,X3),X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1875]) ).

cnf(c_0_1875_2,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_lessequals(X1,c_Orderings_Oord__class_Omax(X2,X4,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1875]) ).

cnf(c_0_1876_0,axiom,
    ( c_lessequals(X1,c_Orderings_Oord__class_Omax(X4,X2,X3),X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1876]) ).

cnf(c_0_1876_1,axiom,
    ( ~ c_lessequals(X1,X2,X3)
    | c_lessequals(X1,c_Orderings_Oord__class_Omax(X4,X2,X3),X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1876]) ).

cnf(c_0_1876_2,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_lessequals(X1,c_Orderings_Oord__class_Omax(X4,X2,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1876]) ).

cnf(c_0_1877_0,axiom,
    ( c_lessequals(X1,c_Orderings_Oord__class_Omax(X2,X4,X3),X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1877]) ).

cnf(c_0_1877_1,axiom,
    ( ~ c_lessequals(X1,X2,X3)
    | c_lessequals(X1,c_Orderings_Oord__class_Omax(X2,X4,X3),X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1877]) ).

cnf(c_0_1877_2,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_lessequals(X1,c_Orderings_Oord__class_Omax(X2,X4,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1877]) ).

cnf(c_0_1878_0,axiom,
    ( c_lessequals(X1,c_Orderings_Oord__class_Omax(X4,X2,X3),X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1878]) ).

cnf(c_0_1878_1,axiom,
    ( ~ c_lessequals(X1,X2,X3)
    | c_lessequals(X1,c_Orderings_Oord__class_Omax(X4,X2,X3),X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1878]) ).

cnf(c_0_1878_2,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_lessequals(X1,c_Orderings_Oord__class_Omax(X4,X2,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1878]) ).

cnf(c_0_1879_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X4,X2,X3),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1879]) ).

cnf(c_0_1879_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X4,X2,X3),X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1879]) ).

cnf(c_0_1879_2,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X4,X2,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1879]) ).

cnf(c_0_1880_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X2,X4,X3),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1880]) ).

cnf(c_0_1880_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X2,X4,X3),X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1880]) ).

cnf(c_0_1880_2,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X2,X4,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1880]) ).

cnf(c_0_1881_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X4,X2,X3),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1881]) ).

cnf(c_0_1881_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X4,X2,X3),X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1881]) ).

cnf(c_0_1881_2,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X4,X2,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1881]) ).

cnf(c_0_1882_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X2,X4,X3),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1882]) ).

cnf(c_0_1882_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X2,X4,X3),X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1882]) ).

cnf(c_0_1882_2,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X2,X4,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1882]) ).

cnf(c_0_1883_0,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_Nat_Osemiring__1__class_Oof__nat(X1,X3)),c_Nat_Osemiring__1__class_Oof__nat(X2,X3)) = c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X3)
    | ~ class_Ring__and__Field_Osemiring__1(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1883]) ).

cnf(c_0_1883_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring__1(X3)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_Nat_Osemiring__1__class_Oof__nat(X1,X3)),c_Nat_Osemiring__1__class_Oof__nat(X2,X3)) = c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1883]) ).

cnf(c_0_1884_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_1884]) ).

cnf(c_0_1884_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_1884]) ).

cnf(c_0_1885_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_1885]) ).

cnf(c_0_1885_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_1885]) ).

cnf(c_0_1886_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,X4,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_lessequals(X2,X4,X3)
    | ~ class_Orderings_Opreorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1886]) ).

cnf(c_0_1886_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X1,X4,X3)
    | ~ c_lessequals(X2,X4,X3)
    | ~ class_Orderings_Opreorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1886]) ).

cnf(c_0_1886_2,axiom,
    ( ~ c_lessequals(X2,X4,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X1,X4,X3)
    | ~ class_Orderings_Opreorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1886]) ).

cnf(c_0_1886_3,axiom,
    ( ~ class_Orderings_Opreorder(X3)
    | ~ c_lessequals(X2,X4,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X1,X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1886]) ).

cnf(c_0_1887_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,X4,X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X2,X4,X3)
    | ~ class_Orderings_Opreorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1887]) ).

cnf(c_0_1887_1,axiom,
    ( ~ c_lessequals(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X1,X4,X3)
    | ~ c_HOL_Oord__class_Oless(X2,X4,X3)
    | ~ class_Orderings_Opreorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1887]) ).

cnf(c_0_1887_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(X2,X4,X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X1,X4,X3)
    | ~ class_Orderings_Opreorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1887]) ).

cnf(c_0_1887_3,axiom,
    ( ~ class_Orderings_Opreorder(X3)
    | ~ c_HOL_Oord__class_Oless(X2,X4,X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X1,X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1887]) ).

cnf(c_0_1888_0,axiom,
    ( c_lessequals(X1,X4,X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_lessequals(X2,X4,X3)
    | ~ class_Orderings_Opreorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1888]) ).

cnf(c_0_1888_1,axiom,
    ( ~ c_lessequals(X1,X2,X3)
    | c_lessequals(X1,X4,X3)
    | ~ c_lessequals(X2,X4,X3)
    | ~ class_Orderings_Opreorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1888]) ).

cnf(c_0_1888_2,axiom,
    ( ~ c_lessequals(X2,X4,X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_lessequals(X1,X4,X3)
    | ~ class_Orderings_Opreorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1888]) ).

cnf(c_0_1888_3,axiom,
    ( ~ class_Orderings_Opreorder(X3)
    | ~ c_lessequals(X2,X4,X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_lessequals(X1,X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1888]) ).

cnf(c_0_1889_0,axiom,
    ( c_HOL_Oord__class_Oless(X4,X2,X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X4,X1,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1889]) ).

cnf(c_0_1889_1,axiom,
    ( ~ c_lessequals(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X4,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X4,X1,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1889]) ).

cnf(c_0_1889_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(X4,X1,X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X4,X2,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1889]) ).

cnf(c_0_1889_3,axiom,
    ( ~ class_Orderings_Oorder(X3)
    | ~ c_HOL_Oord__class_Oless(X4,X1,X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X4,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1889]) ).

cnf(c_0_1890_0,axiom,
    ( c_HOL_Oord__class_Oless(X4,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_lessequals(X4,X1,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1890]) ).

cnf(c_0_1890_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X4,X2,X3)
    | ~ c_lessequals(X4,X1,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1890]) ).

cnf(c_0_1890_2,axiom,
    ( ~ c_lessequals(X4,X1,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X4,X2,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1890]) ).

cnf(c_0_1890_3,axiom,
    ( ~ class_Orderings_Oorder(X3)
    | ~ c_lessequals(X4,X1,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X4,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1890]) ).

cnf(c_0_1891_0,axiom,
    ( c_lessequals(X4,X2,X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_lessequals(X4,X1,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1891]) ).

cnf(c_0_1891_1,axiom,
    ( ~ c_lessequals(X1,X2,X3)
    | c_lessequals(X4,X2,X3)
    | ~ c_lessequals(X4,X1,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1891]) ).

cnf(c_0_1891_2,axiom,
    ( ~ c_lessequals(X4,X1,X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_lessequals(X4,X2,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1891]) ).

cnf(c_0_1891_3,axiom,
    ( ~ class_Orderings_Oorder(X3)
    | ~ c_lessequals(X4,X1,X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_lessequals(X4,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1891]) ).

cnf(c_0_1892_0,axiom,
    ( c_HOL_Oord__class_Oless(X4,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X4,X1,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1892]) ).

cnf(c_0_1892_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X4,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X4,X1,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1892]) ).

cnf(c_0_1892_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(X4,X1,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X4,X2,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1892]) ).

cnf(c_0_1892_3,axiom,
    ( ~ class_Orderings_Oorder(X3)
    | ~ c_HOL_Oord__class_Oless(X4,X1,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X4,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1892]) ).

cnf(c_0_1893_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,X4,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X2,X4,X3)
    | ~ class_Orderings_Opreorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1893]) ).

cnf(c_0_1893_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X1,X4,X3)
    | ~ c_HOL_Oord__class_Oless(X2,X4,X3)
    | ~ class_Orderings_Opreorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1893]) ).

cnf(c_0_1893_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(X2,X4,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X1,X4,X3)
    | ~ class_Orderings_Opreorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1893]) ).

cnf(c_0_1893_3,axiom,
    ( ~ class_Orderings_Opreorder(X3)
    | ~ c_HOL_Oord__class_Oless(X2,X4,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X1,X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1893]) ).

cnf(c_0_1894_0,axiom,
    ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OAbs(X1)),c_Lambda_OdB_OAbs(X2)))
    | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_1894]) ).

cnf(c_0_1894_1,axiom,
    ( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2))
    | hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OAbs(X1)),c_Lambda_OdB_OAbs(X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_1894]) ).

cnf(c_0_1895_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_Nat_Osemiring__1__class_Oof__nat(X3,X2),X2)
    | ~ class_Ring__and__Field_Oordered__semidom(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1895]) ).

cnf(c_0_1895_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_Nat_Osemiring__1__class_Oof__nat(X3,X2),X2)
    | c_HOL_Oord__class_Oless(X1,X3,tc_nat)
    | ~ class_Ring__and__Field_Oordered__semidom(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1895]) ).

cnf(c_0_1895_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X2)
    | ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_Nat_Osemiring__1__class_Oof__nat(X3,X2),X2)
    | c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_1895]) ).

cnf(c_0_1896_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_1896]) ).

cnf(c_0_1896_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_1896]) ).

cnf(c_0_1897_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_1897]) ).

cnf(c_0_1897_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_1897]) ).

cnf(c_0_1898_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_1898]) ).

cnf(c_0_1898_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_1898]) ).

cnf(c_0_1899_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_1899]) ).

cnf(c_0_1899_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_1899]) ).

cnf(c_0_1900_0,axiom,
    ( c_Orderings_Oord__class_Omax(X1,c_Orderings_Oord__class_Omax(X1,X2,X3),X3) = c_Orderings_Oord__class_Omax(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1900]) ).

cnf(c_0_1900_1,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | c_Orderings_Oord__class_Omax(X1,c_Orderings_Oord__class_Omax(X1,X2,X3),X3) = c_Orderings_Oord__class_Omax(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1900]) ).

cnf(c_0_1901_0,axiom,
    ( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_Olift,X1),X2)))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_1901]) ).

cnf(c_0_1901_1,axiom,
    ( ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
    | hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_Olift,X1),X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_1901]) ).

cnf(c_0_1902_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_Lambda_Oliftn(X3,c_Lambda_OdB_OVar(X1),X2) = c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_1902]) ).

cnf(c_0_1902_1,axiom,
    ( c_Lambda_Oliftn(X3,c_Lambda_OdB_OVar(X1),X2) = c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3))
    | c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_1902]) ).

cnf(c_0_1903_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Oone__class_Oone(X1)),c_HOL_Oone__class_Oone(X1)),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1903]) ).

cnf(c_0_1903_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Oone__class_Oone(X1)),c_HOL_Oone__class_Oone(X1)),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1903]) ).

cnf(c_0_1904_0,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),c_List_Olistsum(X2,X3)) = c_List_Olistsum(c_List_Olist_OCons(X1,X2,X3),X3)
    | ~ class_OrderedGroup_Omonoid__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1904]) ).

cnf(c_0_1904_1,axiom,
    ( ~ class_OrderedGroup_Omonoid__add(X3)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),c_List_Olistsum(X2,X3)) = c_List_Olistsum(c_List_Olist_OCons(X1,X2,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1904]) ).

cnf(c_0_1905_0,axiom,
    ( c_lessequals(X2,X1,X3)
    | c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Opreorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1905]) ).

cnf(c_0_1905_1,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_lessequals(X2,X1,X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Opreorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1905]) ).

cnf(c_0_1905_2,axiom,
    ( ~ c_lessequals(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_lessequals(X2,X1,X3)
    | ~ class_Orderings_Opreorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1905]) ).

cnf(c_0_1905_3,axiom,
    ( ~ class_Orderings_Opreorder(X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_lessequals(X2,X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1905]) ).

cnf(c_0_1906_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(X1)),X2) = c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat))) ),
    inference(literals_permutation,[status(thm)],[c_0_1906]) ).

cnf(c_0_1906_1,axiom,
    ( hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(X1)),X2) = c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)))
    | c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_1906]) ).

cnf(c_0_1907_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1907]) ).

cnf(c_0_1907_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1),X1)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1907]) ).

cnf(c_0_1907_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1),X1)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_1907]) ).

cnf(c_0_1908_0,axiom,
    ( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X1)),X3),X2) = c_Lambda_OdB_OVar(X1)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_1908]) ).

cnf(c_0_1908_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X1)),X3),X2) = c_Lambda_OdB_OVar(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1908]) ).

cnf(c_0_1909_0,axiom,
    ( c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X3),c_Nat_Osemiring__1__class_Oof__nat(X2,X3),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ class_Ring__and__Field_Oordered__semidom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1909]) ).

cnf(c_0_1909_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X3),c_Nat_Osemiring__1__class_Oof__nat(X2,X3),X3)
    | ~ class_Ring__and__Field_Oordered__semidom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1909]) ).

cnf(c_0_1909_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X3),c_Nat_Osemiring__1__class_Oof__nat(X2,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1909]) ).

cnf(c_0_1910_0,axiom,
    ( c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X1,tc_Lambda_OdB)
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_1910]) ).

cnf(c_0_1910_1,axiom,
    ( ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
    | c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X1,tc_Lambda_OdB) ),
    inference(literals_permutation,[status(thm)],[c_0_1910]) ).

cnf(c_0_1911_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | X1 = X2
    | c_HOL_Oord__class_Oless(X2,X1,tc_nat)
    | hBOOL(hAPP(hAPP(X3,X2),X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_1911]) ).

cnf(c_0_1911_1,axiom,
    ( X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(X2,X1,tc_nat)
    | hBOOL(hAPP(hAPP(X3,X2),X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_1911]) ).

cnf(c_0_1911_2,axiom,
    ( c_HOL_Oord__class_Oless(X2,X1,tc_nat)
    | X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | hBOOL(hAPP(hAPP(X3,X2),X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_1911]) ).

cnf(c_0_1911_3,axiom,
    ( hBOOL(hAPP(hAPP(X3,X2),X1))
    | c_HOL_Oord__class_Oless(X2,X1,tc_nat)
    | X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_1911]) ).

cnf(c_0_1912_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_Nat_Osemiring__1__class_Oof__nat(X1,X2),X2)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | ~ class_Ring__and__Field_Oordered__semidom(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1912]) ).

cnf(c_0_1912_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_Nat_Osemiring__1__class_Oof__nat(X1,X2),X2)
    | ~ class_Ring__and__Field_Oordered__semidom(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1912]) ).

cnf(c_0_1912_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X2)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_Nat_Osemiring__1__class_Oof__nat(X1,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1912]) ).

cnf(c_0_1913_0,axiom,
    ( X2 = X1
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_lessequals(X2,X1,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1913]) ).

cnf(c_0_1913_1,axiom,
    ( ~ c_lessequals(X1,X2,X3)
    | X2 = X1
    | ~ c_lessequals(X2,X1,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1913]) ).

cnf(c_0_1913_2,axiom,
    ( ~ c_lessequals(X2,X1,X3)
    | ~ c_lessequals(X1,X2,X3)
    | X2 = X1
    | ~ class_Orderings_Oorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1913]) ).

cnf(c_0_1913_3,axiom,
    ( ~ class_Orderings_Oorder(X3)
    | ~ c_lessequals(X2,X1,X3)
    | ~ c_lessequals(X1,X2,X3)
    | X2 = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_1913]) ).

cnf(c_0_1914_0,axiom,
    ( X1 = X2
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_lessequals(X2,X1,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1914]) ).

cnf(c_0_1914_1,axiom,
    ( ~ c_lessequals(X1,X2,X3)
    | X1 = X2
    | ~ c_lessequals(X2,X1,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1914]) ).

cnf(c_0_1914_2,axiom,
    ( ~ c_lessequals(X2,X1,X3)
    | ~ c_lessequals(X1,X2,X3)
    | X1 = X2
    | ~ class_Orderings_Oorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1914]) ).

cnf(c_0_1914_3,axiom,
    ( ~ class_Orderings_Oorder(X3)
    | ~ c_lessequals(X2,X1,X3)
    | ~ c_lessequals(X1,X2,X3)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_1914]) ).

cnf(c_0_1915_0,axiom,
    ( X1 = X2
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_lessequals(X2,X1,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1915]) ).

cnf(c_0_1915_1,axiom,
    ( ~ c_lessequals(X1,X2,X3)
    | X1 = X2
    | ~ c_lessequals(X2,X1,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1915]) ).

cnf(c_0_1915_2,axiom,
    ( ~ c_lessequals(X2,X1,X3)
    | ~ c_lessequals(X1,X2,X3)
    | X1 = X2
    | ~ class_Orderings_Oorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1915]) ).

cnf(c_0_1915_3,axiom,
    ( ~ class_Orderings_Oorder(X3)
    | ~ c_lessequals(X2,X1,X3)
    | ~ c_lessequals(X1,X2,X3)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_1915]) ).

cnf(c_0_1916_0,axiom,
    ( X1 = X2
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2)
    | ~ class_Int_Onumber__ring(X3)
    | ~ class_Ring__and__Field_Oidom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1916]) ).

cnf(c_0_1916_1,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2)
    | X1 = X2
    | ~ class_Int_Onumber__ring(X3)
    | ~ class_Ring__and__Field_Oidom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1916]) ).

cnf(c_0_1916_2,axiom,
    ( ~ class_Int_Onumber__ring(X3)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2)
    | X1 = X2
    | ~ class_Ring__and__Field_Oidom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1916]) ).

cnf(c_0_1916_3,axiom,
    ( ~ class_Ring__and__Field_Oidom(X3)
    | ~ class_Int_Onumber__ring(X3)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_1916]) ).

cnf(c_0_1917_0,axiom,
    ( c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB)
    | hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X1)))
    | hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__5(X1)))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_1917]) ).

cnf(c_0_1917_1,axiom,
    ( hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X1)))
    | c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB)
    | hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__5(X1)))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_1917]) ).

cnf(c_0_1917_2,axiom,
    ( hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__5(X1)))
    | hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X1)))
    | c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB)
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_1917]) ).

cnf(c_0_1917_3,axiom,
    ( ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
    | hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__5(X1)))
    | hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X1)))
    | c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB) ),
    inference(literals_permutation,[status(thm)],[c_0_1917]) ).

cnf(c_0_1918_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
    | ~ c_lessequals(X1,X1,X2)
    | ~ class_Orderings_Olinorder(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1918]) ).

cnf(c_0_1918_1,axiom,
    ( ~ c_lessequals(X1,X1,X2)
    | ~ c_HOL_Oord__class_Oless(X1,X1,X2)
    | ~ class_Orderings_Olinorder(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1918]) ).

cnf(c_0_1918_2,axiom,
    ( ~ class_Orderings_Olinorder(X2)
    | ~ c_lessequals(X1,X1,X2)
    | ~ c_HOL_Oord__class_Oless(X1,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1918]) ).

cnf(c_0_1919_0,axiom,
    ( ~ c_lessequals(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X2,X1,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1919]) ).

cnf(c_0_1919_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X2,X1,X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1919]) ).

cnf(c_0_1919_2,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | ~ c_HOL_Oord__class_Oless(X2,X1,X3)
    | ~ c_lessequals(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1919]) ).

cnf(c_0_1920_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_lessequals(X2,X1,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1920]) ).

cnf(c_0_1920_1,axiom,
    ( ~ c_lessequals(X2,X1,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1920]) ).

cnf(c_0_1920_2,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | ~ c_lessequals(X2,X1,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1920]) ).

cnf(c_0_1921_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_lessequals(X2,X1,X3)
    | ~ class_Orderings_Opreorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1921]) ).

cnf(c_0_1921_1,axiom,
    ( ~ c_lessequals(X2,X1,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ class_Orderings_Opreorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1921]) ).

cnf(c_0_1921_2,axiom,
    ( ~ class_Orderings_Opreorder(X3)
    | ~ c_lessequals(X2,X1,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1921]) ).

cnf(c_0_1922_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X2,X1,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1922]) ).

cnf(c_0_1922_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X2,X1,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1922]) ).

cnf(c_0_1922_2,axiom,
    ( ~ class_Orderings_Oorder(X3)
    | ~ c_HOL_Oord__class_Oless(X2,X1,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1922]) ).

cnf(c_0_1923_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X2,X1,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1923]) ).

cnf(c_0_1923_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X2,X1,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1923]) ).

cnf(c_0_1923_2,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | ~ c_HOL_Oord__class_Oless(X2,X1,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1923]) ).

cnf(c_0_1924_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X2,X1,X3)
    | ~ class_Orderings_Opreorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1924]) ).

cnf(c_0_1924_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X2,X1,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ class_Orderings_Opreorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1924]) ).

cnf(c_0_1924_2,axiom,
    ( ~ class_Orderings_Opreorder(X3)
    | ~ c_HOL_Oord__class_Oless(X2,X1,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1924]) ).

cnf(c_0_1925_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X2,X1,X3)
    | ~ class_Orderings_Opreorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1925]) ).

cnf(c_0_1925_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X2,X1,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ class_Orderings_Opreorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1925]) ).

cnf(c_0_1925_2,axiom,
    ( ~ class_Orderings_Opreorder(X3)
    | ~ c_HOL_Oord__class_Oless(X2,X1,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1925]) ).

cnf(c_0_1926_0,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X2 = X3
    | c_List_Oreplicate(X1,X2,X4) != c_List_Oreplicate(X5,X3,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_1926]) ).

cnf(c_0_1926_1,axiom,
    ( X2 = X3
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_List_Oreplicate(X1,X2,X4) != c_List_Oreplicate(X5,X3,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_1926]) ).

cnf(c_0_1926_2,axiom,
    ( c_List_Oreplicate(X1,X2,X4) != c_List_Oreplicate(X5,X3,X4)
    | X2 = X3
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_1926]) ).

cnf(c_0_1927_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),c_HOL_Oone__class_Oone(X2)),X2)
    | ~ class_Ring__and__Field_Oordered__semidom(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1927]) ).

cnf(c_0_1927_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X2)
    | c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),c_HOL_Oone__class_Oone(X2)),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1927]) ).

cnf(c_0_1928_0,axiom,
    ( X1 = X2
    | c_List_Oreplicate(X1,X3,X4) != c_List_Oreplicate(X2,X5,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_1928]) ).

cnf(c_0_1928_1,axiom,
    ( c_List_Oreplicate(X1,X3,X4) != c_List_Oreplicate(X2,X5,X4)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_1928]) ).

cnf(c_0_1929_0,axiom,
    ( X1 = X2
    | c_List_Oappend(X1,X3,X4) != c_List_Oappend(X2,X3,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_1929]) ).

cnf(c_0_1929_1,axiom,
    ( c_List_Oappend(X1,X3,X4) != c_List_Oappend(X2,X3,X4)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_1929]) ).

cnf(c_0_1930_0,axiom,
    ( X1 = X2
    | c_List_Oappend(X3,X1,X4) != c_List_Oappend(X3,X2,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_1930]) ).

cnf(c_0_1930_1,axiom,
    ( c_List_Oappend(X3,X1,X4) != c_List_Oappend(X3,X2,X4)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_1930]) ).

cnf(c_0_1931_0,axiom,
    ( X1 = X2
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2)
    | ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1931]) ).

cnf(c_0_1931_1,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2)
    | X1 = X2
    | ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1931]) ).

cnf(c_0_1931_2,axiom,
    ( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X3)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_1931]) ).

cnf(c_0_1932_0,axiom,
    ( X1 = X2
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2)
    | ~ class_OrderedGroup_Ocancel__semigroup__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1932]) ).

cnf(c_0_1932_1,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2)
    | X1 = X2
    | ~ class_OrderedGroup_Ocancel__semigroup__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1932]) ).

cnf(c_0_1932_2,axiom,
    ( ~ class_OrderedGroup_Ocancel__semigroup__add(X3)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_1932]) ).

cnf(c_0_1933_0,axiom,
    ( X1 = X2
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4)
    | ~ class_OrderedGroup_Ocancel__semigroup__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1933]) ).

cnf(c_0_1933_1,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4)
    | X1 = X2
    | ~ class_OrderedGroup_Ocancel__semigroup__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1933]) ).

cnf(c_0_1933_2,axiom,
    ( ~ class_OrderedGroup_Ocancel__semigroup__add(X3)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_1933]) ).

cnf(c_0_1934_0,axiom,
    ( X1 = X2
    | c_List_Olist_OCons(X1,X3,X4) != c_List_Olist_OCons(X2,X5,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_1934]) ).

cnf(c_0_1934_1,axiom,
    ( c_List_Olist_OCons(X1,X3,X4) != c_List_Olist_OCons(X2,X5,X4)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_1934]) ).

cnf(c_0_1935_0,axiom,
    ( X1 = X2
    | c_List_Olist_OCons(X3,X1,X4) != c_List_Olist_OCons(X5,X2,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_1935]) ).

cnf(c_0_1935_1,axiom,
    ( c_List_Olist_OCons(X3,X1,X4) != c_List_Olist_OCons(X5,X2,X4)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_1935]) ).

cnf(c_0_1936_0,axiom,
    ( c_Lambda_Osubstn(c_Lambda_OdB_OVar(X1),X2,X1) = c_Lambda_Oliftn(X1,X2,c_HOL_Ozero__class_Ozero(tc_nat))
    | c_HOL_Oord__class_Oless(X1,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_1936]) ).

cnf(c_0_1936_1,axiom,
    ( c_HOL_Oord__class_Oless(X1,X1,tc_nat)
    | c_Lambda_Osubstn(c_Lambda_OdB_OVar(X1),X2,X1) = c_Lambda_Oliftn(X1,X2,c_HOL_Ozero__class_Ozero(tc_nat)) ),
    inference(literals_permutation,[status(thm)],[c_0_1936]) ).

cnf(c_0_1937_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | X2 = X1
    | hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X2)),X3),X1) = c_Lambda_OdB_OVar(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1937]) ).

cnf(c_0_1937_1,axiom,
    ( X2 = X1
    | c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X2)),X3),X1) = c_Lambda_OdB_OVar(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1937]) ).

cnf(c_0_1937_2,axiom,
    ( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X2)),X3),X1) = c_Lambda_OdB_OVar(X2)
    | X2 = X1
    | c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_1937]) ).

cnf(c_0_1938_0,axiom,
    ( X2 = X3
    | ~ hBOOL(hAPP(hAPP(c_fequal(X1),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_1938]) ).

cnf(c_0_1938_1,axiom,
    ( ~ hBOOL(hAPP(hAPP(c_fequal(X1),X2),X3))
    | X2 = X3 ),
    inference(literals_permutation,[status(thm)],[c_0_1938]) ).

cnf(c_0_1939_0,axiom,
    ( c_lessequals(X1,c_Orderings_Oord__class_Omax(X2,X1,X3),X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1939]) ).

cnf(c_0_1939_1,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | c_lessequals(X1,c_Orderings_Oord__class_Omax(X2,X1,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1939]) ).

cnf(c_0_1940_0,axiom,
    ( c_lessequals(X1,c_Orderings_Oord__class_Omax(X1,X2,X3),X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1940]) ).

cnf(c_0_1940_1,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | c_lessequals(X1,c_Orderings_Oord__class_Omax(X1,X2,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1940]) ).

cnf(c_0_1941_0,axiom,
    ( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X1)),X2),X1) = X2
    | c_HOL_Oord__class_Oless(X1,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_1941]) ).

cnf(c_0_1941_1,axiom,
    ( c_HOL_Oord__class_Oless(X1,X1,tc_nat)
    | hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X1)),X2),X1) = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_1941]) ).

cnf(c_0_1942_0,axiom,
    ( c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB)
    | c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X1)) = X1
    | hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__5(X1)))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_1942]) ).

cnf(c_0_1942_1,axiom,
    ( c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X1)) = X1
    | c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB)
    | hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__5(X1)))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_1942]) ).

cnf(c_0_1942_2,axiom,
    ( hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__5(X1)))
    | c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X1)) = X1
    | c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB)
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_1942]) ).

cnf(c_0_1942_3,axiom,
    ( ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
    | hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__5(X1)))
    | c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X1)) = X1
    | c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB) ),
    inference(literals_permutation,[status(thm)],[c_0_1942]) ).

cnf(c_0_1943_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,X3)
    | X1 = X2
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1943]) ).

cnf(c_0_1943_1,axiom,
    ( X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1943]) ).

cnf(c_0_1943_2,axiom,
    ( ~ c_lessequals(X1,X2,X3)
    | X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1943]) ).

cnf(c_0_1943_3,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | ~ c_lessequals(X1,X2,X3)
    | X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1943]) ).

cnf(c_0_1944_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,X3)
    | X1 = X2
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1944]) ).

cnf(c_0_1944_1,axiom,
    ( X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1944]) ).

cnf(c_0_1944_2,axiom,
    ( ~ c_lessequals(X1,X2,X3)
    | X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1944]) ).

cnf(c_0_1944_3,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | ~ c_lessequals(X1,X2,X3)
    | X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1944]) ).

cnf(c_0_1945_0,axiom,
    ( X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1945]) ).

cnf(c_0_1945_1,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,X3)
    | X1 = X2
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1945]) ).

cnf(c_0_1945_2,axiom,
    ( ~ c_lessequals(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X1,X2,X3)
    | X1 = X2
    | ~ class_Orderings_Oorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1945]) ).

cnf(c_0_1945_3,axiom,
    ( ~ class_Orderings_Oorder(X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X1,X2,X3)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_1945]) ).

cnf(c_0_1946_0,axiom,
    ( X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1946]) ).

cnf(c_0_1946_1,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,X3)
    | X1 = X2
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1946]) ).

cnf(c_0_1946_2,axiom,
    ( ~ c_lessequals(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X1,X2,X3)
    | X1 = X2
    | ~ class_Orderings_Oorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1946]) ).

cnf(c_0_1946_3,axiom,
    ( ~ class_Orderings_Oorder(X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X1,X2,X3)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_1946]) ).

cnf(c_0_1947_0,axiom,
    ( X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1947]) ).

cnf(c_0_1947_1,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,X3)
    | X1 = X2
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1947]) ).

cnf(c_0_1947_2,axiom,
    ( ~ c_lessequals(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X1,X2,X3)
    | X1 = X2
    | ~ class_Orderings_Oorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1947]) ).

cnf(c_0_1947_3,axiom,
    ( ~ class_Orderings_Oorder(X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X1,X2,X3)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_1947]) ).

cnf(c_0_1948_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,X3)
    | X1 = X2
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1948]) ).

cnf(c_0_1948_1,axiom,
    ( X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1948]) ).

cnf(c_0_1948_2,axiom,
    ( ~ c_lessequals(X1,X2,X3)
    | X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1948]) ).

cnf(c_0_1948_3,axiom,
    ( ~ class_Orderings_Oorder(X3)
    | ~ c_lessequals(X1,X2,X3)
    | X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1948]) ).

cnf(c_0_1949_0,axiom,
    ( X1 = X2
    | c_HOL_Oord__class_Oless(X2,X1,X3)
    | ~ c_lessequals(X2,X1,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1949]) ).

cnf(c_0_1949_1,axiom,
    ( c_HOL_Oord__class_Oless(X2,X1,X3)
    | X1 = X2
    | ~ c_lessequals(X2,X1,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1949]) ).

cnf(c_0_1949_2,axiom,
    ( ~ c_lessequals(X2,X1,X3)
    | c_HOL_Oord__class_Oless(X2,X1,X3)
    | X1 = X2
    | ~ class_Orderings_Oorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1949]) ).

cnf(c_0_1949_3,axiom,
    ( ~ class_Orderings_Oorder(X3)
    | ~ c_lessequals(X2,X1,X3)
    | c_HOL_Oord__class_Oless(X2,X1,X3)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_1949]) ).

cnf(c_0_1950_0,axiom,
    ( X2 = X1
    | c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1950]) ).

cnf(c_0_1950_1,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,X3)
    | X2 = X1
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1950]) ).

cnf(c_0_1950_2,axiom,
    ( ~ c_lessequals(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X1,X2,X3)
    | X2 = X1
    | ~ class_Orderings_Oorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1950]) ).

cnf(c_0_1950_3,axiom,
    ( ~ class_Orderings_Oorder(X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X1,X2,X3)
    | X2 = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_1950]) ).

cnf(c_0_1951_0,axiom,
    ( c_lessequals(X1,X2,X3)
    | c_Orderings_Oord__class_Omax(X1,X2,X3) != X2
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1951]) ).

cnf(c_0_1951_1,axiom,
    ( c_Orderings_Oord__class_Omax(X1,X2,X3) != X2
    | c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1951]) ).

cnf(c_0_1951_2,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | c_Orderings_Oord__class_Omax(X1,X2,X3) != X2
    | c_lessequals(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1951]) ).

cnf(c_0_1952_0,axiom,
    ( c_Orderings_Oord__class_Omax(X1,X2,X3) = X2
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1952]) ).

cnf(c_0_1952_1,axiom,
    ( ~ c_lessequals(X1,X2,X3)
    | c_Orderings_Oord__class_Omax(X1,X2,X3) = X2
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1952]) ).

cnf(c_0_1952_2,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_Orderings_Oord__class_Omax(X1,X2,X3) = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_1952]) ).

cnf(c_0_1953_0,axiom,
    ( c_Orderings_Oord__class_Omax(X2,X1,X3) = X2
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1953]) ).

cnf(c_0_1953_1,axiom,
    ( ~ c_lessequals(X1,X2,X3)
    | c_Orderings_Oord__class_Omax(X2,X1,X3) = X2
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1953]) ).

cnf(c_0_1953_2,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_Orderings_Oord__class_Omax(X2,X1,X3) = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_1953]) ).

cnf(c_0_1954_0,axiom,
    ( c_Lambda_Oliftn(X3,c_Lambda_OdB_OVar(X1),X2) = c_Lambda_OdB_OVar(X1)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_1954]) ).

cnf(c_0_1954_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_Lambda_Oliftn(X3,c_Lambda_OdB_OVar(X1),X2) = c_Lambda_OdB_OVar(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1954]) ).

cnf(c_0_1955_0,axiom,
    ( c_lessequals(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ class_Orderings_Opreorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1955]) ).

cnf(c_0_1955_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Opreorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1955]) ).

cnf(c_0_1955_2,axiom,
    ( ~ class_Orderings_Opreorder(X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_lessequals(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1955]) ).

cnf(c_0_1956_0,axiom,
    ( c_lessequals(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1956]) ).

cnf(c_0_1956_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1956]) ).

cnf(c_0_1956_2,axiom,
    ( ~ class_Orderings_Oorder(X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_lessequals(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1956]) ).

cnf(c_0_1957_0,axiom,
    ( X1 = X2
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1957]) ).

cnf(c_0_1957_1,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_1957]) ).

cnf(c_0_1958_0,axiom,
    ( X1 = X2
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1958]) ).

cnf(c_0_1958_1,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_1958]) ).

cnf(c_0_1959_0,axiom,
    ( X1 = X2
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1959]) ).

cnf(c_0_1959_1,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_1959]) ).

cnf(c_0_1960_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_Ring__and__Field_Oordered__semidom(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1960]) ).

cnf(c_0_1960_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X2)
    | ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1960]) ).

cnf(c_0_1961_0,axiom,
    ( hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(X1)),X2) = c_Lambda_OdB_OVar(X1)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_1961]) ).

cnf(c_0_1961_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(X1)),X2) = c_Lambda_OdB_OVar(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1961]) ).

cnf(c_0_1962_0,axiom,
    ( hAPP(hAPP(X2,X4),X1) = X4
    | ~ c_OrderedGroup_Omonoid__add(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1962]) ).

cnf(c_0_1962_1,axiom,
    ( ~ c_OrderedGroup_Omonoid__add(X1,X2,X3)
    | hAPP(hAPP(X2,X4),X1) = X4 ),
    inference(literals_permutation,[status(thm)],[c_0_1962]) ).

cnf(c_0_1963_0,axiom,
    ( hAPP(hAPP(X2,X1),X4) = X4
    | ~ c_OrderedGroup_Omonoid__add(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1963]) ).

cnf(c_0_1963_1,axiom,
    ( ~ c_OrderedGroup_Omonoid__add(X1,X2,X3)
    | hAPP(hAPP(X2,X1),X4) = X4 ),
    inference(literals_permutation,[status(thm)],[c_0_1963]) ).

cnf(c_0_1964_0,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(X2)
    | c_Power_Opower__class_Opower(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
    | ~ class_Power_Opower(X2)
    | ~ class_Ring__and__Field_Omult__zero(X2)
    | ~ class_Ring__and__Field_Ono__zero__divisors(X2)
    | ~ class_Ring__and__Field_Ozero__neq__one(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1964]) ).

cnf(c_0_1964_1,axiom,
    ( c_Power_Opower__class_Opower(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
    | X1 = c_HOL_Ozero__class_Ozero(X2)
    | ~ class_Power_Opower(X2)
    | ~ class_Ring__and__Field_Omult__zero(X2)
    | ~ class_Ring__and__Field_Ono__zero__divisors(X2)
    | ~ class_Ring__and__Field_Ozero__neq__one(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1964]) ).

cnf(c_0_1964_2,axiom,
    ( ~ class_Power_Opower(X2)
    | c_Power_Opower__class_Opower(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
    | X1 = c_HOL_Ozero__class_Ozero(X2)
    | ~ class_Ring__and__Field_Omult__zero(X2)
    | ~ class_Ring__and__Field_Ono__zero__divisors(X2)
    | ~ class_Ring__and__Field_Ozero__neq__one(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1964]) ).

cnf(c_0_1964_3,axiom,
    ( ~ class_Ring__and__Field_Omult__zero(X2)
    | ~ class_Power_Opower(X2)
    | c_Power_Opower__class_Opower(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
    | X1 = c_HOL_Ozero__class_Ozero(X2)
    | ~ class_Ring__and__Field_Ono__zero__divisors(X2)
    | ~ class_Ring__and__Field_Ozero__neq__one(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1964]) ).

cnf(c_0_1964_4,axiom,
    ( ~ class_Ring__and__Field_Ono__zero__divisors(X2)
    | ~ class_Ring__and__Field_Omult__zero(X2)
    | ~ class_Power_Opower(X2)
    | c_Power_Opower__class_Opower(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
    | X1 = c_HOL_Ozero__class_Ozero(X2)
    | ~ class_Ring__and__Field_Ozero__neq__one(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1964]) ).

cnf(c_0_1964_5,axiom,
    ( ~ class_Ring__and__Field_Ozero__neq__one(X2)
    | ~ class_Ring__and__Field_Ono__zero__divisors(X2)
    | ~ class_Ring__and__Field_Omult__zero(X2)
    | ~ class_Power_Opower(X2)
    | c_Power_Opower__class_Opower(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
    | X1 = c_HOL_Ozero__class_Ozero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1964]) ).

cnf(c_0_1965_0,axiom,
    ( c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X2) != c_HOL_Ozero__class_Ozero(X2)
    | ~ class_Power_Opower(X2)
    | ~ class_Ring__and__Field_Omult__zero(X2)
    | ~ class_Ring__and__Field_Ono__zero__divisors(X2)
    | ~ class_Ring__and__Field_Ozero__neq__one(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1965]) ).

cnf(c_0_1965_1,axiom,
    ( ~ class_Power_Opower(X2)
    | c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X2) != c_HOL_Ozero__class_Ozero(X2)
    | ~ class_Ring__and__Field_Omult__zero(X2)
    | ~ class_Ring__and__Field_Ono__zero__divisors(X2)
    | ~ class_Ring__and__Field_Ozero__neq__one(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1965]) ).

cnf(c_0_1965_2,axiom,
    ( ~ class_Ring__and__Field_Omult__zero(X2)
    | ~ class_Power_Opower(X2)
    | c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X2) != c_HOL_Ozero__class_Ozero(X2)
    | ~ class_Ring__and__Field_Ono__zero__divisors(X2)
    | ~ class_Ring__and__Field_Ozero__neq__one(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1965]) ).

cnf(c_0_1965_3,axiom,
    ( ~ class_Ring__and__Field_Ono__zero__divisors(X2)
    | ~ class_Ring__and__Field_Omult__zero(X2)
    | ~ class_Power_Opower(X2)
    | c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X2) != c_HOL_Ozero__class_Ozero(X2)
    | ~ class_Ring__and__Field_Ozero__neq__one(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1965]) ).

cnf(c_0_1965_4,axiom,
    ( ~ class_Ring__and__Field_Ozero__neq__one(X2)
    | ~ class_Ring__and__Field_Ono__zero__divisors(X2)
    | ~ class_Ring__and__Field_Omult__zero(X2)
    | ~ class_Power_Opower(X2)
    | c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X2) != c_HOL_Ozero__class_Ozero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1965]) ).

cnf(c_0_1966_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | X2 = X1
    | c_Lambda_Osubstn(c_Lambda_OdB_OVar(X2),X3,X1) = c_Lambda_OdB_OVar(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1966]) ).

cnf(c_0_1966_1,axiom,
    ( X2 = X1
    | c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_Lambda_Osubstn(c_Lambda_OdB_OVar(X2),X3,X1) = c_Lambda_OdB_OVar(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1966]) ).

cnf(c_0_1966_2,axiom,
    ( c_Lambda_Osubstn(c_Lambda_OdB_OVar(X2),X3,X1) = c_Lambda_OdB_OVar(X2)
    | X2 = X1
    | c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_1966]) ).

cnf(c_0_1967_0,axiom,
    ( X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X2,X1,X3)
    | ~ class_Ring__and__Field_Oordered__idom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1967]) ).

cnf(c_0_1967_1,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,X3)
    | X1 = X2
    | c_HOL_Oord__class_Oless(X2,X1,X3)
    | ~ class_Ring__and__Field_Oordered__idom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1967]) ).

cnf(c_0_1967_2,axiom,
    ( c_HOL_Oord__class_Oless(X2,X1,X3)
    | c_HOL_Oord__class_Oless(X1,X2,X3)
    | X1 = X2
    | ~ class_Ring__and__Field_Oordered__idom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1967]) ).

cnf(c_0_1967_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X3)
    | c_HOL_Oord__class_Oless(X2,X1,X3)
    | c_HOL_Oord__class_Oless(X1,X2,X3)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_1967]) ).

cnf(c_0_1968_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X2,X1,X3)
    | X1 = X2
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1968]) ).

cnf(c_0_1968_1,axiom,
    ( c_HOL_Oord__class_Oless(X2,X1,X3)
    | c_HOL_Oord__class_Oless(X1,X2,X3)
    | X1 = X2
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1968]) ).

cnf(c_0_1968_2,axiom,
    ( X1 = X2
    | c_HOL_Oord__class_Oless(X2,X1,X3)
    | c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1968]) ).

cnf(c_0_1968_3,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | X1 = X2
    | c_HOL_Oord__class_Oless(X2,X1,X3)
    | c_HOL_Oord__class_Oless(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1968]) ).

cnf(c_0_1969_0,axiom,
    ( X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X2,X1,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1969]) ).

cnf(c_0_1969_1,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,X3)
    | X1 = X2
    | c_HOL_Oord__class_Oless(X2,X1,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1969]) ).

cnf(c_0_1969_2,axiom,
    ( c_HOL_Oord__class_Oless(X2,X1,X3)
    | c_HOL_Oord__class_Oless(X1,X2,X3)
    | X1 = X2
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1969]) ).

cnf(c_0_1969_3,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | c_HOL_Oord__class_Oless(X2,X1,X3)
    | c_HOL_Oord__class_Oless(X1,X2,X3)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_1969]) ).

cnf(c_0_1970_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,X3)
    | X1 = X2
    | c_HOL_Oord__class_Oless(X2,X1,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1970]) ).

cnf(c_0_1970_1,axiom,
    ( X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X2,X1,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1970]) ).

cnf(c_0_1970_2,axiom,
    ( c_HOL_Oord__class_Oless(X2,X1,X3)
    | X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1970]) ).

cnf(c_0_1970_3,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | c_HOL_Oord__class_Oless(X2,X1,X3)
    | X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1970]) ).

cnf(c_0_1971_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X2,X1,X3)
    | X2 = X1
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1971]) ).

cnf(c_0_1971_1,axiom,
    ( c_HOL_Oord__class_Oless(X2,X1,X3)
    | c_HOL_Oord__class_Oless(X1,X2,X3)
    | X2 = X1
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1971]) ).

cnf(c_0_1971_2,axiom,
    ( X2 = X1
    | c_HOL_Oord__class_Oless(X2,X1,X3)
    | c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1971]) ).

cnf(c_0_1971_3,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | X2 = X1
    | c_HOL_Oord__class_Oless(X2,X1,X3)
    | c_HOL_Oord__class_Oless(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1971]) ).

cnf(c_0_1972_0,axiom,
    ( X1 = X2
    | hAPP(hAPP(c_Lambda_OdB_OApp,X1),X3) != hAPP(hAPP(c_Lambda_OdB_OApp,X2),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_1972]) ).

cnf(c_0_1972_1,axiom,
    ( hAPP(hAPP(c_Lambda_OdB_OApp,X1),X3) != hAPP(hAPP(c_Lambda_OdB_OApp,X2),X4)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_1972]) ).

cnf(c_0_1973_0,axiom,
    ( X1 = X2
    | hAPP(hAPP(c_Lambda_OdB_OApp,X3),X1) != hAPP(hAPP(c_Lambda_OdB_OApp,X4),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1973]) ).

cnf(c_0_1973_1,axiom,
    ( hAPP(hAPP(c_Lambda_OdB_OApp,X3),X1) != hAPP(hAPP(c_Lambda_OdB_OApp,X4),X2)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_1973]) ).

cnf(c_0_1974_0,axiom,
    ( c_lessequals(X1,X2,X3)
    | c_lessequals(X2,X1,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1974]) ).

cnf(c_0_1974_1,axiom,
    ( c_lessequals(X2,X1,X3)
    | c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1974]) ).

cnf(c_0_1974_2,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | c_lessequals(X2,X1,X3)
    | c_lessequals(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1974]) ).

cnf(c_0_1975_0,axiom,
    ( c_lessequals(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X2,X1,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1975]) ).

cnf(c_0_1975_1,axiom,
    ( c_HOL_Oord__class_Oless(X2,X1,X3)
    | c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1975]) ).

cnf(c_0_1975_2,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | c_HOL_Oord__class_Oless(X2,X1,X3)
    | c_lessequals(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1975]) ).

cnf(c_0_1976_0,axiom,
    ( c_lessequals(X1,X1,X2)
    | c_HOL_Oord__class_Oless(X1,X1,X2)
    | ~ class_Orderings_Olinorder(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1976]) ).

cnf(c_0_1976_1,axiom,
    ( c_HOL_Oord__class_Oless(X1,X1,X2)
    | c_lessequals(X1,X1,X2)
    | ~ class_Orderings_Olinorder(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1976]) ).

cnf(c_0_1976_2,axiom,
    ( ~ class_Orderings_Olinorder(X2)
    | c_HOL_Oord__class_Oless(X1,X1,X2)
    | c_lessequals(X1,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1976]) ).

cnf(c_0_1977_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_lessequals(X2,X1,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1977]) ).

cnf(c_0_1977_1,axiom,
    ( c_lessequals(X2,X1,X3)
    | c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1977]) ).

cnf(c_0_1977_2,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | c_lessequals(X2,X1,X3)
    | c_HOL_Oord__class_Oless(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1977]) ).

cnf(c_0_1978_0,axiom,
    ( c_lessequals(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X2,X1,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1978]) ).

cnf(c_0_1978_1,axiom,
    ( c_HOL_Oord__class_Oless(X2,X1,X3)
    | c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1978]) ).

cnf(c_0_1978_2,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | c_HOL_Oord__class_Oless(X2,X1,X3)
    | c_lessequals(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1978]) ).

cnf(c_0_1979_0,axiom,
    ( c_Orderings_Oord__class_Omax(X1,X2,X3) = c_Orderings_Oord__class_Omax(X2,X1,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1979]) ).

cnf(c_0_1979_1,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | c_Orderings_Oord__class_Omax(X1,X2,X3) = c_Orderings_Oord__class_Omax(X2,X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1979]) ).

cnf(c_0_1980_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1980]) ).

cnf(c_0_1980_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1980]) ).

cnf(c_0_1981_0,axiom,
    ( ~ c_lessequals(c_HOL_Oone__class_Oone(X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1981]) ).

cnf(c_0_1981_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | ~ c_lessequals(c_HOL_Oone__class_Oone(X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1981]) ).

cnf(c_0_1982_0,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X2)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1982]) ).

cnf(c_0_1982_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1982]) ).

cnf(c_0_1983_0,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X2)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1983]) ).

cnf(c_0_1983_1,axiom,
    ( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1983]) ).

cnf(c_0_1984_0,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X2)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1984]) ).

cnf(c_0_1984_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1984]) ).

cnf(c_0_1985_0,axiom,
    ( hAPP(X1,X2) = X3
    | ~ c_Type_Otyping(X1,c_Lambda_OdB_OVar(X2),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1985]) ).

cnf(c_0_1985_1,axiom,
    ( ~ c_Type_Otyping(X1,c_Lambda_OdB_OVar(X2),X3)
    | hAPP(X1,X2) = X3 ),
    inference(literals_permutation,[status(thm)],[c_0_1985]) ).

cnf(c_0_1986_0,axiom,
    ( X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_1986]) ).

cnf(c_0_1986_1,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | X1 = X2
    | c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_1986]) ).

cnf(c_0_1986_2,axiom,
    ( c_HOL_Oord__class_Oless(X2,X1,tc_nat)
    | c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_1986]) ).

cnf(c_0_1987_0,axiom,
    ( X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_1987]) ).

cnf(c_0_1987_1,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | X1 = X2
    | c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_1987]) ).

cnf(c_0_1987_2,axiom,
    ( c_HOL_Oord__class_Oless(X2,X1,tc_nat)
    | c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_1987]) ).

cnf(c_0_1988_0,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(X2)
    | c_Power_Opower__class_Opower(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
    | ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1988]) ).

cnf(c_0_1988_1,axiom,
    ( c_Power_Opower__class_Opower(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
    | X1 = c_HOL_Ozero__class_Ozero(X2)
    | ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1988]) ).

cnf(c_0_1988_2,axiom,
    ( ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X2)
    | c_Power_Opower__class_Opower(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
    | X1 = c_HOL_Ozero__class_Ozero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1988]) ).

cnf(c_0_1989_0,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(X2)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),X1) != X3
    | ~ class_Int_Onumber__ring(X2)
    | ~ class_Ring__and__Field_Oidom(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1989]) ).

cnf(c_0_1989_1,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),X1) != X3
    | X1 = c_HOL_Ozero__class_Ozero(X2)
    | ~ class_Int_Onumber__ring(X2)
    | ~ class_Ring__and__Field_Oidom(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1989]) ).

cnf(c_0_1989_2,axiom,
    ( ~ class_Int_Onumber__ring(X2)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),X1) != X3
    | X1 = c_HOL_Ozero__class_Ozero(X2)
    | ~ class_Ring__and__Field_Oidom(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1989]) ).

cnf(c_0_1989_3,axiom,
    ( ~ class_Ring__and__Field_Oidom(X2)
    | ~ class_Int_Onumber__ring(X2)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),X1) != X3
    | X1 = c_HOL_Ozero__class_Ozero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1989]) ).

cnf(c_0_1990_0,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(X2)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X1) != c_HOL_Ozero__class_Ozero(X2)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1990]) ).

cnf(c_0_1990_1,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X1) != c_HOL_Ozero__class_Ozero(X2)
    | X1 = c_HOL_Ozero__class_Ozero(X2)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1990]) ).

cnf(c_0_1990_2,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__add(X2)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X1) != c_HOL_Ozero__class_Ozero(X2)
    | X1 = c_HOL_Ozero__class_Ozero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1990]) ).

cnf(c_0_1991_0,axiom,
    ( X1 = c_List_Olist_ONil(X2)
    | c_List_Oappend(X1,X3,X2) != c_List_Olist_ONil(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1991]) ).

cnf(c_0_1991_1,axiom,
    ( c_List_Oappend(X1,X3,X2) != c_List_Olist_ONil(X2)
    | X1 = c_List_Olist_ONil(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1991]) ).

cnf(c_0_1992_0,axiom,
    ( X1 = c_List_Olist_ONil(X2)
    | c_List_Oappend(X3,X1,X2) != c_List_Olist_ONil(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1992]) ).

cnf(c_0_1992_1,axiom,
    ( c_List_Oappend(X3,X1,X2) != c_List_Olist_ONil(X2)
    | X1 = c_List_Olist_ONil(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1992]) ).

cnf(c_0_1993_0,axiom,
    ( X1 = c_List_Olist_ONil(X2)
    | c_List_Oappend(X1,X3,X2) != c_List_Olist_ONil(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1993]) ).

cnf(c_0_1993_1,axiom,
    ( c_List_Oappend(X1,X3,X2) != c_List_Olist_ONil(X2)
    | X1 = c_List_Olist_ONil(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1993]) ).

cnf(c_0_1994_0,axiom,
    ( X1 = c_List_Olist_ONil(X2)
    | c_List_Oappend(X3,X1,X2) != c_List_Olist_ONil(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1994]) ).

cnf(c_0_1994_1,axiom,
    ( c_List_Oappend(X3,X1,X2) != c_List_Olist_ONil(X2)
    | X1 = c_List_Olist_ONil(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1994]) ).

cnf(c_0_1995_0,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X2),X1,X2) = c_HOL_Ozero__class_Ozero(X2)
    | ~ class_Power_Opower(X2)
    | ~ class_Ring__and__Field_Omult__zero(X2)
    | ~ class_Ring__and__Field_Ono__zero__divisors(X2)
    | ~ class_Ring__and__Field_Ozero__neq__one(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1995]) ).

cnf(c_0_1995_1,axiom,
    ( c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X2),X1,X2) = c_HOL_Ozero__class_Ozero(X2)
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | ~ class_Power_Opower(X2)
    | ~ class_Ring__and__Field_Omult__zero(X2)
    | ~ class_Ring__and__Field_Ono__zero__divisors(X2)
    | ~ class_Ring__and__Field_Ozero__neq__one(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1995]) ).

cnf(c_0_1995_2,axiom,
    ( ~ class_Power_Opower(X2)
    | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X2),X1,X2) = c_HOL_Ozero__class_Ozero(X2)
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | ~ class_Ring__and__Field_Omult__zero(X2)
    | ~ class_Ring__and__Field_Ono__zero__divisors(X2)
    | ~ class_Ring__and__Field_Ozero__neq__one(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1995]) ).

cnf(c_0_1995_3,axiom,
    ( ~ class_Ring__and__Field_Omult__zero(X2)
    | ~ class_Power_Opower(X2)
    | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X2),X1,X2) = c_HOL_Ozero__class_Ozero(X2)
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | ~ class_Ring__and__Field_Ono__zero__divisors(X2)
    | ~ class_Ring__and__Field_Ozero__neq__one(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1995]) ).

cnf(c_0_1995_4,axiom,
    ( ~ class_Ring__and__Field_Ono__zero__divisors(X2)
    | ~ class_Ring__and__Field_Omult__zero(X2)
    | ~ class_Power_Opower(X2)
    | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X2),X1,X2) = c_HOL_Ozero__class_Ozero(X2)
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | ~ class_Ring__and__Field_Ozero__neq__one(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1995]) ).

cnf(c_0_1995_5,axiom,
    ( ~ class_Ring__and__Field_Ozero__neq__one(X2)
    | ~ class_Ring__and__Field_Ono__zero__divisors(X2)
    | ~ class_Ring__and__Field_Omult__zero(X2)
    | ~ class_Power_Opower(X2)
    | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X2),X1,X2) = c_HOL_Ozero__class_Ozero(X2)
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_1995]) ).

cnf(c_0_1996_0,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_List_Oreplicate(X1,X2,X3) != c_List_Olist_ONil(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1996]) ).

cnf(c_0_1996_1,axiom,
    ( c_List_Oreplicate(X1,X2,X3) != c_List_Olist_ONil(X3)
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_1996]) ).

cnf(c_0_1997_0,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_List_Oreplicate(X1,X3,X2) != c_List_Olist_ONil(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1997]) ).

cnf(c_0_1997_1,axiom,
    ( c_List_Oreplicate(X1,X3,X2) != c_List_Olist_ONil(X2)
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_1997]) ).

cnf(c_0_1998_0,axiom,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1998]) ).

cnf(c_0_1998_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1998]) ).

cnf(c_0_1999_0,axiom,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1999]) ).

cnf(c_0_1999_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1999]) ).

cnf(c_0_2000_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
    | ~ class_Orderings_Oorder(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2000]) ).

cnf(c_0_2000_1,axiom,
    ( ~ class_Orderings_Oorder(X2)
    | ~ c_HOL_Oord__class_Oless(X1,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2000]) ).

cnf(c_0_2001_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
    | ~ class_Orderings_Olinorder(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2001]) ).

cnf(c_0_2001_1,axiom,
    ( ~ class_Orderings_Olinorder(X2)
    | ~ c_HOL_Oord__class_Oless(X1,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2001]) ).

cnf(c_0_2002_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
    | ~ class_Orderings_Opreorder(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2002]) ).

cnf(c_0_2002_1,axiom,
    ( ~ class_Orderings_Opreorder(X2)
    | ~ c_HOL_Oord__class_Oless(X1,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2002]) ).

cnf(c_0_2003_0,axiom,
    ( X1 = c_List_Olist_ONil(X2)
    | c_List_Oappend(X3,X1,X2) != X3 ),
    inference(literals_permutation,[status(thm)],[c_0_2003]) ).

cnf(c_0_2003_1,axiom,
    ( c_List_Oappend(X3,X1,X2) != X3
    | X1 = c_List_Olist_ONil(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2003]) ).

cnf(c_0_2004_0,axiom,
    ( X1 = c_List_Olist_ONil(X2)
    | c_List_Oappend(X3,X1,X2) != X3 ),
    inference(literals_permutation,[status(thm)],[c_0_2004]) ).

cnf(c_0_2004_1,axiom,
    ( c_List_Oappend(X3,X1,X2) != X3
    | X1 = c_List_Olist_ONil(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2004]) ).

cnf(c_0_2005_0,axiom,
    ( X1 = c_List_Olist_ONil(X2)
    | c_List_Oappend(X1,X3,X2) != X3 ),
    inference(literals_permutation,[status(thm)],[c_0_2005]) ).

cnf(c_0_2005_1,axiom,
    ( c_List_Oappend(X1,X3,X2) != X3
    | X1 = c_List_Olist_ONil(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2005]) ).

cnf(c_0_2006_0,axiom,
    ( X1 = c_List_Olist_ONil(X2)
    | c_List_Oappend(X1,X3,X2) != X3 ),
    inference(literals_permutation,[status(thm)],[c_0_2006]) ).

cnf(c_0_2006_1,axiom,
    ( c_List_Oappend(X1,X3,X2) != X3
    | X1 = c_List_Olist_ONil(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2006]) ).

cnf(c_0_2007_0,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X2),X1,X2) = c_HOL_Ozero__class_Ozero(X2)
    | ~ class_Power_Opower(X2)
    | ~ class_Ring__and__Field_Osemiring__0(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2007]) ).

cnf(c_0_2007_1,axiom,
    ( c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X2),X1,X2) = c_HOL_Ozero__class_Ozero(X2)
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | ~ class_Power_Opower(X2)
    | ~ class_Ring__and__Field_Osemiring__0(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2007]) ).

cnf(c_0_2007_2,axiom,
    ( ~ class_Power_Opower(X2)
    | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X2),X1,X2) = c_HOL_Ozero__class_Ozero(X2)
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | ~ class_Ring__and__Field_Osemiring__0(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2007]) ).

cnf(c_0_2007_3,axiom,
    ( ~ class_Ring__and__Field_Osemiring__0(X2)
    | ~ class_Power_Opower(X2)
    | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X2),X1,X2) = c_HOL_Ozero__class_Ozero(X2)
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2007]) ).

cnf(c_0_2008_0,axiom,
    ( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(X1)))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_2008]) ).

cnf(c_0_2008_1,axiom,
    ( ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
    | hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_2008]) ).

cnf(c_0_2009_0,axiom,
    ( c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(tc_nat),X1) = c_HOL_Oone__class_Oone(X1)
    | ~ class_Power_Opower(X1)
    | ~ class_Ring__and__Field_Osemiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2009]) ).

cnf(c_0_2009_1,axiom,
    ( ~ class_Power_Opower(X1)
    | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(tc_nat),X1) = c_HOL_Oone__class_Oone(X1)
    | ~ class_Ring__and__Field_Osemiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2009]) ).

cnf(c_0_2009_2,axiom,
    ( ~ class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Power_Opower(X1)
    | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(tc_nat),X1) = c_HOL_Oone__class_Oone(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2009]) ).

cnf(c_0_2010_0,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1)) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2010]) ).

cnf(c_0_2010_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__add(X1)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1)) = c_HOL_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2010]) ).

cnf(c_0_2011_0,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2011]) ).

cnf(c_0_2011_1,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != c_HOL_Ozero__class_Ozero(tc_nat)
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2011]) ).

cnf(c_0_2012_0,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2012]) ).

cnf(c_0_2012_1,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_HOL_Ozero__class_Ozero(tc_nat)
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2012]) ).

cnf(c_0_2013_0,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != X2 ),
    inference(literals_permutation,[status(thm)],[c_0_2013]) ).

cnf(c_0_2013_1,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != X2
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2013]) ).

cnf(c_0_2014_0,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != X2 ),
    inference(literals_permutation,[status(thm)],[c_0_2014]) ).

cnf(c_0_2014_1,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != X2
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2014]) ).

cnf(c_0_2015_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oone__class_Oone(X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2015]) ).

cnf(c_0_2015_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oone__class_Oone(X1),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2015]) ).

cnf(c_0_2016_0,axiom,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oone__class_Oone(X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2016]) ).

cnf(c_0_2016_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oone__class_Oone(X1),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2016]) ).

cnf(c_0_2017_0,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),c_HOL_Ozero__class_Ozero(X2)) = X1
    | ~ class_Int_Onumber__ring(X2)
    | ~ class_Ring__and__Field_Oidom(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2017]) ).

cnf(c_0_2017_1,axiom,
    ( ~ class_Int_Onumber__ring(X2)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),c_HOL_Ozero__class_Ozero(X2)) = X1
    | ~ class_Ring__and__Field_Oidom(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2017]) ).

cnf(c_0_2017_2,axiom,
    ( ~ class_Ring__and__Field_Oidom(X2)
    | ~ class_Int_Onumber__ring(X2)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),c_HOL_Ozero__class_Ozero(X2)) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_2017]) ).

cnf(c_0_2018_0,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2018]) ).

cnf(c_0_2018_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_2018]) ).

cnf(c_0_2019_0,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2019]) ).

cnf(c_0_2019_1,axiom,
    ( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_2019]) ).

cnf(c_0_2020_0,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
    | ~ class_OrderedGroup_Omonoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2020]) ).

cnf(c_0_2020_1,axiom,
    ( ~ class_OrderedGroup_Omonoid__add(X1)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_2020]) ).

cnf(c_0_2021_0,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2021]) ).

cnf(c_0_2021_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_2021]) ).

cnf(c_0_2022_0,axiom,
    ( c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X1),X2,X1) = c_HOL_Oone__class_Oone(X1)
    | ~ class_OrderedGroup_Omonoid__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2022]) ).

cnf(c_0_2022_1,axiom,
    ( ~ class_OrderedGroup_Omonoid__mult(X1)
    | c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X1),X2,X1) = c_HOL_Oone__class_Oone(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2022]) ).

cnf(c_0_2023_0,axiom,
    ( c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X2) = c_HOL_Oone__class_Oone(X2)
    | ~ class_Power_Opower(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2023]) ).

cnf(c_0_2023_1,axiom,
    ( ~ class_Power_Opower(X2)
    | c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X2) = c_HOL_Oone__class_Oone(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2023]) ).

cnf(c_0_2024_0,axiom,
    ( c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X2) = c_HOL_Oone__class_Oone(X2)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2024]) ).

cnf(c_0_2024_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
    | c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X2) = c_HOL_Oone__class_Oone(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2024]) ).

cnf(c_0_2025_0,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = X2
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2025]) ).

cnf(c_0_2025_1,axiom,
    ( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_2025]) ).

cnf(c_0_2026_0,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = X2
    | ~ class_OrderedGroup_Omonoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2026]) ).

cnf(c_0_2026_1,axiom,
    ( ~ class_OrderedGroup_Omonoid__add(X1)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_2026]) ).

cnf(c_0_2027_0,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = X2
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2027]) ).

cnf(c_0_2027_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_2027]) ).

cnf(c_0_2028_0,axiom,
    ( c_Power_Opower__class_Opower(X1,c_HOL_Oone__class_Oone(tc_nat),X2) = X1
    | ~ class_OrderedGroup_Omonoid__mult(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2028]) ).

cnf(c_0_2028_1,axiom,
    ( ~ class_OrderedGroup_Omonoid__mult(X2)
    | c_Power_Opower__class_Opower(X1,c_HOL_Oone__class_Oone(tc_nat),X2) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_2028]) ).

cnf(c_0_2029_0,axiom,
    ( c_Power_Opower__class_Opower(X1,c_HOL_Oone__class_Oone(tc_nat),X2) = X1
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2029]) ).

cnf(c_0_2029_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
    | c_Power_Opower__class_Opower(X1,c_HOL_Oone__class_Oone(tc_nat),X2) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_2029]) ).

cnf(c_0_2030_0,axiom,
    ( c_Orderings_Oord__class_Omax(X1,X1,X2) = X1
    | ~ class_Orderings_Olinorder(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2030]) ).

cnf(c_0_2030_1,axiom,
    ( ~ class_Orderings_Olinorder(X2)
    | c_Orderings_Oord__class_Omax(X1,X1,X2) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_2030]) ).

cnf(c_0_2031_0,axiom,
    ( c_lessequals(X1,X1,X2)
    | ~ class_Orderings_Opreorder(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2031]) ).

cnf(c_0_2031_1,axiom,
    ( ~ class_Orderings_Opreorder(X2)
    | c_lessequals(X1,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2031]) ).

cnf(c_0_2032_0,axiom,
    ( c_lessequals(X1,X1,X2)
    | ~ class_Orderings_Oorder(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2032]) ).

cnf(c_0_2032_1,axiom,
    ( ~ class_Orderings_Oorder(X2)
    | c_lessequals(X1,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2032]) ).

cnf(c_0_2033_0,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2033]) ).

cnf(c_0_2033_1,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2033]) ).

cnf(c_0_2034_0,axiom,
    ( X1 = X2
    | c_Nat_Osemiring__1__class_Oof__nat(X1,X3) != c_Nat_Osemiring__1__class_Oof__nat(X2,X3)
    | ~ class_Nat_Osemiring__char__0(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2034]) ).

cnf(c_0_2034_1,axiom,
    ( c_Nat_Osemiring__1__class_Oof__nat(X1,X3) != c_Nat_Osemiring__1__class_Oof__nat(X2,X3)
    | X1 = X2
    | ~ class_Nat_Osemiring__char__0(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2034]) ).

cnf(c_0_2034_2,axiom,
    ( ~ class_Nat_Osemiring__char__0(X3)
    | c_Nat_Osemiring__1__class_Oof__nat(X1,X3) != c_Nat_Osemiring__1__class_Oof__nat(X2,X3)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_2034]) ).

cnf(c_0_2035_0,axiom,
    ( class_Orderings_Opreorder(tc_fun(X2,X1))
    | ~ class_Orderings_Opreorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2035]) ).

cnf(c_0_2035_1,axiom,
    ( ~ class_Orderings_Opreorder(X1)
    | class_Orderings_Opreorder(tc_fun(X2,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_2035]) ).

cnf(c_0_2036_0,axiom,
    ( class_Orderings_Oorder(tc_fun(X2,X1))
    | ~ class_Orderings_Oorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2036]) ).

cnf(c_0_2036_1,axiom,
    ( ~ class_Orderings_Oorder(X1)
    | class_Orderings_Oorder(tc_fun(X2,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_2036]) ).

cnf(c_0_2037_0,axiom,
    ( c_List_Olistsum(c_List_Olist_ONil(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_OrderedGroup_Omonoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2037]) ).

cnf(c_0_2037_1,axiom,
    ( ~ class_OrderedGroup_Omonoid__add(X1)
    | c_List_Olistsum(c_List_Olist_ONil(X1),X1) = c_HOL_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2037]) ).

cnf(c_0_2038_0,axiom,
    ( c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),X1) = c_HOL_Oone__class_Oone(X1)
    | ~ class_Ring__and__Field_Osemiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2038]) ).

cnf(c_0_2038_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring__1(X1)
    | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),X1) = c_HOL_Oone__class_Oone(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2038]) ).

cnf(c_0_2039_0,axiom,
    ( c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Osemiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2039]) ).

cnf(c_0_2039_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring__1(X1)
    | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X1) = c_HOL_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2039]) ).

cnf(c_0_2040_0,axiom,
    ( c_OrderedGroup_Osemigroup__add(c_HOL_Oplus__class_Oplus(X1),X1)
    | ~ class_OrderedGroup_Osemigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2040]) ).

cnf(c_0_2040_1,axiom,
    ( ~ class_OrderedGroup_Osemigroup__add(X1)
    | c_OrderedGroup_Osemigroup__add(c_HOL_Oplus__class_Oplus(X1),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2040]) ).

cnf(c_0_2041_0,axiom,
    ( c_HOL_Oone__class_Oone(X1) != c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Ozero__neq__one(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2041]) ).

cnf(c_0_2041_1,axiom,
    ( ~ class_Ring__and__Field_Ozero__neq__one(X1)
    | c_HOL_Oone__class_Oone(X1) != c_HOL_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2041]) ).

cnf(c_0_2042_0,axiom,
    ( c_HOL_Oone__class_Oone(X1) != c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Ozero__neq__one(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2042]) ).

cnf(c_0_2042_1,axiom,
    ( ~ class_Ring__and__Field_Ozero__neq__one(X1)
    | c_HOL_Oone__class_Oone(X1) != c_HOL_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2042]) ).

cnf(c_0_2043_0,axiom,
    ( X1 = X2
    | c_Lambda_OdB_OAbs(X1) != c_Lambda_OdB_OAbs(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2043]) ).

cnf(c_0_2043_1,axiom,
    ( c_Lambda_OdB_OAbs(X1) != c_Lambda_OdB_OAbs(X2)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_2043]) ).

cnf(c_0_2044_0,axiom,
    ( X1 = X2
    | c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OVar(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2044]) ).

cnf(c_0_2044_1,axiom,
    ( c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OVar(X2)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_2044]) ).

% CNF of non-axioms
% Start CNF derivation
fof(c_0_0_676,negated_conjecture,
    ~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r),v_s),c_HOL_Ozero__class_Ozero(tc_nat)),v_ss,tc_Lambda_OdB,tc_Lambda_OdB)),c_Lambda_OdB_OVar(v_i)))),
    file('<stdin>',cls_conjecture_4) ).

fof(c_0_1_677,negated_conjecture,
    hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r),v_s),c_HOL_Ozero__class_Ozero(tc_nat)),v_ss,tc_Lambda_OdB,tc_Lambda_OdB)),c_Lambda_OdB_OVar(v_i)))),
    file('<stdin>',cls_conjecture_1) ).

fof(c_0_2_678,negated_conjecture,
    hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r),v_s),c_HOL_Ozero__class_Ozero(tc_nat)),v_ss,tc_Lambda_OdB,tc_Lambda_OdB))),
    file('<stdin>',cls_conjecture_0) ).

fof(c_0_3_679,negated_conjecture,
    hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,v_s),c_Lambda_OdB_OVar(v_i)))),
    file('<stdin>',cls_conjecture_3) ).

fof(c_0_4_680,negated_conjecture,
    hBOOL(hAPP(c_InductTermi_OIT,v_s)),
    file('<stdin>',cls_conjecture_2) ).

fof(c_0_5_681,negated_conjecture,
    ~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r),v_s),c_HOL_Ozero__class_Ozero(tc_nat)),v_ss,tc_Lambda_OdB,tc_Lambda_OdB)),c_Lambda_OdB_OVar(v_i)))),
    inference(fof_simplification,[status(thm)],[c_0_0]) ).

fof(c_0_6_682,negated_conjecture,
    hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r),v_s),c_HOL_Ozero__class_Ozero(tc_nat)),v_ss,tc_Lambda_OdB,tc_Lambda_OdB)),c_Lambda_OdB_OVar(v_i)))),
    c_0_1 ).

fof(c_0_7_683,negated_conjecture,
    hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r),v_s),c_HOL_Ozero__class_Ozero(tc_nat)),v_ss,tc_Lambda_OdB,tc_Lambda_OdB))),
    c_0_2 ).

fof(c_0_8_684,negated_conjecture,
    hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,v_s),c_Lambda_OdB_OVar(v_i)))),
    c_0_3 ).

fof(c_0_9_685,negated_conjecture,
    hBOOL(hAPP(c_InductTermi_OIT,v_s)),
    c_0_4 ).

fof(c_0_10_686,negated_conjecture,
    ~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r),v_s),c_HOL_Ozero__class_Ozero(tc_nat)),v_ss,tc_Lambda_OdB,tc_Lambda_OdB)),c_Lambda_OdB_OVar(v_i)))),
    c_0_5 ).

fof(c_0_11_687,negated_conjecture,
    hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r),v_s),c_HOL_Ozero__class_Ozero(tc_nat)),v_ss,tc_Lambda_OdB,tc_Lambda_OdB)),c_Lambda_OdB_OVar(v_i)))),
    c_0_6 ).

fof(c_0_12_688,negated_conjecture,
    hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r),v_s),c_HOL_Ozero__class_Ozero(tc_nat)),v_ss,tc_Lambda_OdB,tc_Lambda_OdB))),
    c_0_7 ).

fof(c_0_13_689,negated_conjecture,
    hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,v_s),c_Lambda_OdB_OVar(v_i)))),
    c_0_8 ).

fof(c_0_14_690,negated_conjecture,
    hBOOL(hAPP(c_InductTermi_OIT,v_s)),
    c_0_9 ).

cnf(c_0_15_691,negated_conjecture,
    ~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r),v_s),c_HOL_Ozero__class_Ozero(tc_nat)),v_ss,tc_Lambda_OdB,tc_Lambda_OdB)),c_Lambda_OdB_OVar(v_i)))),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_16_692,negated_conjecture,
    hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r),v_s),c_HOL_Ozero__class_Ozero(tc_nat)),v_ss,tc_Lambda_OdB,tc_Lambda_OdB)),c_Lambda_OdB_OVar(v_i)))),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_17_693,negated_conjecture,
    hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r),v_s),c_HOL_Ozero__class_Ozero(tc_nat)),v_ss,tc_Lambda_OdB,tc_Lambda_OdB))),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_18_694,negated_conjecture,
    hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,v_s),c_Lambda_OdB_OVar(v_i)))),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_19_695,negated_conjecture,
    hBOOL(hAPP(c_InductTermi_OIT,v_s)),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_20_696,negated_conjecture,
    ~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r),v_s),c_HOL_Ozero__class_Ozero(tc_nat)),v_ss,tc_Lambda_OdB,tc_Lambda_OdB)),c_Lambda_OdB_OVar(v_i)))),
    c_0_15,
    [final] ).

cnf(c_0_21_697,negated_conjecture,
    hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r),v_s),c_HOL_Ozero__class_Ozero(tc_nat)),v_ss,tc_Lambda_OdB,tc_Lambda_OdB)),c_Lambda_OdB_OVar(v_i)))),
    c_0_16,
    [final] ).

cnf(c_0_22_698,negated_conjecture,
    hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r),v_s),c_HOL_Ozero__class_Ozero(tc_nat)),v_ss,tc_Lambda_OdB,tc_Lambda_OdB))),
    c_0_17,
    [final] ).

cnf(c_0_23_699,negated_conjecture,
    hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,v_s),c_Lambda_OdB_OVar(v_i)))),
    c_0_18,
    [final] ).

cnf(c_0_24_700,negated_conjecture,
    hBOOL(hAPP(c_InductTermi_OIT,v_s)),
    c_0_19,
    [final] ).

% End CNF derivation

%-------------------------------------------------------------
% Proof by iprover

cnf(c_1241,negated_conjecture,
    ~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r),v_s),c_HOL_Ozero__class_Ozero(tc_nat)),v_ss,tc_Lambda_OdB,tc_Lambda_OdB)),c_Lambda_OdB_OVar(v_i)))),
    file('/export/starexec/sandbox2/tmp/iprover_modulo_2d5469.p',c_0_20) ).

cnf(c_1242,negated_conjecture,
    hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r),v_s),c_HOL_Ozero__class_Ozero(tc_nat)),v_ss,tc_Lambda_OdB,tc_Lambda_OdB)),c_Lambda_OdB_OVar(v_i)))),
    file('/export/starexec/sandbox2/tmp/iprover_modulo_2d5469.p',c_0_21) ).

cnf(contradiction,plain,
    $false,
    inference(minisat,[status(thm)],[c_1241,c_1242]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : LCL778-1 : TPTP v8.1.0. Released v4.1.0.
% 0.12/0.13  % Command  : iprover_modulo %s %d
% 0.12/0.34  % Computer : n004.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Mon Jul  4 05:55:53 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.12/0.34  % Running in mono-core mode
% 0.20/0.50  % Orienting using strategy Equiv(ClausalAll)
% 0.20/0.50  % Orientation found
% 0.20/0.50  % Executing iprover_moduloopt --modulo true --schedule none --sub_typing false --res_to_prop_solver none --res_prop_simpl_given false --res_lit_sel kbo_max --large_theory_mode false --res_time_limit 1000 --res_orphan_elimination false --prep_sem_filter none --prep_unflatten false --comb_res_mult 1000 --comb_inst_mult 300 --clausifier .//eprover --clausifier_options "--tstp-format  " --proof_out_file /export/starexec/sandbox2/tmp/iprover_proof_126608.s --tptp_safe_out true --time_out_real 150 /export/starexec/sandbox2/tmp/iprover_modulo_2d5469.p | tee /export/starexec/sandbox2/tmp/iprover_modulo_out_945de7 | grep -v "SZS"
% 0.20/0.52  
% 0.20/0.52  %---------------- iProver v2.5 (CASC-J8 2016) ----------------%
% 0.20/0.52  
% 0.20/0.52  % 
% 0.20/0.52  % ------  iProver source info 
% 0.20/0.52  
% 0.20/0.52  % git: sha1: 57accf6c58032223c7708532cf852a99fa48c1b3
% 0.20/0.52  % git: non_committed_changes: true
% 0.20/0.52  % git: last_make_outside_of_git: true
% 0.20/0.52  
% 0.20/0.52  % 
% 0.20/0.52  % ------ Input Options
% 0.20/0.52  
% 0.20/0.52  % --out_options                         all
% 0.20/0.52  % --tptp_safe_out                       true
% 0.20/0.52  % --problem_path                        ""
% 0.20/0.52  % --include_path                        ""
% 0.20/0.52  % --clausifier                          .//eprover
% 0.20/0.52  % --clausifier_options                  --tstp-format  
% 0.20/0.52  % --stdin                               false
% 0.20/0.52  % --dbg_backtrace                       false
% 0.20/0.52  % --dbg_dump_prop_clauses               false
% 0.20/0.52  % --dbg_dump_prop_clauses_file          -
% 0.20/0.52  % --dbg_out_stat                        false
% 0.20/0.52  
% 0.20/0.52  % ------ General Options
% 0.20/0.52  
% 0.20/0.52  % --fof                                 false
% 0.20/0.52  % --time_out_real                       150.
% 0.20/0.52  % --time_out_prep_mult                  0.2
% 0.20/0.52  % --time_out_virtual                    -1.
% 0.20/0.52  % --schedule                            none
% 0.20/0.52  % --ground_splitting                    input
% 0.20/0.52  % --splitting_nvd                       16
% 0.20/0.52  % --non_eq_to_eq                        false
% 0.20/0.52  % --prep_gs_sim                         true
% 0.20/0.52  % --prep_unflatten                      false
% 0.20/0.52  % --prep_res_sim                        true
% 0.20/0.52  % --prep_upred                          true
% 0.20/0.52  % --res_sim_input                       true
% 0.20/0.52  % --clause_weak_htbl                    true
% 0.20/0.52  % --gc_record_bc_elim                   false
% 0.20/0.52  % --symbol_type_check                   false
% 0.20/0.52  % --clausify_out                        false
% 0.20/0.52  % --large_theory_mode                   false
% 0.20/0.52  % --prep_sem_filter                     none
% 0.20/0.52  % --prep_sem_filter_out                 false
% 0.20/0.52  % --preprocessed_out                    false
% 0.20/0.52  % --sub_typing                          false
% 0.20/0.52  % --brand_transform                     false
% 0.20/0.52  % --pure_diseq_elim                     true
% 0.20/0.52  % --min_unsat_core                      false
% 0.20/0.52  % --pred_elim                           true
% 0.20/0.52  % --add_important_lit                   false
% 0.20/0.52  % --soft_assumptions                    false
% 0.20/0.52  % --reset_solvers                       false
% 0.20/0.52  % --bc_imp_inh                          []
% 0.20/0.52  % --conj_cone_tolerance                 1.5
% 0.20/0.52  % --prolific_symb_bound                 500
% 0.20/0.52  % --lt_threshold                        2000
% 0.20/0.52  
% 0.20/0.52  % ------ SAT Options
% 0.20/0.52  
% 0.20/0.52  % --sat_mode                            false
% 0.20/0.52  % --sat_fm_restart_options              ""
% 0.20/0.52  % --sat_gr_def                          false
% 0.20/0.52  % --sat_epr_types                       true
% 0.20/0.52  % --sat_non_cyclic_types                false
% 0.20/0.52  % --sat_finite_models                   false
% 0.20/0.52  % --sat_fm_lemmas                       false
% 0.20/0.52  % --sat_fm_prep                         false
% 0.20/0.52  % --sat_fm_uc_incr                      true
% 0.20/0.52  % --sat_out_model                       small
% 0.20/0.52  % --sat_out_clauses                     false
% 0.20/0.52  
% 0.20/0.52  % ------ QBF Options
% 0.20/0.52  
% 0.20/0.52  % --qbf_mode                            false
% 0.20/0.52  % --qbf_elim_univ                       true
% 0.20/0.52  % --qbf_sk_in                           true
% 0.20/0.52  % --qbf_pred_elim                       true
% 0.20/0.52  % --qbf_split                           32
% 0.20/0.52  
% 0.20/0.52  % ------ BMC1 Options
% 0.20/0.52  
% 0.20/0.52  % --bmc1_incremental                    false
% 0.20/0.52  % --bmc1_axioms                         reachable_all
% 0.20/0.52  % --bmc1_min_bound                      0
% 0.20/0.52  % --bmc1_max_bound                      -1
% 0.20/0.52  % --bmc1_max_bound_default              -1
% 0.20/0.52  % --bmc1_symbol_reachability            true
% 0.20/0.52  % --bmc1_property_lemmas                false
% 0.20/0.52  % --bmc1_k_induction                    false
% 0.20/0.52  % --bmc1_non_equiv_states               false
% 0.20/0.52  % --bmc1_deadlock                       false
% 0.20/0.52  % --bmc1_ucm                            false
% 0.20/0.52  % --bmc1_add_unsat_core                 none
% 0.20/0.52  % --bmc1_unsat_core_children            false
% 0.20/0.52  % --bmc1_unsat_core_extrapolate_axioms  false
% 0.20/0.52  % --bmc1_out_stat                       full
% 0.20/0.52  % --bmc1_ground_init                    false
% 0.20/0.52  % --bmc1_pre_inst_next_state            false
% 0.20/0.52  % --bmc1_pre_inst_state                 false
% 0.20/0.52  % --bmc1_pre_inst_reach_state           false
% 0.20/0.52  % --bmc1_out_unsat_core                 false
% 0.20/0.52  % --bmc1_aig_witness_out                false
% 0.20/0.52  % --bmc1_verbose                        false
% 0.20/0.52  % --bmc1_dump_clauses_tptp              false
% 0.42/0.60  % --bmc1_dump_unsat_core_tptp           false
% 0.42/0.60  % --bmc1_dump_file                      -
% 0.42/0.60  % --bmc1_ucm_expand_uc_limit            128
% 0.42/0.60  % --bmc1_ucm_n_expand_iterations        6
% 0.42/0.60  % --bmc1_ucm_extend_mode                1
% 0.42/0.60  % --bmc1_ucm_init_mode                  2
% 0.42/0.60  % --bmc1_ucm_cone_mode                  none
% 0.42/0.60  % --bmc1_ucm_reduced_relation_type      0
% 0.42/0.60  % --bmc1_ucm_relax_model                4
% 0.42/0.60  % --bmc1_ucm_full_tr_after_sat          true
% 0.42/0.60  % --bmc1_ucm_expand_neg_assumptions     false
% 0.42/0.60  % --bmc1_ucm_layered_model              none
% 0.42/0.60  % --bmc1_ucm_max_lemma_size             10
% 0.42/0.60  
% 0.42/0.60  % ------ AIG Options
% 0.42/0.60  
% 0.42/0.60  % --aig_mode                            false
% 0.42/0.60  
% 0.42/0.60  % ------ Instantiation Options
% 0.42/0.60  
% 0.42/0.60  % --instantiation_flag                  true
% 0.42/0.60  % --inst_lit_sel                        [+prop;+sign;+ground;-num_var;-num_symb]
% 0.42/0.60  % --inst_solver_per_active              750
% 0.42/0.60  % --inst_solver_calls_frac              0.5
% 0.42/0.60  % --inst_passive_queue_type             priority_queues
% 0.42/0.60  % --inst_passive_queues                 [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 0.42/0.60  % --inst_passive_queues_freq            [25;2]
% 0.42/0.60  % --inst_dismatching                    true
% 0.42/0.60  % --inst_eager_unprocessed_to_passive   true
% 0.42/0.60  % --inst_prop_sim_given                 true
% 0.42/0.60  % --inst_prop_sim_new                   false
% 0.42/0.60  % --inst_orphan_elimination             true
% 0.42/0.60  % --inst_learning_loop_flag             true
% 0.42/0.60  % --inst_learning_start                 3000
% 0.42/0.60  % --inst_learning_factor                2
% 0.42/0.60  % --inst_start_prop_sim_after_learn     3
% 0.42/0.60  % --inst_sel_renew                      solver
% 0.42/0.60  % --inst_lit_activity_flag              true
% 0.42/0.60  % --inst_out_proof                      true
% 0.42/0.60  
% 0.42/0.60  % ------ Resolution Options
% 0.42/0.60  
% 0.42/0.60  % --resolution_flag                     true
% 0.42/0.60  % --res_lit_sel                         kbo_max
% 0.42/0.60  % --res_to_prop_solver                  none
% 0.42/0.60  % --res_prop_simpl_new                  false
% 0.42/0.60  % --res_prop_simpl_given                false
% 0.42/0.60  % --res_passive_queue_type              priority_queues
% 0.42/0.60  % --res_passive_queues                  [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 0.42/0.60  % --res_passive_queues_freq             [15;5]
% 0.42/0.60  % --res_forward_subs                    full
% 0.42/0.60  % --res_backward_subs                   full
% 0.42/0.60  % --res_forward_subs_resolution         true
% 0.42/0.60  % --res_backward_subs_resolution        true
% 0.42/0.60  % --res_orphan_elimination              false
% 0.42/0.60  % --res_time_limit                      1000.
% 0.42/0.60  % --res_out_proof                       true
% 0.42/0.60  % --proof_out_file                      /export/starexec/sandbox2/tmp/iprover_proof_126608.s
% 0.42/0.60  % --modulo                              true
% 0.42/0.60  
% 0.42/0.60  % ------ Combination Options
% 0.42/0.60  
% 0.42/0.60  % --comb_res_mult                       1000
% 0.42/0.60  % --comb_inst_mult                      300
% 0.42/0.60  % ------ 
% 0.42/0.60  
% 0.42/0.60  % ------ Parsing...% successful
% 0.42/0.60  
% 0.42/0.60  % 
% 0.42/0.60  
% 0.42/0.60  
% 0.42/0.60  % ------                             Statistics
% 0.42/0.60  
% 0.42/0.60  % ------ General
% 0.42/0.60  
% 0.42/0.60  % num_of_input_clauses:                 1246
% 0.42/0.60  % num_of_input_neg_conjectures:         5
% 0.42/0.60  % num_of_splits:                        0
% 0.42/0.60  % num_of_split_atoms:                   0
% 0.42/0.60  % num_of_sem_filtered_clauses:          0
% 0.42/0.60  % num_of_subtypes:                      0
% 0.42/0.60  % monotx_restored_types:                0
% 0.42/0.60  % sat_num_of_epr_types:                 0
% 0.42/0.60  % sat_num_of_non_cyclic_types:          0
% 0.42/0.60  % sat_guarded_non_collapsed_types:      0
% 0.42/0.60  % is_epr:                               0
% 0.42/0.60  % is_horn:                              0
% 0.42/0.60  % has_eq:                               0
% 0.42/0.60  % num_pure_diseq_elim:                  0
% 0.42/0.60  % simp_replaced_by:                     0
% 0.42/0.60  % res_preprocessed:                     0
% 0.42/0.60  % prep_upred:                           0
% 0.42/0.60  % prep_unflattend:                      0
% 0.42/0.60  % pred_elim_cands:                      0
% 0.42/0.60  % pred_elim:                            0
% 0.42/0.60  % pred_elim_cl:                         0
% 0.42/0.60  % pred_elim_cycles:                     0
% 0.42/0.60  % forced_gc_time:                       0
% 0.42/0.60  % gc_basic_clause_elim:                 0
% 0.42/0.60  % parsing_time:                         0.074
% 0.42/0.60  % sem_filter_time:                      0.
% 0.42/0.60  % pred_elim_time:                       0.
% 0.42/0.60  % out_proof_time:                       0.
% 0.42/0.60  % monotx_time:                          0.
% 0.42/0.60  % subtype_inf_time:                     0.
% 0.42/0.60  % unif_index_cands_time:                0.
% 0.42/0.60  % unif_index_add_time:                  0.
% 0.42/0.60  % total_time:                           0.096
% 0.42/0.60  % num_of_symbols:                       130
% 0.42/0.60  % num_of_terms:                         2518
% 0.42/0.60  
% 0.42/0.60  % ------ Propositional Solver
% 0.42/0.60  
% 0.42/0.60  % prop_solver_calls:                    0
% 0.42/0.60  % prop_fast_solver_calls:               0
% 0.42/0.60  % prop_num_of_clauses:                  4
% 0.42/0.60  % prop_preprocess_simplified:           0
% 0.42/0.60  % prop_fo_subsumed:                     0
% 0.42/0.60  % prop_solver_time:                     0.
% 0.42/0.60  % prop_fast_solver_time:                0.
% 0.42/0.60  % prop_unsat_core_time:                 0.
% 0.42/0.60  
% 0.42/0.60  % ------ QBF 
% 0.42/0.60  
% 0.42/0.60  % qbf_q_res:                            0
% 0.42/0.60  % qbf_num_tautologies:                  0
% 0.42/0.60  % qbf_prep_cycles:                      0
% 0.42/0.60  
% 0.42/0.60  % ------ BMC1
% 0.42/0.60  
% 0.42/0.60  % bmc1_current_bound:                   -1
% 0.42/0.60  % bmc1_last_solved_bound:               -1
% 0.42/0.60  % bmc1_unsat_core_size:                 -1
% 0.42/0.60  % bmc1_unsat_core_parents_size:         -1
% 0.42/0.60  % bmc1_merge_next_fun:                  0
% 0.42/0.60  % bmc1_unsat_core_clauses_time:         0.
% 0.42/0.60  
% 0.42/0.60  % ------ Instantiation
% 0.42/0.60  
% 0.42/0.60  % inst_num_of_clauses:                  undef
% 0.42/0.60  % inst_num_in_passive:                  undef
% 0.42/0.60  % inst_num_in_active:                   0
% 0.42/0.60  % inst_num_in_unprocessed:              0
% 0.42/0.60  % inst_num_of_loops:                    0
% 0.42/0.60  % inst_num_of_learning_restarts:        0
% 0.42/0.60  % inst_num_moves_active_passive:        0
% 0.42/0.60  % inst_lit_activity:                    0
% 0.42/0.60  % inst_lit_activity_moves:              0
% 0.42/0.60  % inst_num_tautologies:                 0
% 0.42/0.60  % inst_num_prop_implied:                0
% 0.42/0.60  % inst_num_existing_simplified:         0
% 0.42/0.60  % inst_num_eq_res_simplified:           0
% 0.42/0.60  % inst_num_child_elim:                  0
% 0.42/0.60  % inst_num_of_dismatching_blockings:    0
% 0.42/0.60  % inst_num_of_non_proper_insts:         0
% 0.42/0.60  % inst_num_of_duplicates:               0
% 0.42/0.60  % inst_inst_num_from_inst_to_res:       0
% 0.42/0.60  % inst_dismatching_checking_time:       0.
% 0.42/0.60  
% 0.42/0.60  % ------ Resolution
% 0.42/0.60  
% 0.42/0.60  % res_num_of_clauses:                   undef
% 0.42/0.60  % res_num_in_passive:                   undef
% 0.42/0.60  % res_num_in_active:                    0
% 0.42/0.60  % res_num_of_loops:                     0
% 0.42/0.60  % res_forward_subset_subsumed:          0
% 0.42/0.60  % res_backward_subset_subsumed:         0
% 0.42/0.60  % res_forward_subsumed:                 0
% 0.42/0.60  % res_backward_subsumed:                0
% 0.42/0.60  % res_forward_subsumption_resolution:   0
% 0.42/0.60  % res_backward_subsumption_resolution:  0
% 0.42/0.60  % res_clause_to_clause_subsumption:     0
% 0.42/0.60  % res_orphan_elimination:               0
% 0.42/0.60  % res_tautology_del:                    0
% 0.42/0.60  % res_num_eq_res_simplified:            0
% 0.42/0.60  % res_num_sel_changes:                  0
% 0.42/0.60  % res_moves_from_active_to_pass:        0
% 0.42/0.60  
% 0.42/0.60  % Status Unsatisfiable
% 0.42/0.60  % SZS status Unsatisfiable
% 0.42/0.60  % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------