%------------------------------------------------------------------------------
% File     : iProverMo---2.5-0.1
% Problem  : LCL854-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : iprover_modulo %s %d

% Computer : n025.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 11:40:49 EDT 2022

% Result   : Unsatisfiable 0.19s 0.48s
% Output   : CNFRefutation 0.19s
% 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(cls_type_Osimps_I3_J_0,axiom,
    c_Type_Otype_OAtom(V_nat) != hAPP(hAPP(c_Type_Otype_OFun,V_type1_H),V_type2_H),
    input ).

fof(cls_type_Osimps_I3_J_0_0,plain,
    ! [V_nat,V_type1_H,V_type2_H] :
      ( c_Type_Otype_OAtom(V_nat) != hAPP(hAPP(c_Type_Otype_OFun,V_type1_H),V_type2_H)
      | $false ),
    inference(orientation,[status(thm)],[cls_type_Osimps_I3_J_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_App_I1_J_0,axiom,
    c_Type_Otyping(v_ea____,v_s____,hAPP(hAPP(c_Type_Otype_OFun,v_Ta____),v_U____)),
    input ).

fof(cls_App_I1_J_0_0,plain,
    ( c_Type_Otyping(v_ea____,v_s____,hAPP(hAPP(c_Type_Otype_OFun,v_Ta____),v_U____))
    | $false ),
    inference(orientation,[status(thm)],[cls_App_I1_J_0]) ).

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

fof(cls_type_Osimps_I6_J_0_0,plain,
    ! [T_a,V_f1,V_f2,V_type1,V_type2] :
      ( c_Type_Otype_Otype__case(V_f1,V_f2,hAPP(hAPP(c_Type_Otype_OFun,V_type1),V_type2),T_a) = hAPP(hAPP(V_f2,V_type1),V_type2)
      | $false ),
    inference(orientation,[status(thm)],[cls_type_Osimps_I6_J_0]) ).

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

fof(cls_type_Orecs_I2_J_0_0,plain,
    ! [T_a,V_f1,V_f2,V_type1,V_type2] :
      ( c_Type_Otype_Otype__rec(V_f1,V_f2,hAPP(hAPP(c_Type_Otype_OFun,V_type1),V_type2),T_a) = hAPP(hAPP(hAPP(hAPP(V_f2,V_type1),V_type2),c_Type_Otype_Otype__rec(V_f1,V_f2,V_type1,T_a)),c_Type_Otype_Otype__rec(V_f1,V_f2,V_type2,T_a))
      | $false ),
    inference(orientation,[status(thm)],[cls_type_Orecs_I2_J_0]) ).

cnf(cls_App_I3_J_0,axiom,
    c_Type_Otyping(v_ea____,v_ta____,v_Ta____),
    input ).

fof(cls_App_I3_J_0_0,plain,
    ( c_Type_Otyping(v_ea____,v_ta____,v_Ta____)
    | $false ),
    inference(orientation,[status(thm)],[cls_App_I3_J_0]) ).

cnf(cls_App_I2_J_0,axiom,
    hBOOL(hAPP(c_InductTermi_OIT,v_s____)),
    input ).

fof(cls_App_I2_J_0_0,plain,
    ( hBOOL(hAPP(c_InductTermi_OIT,v_s____))
    | $false ),
    inference(orientation,[status(thm)],[cls_App_I2_J_0]) ).

cnf(cls_type_Osimps_I4_J_0,axiom,
    hAPP(hAPP(c_Type_Otype_OFun,V_type1_H),V_type2_H) != c_Type_Otype_OAtom(V_nat),
    input ).

fof(cls_type_Osimps_I4_J_0_0,plain,
    ! [V_nat,V_type1_H,V_type2_H] :
      ( hAPP(hAPP(c_Type_Otype_OFun,V_type1_H),V_type2_H) != c_Type_Otype_OAtom(V_nat)
      | $false ),
    inference(orientation,[status(thm)],[cls_type_Osimps_I4_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_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_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_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_type_Osize_I3_J_0,axiom,
    c_Nat_Osize__class_Osize(c_Type_Otype_OAtom(V_nat),tc_Type_Otype) = c_HOL_Ozero__class_Ozero(tc_nat),
    input ).

fof(cls_type_Osize_I3_J_0_0,plain,
    ! [V_nat] :
      ( c_Nat_Osize__class_Osize(c_Type_Otype_OAtom(V_nat),tc_Type_Otype) = c_HOL_Ozero__class_Ozero(tc_nat)
      | $false ),
    inference(orientation,[status(thm)],[cls_type_Osize_I3_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_beta_0,axiom,
    hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_s)),V_t)),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)),c_Lambda_Osubst(V_s,V_t,c_HOL_Ozero__class_Ozero(tc_nat))))
      | $false ),
    inference(orientation,[status(thm)],[cls_beta_0]) ).

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

fof(cls_type_Orecs_I1_J_0_0,plain,
    ! [T_a,V_f1,V_f2,V_nat] :
      ( c_Type_Otype_Otype__rec(V_f1,V_f2,c_Type_Otype_OAtom(V_nat),T_a) = hAPP(V_f1,V_nat)
      | $false ),
    inference(orientation,[status(thm)],[cls_type_Orecs_I1_J_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_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_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]) ).

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_shift__commute_0,axiom,
    c_Type_Oshift(c_Type_Oshift(V_e,V_i,V_U,T_a),c_HOL_Ozero__class_Ozero(tc_nat),V_T,T_a) = c_Type_Oshift(c_Type_Oshift(V_e,c_HOL_Ozero__class_Ozero(tc_nat),V_T,T_a),c_Suc(V_i),V_U,T_a),
    input ).

fof(cls_shift__commute_0_0,plain,
    ! [T_a,V_T,V_U,V_e,V_i] :
      ( c_Type_Oshift(c_Type_Oshift(V_e,V_i,V_U,T_a),c_HOL_Ozero__class_Ozero(tc_nat),V_T,T_a) = c_Type_Oshift(c_Type_Oshift(V_e,c_HOL_Ozero__class_Ozero(tc_nat),V_T,T_a),c_Suc(V_i),V_U,T_a)
      | $false ),
    inference(orientation,[status(thm)],[cls_shift__commute_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_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_App_I4_J_0,axiom,
    hBOOL(hAPP(c_InductTermi_OIT,v_ta____)),
    input ).

fof(cls_App_I4_J_0_0,plain,
    ( hBOOL(hAPP(c_InductTermi_OIT,v_ta____))
    | $false ),
    inference(orientation,[status(thm)],[cls_App_I4_J_0]) ).

cnf(cls_type_Osize_I1_J_0,axiom,
    c_Type_Otype_Otype__size(c_Type_Otype_OAtom(V_nat)) = c_HOL_Ozero__class_Ozero(tc_nat),
    input ).

fof(cls_type_Osize_I1_J_0_0,plain,
    ! [V_nat] :
      ( c_Type_Otype_Otype__size(c_Type_Otype_OAtom(V_nat)) = c_HOL_Ozero__class_Ozero(tc_nat)
      | $false ),
    inference(orientation,[status(thm)],[cls_type_Osize_I1_J_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_type_Osimps_I5_J_0,axiom,
    c_Type_Otype_Otype__case(V_f1,V_f2,c_Type_Otype_OAtom(V_nat),T_a) = hAPP(V_f1,V_nat),
    input ).

fof(cls_type_Osimps_I5_J_0_0,plain,
    ! [T_a,V_f1,V_f2,V_nat] :
      ( c_Type_Otype_Otype__case(V_f1,V_f2,c_Type_Otype_OAtom(V_nat),T_a) = hAPP(V_f1,V_nat)
      | $false ),
    inference(orientation,[status(thm)],[cls_type_Osimps_I5_J_0]) ).

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_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_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_subst__lift_0,axiom,
    c_Lambda_Osubst(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] :
      ( c_Lambda_Osubst(c_Lambda_Olift(V_t,V_k),V_s,V_k) = V_t
      | $false ),
    inference(orientation,[status(thm)],[cls_subst__lift_0]) ).

cnf(cls_dB_Osize_I6_J_0,axiom,
    c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(V_dB),tc_Lambda_OdB) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(V_dB,tc_Lambda_OdB)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
    input ).

fof(cls_dB_Osize_I6_J_0_0,plain,
    ! [V_dB] :
      ( c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(V_dB),tc_Lambda_OdB) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(V_dB,tc_Lambda_OdB)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)))
      | $false ),
    inference(orientation,[status(thm)],[cls_dB_Osize_I6_J_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_dB_Osize_I5_J_0,axiom,
    c_Nat_Osize__class_Osize(hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2),tc_Lambda_OdB) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(V_dB1,tc_Lambda_OdB)),c_Nat_Osize__class_Osize(V_dB2,tc_Lambda_OdB))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
    input ).

fof(cls_dB_Osize_I5_J_0_0,plain,
    ! [V_dB1,V_dB2] :
      ( c_Nat_Osize__class_Osize(hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2),tc_Lambda_OdB) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(V_dB1,tc_Lambda_OdB)),c_Nat_Osize__class_Osize(V_dB2,tc_Lambda_OdB))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)))
      | $false ),
    inference(orientation,[status(thm)],[cls_dB_Osize_I5_J_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_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_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_nat_Osimps_I2_J_0,axiom,
    c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(V_nat_H),
    input ).

fof(cls_nat_Osimps_I2_J_0_0,plain,
    ! [V_nat_H] :
      ( c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(V_nat_H)
      | $false ),
    inference(orientation,[status(thm)],[cls_nat_Osimps_I2_J_0]) ).

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

fof(cls_Zero__neq__Suc_0_0,plain,
    ! [V_m] :
      ( c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(V_m)
      | $false ),
    inference(orientation,[status(thm)],[cls_Zero__neq__Suc_0]) ).

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

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

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

fof(cls_nat_Osimps_I3_J_0_0,plain,
    ! [V_nat_H] :
      ( c_Suc(V_nat_H) != c_HOL_Ozero__class_Ozero(tc_nat)
      | $false ),
    inference(orientation,[status(thm)],[cls_nat_Osimps_I3_J_0]) ).

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

fof(cls_Suc__neq__Zero_0_0,plain,
    ! [V_m] :
      ( c_Suc(V_m) != c_HOL_Ozero__class_Ozero(tc_nat)
      | $false ),
    inference(orientation,[status(thm)],[cls_Suc__neq__Zero_0]) ).

cnf(cls_type_Osize_I2_J_0,axiom,
    c_Type_Otype_Otype__size(hAPP(hAPP(c_Type_Otype_OFun,V_type1),V_type2)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Type_Otype_Otype__size(V_type1)),c_Type_Otype_Otype__size(V_type2))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
    input ).

fof(cls_type_Osize_I2_J_0_0,plain,
    ! [V_type1,V_type2] :
      ( c_Type_Otype_Otype__size(hAPP(hAPP(c_Type_Otype_OFun,V_type1),V_type2)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Type_Otype_Otype__size(V_type1)),c_Type_Otype_Otype__size(V_type2))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)))
      | $false ),
    inference(orientation,[status(thm)],[cls_type_Osize_I2_J_0]) ).

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

fof(cls_Suc__n__not__n_0_0,plain,
    ! [V_n] :
      ( c_Suc(V_n) != V_n
      | $false ),
    inference(orientation,[status(thm)],[cls_Suc__n__not__n_0]) ).

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

fof(cls_n__not__Suc__n_0_0,plain,
    ! [V_n] :
      ( V_n != c_Suc(V_n)
      | $false ),
    inference(orientation,[status(thm)],[cls_n__not__Suc__n_0]) ).

cnf(cls_subst__eq_0,axiom,
    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] :
      ( 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_type_Osize_I4_J_0,axiom,
    c_Nat_Osize__class_Osize(hAPP(hAPP(c_Type_Otype_OFun,V_type1),V_type2),tc_Type_Otype) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(V_type1,tc_Type_Otype)),c_Nat_Osize__class_Osize(V_type2,tc_Type_Otype))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
    input ).

fof(cls_type_Osize_I4_J_0_0,plain,
    ! [V_type1,V_type2] :
      ( c_Nat_Osize__class_Osize(hAPP(hAPP(c_Type_Otype_OFun,V_type1),V_type2),tc_Type_Otype) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(V_type1,tc_Type_Otype)),c_Nat_Osize__class_Osize(V_type2,tc_Type_Otype))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)))
      | $false ),
    inference(orientation,[status(thm)],[cls_type_Osize_I4_J_0]) ).

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

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

cnf(cls_dB_Osize_I2_J_0,axiom,
    c_Lambda_OdB_OdB__size(hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(V_dB1)),c_Lambda_OdB_OdB__size(V_dB2))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
    input ).

fof(cls_dB_Osize_I2_J_0_0,plain,
    ! [V_dB1,V_dB2] :
      ( c_Lambda_OdB_OdB__size(hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(V_dB1)),c_Lambda_OdB_OdB__size(V_dB2))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)))
      | $false ),
    inference(orientation,[status(thm)],[cls_dB_Osize_I2_J_0]) ).

cnf(cls_dB_Osize_I3_J_0,axiom,
    c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(V_dB)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(V_dB)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
    input ).

fof(cls_dB_Osize_I3_J_0_0,plain,
    ! [V_dB] :
      ( c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(V_dB)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(V_dB)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)))
      | $false ),
    inference(orientation,[status(thm)],[cls_dB_Osize_I3_J_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_add__is__1_5,axiom,
    hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
    input ).

fof(cls_add__is__1_5_0,plain,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | $false ),
    inference(orientation,[status(thm)],[cls_add__is__1_5]) ).

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

fof(cls_one__is__add_4_0,plain,
    ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat))
    | $false ),
    inference(orientation,[status(thm)],[cls_one__is__add_4]) ).

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_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_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_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_add__Suc_0,axiom,
    hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(V_m)),V_n) = c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)),
    input ).

fof(cls_add__Suc_0_0,plain,
    ! [V_m,V_n] :
      ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(V_m)),V_n) = c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n))
      | $false ),
    inference(orientation,[status(thm)],[cls_add__Suc_0]) ).

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

fof(cls_add__Suc__right_0_0,plain,
    ! [V_m,V_n] :
      ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),c_Suc(V_n)) = c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n))
      | $false ),
    inference(orientation,[status(thm)],[cls_add__Suc__right_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_add__is__1_4,axiom,
    hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat)) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
    input ).

fof(cls_add__is__1_4_0,plain,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat)) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | $false ),
    inference(orientation,[status(thm)],[cls_add__is__1_4]) ).

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_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_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_one__is__add_5,axiom,
    c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
    input ).

fof(cls_one__is__add_5_0,plain,
    ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)))
    | $false ),
    inference(orientation,[status(thm)],[cls_one__is__add_5]) ).

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

fof(cls_add__Suc__shift_0_0,plain,
    ! [V_m,V_n] :
      ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(V_m)),V_n) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),c_Suc(V_n))
      | $false ),
    inference(orientation,[status(thm)],[cls_add__Suc__shift_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]) ).

fof(def_lhs_atom1,axiom,
    ! [V_x] :
      ( lhs_atom1(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_0,plain,
    ! [V_x] :
      ( lhs_atom1(V_x)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_natgb_Oadd__r0__iff_1_0,def_lhs_atom1]) ).

fof(def_lhs_atom2,axiom,
    ! [V_n] :
      ( lhs_atom2(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_1,plain,
    ! [V_n] :
      ( lhs_atom2(V_n)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_plus__nat_Oadd__0_0_0,def_lhs_atom2]) ).

fof(def_lhs_atom3,axiom,
    ! [V_m] :
      ( lhs_atom3(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_2,plain,
    ! [V_m] :
      ( lhs_atom3(V_m)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_Nat_Oadd__0__right_0_0,def_lhs_atom3]) ).

fof(def_lhs_atom4,axiom,
    ! [V_n,V_m] :
      ( lhs_atom4(V_n,V_m)
    <=> hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(V_m)),V_n) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),c_Suc(V_n)) ),
    inference(definition,[],]) ).

fof(to_be_clausified_3,plain,
    ! [V_m,V_n] :
      ( lhs_atom4(V_n,V_m)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_add__Suc__shift_0_0,def_lhs_atom4]) ).

fof(def_lhs_atom5,axiom,
    ( lhs_atom5
  <=> c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) ),
    inference(definition,[],]) ).

fof(to_be_clausified_4,plain,
    ( lhs_atom5
    | $false ),
    inference(fold_definition,[status(thm)],[cls_one__is__add_5_0,def_lhs_atom5]) ).

fof(def_lhs_atom6,axiom,
    ! [V_f,V_a,T_b,T_a] :
      ( lhs_atom6(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_5,plain,
    ! [T_a,T_b,V_a,V_f] :
      ( lhs_atom6(V_f,V_a,T_b,T_a)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_foldr_Osimps_I1_J_0_0,def_lhs_atom6]) ).

fof(def_lhs_atom7,axiom,
    ! [V_n,V_m,V_k] :
      ( lhs_atom7(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_6,plain,
    ! [V_k,V_m,V_n] :
      ( lhs_atom7(V_n,V_m,V_k)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_nat__add__assoc_0_0,def_lhs_atom7]) ).

fof(def_lhs_atom8,axiom,
    ! [V_z,V_y,V_x] :
      ( lhs_atom8(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_7,plain,
    ! [V_x,V_y,V_z] :
      ( lhs_atom8(V_z,V_y,V_x)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_nat__add__left__commute_0_0,def_lhs_atom8]) ).

fof(def_lhs_atom9,axiom,
    ( lhs_atom9
  <=> 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_8,plain,
    ( lhs_atom9
    | $false ),
    inference(fold_definition,[status(thm)],[cls_add__is__0_2_0,def_lhs_atom9]) ).

fof(def_lhs_atom10,axiom,
    ( lhs_atom10
  <=> hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat)) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    inference(definition,[],]) ).

fof(to_be_clausified_9,plain,
    ( lhs_atom10
    | $false ),
    inference(fold_definition,[status(thm)],[cls_add__is__1_4_0,def_lhs_atom10]) ).

fof(def_lhs_atom11,axiom,
    ! [V_A,T_a] :
      ( lhs_atom11(V_A,T_a)
    <=> c_List_Olistsp(V_A,c_List_Olist_ONil(T_a),T_a) ),
    inference(definition,[],]) ).

fof(to_be_clausified_10,plain,
    ! [T_a,V_A] :
      ( lhs_atom11(V_A,T_a)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_listsp_ONil_0_0,def_lhs_atom11]) ).

fof(def_lhs_atom12,axiom,
    ! [V_n,V_m] :
      ( lhs_atom12(V_n,V_m)
    <=> hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),c_Suc(V_n)) = c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)) ),
    inference(definition,[],]) ).

fof(to_be_clausified_11,plain,
    ! [V_m,V_n] :
      ( lhs_atom12(V_n,V_m)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_add__Suc__right_0_0,def_lhs_atom12]) ).

fof(def_lhs_atom13,axiom,
    ! [V_n,V_m] :
      ( lhs_atom13(V_n,V_m)
    <=> hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(V_m)),V_n) = c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)) ),
    inference(definition,[],]) ).

fof(to_be_clausified_12,plain,
    ! [V_m,V_n] :
      ( lhs_atom13(V_n,V_m)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_add__Suc_0_0,def_lhs_atom13]) ).

fof(def_lhs_atom14,axiom,
    ! [V_n,V_m] :
      ( lhs_atom14(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_13,plain,
    ! [V_m,V_n] :
      ( lhs_atom14(V_n,V_m)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_nat__add__commute_0_0,def_lhs_atom14]) ).

fof(def_lhs_atom15,axiom,
    ! [V_xs,V_r,T_a] :
      ( lhs_atom15(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_14,plain,
    ! [T_a,V_r,V_xs] :
      ( lhs_atom15(V_xs,V_r,T_a)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_not__Nil__step1_0_0,def_lhs_atom15]) ).

fof(def_lhs_atom16,axiom,
    ! [V_xs,V_r,T_a] :
      ( lhs_atom16(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_15,plain,
    ! [T_a,V_r,V_xs] :
      ( lhs_atom16(V_xs,V_r,T_a)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_not__step1__Nil_0_0,def_lhs_atom16]) ).

fof(def_lhs_atom17,axiom,
    ! [V_f,V_a,T_b,T_a] :
      ( lhs_atom17(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_16,plain,
    ! [T_a,T_b,V_a,V_f] :
      ( lhs_atom17(V_f,V_a,T_b,T_a)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_foldl__Nil_0_0,def_lhs_atom17]) ).

fof(def_lhs_atom18,axiom,
    ! [T_a] :
      ( lhs_atom18(T_a)
    <=> c_Predicate_Oconversep(c_fequal(T_a),T_a,T_a) = c_fequal(T_a) ),
    inference(definition,[],]) ).

fof(to_be_clausified_17,plain,
    ! [T_a] :
      ( lhs_atom18(T_a)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_conversep__eq_0_0,def_lhs_atom18]) ).

fof(def_lhs_atom19,axiom,
    ( lhs_atom19
  <=> c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat)) ),
    inference(definition,[],]) ).

fof(to_be_clausified_18,plain,
    ( lhs_atom19
    | $false ),
    inference(fold_definition,[status(thm)],[cls_one__is__add_4_0,def_lhs_atom19]) ).

fof(def_lhs_atom20,axiom,
    ! [V_r,T_b,T_a] :
      ( lhs_atom20(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_19,plain,
    ! [T_a,T_b,V_r] :
      ( lhs_atom20(V_r,T_b,T_a)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_conversep__conversep_0_0,def_lhs_atom20]) ).

fof(def_lhs_atom21,axiom,
    ( lhs_atom21
  <=> hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    inference(definition,[],]) ).

fof(to_be_clausified_20,plain,
    ( lhs_atom21
    | $false ),
    inference(fold_definition,[status(thm)],[cls_add__is__1_5_0,def_lhs_atom21]) ).

fof(def_lhs_atom22,axiom,
    ! [V_s,V_r] :
      ( lhs_atom22(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_21,plain,
    ! [V_r,V_s] :
      ( lhs_atom22(V_s,V_r)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_App__eq__foldl__conv_4_0,def_lhs_atom22]) ).

fof(def_lhs_atom23,axiom,
    ! [V_dB] :
      ( lhs_atom23(V_dB)
    <=> c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(V_dB)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(V_dB)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) ),
    inference(definition,[],]) ).

fof(to_be_clausified_22,plain,
    ! [V_dB] :
      ( lhs_atom23(V_dB)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_dB_Osize_I3_J_0_0,def_lhs_atom23]) ).

fof(def_lhs_atom24,axiom,
    ! [V_dB2,V_dB1] :
      ( lhs_atom24(V_dB2,V_dB1)
    <=> c_Lambda_OdB_OdB__size(hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(V_dB1)),c_Lambda_OdB_OdB__size(V_dB2))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) ),
    inference(definition,[],]) ).

fof(to_be_clausified_23,plain,
    ! [V_dB1,V_dB2] :
      ( lhs_atom24(V_dB2,V_dB1)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_dB_Osize_I2_J_0_0,def_lhs_atom24]) ).

fof(def_lhs_atom25,axiom,
    ! [V_u,V_t,V_s,V_k] :
      ( lhs_atom25(V_u,V_t,V_s,V_k)
    <=> c_Lambda_Osubst(hAPP(hAPP(c_Lambda_OdB_OApp,V_t),V_u),V_s,V_k) = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Osubst(V_t,V_s,V_k)),c_Lambda_Osubst(V_u,V_s,V_k)) ),
    inference(definition,[],]) ).

fof(to_be_clausified_24,plain,
    ! [V_k,V_s,V_t,V_u] :
      ( lhs_atom25(V_u,V_t,V_s,V_k)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_subst__App_0_0,def_lhs_atom25]) ).

fof(def_lhs_atom26,axiom,
    ! [V_type2,V_type1] :
      ( lhs_atom26(V_type2,V_type1)
    <=> c_Nat_Osize__class_Osize(hAPP(hAPP(c_Type_Otype_OFun,V_type1),V_type2),tc_Type_Otype) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(V_type1,tc_Type_Otype)),c_Nat_Osize__class_Osize(V_type2,tc_Type_Otype))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) ),
    inference(definition,[],]) ).

fof(to_be_clausified_25,plain,
    ! [V_type1,V_type2] :
      ( lhs_atom26(V_type2,V_type1)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_type_Osize_I4_J_0_0,def_lhs_atom26]) ).

fof(def_lhs_atom27,axiom,
    ! [V_u,V_k] :
      ( lhs_atom27(V_u,V_k)
    <=> c_Lambda_Osubst(c_Lambda_OdB_OVar(V_k),V_u,V_k) = V_u ),
    inference(definition,[],]) ).

fof(to_be_clausified_26,plain,
    ! [V_k,V_u] :
      ( lhs_atom27(V_u,V_k)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_subst__eq_0_0,def_lhs_atom27]) ).

fof(def_lhs_atom28,axiom,
    ! [V_n] :
      ( lhs_atom28(V_n)
    <=> V_n != c_Suc(V_n) ),
    inference(definition,[],]) ).

fof(to_be_clausified_27,plain,
    ! [V_n] :
      ( lhs_atom28(V_n)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_n__not__Suc__n_0_0,def_lhs_atom28]) ).

fof(def_lhs_atom29,axiom,
    ! [V_n] :
      ( lhs_atom29(V_n)
    <=> c_Suc(V_n) != V_n ),
    inference(definition,[],]) ).

fof(to_be_clausified_28,plain,
    ! [V_n] :
      ( lhs_atom29(V_n)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_Suc__n__not__n_0_0,def_lhs_atom29]) ).

fof(def_lhs_atom30,axiom,
    ! [V_type2,V_type1] :
      ( lhs_atom30(V_type2,V_type1)
    <=> c_Type_Otype_Otype__size(hAPP(hAPP(c_Type_Otype_OFun,V_type1),V_type2)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Type_Otype_Otype__size(V_type1)),c_Type_Otype_Otype__size(V_type2))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) ),
    inference(definition,[],]) ).

fof(to_be_clausified_29,plain,
    ! [V_type1,V_type2] :
      ( lhs_atom30(V_type2,V_type1)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_type_Osize_I2_J_0_0,def_lhs_atom30]) ).

fof(def_lhs_atom31,axiom,
    ! [V_m] :
      ( lhs_atom31(V_m)
    <=> c_Suc(V_m) != c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_30,plain,
    ! [V_m] :
      ( lhs_atom31(V_m)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_Suc__neq__Zero_0_0,def_lhs_atom31]) ).

fof(def_lhs_atom32,axiom,
    ! [V_nat_H] :
      ( lhs_atom32(V_nat_H)
    <=> c_Suc(V_nat_H) != c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_31,plain,
    ! [V_nat_H] :
      ( lhs_atom32(V_nat_H)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_nat_Osimps_I3_J_0_0,def_lhs_atom32]) ).

fof(def_lhs_atom33,axiom,
    ! [V_t,V_s,V_k] :
      ( lhs_atom33(V_t,V_s,V_k)
    <=> c_Lambda_Olift(hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_t),V_k) = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Olift(V_s,V_k)),c_Lambda_Olift(V_t,V_k)) ),
    inference(definition,[],]) ).

fof(to_be_clausified_32,plain,
    ! [V_k,V_s,V_t] :
      ( lhs_atom33(V_t,V_s,V_k)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_lift_Osimps_I2_J_0_0,def_lhs_atom33]) ).

fof(def_lhs_atom34,axiom,
    ! [V_m] :
      ( lhs_atom34(V_m)
    <=> c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(V_m) ),
    inference(definition,[],]) ).

fof(to_be_clausified_33,plain,
    ! [V_m] :
      ( lhs_atom34(V_m)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_Zero__neq__Suc_0_0,def_lhs_atom34]) ).

fof(def_lhs_atom35,axiom,
    ! [V_nat_H] :
      ( lhs_atom35(V_nat_H)
    <=> c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(V_nat_H) ),
    inference(definition,[],]) ).

fof(to_be_clausified_34,plain,
    ! [V_nat_H] :
      ( lhs_atom35(V_nat_H)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_nat_Osimps_I2_J_0_0,def_lhs_atom35]) ).

fof(def_lhs_atom36,axiom,
    ! [V_x,V_r,T_a] :
      ( lhs_atom36(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_35,plain,
    ! [T_a,V_r,V_x] :
      ( lhs_atom36(V_x,V_r,T_a)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_Nitpick_Ortranclp__def_1_0,def_lhs_atom36]) ).

fof(def_lhs_atom37,axiom,
    ! [V_r,V_a,T_a] :
      ( lhs_atom37(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_36,plain,
    ! [T_a,V_a,V_r] :
      ( lhs_atom37(V_r,V_a,T_a)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_rtranclp_Ortrancl__refl_0_0,def_lhs_atom37]) ).

fof(def_lhs_atom38,axiom,
    ! [V_m] :
      ( lhs_atom38(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_37,plain,
    ! [V_m] :
      ( lhs_atom38(V_m)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_Var__eq__apps__conv_2_0,def_lhs_atom38]) ).

fof(def_lhs_atom39,axiom,
    ! [V_dB2,V_dB1] :
      ( lhs_atom39(V_dB2,V_dB1)
    <=> c_Nat_Osize__class_Osize(hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2),tc_Lambda_OdB) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(V_dB1,tc_Lambda_OdB)),c_Nat_Osize__class_Osize(V_dB2,tc_Lambda_OdB))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) ),
    inference(definition,[],]) ).

fof(to_be_clausified_38,plain,
    ! [V_dB1,V_dB2] :
      ( lhs_atom39(V_dB2,V_dB1)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_dB_Osize_I5_J_0_0,def_lhs_atom39]) ).

fof(def_lhs_atom40,axiom,
    ! [V_r] :
      ( lhs_atom40(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_39,plain,
    ! [V_r] :
      ( lhs_atom40(V_r)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_Abs__eq__apps__conv_2_0,def_lhs_atom40]) ).

fof(def_lhs_atom41,axiom,
    ! [V_dB] :
      ( lhs_atom41(V_dB)
    <=> c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(V_dB),tc_Lambda_OdB) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(V_dB,tc_Lambda_OdB)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) ),
    inference(definition,[],]) ).

fof(to_be_clausified_40,plain,
    ! [V_dB] :
      ( lhs_atom41(V_dB)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_dB_Osize_I6_J_0_0,def_lhs_atom41]) ).

fof(def_lhs_atom42,axiom,
    ! [V_t,V_s,V_k] :
      ( lhs_atom42(V_t,V_s,V_k)
    <=> c_Lambda_Osubst(c_Lambda_Olift(V_t,V_k),V_s,V_k) = V_t ),
    inference(definition,[],]) ).

fof(to_be_clausified_41,plain,
    ! [V_k,V_s,V_t] :
      ( lhs_atom42(V_t,V_s,V_k)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_subst__lift_0_0,def_lhs_atom42]) ).

fof(def_lhs_atom43,axiom,
    ! [V_r] :
      ( lhs_atom43(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_42,plain,
    ! [V_r] :
      ( lhs_atom43(V_r)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_apps__eq__Abs__conv_2_0,def_lhs_atom43]) ).

fof(def_lhs_atom44,axiom,
    ! [V_r,T_a] :
      ( lhs_atom44(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_43,plain,
    ! [T_a,V_r] :
      ( lhs_atom44(V_r,T_a)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_rtranclp__idemp_0_0,def_lhs_atom44]) ).

fof(def_lhs_atom45,axiom,
    ! [V_nat,V_dB2_H,V_dB1_H] :
      ( lhs_atom45(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_44,plain,
    ! [V_dB1_H,V_dB2_H,V_nat] :
      ( lhs_atom45(V_nat,V_dB2_H,V_dB1_H)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_dB_Osimps_I5_J_0_0,def_lhs_atom45]) ).

fof(def_lhs_atom46,axiom,
    ! [V_nat,V_f2,V_f1,T_a] :
      ( lhs_atom46(V_nat,V_f2,V_f1,T_a)
    <=> c_Type_Otype_Otype__case(V_f1,V_f2,c_Type_Otype_OAtom(V_nat),T_a) = hAPP(V_f1,V_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_45,plain,
    ! [T_a,V_f1,V_f2,V_nat] :
      ( lhs_atom46(V_nat,V_f2,V_f1,T_a)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_type_Osimps_I5_J_0_0,def_lhs_atom46]) ).

fof(def_lhs_atom47,axiom,
    ! [V_t,V_ss,V_s,V_n] :
      ( lhs_atom47(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_46,plain,
    ! [V_n,V_s,V_ss,V_t] :
      ( lhs_atom47(V_t,V_ss,V_s,V_n)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_Abs__App__neq__Var__apps_0_0,def_lhs_atom47]) ).

fof(def_lhs_atom48,axiom,
    ! [V_nat] :
      ( lhs_atom48(V_nat)
    <=> c_Type_Otype_Otype__size(c_Type_Otype_OAtom(V_nat)) = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_47,plain,
    ! [V_nat] :
      ( lhs_atom48(V_nat)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_type_Osize_I1_J_0_0,def_lhs_atom48]) ).

fof(def_lhs_atom49,axiom,
    ( lhs_atom49
  <=> hBOOL(hAPP(c_InductTermi_OIT,v_ta____)) ),
    inference(definition,[],]) ).

fof(to_be_clausified_48,plain,
    ( lhs_atom49
    | $false ),
    inference(fold_definition,[status(thm)],[cls_App_I4_J_0_0,def_lhs_atom49]) ).

fof(def_lhs_atom50,axiom,
    ! [V_nat] :
      ( lhs_atom50(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_49,plain,
    ! [V_nat] :
      ( lhs_atom50(V_nat)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_dB_Osize_I1_J_0_0,def_lhs_atom50]) ).

fof(def_lhs_atom51,axiom,
    ! [V_n] :
      ( lhs_atom51(V_n)
    <=> hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(V_n))) ),
    inference(definition,[],]) ).

fof(to_be_clausified_50,plain,
    ! [V_n] :
      ( lhs_atom51(V_n)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_Var__IT_0_0,def_lhs_atom51]) ).

fof(def_lhs_atom52,axiom,
    ! [V_i,V_e,V_U,V_T,T_a] :
      ( lhs_atom52(V_i,V_e,V_U,V_T,T_a)
    <=> c_Type_Oshift(c_Type_Oshift(V_e,V_i,V_U,T_a),c_HOL_Ozero__class_Ozero(tc_nat),V_T,T_a) = c_Type_Oshift(c_Type_Oshift(V_e,c_HOL_Ozero__class_Ozero(tc_nat),V_T,T_a),c_Suc(V_i),V_U,T_a) ),
    inference(definition,[],]) ).

fof(to_be_clausified_51,plain,
    ! [T_a,V_T,V_U,V_e,V_i] :
      ( lhs_atom52(V_i,V_e,V_U,V_T,T_a)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_shift__commute_0_0,def_lhs_atom52]) ).

fof(def_lhs_atom53,axiom,
    ! [V_nat,V_dB_H] :
      ( lhs_atom53(V_nat,V_dB_H)
    <=> c_Lambda_OdB_OVar(V_nat) != c_Lambda_OdB_OAbs(V_dB_H) ),
    inference(definition,[],]) ).

fof(to_be_clausified_52,plain,
    ! [V_dB_H,V_nat] :
      ( lhs_atom53(V_nat,V_dB_H)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_dB_Osimps_I6_J_0_0,def_lhs_atom53]) ).

fof(def_lhs_atom54,axiom,
    ! [V_x,V_e,V_T,T_a] :
      ( lhs_atom54(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_53,plain,
    ! [T_a,V_T,V_e,V_x] :
      ( lhs_atom54(V_x,V_e,V_T,T_a)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_shift__eq_0_0,def_lhs_atom54]) ).

fof(def_lhs_atom55,axiom,
    ! [V_ts,V_ss,V_r,V_n] :
      ( lhs_atom55(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_54,plain,
    ! [V_n,V_r,V_ss,V_ts] :
      ( lhs_atom55(V_ts,V_ss,V_r,V_n)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_Var__apps__neq__Abs__apps_0_0,def_lhs_atom55]) ).

fof(def_lhs_atom56,axiom,
    ! [V_nat,V_dB2_H,V_dB1_H] :
      ( lhs_atom56(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_55,plain,
    ! [V_dB1_H,V_dB2_H,V_nat] :
      ( lhs_atom56(V_nat,V_dB2_H,V_dB1_H)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_dB_Osimps_I4_J_0_0,def_lhs_atom56]) ).

fof(def_lhs_atom57,axiom,
    ! [V_nat,V_f2,V_f1,T_a] :
      ( lhs_atom57(V_nat,V_f2,V_f1,T_a)
    <=> c_Type_Otype_Otype__rec(V_f1,V_f2,c_Type_Otype_OAtom(V_nat),T_a) = hAPP(V_f1,V_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_56,plain,
    ! [T_a,V_f1,V_f2,V_nat] :
      ( lhs_atom57(V_nat,V_f2,V_f1,T_a)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_type_Orecs_I1_J_0_0,def_lhs_atom57]) ).

fof(def_lhs_atom58,axiom,
    ! [V_t,V_s] :
      ( lhs_atom58(V_t,V_s)
    <=> hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_s)),V_t)),c_Lambda_Osubst(V_s,V_t,c_HOL_Ozero__class_Ozero(tc_nat)))) ),
    inference(definition,[],]) ).

fof(to_be_clausified_57,plain,
    ! [V_s,V_t] :
      ( lhs_atom58(V_t,V_s)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_beta_0_0,def_lhs_atom58]) ).

fof(def_lhs_atom59,axiom,
    ! [V_t,V_i] :
      ( lhs_atom59(V_t,V_i)
    <=> ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OVar(V_i)),V_t)) ),
    inference(definition,[],]) ).

fof(to_be_clausified_58,plain,
    ! [V_i,V_t] :
      ( lhs_atom59(V_t,V_i)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_beta__cases_I1_J_0_0,def_lhs_atom59]) ).

fof(def_lhs_atom60,axiom,
    ! [V_nat] :
      ( lhs_atom60(V_nat)
    <=> c_Nat_Osize__class_Osize(c_Type_Otype_OAtom(V_nat),tc_Type_Otype) = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_59,plain,
    ! [V_nat] :
      ( lhs_atom60(V_nat)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_type_Osize_I3_J_0_0,def_lhs_atom60]) ).

fof(def_lhs_atom61,axiom,
    ! [V_dB_H,V_dB2,V_dB1] :
      ( lhs_atom61(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_60,plain,
    ! [V_dB1,V_dB2,V_dB_H] :
      ( lhs_atom61(V_dB_H,V_dB2,V_dB1)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_dB_Osimps_I9_J_0_0,def_lhs_atom61]) ).

fof(def_lhs_atom62,axiom,
    ! [V_dB_H,V_dB2,V_dB1] :
      ( lhs_atom62(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_61,plain,
    ! [V_dB1,V_dB2,V_dB_H] :
      ( lhs_atom62(V_dB_H,V_dB2,V_dB1)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_dB_Osimps_I8_J_0_0,def_lhs_atom62]) ).

fof(def_lhs_atom63,axiom,
    ! [V_nat,V_dB_H] :
      ( lhs_atom63(V_nat,V_dB_H)
    <=> c_Lambda_OdB_OAbs(V_dB_H) != c_Lambda_OdB_OVar(V_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_62,plain,
    ! [V_dB_H,V_nat] :
      ( lhs_atom63(V_nat,V_dB_H)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_dB_Osimps_I7_J_0_0,def_lhs_atom63]) ).

fof(def_lhs_atom64,axiom,
    ! [V_nat] :
      ( lhs_atom64(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_63,plain,
    ! [V_nat] :
      ( lhs_atom64(V_nat)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_dB_Osize_I4_J_0_0,def_lhs_atom64]) ).

fof(def_lhs_atom65,axiom,
    ! [V_type2_H,V_type1_H,V_nat] :
      ( lhs_atom65(V_type2_H,V_type1_H,V_nat)
    <=> hAPP(hAPP(c_Type_Otype_OFun,V_type1_H),V_type2_H) != c_Type_Otype_OAtom(V_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_64,plain,
    ! [V_nat,V_type1_H,V_type2_H] :
      ( lhs_atom65(V_type2_H,V_type1_H,V_nat)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_type_Osimps_I4_J_0_0,def_lhs_atom65]) ).

fof(def_lhs_atom66,axiom,
    ( lhs_atom66
  <=> hBOOL(hAPP(c_InductTermi_OIT,v_s____)) ),
    inference(definition,[],]) ).

fof(to_be_clausified_65,plain,
    ( lhs_atom66
    | $false ),
    inference(fold_definition,[status(thm)],[cls_App_I2_J_0_0,def_lhs_atom66]) ).

fof(def_lhs_atom67,axiom,
    ( lhs_atom67
  <=> c_Type_Otyping(v_ea____,v_ta____,v_Ta____) ),
    inference(definition,[],]) ).

fof(to_be_clausified_66,plain,
    ( lhs_atom67
    | $false ),
    inference(fold_definition,[status(thm)],[cls_App_I3_J_0_0,def_lhs_atom67]) ).

fof(def_lhs_atom68,axiom,
    ! [V_type2,V_type1,V_f2,V_f1,T_a] :
      ( lhs_atom68(V_type2,V_type1,V_f2,V_f1,T_a)
    <=> c_Type_Otype_Otype__rec(V_f1,V_f2,hAPP(hAPP(c_Type_Otype_OFun,V_type1),V_type2),T_a) = hAPP(hAPP(hAPP(hAPP(V_f2,V_type1),V_type2),c_Type_Otype_Otype__rec(V_f1,V_f2,V_type1,T_a)),c_Type_Otype_Otype__rec(V_f1,V_f2,V_type2,T_a)) ),
    inference(definition,[],]) ).

fof(to_be_clausified_67,plain,
    ! [T_a,V_f1,V_f2,V_type1,V_type2] :
      ( lhs_atom68(V_type2,V_type1,V_f2,V_f1,T_a)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_type_Orecs_I2_J_0_0,def_lhs_atom68]) ).

fof(def_lhs_atom69,axiom,
    ! [V_type2,V_type1,V_f2,V_f1,T_a] :
      ( lhs_atom69(V_type2,V_type1,V_f2,V_f1,T_a)
    <=> c_Type_Otype_Otype__case(V_f1,V_f2,hAPP(hAPP(c_Type_Otype_OFun,V_type1),V_type2),T_a) = hAPP(hAPP(V_f2,V_type1),V_type2) ),
    inference(definition,[],]) ).

fof(to_be_clausified_68,plain,
    ! [T_a,V_f1,V_f2,V_type1,V_type2] :
      ( lhs_atom69(V_type2,V_type1,V_f2,V_f1,T_a)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_type_Osimps_I6_J_0_0,def_lhs_atom69]) ).

fof(def_lhs_atom70,axiom,
    ( lhs_atom70
  <=> c_Type_Otyping(v_ea____,v_s____,hAPP(hAPP(c_Type_Otype_OFun,v_Ta____),v_U____)) ),
    inference(definition,[],]) ).

fof(to_be_clausified_69,plain,
    ( lhs_atom70
    | $false ),
    inference(fold_definition,[status(thm)],[cls_App_I1_J_0_0,def_lhs_atom70]) ).

fof(def_lhs_atom71,axiom,
    ! [V_x,V_env] :
      ( lhs_atom71(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_70,plain,
    ! [V_env,V_x] :
      ( lhs_atom71(V_x,V_env)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_typing_OVar_0_0,def_lhs_atom71]) ).

fof(def_lhs_atom72,axiom,
    ! [V_type2_H,V_type1_H,V_nat] :
      ( lhs_atom72(V_type2_H,V_type1_H,V_nat)
    <=> c_Type_Otype_OAtom(V_nat) != hAPP(hAPP(c_Type_Otype_OFun,V_type1_H),V_type2_H) ),
    inference(definition,[],]) ).

fof(to_be_clausified_71,plain,
    ! [V_nat,V_type1_H,V_type2_H] :
      ( lhs_atom72(V_type2_H,V_type1_H,V_nat)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_type_Osimps_I3_J_0_0,def_lhs_atom72]) ).

fof(def_lhs_atom73,axiom,
    ( lhs_atom73
  <=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_72,plain,
    ( lhs_atom73
    | $false ),
    inference(fold_definition,[status(thm)],[clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le_0,def_lhs_atom73]) ).

fof(def_lhs_atom74,axiom,
    ( lhs_atom74
  <=> class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_73,plain,
    ( lhs_atom74
    | $false ),
    inference(fold_definition,[status(thm)],[clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add_0,def_lhs_atom74]) ).

fof(def_lhs_atom75,axiom,
    ( lhs_atom75
  <=> class_OrderedGroup_Opordered__comm__monoid__add(tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_74,plain,
    ( lhs_atom75
    | $false ),
    inference(fold_definition,[status(thm)],[clsarity_nat__OrderedGroup_Opordered__comm__monoid__add_0,def_lhs_atom75]) ).

fof(def_lhs_atom76,axiom,
    ( lhs_atom76
  <=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_75,plain,
    ( lhs_atom76
    | $false ),
    inference(fold_definition,[status(thm)],[clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add_0,def_lhs_atom76]) ).

fof(def_lhs_atom77,axiom,
    ( lhs_atom77
  <=> class_OrderedGroup_Ocancel__semigroup__add(tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_76,plain,
    ( lhs_atom77
    | $false ),
    inference(fold_definition,[status(thm)],[clsarity_nat__OrderedGroup_Ocancel__semigroup__add_0,def_lhs_atom77]) ).

fof(def_lhs_atom78,axiom,
    ( lhs_atom78
  <=> class_Ring__and__Field_Ono__zero__divisors(tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_77,plain,
    ( lhs_atom78
    | $false ),
    inference(fold_definition,[status(thm)],[clsarity_nat__Ring__and__Field_Ono__zero__divisors_0,def_lhs_atom78]) ).

fof(def_lhs_atom79,axiom,
    ( lhs_atom79
  <=> class_Ring__and__Field_Oordered__semidom(tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_78,plain,
    ( lhs_atom79
    | $false ),
    inference(fold_definition,[status(thm)],[clsarity_nat__Ring__and__Field_Oordered__semidom_0,def_lhs_atom79]) ).

fof(def_lhs_atom80,axiom,
    ( lhs_atom80
  <=> class_Ring__and__Field_Ocomm__semiring__1(tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_79,plain,
    ( lhs_atom80
    | $false ),
    inference(fold_definition,[status(thm)],[clsarity_nat__Ring__and__Field_Ocomm__semiring__1_0,def_lhs_atom80]) ).

fof(def_lhs_atom81,axiom,
    ( lhs_atom81
  <=> class_OrderedGroup_Oab__semigroup__add(tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_80,plain,
    ( lhs_atom81
    | $false ),
    inference(fold_definition,[status(thm)],[clsarity_nat__OrderedGroup_Oab__semigroup__add_0,def_lhs_atom81]) ).

fof(def_lhs_atom82,axiom,
    ( lhs_atom82
  <=> class_OrderedGroup_Ocomm__monoid__add(tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_81,plain,
    ( lhs_atom82
    | $false ),
    inference(fold_definition,[status(thm)],[clsarity_nat__OrderedGroup_Ocomm__monoid__add_0,def_lhs_atom82]) ).

fof(def_lhs_atom83,axiom,
    ( lhs_atom83
  <=> class_Ring__and__Field_Ozero__neq__one(tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_82,plain,
    ( lhs_atom83
    | $false ),
    inference(fold_definition,[status(thm)],[clsarity_nat__Ring__and__Field_Ozero__neq__one_0,def_lhs_atom83]) ).

fof(def_lhs_atom84,axiom,
    ( lhs_atom84
  <=> class_OrderedGroup_Osemigroup__add(tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_83,plain,
    ( lhs_atom84
    | $false ),
    inference(fold_definition,[status(thm)],[clsarity_nat__OrderedGroup_Osemigroup__add_0,def_lhs_atom84]) ).

fof(def_lhs_atom85,axiom,
    ( lhs_atom85
  <=> class_Ring__and__Field_Osemiring__1(tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_84,plain,
    ( lhs_atom85
    | $false ),
    inference(fold_definition,[status(thm)],[clsarity_nat__Ring__and__Field_Osemiring__1_0,def_lhs_atom85]) ).

fof(def_lhs_atom86,axiom,
    ( lhs_atom86
  <=> class_Ring__and__Field_Osemiring__0(tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_85,plain,
    ( lhs_atom86
    | $false ),
    inference(fold_definition,[status(thm)],[clsarity_nat__Ring__and__Field_Osemiring__0_0,def_lhs_atom86]) ).

fof(def_lhs_atom87,axiom,
    ( lhs_atom87
  <=> class_Ring__and__Field_Omult__zero(tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_86,plain,
    ( lhs_atom87
    | $false ),
    inference(fold_definition,[status(thm)],[clsarity_nat__Ring__and__Field_Omult__zero_0,def_lhs_atom87]) ).

fof(def_lhs_atom88,axiom,
    ( lhs_atom88
  <=> class_OrderedGroup_Omonoid__mult(tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_87,plain,
    ( lhs_atom88
    | $false ),
    inference(fold_definition,[status(thm)],[clsarity_nat__OrderedGroup_Omonoid__mult_0,def_lhs_atom88]) ).

fof(def_lhs_atom89,axiom,
    ( lhs_atom89
  <=> class_OrderedGroup_Omonoid__add(tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_88,plain,
    ( lhs_atom89
    | $false ),
    inference(fold_definition,[status(thm)],[clsarity_nat__OrderedGroup_Omonoid__add_0,def_lhs_atom89]) ).

fof(def_lhs_atom90,axiom,
    ( lhs_atom90
  <=> class_Nat_Osemiring__char__0(tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_89,plain,
    ( lhs_atom90
    | $false ),
    inference(fold_definition,[status(thm)],[clsarity_nat__Nat_Osemiring__char__0_0,def_lhs_atom90]) ).

fof(def_lhs_atom91,axiom,
    ( lhs_atom91
  <=> class_Orderings_Opreorder(tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_90,plain,
    ( lhs_atom91
    | $false ),
    inference(fold_definition,[status(thm)],[clsarity_nat__Orderings_Opreorder_0,def_lhs_atom91]) ).

fof(def_lhs_atom92,axiom,
    ( lhs_atom92
  <=> class_Orderings_Olinorder(tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_91,plain,
    ( lhs_atom92
    | $false ),
    inference(fold_definition,[status(thm)],[clsarity_nat__Orderings_Olinorder_0,def_lhs_atom92]) ).

fof(def_lhs_atom93,axiom,
    ( lhs_atom93
  <=> class_Orderings_Oorder(tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_92,plain,
    ( lhs_atom93
    | $false ),
    inference(fold_definition,[status(thm)],[clsarity_nat__Orderings_Oorder_0,def_lhs_atom93]) ).

fof(def_lhs_atom94,axiom,
    ( lhs_atom94
  <=> class_Power_Opower(tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_93,plain,
    ( lhs_atom94
    | $false ),
    inference(fold_definition,[status(thm)],[clsarity_nat__Power_Opower_0,def_lhs_atom94]) ).

fof(def_lhs_atom95,axiom,
    ( lhs_atom95
  <=> class_Orderings_Opreorder(tc_bool) ),
    inference(definition,[],]) ).

fof(to_be_clausified_94,plain,
    ( lhs_atom95
    | $false ),
    inference(fold_definition,[status(thm)],[clsarity_bool__Orderings_Opreorder_0,def_lhs_atom95]) ).

fof(def_lhs_atom96,axiom,
    ( lhs_atom96
  <=> class_Orderings_Oorder(tc_bool) ),
    inference(definition,[],]) ).

fof(to_be_clausified_95,plain,
    ( lhs_atom96
    | $false ),
    inference(fold_definition,[status(thm)],[clsarity_bool__Orderings_Oorder_0,def_lhs_atom96]) ).

fof(def_lhs_atom97,axiom,
    ! [V_x,T_a] :
      ( lhs_atom97(V_x,T_a)
    <=> hBOOL(hAPP(hAPP(c_fequal(T_a),V_x),V_x)) ),
    inference(definition,[],]) ).

fof(to_be_clausified_96,plain,
    ! [T_a,V_x] :
      ( lhs_atom97(V_x,T_a)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_ATP__Linkup_Oequal__imp__fequal_0_0,def_lhs_atom97]) ).

% Start CNF derivation
fof(c_0_0,axiom,
    ! [X20,X21,X26,X27,X7] :
      ( lhs_atom69(X20,X21,X26,X27,X7)
      | ~ $true ),
    file('<stdin>',to_be_clausified_68) ).

fof(c_0_1,axiom,
    ! [X20,X21,X26,X27,X7] :
      ( lhs_atom68(X20,X21,X26,X27,X7)
      | ~ $true ),
    file('<stdin>',to_be_clausified_67) ).

fof(c_0_2,axiom,
    ! [X29,X30,X31,X32,X7] :
      ( lhs_atom52(X29,X30,X31,X32,X7)
      | ~ $true ),
    file('<stdin>',to_be_clausified_51) ).

fof(c_0_3,axiom,
    ! [X23,X26,X27,X7] :
      ( lhs_atom57(X23,X26,X27,X7)
      | ~ $true ),
    file('<stdin>',to_be_clausified_56) ).

fof(c_0_4,axiom,
    ! [X34,X28,X13,X2] :
      ( lhs_atom55(X34,X28,X13,X2)
      | ~ $true ),
    file('<stdin>',to_be_clausified_54) ).

fof(c_0_5,axiom,
    ! [X1,X30,X32,X7] :
      ( lhs_atom54(X1,X30,X32,X7)
      | ~ $true ),
    file('<stdin>',to_be_clausified_53) ).

fof(c_0_6,axiom,
    ! [X19,X28,X14,X2] :
      ( lhs_atom47(X19,X28,X14,X2)
      | ~ $true ),
    file('<stdin>',to_be_clausified_46) ).

fof(c_0_7,axiom,
    ! [X23,X26,X27,X7] :
      ( lhs_atom46(X23,X26,X27,X7)
      | ~ $true ),
    file('<stdin>',to_be_clausified_45) ).

fof(c_0_8,axiom,
    ! [X18,X19,X14,X8] :
      ( lhs_atom25(X18,X19,X14,X8)
      | ~ $true ),
    file('<stdin>',to_be_clausified_24) ).

fof(c_0_9,axiom,
    ! [X4,X5,X6,X7] :
      ( lhs_atom17(X4,X5,X6,X7)
      | ~ $true ),
    file('<stdin>',to_be_clausified_16) ).

fof(c_0_10,axiom,
    ! [X4,X5,X6,X7] :
      ( lhs_atom6(X4,X5,X6,X7)
      | ~ $true ),
    file('<stdin>',to_be_clausified_5) ).

fof(c_0_11,axiom,
    ! [X35,X36,X23] :
      ( lhs_atom72(X35,X36,X23)
      | ~ $true ),
    file('<stdin>',to_be_clausified_71) ).

fof(c_0_12,axiom,
    ! [X35,X36,X23] :
      ( lhs_atom65(X35,X36,X23)
      | ~ $true ),
    file('<stdin>',to_be_clausified_64) ).

fof(c_0_13,axiom,
    ! [X33,X16,X17] :
      ( lhs_atom62(X33,X16,X17)
      | ~ $true ),
    file('<stdin>',to_be_clausified_61) ).

fof(c_0_14,axiom,
    ! [X33,X16,X17] :
      ( lhs_atom61(X33,X16,X17)
      | ~ $true ),
    file('<stdin>',to_be_clausified_60) ).

fof(c_0_15,axiom,
    ! [X23,X24,X25] :
      ( lhs_atom56(X23,X24,X25)
      | ~ $true ),
    file('<stdin>',to_be_clausified_55) ).

fof(c_0_16,axiom,
    ! [X23,X24,X25] :
      ( lhs_atom45(X23,X24,X25)
      | ~ $true ),
    file('<stdin>',to_be_clausified_44) ).

fof(c_0_17,axiom,
    ! [X19,X14,X8] :
      ( lhs_atom42(X19,X14,X8)
      | ~ $true ),
    file('<stdin>',to_be_clausified_41) ).

fof(c_0_18,axiom,
    ! [X13,X5,X7] :
      ( lhs_atom37(X13,X5,X7)
      | ~ $true ),
    file('<stdin>',to_be_clausified_36) ).

fof(c_0_19,axiom,
    ! [X1,X13,X7] :
      ( lhs_atom36(X1,X13,X7)
      | ~ $true ),
    file('<stdin>',to_be_clausified_35) ).

fof(c_0_20,axiom,
    ! [X19,X14,X8] :
      ( lhs_atom33(X19,X14,X8)
      | ~ $true ),
    file('<stdin>',to_be_clausified_32) ).

fof(c_0_21,axiom,
    ! [X13,X6,X7] :
      ( lhs_atom20(X13,X6,X7)
      | ~ $true ),
    file('<stdin>',to_be_clausified_19) ).

fof(c_0_22,axiom,
    ! [X12,X13,X7] :
      ( lhs_atom16(X12,X13,X7)
      | ~ $true ),
    file('<stdin>',to_be_clausified_15) ).

fof(c_0_23,axiom,
    ! [X12,X13,X7] :
      ( lhs_atom15(X12,X13,X7)
      | ~ $true ),
    file('<stdin>',to_be_clausified_14) ).

fof(c_0_24,axiom,
    ! [X9,X10,X1] :
      ( lhs_atom8(X9,X10,X1)
      | ~ $true ),
    file('<stdin>',to_be_clausified_7) ).

fof(c_0_25,axiom,
    ! [X2,X3,X8] :
      ( lhs_atom7(X2,X3,X8)
      | ~ $true ),
    file('<stdin>',to_be_clausified_6) ).

fof(c_0_26,axiom,
    ! [X1,X7] :
      ( lhs_atom97(X1,X7)
      | ~ $true ),
    file('<stdin>',to_be_clausified_96) ).

fof(c_0_27,axiom,
    ! [X1,X37] :
      ( lhs_atom71(X1,X37)
      | ~ $true ),
    file('<stdin>',to_be_clausified_70) ).

fof(c_0_28,axiom,
    ! [X23,X33] :
      ( lhs_atom63(X23,X33)
      | ~ $true ),
    file('<stdin>',to_be_clausified_62) ).

fof(c_0_29,axiom,
    ! [X19,X29] :
      ( lhs_atom59(X19,X29)
      | ~ $true ),
    file('<stdin>',to_be_clausified_58) ).

fof(c_0_30,axiom,
    ! [X19,X14] :
      ( lhs_atom58(X19,X14)
      | ~ $true ),
    file('<stdin>',to_be_clausified_57) ).

fof(c_0_31,axiom,
    ! [X23,X33] :
      ( lhs_atom53(X23,X33)
      | ~ $true ),
    file('<stdin>',to_be_clausified_52) ).

fof(c_0_32,axiom,
    ! [X13,X7] :
      ( lhs_atom44(X13,X7)
      | ~ $true ),
    file('<stdin>',to_be_clausified_43) ).

fof(c_0_33,axiom,
    ! [X16,X17] :
      ( lhs_atom39(X16,X17)
      | ~ $true ),
    file('<stdin>',to_be_clausified_38) ).

fof(c_0_34,axiom,
    ! [X20,X21] :
      ( lhs_atom30(X20,X21)
      | ~ $true ),
    file('<stdin>',to_be_clausified_29) ).

fof(c_0_35,axiom,
    ! [X18,X8] :
      ( lhs_atom27(X18,X8)
      | ~ $true ),
    file('<stdin>',to_be_clausified_26) ).

fof(c_0_36,axiom,
    ! [X20,X21] :
      ( lhs_atom26(X20,X21)
      | ~ $true ),
    file('<stdin>',to_be_clausified_25) ).

fof(c_0_37,axiom,
    ! [X16,X17] :
      ( lhs_atom24(X16,X17)
      | ~ $true ),
    file('<stdin>',to_be_clausified_23) ).

fof(c_0_38,axiom,
    ! [X14,X13] :
      ( lhs_atom22(X14,X13)
      | ~ $true ),
    file('<stdin>',to_be_clausified_21) ).

fof(c_0_39,axiom,
    ! [X2,X3] :
      ( lhs_atom14(X2,X3)
      | ~ $true ),
    file('<stdin>',to_be_clausified_13) ).

fof(c_0_40,axiom,
    ! [X2,X3] :
      ( lhs_atom13(X2,X3)
      | ~ $true ),
    file('<stdin>',to_be_clausified_12) ).

fof(c_0_41,axiom,
    ! [X2,X3] :
      ( lhs_atom12(X2,X3)
      | ~ $true ),
    file('<stdin>',to_be_clausified_11) ).

fof(c_0_42,axiom,
    ! [X11,X7] :
      ( lhs_atom11(X11,X7)
      | ~ $true ),
    file('<stdin>',to_be_clausified_10) ).

fof(c_0_43,axiom,
    ! [X2,X3] :
      ( lhs_atom4(X2,X3)
      | ~ $true ),
    file('<stdin>',to_be_clausified_3) ).

fof(c_0_44,axiom,
    ! [X23] :
      ( lhs_atom64(X23)
      | ~ $true ),
    file('<stdin>',to_be_clausified_63) ).

fof(c_0_45,axiom,
    ! [X23] :
      ( lhs_atom60(X23)
      | ~ $true ),
    file('<stdin>',to_be_clausified_59) ).

fof(c_0_46,axiom,
    ! [X2] :
      ( lhs_atom51(X2)
      | ~ $true ),
    file('<stdin>',to_be_clausified_50) ).

fof(c_0_47,axiom,
    ! [X23] :
      ( lhs_atom50(X23)
      | ~ $true ),
    file('<stdin>',to_be_clausified_49) ).

fof(c_0_48,axiom,
    ! [X23] :
      ( lhs_atom48(X23)
      | ~ $true ),
    file('<stdin>',to_be_clausified_47) ).

fof(c_0_49,axiom,
    ! [X13] :
      ( lhs_atom43(X13)
      | ~ $true ),
    file('<stdin>',to_be_clausified_42) ).

fof(c_0_50,axiom,
    ! [X15] :
      ( lhs_atom41(X15)
      | ~ $true ),
    file('<stdin>',to_be_clausified_40) ).

fof(c_0_51,axiom,
    ! [X13] :
      ( lhs_atom40(X13)
      | ~ $true ),
    file('<stdin>',to_be_clausified_39) ).

fof(c_0_52,axiom,
    ! [X3] :
      ( lhs_atom38(X3)
      | ~ $true ),
    file('<stdin>',to_be_clausified_37) ).

fof(c_0_53,axiom,
    ! [X22] :
      ( lhs_atom35(X22)
      | ~ $true ),
    file('<stdin>',to_be_clausified_34) ).

fof(c_0_54,axiom,
    ! [X3] :
      ( lhs_atom34(X3)
      | ~ $true ),
    file('<stdin>',to_be_clausified_33) ).

fof(c_0_55,axiom,
    ! [X22] :
      ( lhs_atom32(X22)
      | ~ $true ),
    file('<stdin>',to_be_clausified_31) ).

fof(c_0_56,axiom,
    ! [X3] :
      ( lhs_atom31(X3)
      | ~ $true ),
    file('<stdin>',to_be_clausified_30) ).

fof(c_0_57,axiom,
    ! [X2] :
      ( lhs_atom29(X2)
      | ~ $true ),
    file('<stdin>',to_be_clausified_28) ).

fof(c_0_58,axiom,
    ! [X2] :
      ( lhs_atom28(X2)
      | ~ $true ),
    file('<stdin>',to_be_clausified_27) ).

fof(c_0_59,axiom,
    ! [X15] :
      ( lhs_atom23(X15)
      | ~ $true ),
    file('<stdin>',to_be_clausified_22) ).

fof(c_0_60,axiom,
    ! [X7] :
      ( lhs_atom18(X7)
      | ~ $true ),
    file('<stdin>',to_be_clausified_17) ).

fof(c_0_61,axiom,
    ! [X3] :
      ( lhs_atom3(X3)
      | ~ $true ),
    file('<stdin>',to_be_clausified_2) ).

fof(c_0_62,axiom,
    ! [X2] :
      ( lhs_atom2(X2)
      | ~ $true ),
    file('<stdin>',to_be_clausified_1) ).

fof(c_0_63,axiom,
    ! [X1] :
      ( lhs_atom1(X1)
      | ~ $true ),
    file('<stdin>',to_be_clausified_0) ).

fof(c_0_64,axiom,
    ( lhs_atom96
    | ~ $true ),
    file('<stdin>',to_be_clausified_95) ).

fof(c_0_65,axiom,
    ( lhs_atom95
    | ~ $true ),
    file('<stdin>',to_be_clausified_94) ).

fof(c_0_66,axiom,
    ( lhs_atom94
    | ~ $true ),
    file('<stdin>',to_be_clausified_93) ).

fof(c_0_67,axiom,
    ( lhs_atom93
    | ~ $true ),
    file('<stdin>',to_be_clausified_92) ).

fof(c_0_68,axiom,
    ( lhs_atom92
    | ~ $true ),
    file('<stdin>',to_be_clausified_91) ).

fof(c_0_69,axiom,
    ( lhs_atom91
    | ~ $true ),
    file('<stdin>',to_be_clausified_90) ).

fof(c_0_70,axiom,
    ( lhs_atom90
    | ~ $true ),
    file('<stdin>',to_be_clausified_89) ).

fof(c_0_71,axiom,
    ( lhs_atom89
    | ~ $true ),
    file('<stdin>',to_be_clausified_88) ).

fof(c_0_72,axiom,
    ( lhs_atom88
    | ~ $true ),
    file('<stdin>',to_be_clausified_87) ).

fof(c_0_73,axiom,
    ( lhs_atom87
    | ~ $true ),
    file('<stdin>',to_be_clausified_86) ).

fof(c_0_74,axiom,
    ( lhs_atom86
    | ~ $true ),
    file('<stdin>',to_be_clausified_85) ).

fof(c_0_75,axiom,
    ( lhs_atom85
    | ~ $true ),
    file('<stdin>',to_be_clausified_84) ).

fof(c_0_76,axiom,
    ( lhs_atom84
    | ~ $true ),
    file('<stdin>',to_be_clausified_83) ).

fof(c_0_77,axiom,
    ( lhs_atom83
    | ~ $true ),
    file('<stdin>',to_be_clausified_82) ).

fof(c_0_78,axiom,
    ( lhs_atom82
    | ~ $true ),
    file('<stdin>',to_be_clausified_81) ).

fof(c_0_79,axiom,
    ( lhs_atom81
    | ~ $true ),
    file('<stdin>',to_be_clausified_80) ).

fof(c_0_80,axiom,
    ( lhs_atom80
    | ~ $true ),
    file('<stdin>',to_be_clausified_79) ).

fof(c_0_81,axiom,
    ( lhs_atom79
    | ~ $true ),
    file('<stdin>',to_be_clausified_78) ).

fof(c_0_82,axiom,
    ( lhs_atom78
    | ~ $true ),
    file('<stdin>',to_be_clausified_77) ).

fof(c_0_83,axiom,
    ( lhs_atom77
    | ~ $true ),
    file('<stdin>',to_be_clausified_76) ).

fof(c_0_84,axiom,
    ( lhs_atom76
    | ~ $true ),
    file('<stdin>',to_be_clausified_75) ).

fof(c_0_85,axiom,
    ( lhs_atom75
    | ~ $true ),
    file('<stdin>',to_be_clausified_74) ).

fof(c_0_86,axiom,
    ( lhs_atom74
    | ~ $true ),
    file('<stdin>',to_be_clausified_73) ).

fof(c_0_87,axiom,
    ( lhs_atom73
    | ~ $true ),
    file('<stdin>',to_be_clausified_72) ).

fof(c_0_88,axiom,
    ( lhs_atom70
    | ~ $true ),
    file('<stdin>',to_be_clausified_69) ).

fof(c_0_89,axiom,
    ( lhs_atom67
    | ~ $true ),
    file('<stdin>',to_be_clausified_66) ).

fof(c_0_90,axiom,
    ( lhs_atom66
    | ~ $true ),
    file('<stdin>',to_be_clausified_65) ).

fof(c_0_91,axiom,
    ( lhs_atom49
    | ~ $true ),
    file('<stdin>',to_be_clausified_48) ).

fof(c_0_92,axiom,
    ( lhs_atom21
    | ~ $true ),
    file('<stdin>',to_be_clausified_20) ).

fof(c_0_93,axiom,
    ( lhs_atom19
    | ~ $true ),
    file('<stdin>',to_be_clausified_18) ).

fof(c_0_94,axiom,
    ( lhs_atom10
    | ~ $true ),
    file('<stdin>',to_be_clausified_9) ).

fof(c_0_95,axiom,
    ( lhs_atom9
    | ~ $true ),
    file('<stdin>',to_be_clausified_8) ).

fof(c_0_96,axiom,
    ( lhs_atom5
    | ~ $true ),
    file('<stdin>',to_be_clausified_4) ).

fof(c_0_97,plain,
    ! [X20,X21,X26,X27,X7] : lhs_atom69(X20,X21,X26,X27,X7),
    inference(fof_simplification,[status(thm)],[c_0_0]) ).

fof(c_0_98,plain,
    ! [X20,X21,X26,X27,X7] : lhs_atom68(X20,X21,X26,X27,X7),
    inference(fof_simplification,[status(thm)],[c_0_1]) ).

fof(c_0_99,plain,
    ! [X29,X30,X31,X32,X7] : lhs_atom52(X29,X30,X31,X32,X7),
    inference(fof_simplification,[status(thm)],[c_0_2]) ).

fof(c_0_100,plain,
    ! [X23,X26,X27,X7] : lhs_atom57(X23,X26,X27,X7),
    inference(fof_simplification,[status(thm)],[c_0_3]) ).

fof(c_0_101,plain,
    ! [X34,X28,X13,X2] : lhs_atom55(X34,X28,X13,X2),
    inference(fof_simplification,[status(thm)],[c_0_4]) ).

fof(c_0_102,plain,
    ! [X1,X30,X32,X7] : lhs_atom54(X1,X30,X32,X7),
    inference(fof_simplification,[status(thm)],[c_0_5]) ).

fof(c_0_103,plain,
    ! [X19,X28,X14,X2] : lhs_atom47(X19,X28,X14,X2),
    inference(fof_simplification,[status(thm)],[c_0_6]) ).

fof(c_0_104,plain,
    ! [X23,X26,X27,X7] : lhs_atom46(X23,X26,X27,X7),
    inference(fof_simplification,[status(thm)],[c_0_7]) ).

fof(c_0_105,plain,
    ! [X18,X19,X14,X8] : lhs_atom25(X18,X19,X14,X8),
    inference(fof_simplification,[status(thm)],[c_0_8]) ).

fof(c_0_106,plain,
    ! [X4,X5,X6,X7] : lhs_atom17(X4,X5,X6,X7),
    inference(fof_simplification,[status(thm)],[c_0_9]) ).

fof(c_0_107,plain,
    ! [X4,X5,X6,X7] : lhs_atom6(X4,X5,X6,X7),
    inference(fof_simplification,[status(thm)],[c_0_10]) ).

fof(c_0_108,plain,
    ! [X35,X36,X23] : lhs_atom72(X35,X36,X23),
    inference(fof_simplification,[status(thm)],[c_0_11]) ).

fof(c_0_109,plain,
    ! [X35,X36,X23] : lhs_atom65(X35,X36,X23),
    inference(fof_simplification,[status(thm)],[c_0_12]) ).

fof(c_0_110,plain,
    ! [X33,X16,X17] : lhs_atom62(X33,X16,X17),
    inference(fof_simplification,[status(thm)],[c_0_13]) ).

fof(c_0_111,plain,
    ! [X33,X16,X17] : lhs_atom61(X33,X16,X17),
    inference(fof_simplification,[status(thm)],[c_0_14]) ).

fof(c_0_112,plain,
    ! [X23,X24,X25] : lhs_atom56(X23,X24,X25),
    inference(fof_simplification,[status(thm)],[c_0_15]) ).

fof(c_0_113,plain,
    ! [X23,X24,X25] : lhs_atom45(X23,X24,X25),
    inference(fof_simplification,[status(thm)],[c_0_16]) ).

fof(c_0_114,plain,
    ! [X19,X14,X8] : lhs_atom42(X19,X14,X8),
    inference(fof_simplification,[status(thm)],[c_0_17]) ).

fof(c_0_115,plain,
    ! [X13,X5,X7] : lhs_atom37(X13,X5,X7),
    inference(fof_simplification,[status(thm)],[c_0_18]) ).

fof(c_0_116,plain,
    ! [X1,X13,X7] : lhs_atom36(X1,X13,X7),
    inference(fof_simplification,[status(thm)],[c_0_19]) ).

fof(c_0_117,plain,
    ! [X19,X14,X8] : lhs_atom33(X19,X14,X8),
    inference(fof_simplification,[status(thm)],[c_0_20]) ).

fof(c_0_118,plain,
    ! [X13,X6,X7] : lhs_atom20(X13,X6,X7),
    inference(fof_simplification,[status(thm)],[c_0_21]) ).

fof(c_0_119,plain,
    ! [X12,X13,X7] : lhs_atom16(X12,X13,X7),
    inference(fof_simplification,[status(thm)],[c_0_22]) ).

fof(c_0_120,plain,
    ! [X12,X13,X7] : lhs_atom15(X12,X13,X7),
    inference(fof_simplification,[status(thm)],[c_0_23]) ).

fof(c_0_121,plain,
    ! [X9,X10,X1] : lhs_atom8(X9,X10,X1),
    inference(fof_simplification,[status(thm)],[c_0_24]) ).

fof(c_0_122,plain,
    ! [X2,X3,X8] : lhs_atom7(X2,X3,X8),
    inference(fof_simplification,[status(thm)],[c_0_25]) ).

fof(c_0_123,plain,
    ! [X1,X7] : lhs_atom97(X1,X7),
    inference(fof_simplification,[status(thm)],[c_0_26]) ).

fof(c_0_124,plain,
    ! [X1,X37] : lhs_atom71(X1,X37),
    inference(fof_simplification,[status(thm)],[c_0_27]) ).

fof(c_0_125,plain,
    ! [X23,X33] : lhs_atom63(X23,X33),
    inference(fof_simplification,[status(thm)],[c_0_28]) ).

fof(c_0_126,plain,
    ! [X19,X29] : lhs_atom59(X19,X29),
    inference(fof_simplification,[status(thm)],[c_0_29]) ).

fof(c_0_127,plain,
    ! [X19,X14] : lhs_atom58(X19,X14),
    inference(fof_simplification,[status(thm)],[c_0_30]) ).

fof(c_0_128,plain,
    ! [X23,X33] : lhs_atom53(X23,X33),
    inference(fof_simplification,[status(thm)],[c_0_31]) ).

fof(c_0_129,plain,
    ! [X13,X7] : lhs_atom44(X13,X7),
    inference(fof_simplification,[status(thm)],[c_0_32]) ).

fof(c_0_130,plain,
    ! [X16,X17] : lhs_atom39(X16,X17),
    inference(fof_simplification,[status(thm)],[c_0_33]) ).

fof(c_0_131,plain,
    ! [X20,X21] : lhs_atom30(X20,X21),
    inference(fof_simplification,[status(thm)],[c_0_34]) ).

fof(c_0_132,plain,
    ! [X18,X8] : lhs_atom27(X18,X8),
    inference(fof_simplification,[status(thm)],[c_0_35]) ).

fof(c_0_133,plain,
    ! [X20,X21] : lhs_atom26(X20,X21),
    inference(fof_simplification,[status(thm)],[c_0_36]) ).

fof(c_0_134,plain,
    ! [X16,X17] : lhs_atom24(X16,X17),
    inference(fof_simplification,[status(thm)],[c_0_37]) ).

fof(c_0_135,plain,
    ! [X14,X13] : lhs_atom22(X14,X13),
    inference(fof_simplification,[status(thm)],[c_0_38]) ).

fof(c_0_136,plain,
    ! [X2,X3] : lhs_atom14(X2,X3),
    inference(fof_simplification,[status(thm)],[c_0_39]) ).

fof(c_0_137,plain,
    ! [X2,X3] : lhs_atom13(X2,X3),
    inference(fof_simplification,[status(thm)],[c_0_40]) ).

fof(c_0_138,plain,
    ! [X2,X3] : lhs_atom12(X2,X3),
    inference(fof_simplification,[status(thm)],[c_0_41]) ).

fof(c_0_139,plain,
    ! [X11,X7] : lhs_atom11(X11,X7),
    inference(fof_simplification,[status(thm)],[c_0_42]) ).

fof(c_0_140,plain,
    ! [X2,X3] : lhs_atom4(X2,X3),
    inference(fof_simplification,[status(thm)],[c_0_43]) ).

fof(c_0_141,plain,
    ! [X23] : lhs_atom64(X23),
    inference(fof_simplification,[status(thm)],[c_0_44]) ).

fof(c_0_142,plain,
    ! [X23] : lhs_atom60(X23),
    inference(fof_simplification,[status(thm)],[c_0_45]) ).

fof(c_0_143,plain,
    ! [X2] : lhs_atom51(X2),
    inference(fof_simplification,[status(thm)],[c_0_46]) ).

fof(c_0_144,plain,
    ! [X23] : lhs_atom50(X23),
    inference(fof_simplification,[status(thm)],[c_0_47]) ).

fof(c_0_145,plain,
    ! [X23] : lhs_atom48(X23),
    inference(fof_simplification,[status(thm)],[c_0_48]) ).

fof(c_0_146,plain,
    ! [X13] : lhs_atom43(X13),
    inference(fof_simplification,[status(thm)],[c_0_49]) ).

fof(c_0_147,plain,
    ! [X15] : lhs_atom41(X15),
    inference(fof_simplification,[status(thm)],[c_0_50]) ).

fof(c_0_148,plain,
    ! [X13] : lhs_atom40(X13),
    inference(fof_simplification,[status(thm)],[c_0_51]) ).

fof(c_0_149,plain,
    ! [X3] : lhs_atom38(X3),
    inference(fof_simplification,[status(thm)],[c_0_52]) ).

fof(c_0_150,plain,
    ! [X22] : lhs_atom35(X22),
    inference(fof_simplification,[status(thm)],[c_0_53]) ).

fof(c_0_151,plain,
    ! [X3] : lhs_atom34(X3),
    inference(fof_simplification,[status(thm)],[c_0_54]) ).

fof(c_0_152,plain,
    ! [X22] : lhs_atom32(X22),
    inference(fof_simplification,[status(thm)],[c_0_55]) ).

fof(c_0_153,plain,
    ! [X3] : lhs_atom31(X3),
    inference(fof_simplification,[status(thm)],[c_0_56]) ).

fof(c_0_154,plain,
    ! [X2] : lhs_atom29(X2),
    inference(fof_simplification,[status(thm)],[c_0_57]) ).

fof(c_0_155,plain,
    ! [X2] : lhs_atom28(X2),
    inference(fof_simplification,[status(thm)],[c_0_58]) ).

fof(c_0_156,plain,
    ! [X15] : lhs_atom23(X15),
    inference(fof_simplification,[status(thm)],[c_0_59]) ).

fof(c_0_157,plain,
    ! [X7] : lhs_atom18(X7),
    inference(fof_simplification,[status(thm)],[c_0_60]) ).

fof(c_0_158,plain,
    ! [X3] : lhs_atom3(X3),
    inference(fof_simplification,[status(thm)],[c_0_61]) ).

fof(c_0_159,plain,
    ! [X2] : lhs_atom2(X2),
    inference(fof_simplification,[status(thm)],[c_0_62]) ).

fof(c_0_160,plain,
    ! [X1] : lhs_atom1(X1),
    inference(fof_simplification,[status(thm)],[c_0_63]) ).

fof(c_0_161,plain,
    lhs_atom96,
    inference(fof_simplification,[status(thm)],[c_0_64]) ).

fof(c_0_162,plain,
    lhs_atom95,
    inference(fof_simplification,[status(thm)],[c_0_65]) ).

fof(c_0_163,plain,
    lhs_atom94,
    inference(fof_simplification,[status(thm)],[c_0_66]) ).

fof(c_0_164,plain,
    lhs_atom93,
    inference(fof_simplification,[status(thm)],[c_0_67]) ).

fof(c_0_165,plain,
    lhs_atom92,
    inference(fof_simplification,[status(thm)],[c_0_68]) ).

fof(c_0_166,plain,
    lhs_atom91,
    inference(fof_simplification,[status(thm)],[c_0_69]) ).

fof(c_0_167,plain,
    lhs_atom90,
    inference(fof_simplification,[status(thm)],[c_0_70]) ).

fof(c_0_168,plain,
    lhs_atom89,
    inference(fof_simplification,[status(thm)],[c_0_71]) ).

fof(c_0_169,plain,
    lhs_atom88,
    inference(fof_simplification,[status(thm)],[c_0_72]) ).

fof(c_0_170,plain,
    lhs_atom87,
    inference(fof_simplification,[status(thm)],[c_0_73]) ).

fof(c_0_171,plain,
    lhs_atom86,
    inference(fof_simplification,[status(thm)],[c_0_74]) ).

fof(c_0_172,plain,
    lhs_atom85,
    inference(fof_simplification,[status(thm)],[c_0_75]) ).

fof(c_0_173,plain,
    lhs_atom84,
    inference(fof_simplification,[status(thm)],[c_0_76]) ).

fof(c_0_174,plain,
    lhs_atom83,
    inference(fof_simplification,[status(thm)],[c_0_77]) ).

fof(c_0_175,plain,
    lhs_atom82,
    inference(fof_simplification,[status(thm)],[c_0_78]) ).

fof(c_0_176,plain,
    lhs_atom81,
    inference(fof_simplification,[status(thm)],[c_0_79]) ).

fof(c_0_177,plain,
    lhs_atom80,
    inference(fof_simplification,[status(thm)],[c_0_80]) ).

fof(c_0_178,plain,
    lhs_atom79,
    inference(fof_simplification,[status(thm)],[c_0_81]) ).

fof(c_0_179,plain,
    lhs_atom78,
    inference(fof_simplification,[status(thm)],[c_0_82]) ).

fof(c_0_180,plain,
    lhs_atom77,
    inference(fof_simplification,[status(thm)],[c_0_83]) ).

fof(c_0_181,plain,
    lhs_atom76,
    inference(fof_simplification,[status(thm)],[c_0_84]) ).

fof(c_0_182,plain,
    lhs_atom75,
    inference(fof_simplification,[status(thm)],[c_0_85]) ).

fof(c_0_183,plain,
    lhs_atom74,
    inference(fof_simplification,[status(thm)],[c_0_86]) ).

fof(c_0_184,plain,
    lhs_atom73,
    inference(fof_simplification,[status(thm)],[c_0_87]) ).

fof(c_0_185,plain,
    lhs_atom70,
    inference(fof_simplification,[status(thm)],[c_0_88]) ).

fof(c_0_186,plain,
    lhs_atom67,
    inference(fof_simplification,[status(thm)],[c_0_89]) ).

fof(c_0_187,plain,
    lhs_atom66,
    inference(fof_simplification,[status(thm)],[c_0_90]) ).

fof(c_0_188,plain,
    lhs_atom49,
    inference(fof_simplification,[status(thm)],[c_0_91]) ).

fof(c_0_189,plain,
    lhs_atom21,
    inference(fof_simplification,[status(thm)],[c_0_92]) ).

fof(c_0_190,plain,
    lhs_atom19,
    inference(fof_simplification,[status(thm)],[c_0_93]) ).

fof(c_0_191,plain,
    lhs_atom10,
    inference(fof_simplification,[status(thm)],[c_0_94]) ).

fof(c_0_192,plain,
    lhs_atom9,
    inference(fof_simplification,[status(thm)],[c_0_95]) ).

fof(c_0_193,plain,
    lhs_atom5,
    inference(fof_simplification,[status(thm)],[c_0_96]) ).

fof(c_0_194,plain,
    ! [X28,X29,X30,X31,X32] : lhs_atom69(X28,X29,X30,X31,X32),
    inference(variable_rename,[status(thm)],[c_0_97]) ).

fof(c_0_195,plain,
    ! [X28,X29,X30,X31,X32] : lhs_atom68(X28,X29,X30,X31,X32),
    inference(variable_rename,[status(thm)],[c_0_98]) ).

fof(c_0_196,plain,
    ! [X33,X34,X35,X36,X37] : lhs_atom52(X33,X34,X35,X36,X37),
    inference(variable_rename,[status(thm)],[c_0_99]) ).

fof(c_0_197,plain,
    ! [X28,X29,X30,X31] : lhs_atom57(X28,X29,X30,X31),
    inference(variable_rename,[status(thm)],[c_0_100]) ).

fof(c_0_198,plain,
    ! [X35,X36,X37,X38] : lhs_atom55(X35,X36,X37,X38),
    inference(variable_rename,[status(thm)],[c_0_101]) ).

fof(c_0_199,plain,
    ! [X33,X34,X35,X36] : lhs_atom54(X33,X34,X35,X36),
    inference(variable_rename,[status(thm)],[c_0_102]) ).

fof(c_0_200,plain,
    ! [X29,X30,X31,X32] : lhs_atom47(X29,X30,X31,X32),
    inference(variable_rename,[status(thm)],[c_0_103]) ).

fof(c_0_201,plain,
    ! [X28,X29,X30,X31] : lhs_atom46(X28,X29,X30,X31),
    inference(variable_rename,[status(thm)],[c_0_104]) ).

fof(c_0_202,plain,
    ! [X20,X21,X22,X23] : lhs_atom25(X20,X21,X22,X23),
    inference(variable_rename,[status(thm)],[c_0_105]) ).

fof(c_0_203,plain,
    ! [X8,X9,X10,X11] : lhs_atom17(X8,X9,X10,X11),
    inference(variable_rename,[status(thm)],[c_0_106]) ).

fof(c_0_204,plain,
    ! [X8,X9,X10,X11] : lhs_atom6(X8,X9,X10,X11),
    inference(variable_rename,[status(thm)],[c_0_107]) ).

fof(c_0_205,plain,
    ! [X37,X38,X39] : lhs_atom72(X37,X38,X39),
    inference(variable_rename,[status(thm)],[c_0_108]) ).

fof(c_0_206,plain,
    ! [X37,X38,X39] : lhs_atom65(X37,X38,X39),
    inference(variable_rename,[status(thm)],[c_0_109]) ).

fof(c_0_207,plain,
    ! [X34,X35,X36] : lhs_atom62(X34,X35,X36),
    inference(variable_rename,[status(thm)],[c_0_110]) ).

fof(c_0_208,plain,
    ! [X34,X35,X36] : lhs_atom61(X34,X35,X36),
    inference(variable_rename,[status(thm)],[c_0_111]) ).

fof(c_0_209,plain,
    ! [X26,X27,X28] : lhs_atom56(X26,X27,X28),
    inference(variable_rename,[status(thm)],[c_0_112]) ).

fof(c_0_210,plain,
    ! [X26,X27,X28] : lhs_atom45(X26,X27,X28),
    inference(variable_rename,[status(thm)],[c_0_113]) ).

fof(c_0_211,plain,
    ! [X20,X21,X22] : lhs_atom42(X20,X21,X22),
    inference(variable_rename,[status(thm)],[c_0_114]) ).

fof(c_0_212,plain,
    ! [X14,X15,X16] : lhs_atom37(X14,X15,X16),
    inference(variable_rename,[status(thm)],[c_0_115]) ).

fof(c_0_213,plain,
    ! [X14,X15,X16] : lhs_atom36(X14,X15,X16),
    inference(variable_rename,[status(thm)],[c_0_116]) ).

fof(c_0_214,plain,
    ! [X20,X21,X22] : lhs_atom33(X20,X21,X22),
    inference(variable_rename,[status(thm)],[c_0_117]) ).

fof(c_0_215,plain,
    ! [X14,X15,X16] : lhs_atom20(X14,X15,X16),
    inference(variable_rename,[status(thm)],[c_0_118]) ).

fof(c_0_216,plain,
    ! [X14,X15,X16] : lhs_atom16(X14,X15,X16),
    inference(variable_rename,[status(thm)],[c_0_119]) ).

fof(c_0_217,plain,
    ! [X14,X15,X16] : lhs_atom15(X14,X15,X16),
    inference(variable_rename,[status(thm)],[c_0_120]) ).

fof(c_0_218,plain,
    ! [X11,X12,X13] : lhs_atom8(X11,X12,X13),
    inference(variable_rename,[status(thm)],[c_0_121]) ).

fof(c_0_219,plain,
    ! [X9,X10,X11] : lhs_atom7(X9,X10,X11),
    inference(variable_rename,[status(thm)],[c_0_122]) ).

fof(c_0_220,plain,
    ! [X8,X9] : lhs_atom97(X8,X9),
    inference(variable_rename,[status(thm)],[c_0_123]) ).

fof(c_0_221,plain,
    ! [X38,X39] : lhs_atom71(X38,X39),
    inference(variable_rename,[status(thm)],[c_0_124]) ).

fof(c_0_222,plain,
    ! [X34,X35] : lhs_atom63(X34,X35),
    inference(variable_rename,[status(thm)],[c_0_125]) ).

fof(c_0_223,plain,
    ! [X30,X31] : lhs_atom59(X30,X31),
    inference(variable_rename,[status(thm)],[c_0_126]) ).

fof(c_0_224,plain,
    ! [X20,X21] : lhs_atom58(X20,X21),
    inference(variable_rename,[status(thm)],[c_0_127]) ).

fof(c_0_225,plain,
    ! [X34,X35] : lhs_atom53(X34,X35),
    inference(variable_rename,[status(thm)],[c_0_128]) ).

fof(c_0_226,plain,
    ! [X14,X15] : lhs_atom44(X14,X15),
    inference(variable_rename,[status(thm)],[c_0_129]) ).

fof(c_0_227,plain,
    ! [X18,X19] : lhs_atom39(X18,X19),
    inference(variable_rename,[status(thm)],[c_0_130]) ).

fof(c_0_228,plain,
    ! [X22,X23] : lhs_atom30(X22,X23),
    inference(variable_rename,[status(thm)],[c_0_131]) ).

fof(c_0_229,plain,
    ! [X19,X20] : lhs_atom27(X19,X20),
    inference(variable_rename,[status(thm)],[c_0_132]) ).

fof(c_0_230,plain,
    ! [X22,X23] : lhs_atom26(X22,X23),
    inference(variable_rename,[status(thm)],[c_0_133]) ).

fof(c_0_231,plain,
    ! [X18,X19] : lhs_atom24(X18,X19),
    inference(variable_rename,[status(thm)],[c_0_134]) ).

fof(c_0_232,plain,
    ! [X15,X16] : lhs_atom22(X15,X16),
    inference(variable_rename,[status(thm)],[c_0_135]) ).

fof(c_0_233,plain,
    ! [X4,X5] : lhs_atom14(X4,X5),
    inference(variable_rename,[status(thm)],[c_0_136]) ).

fof(c_0_234,plain,
    ! [X4,X5] : lhs_atom13(X4,X5),
    inference(variable_rename,[status(thm)],[c_0_137]) ).

fof(c_0_235,plain,
    ! [X4,X5] : lhs_atom12(X4,X5),
    inference(variable_rename,[status(thm)],[c_0_138]) ).

fof(c_0_236,plain,
    ! [X12,X13] : lhs_atom11(X12,X13),
    inference(variable_rename,[status(thm)],[c_0_139]) ).

fof(c_0_237,plain,
    ! [X4,X5] : lhs_atom4(X4,X5),
    inference(variable_rename,[status(thm)],[c_0_140]) ).

fof(c_0_238,plain,
    ! [X24] : lhs_atom64(X24),
    inference(variable_rename,[status(thm)],[c_0_141]) ).

fof(c_0_239,plain,
    ! [X24] : lhs_atom60(X24),
    inference(variable_rename,[status(thm)],[c_0_142]) ).

fof(c_0_240,plain,
    ! [X3] : lhs_atom51(X3),
    inference(variable_rename,[status(thm)],[c_0_143]) ).

fof(c_0_241,plain,
    ! [X24] : lhs_atom50(X24),
    inference(variable_rename,[status(thm)],[c_0_144]) ).

fof(c_0_242,plain,
    ! [X24] : lhs_atom48(X24),
    inference(variable_rename,[status(thm)],[c_0_145]) ).

fof(c_0_243,plain,
    ! [X14] : lhs_atom43(X14),
    inference(variable_rename,[status(thm)],[c_0_146]) ).

fof(c_0_244,plain,
    ! [X16] : lhs_atom41(X16),
    inference(variable_rename,[status(thm)],[c_0_147]) ).

fof(c_0_245,plain,
    ! [X14] : lhs_atom40(X14),
    inference(variable_rename,[status(thm)],[c_0_148]) ).

fof(c_0_246,plain,
    ! [X4] : lhs_atom38(X4),
    inference(variable_rename,[status(thm)],[c_0_149]) ).

fof(c_0_247,plain,
    ! [X23] : lhs_atom35(X23),
    inference(variable_rename,[status(thm)],[c_0_150]) ).

fof(c_0_248,plain,
    ! [X4] : lhs_atom34(X4),
    inference(variable_rename,[status(thm)],[c_0_151]) ).

fof(c_0_249,plain,
    ! [X23] : lhs_atom32(X23),
    inference(variable_rename,[status(thm)],[c_0_152]) ).

fof(c_0_250,plain,
    ! [X4] : lhs_atom31(X4),
    inference(variable_rename,[status(thm)],[c_0_153]) ).

fof(c_0_251,plain,
    ! [X3] : lhs_atom29(X3),
    inference(variable_rename,[status(thm)],[c_0_154]) ).

fof(c_0_252,plain,
    ! [X3] : lhs_atom28(X3),
    inference(variable_rename,[status(thm)],[c_0_155]) ).

fof(c_0_253,plain,
    ! [X16] : lhs_atom23(X16),
    inference(variable_rename,[status(thm)],[c_0_156]) ).

fof(c_0_254,plain,
    ! [X8] : lhs_atom18(X8),
    inference(variable_rename,[status(thm)],[c_0_157]) ).

fof(c_0_255,plain,
    ! [X4] : lhs_atom3(X4),
    inference(variable_rename,[status(thm)],[c_0_158]) ).

fof(c_0_256,plain,
    ! [X3] : lhs_atom2(X3),
    inference(variable_rename,[status(thm)],[c_0_159]) ).

fof(c_0_257,plain,
    ! [X2] : lhs_atom1(X2),
    inference(variable_rename,[status(thm)],[c_0_160]) ).

fof(c_0_258,plain,
    lhs_atom96,
    c_0_161 ).

fof(c_0_259,plain,
    lhs_atom95,
    c_0_162 ).

fof(c_0_260,plain,
    lhs_atom94,
    c_0_163 ).

fof(c_0_261,plain,
    lhs_atom93,
    c_0_164 ).

fof(c_0_262,plain,
    lhs_atom92,
    c_0_165 ).

fof(c_0_263,plain,
    lhs_atom91,
    c_0_166 ).

fof(c_0_264,plain,
    lhs_atom90,
    c_0_167 ).

fof(c_0_265,plain,
    lhs_atom89,
    c_0_168 ).

fof(c_0_266,plain,
    lhs_atom88,
    c_0_169 ).

fof(c_0_267,plain,
    lhs_atom87,
    c_0_170 ).

fof(c_0_268,plain,
    lhs_atom86,
    c_0_171 ).

fof(c_0_269,plain,
    lhs_atom85,
    c_0_172 ).

fof(c_0_270,plain,
    lhs_atom84,
    c_0_173 ).

fof(c_0_271,plain,
    lhs_atom83,
    c_0_174 ).

fof(c_0_272,plain,
    lhs_atom82,
    c_0_175 ).

fof(c_0_273,plain,
    lhs_atom81,
    c_0_176 ).

fof(c_0_274,plain,
    lhs_atom80,
    c_0_177 ).

fof(c_0_275,plain,
    lhs_atom79,
    c_0_178 ).

fof(c_0_276,plain,
    lhs_atom78,
    c_0_179 ).

fof(c_0_277,plain,
    lhs_atom77,
    c_0_180 ).

fof(c_0_278,plain,
    lhs_atom76,
    c_0_181 ).

fof(c_0_279,plain,
    lhs_atom75,
    c_0_182 ).

fof(c_0_280,plain,
    lhs_atom74,
    c_0_183 ).

fof(c_0_281,plain,
    lhs_atom73,
    c_0_184 ).

fof(c_0_282,plain,
    lhs_atom70,
    c_0_185 ).

fof(c_0_283,plain,
    lhs_atom67,
    c_0_186 ).

fof(c_0_284,plain,
    lhs_atom66,
    c_0_187 ).

fof(c_0_285,plain,
    lhs_atom49,
    c_0_188 ).

fof(c_0_286,plain,
    lhs_atom21,
    c_0_189 ).

fof(c_0_287,plain,
    lhs_atom19,
    c_0_190 ).

fof(c_0_288,plain,
    lhs_atom10,
    c_0_191 ).

fof(c_0_289,plain,
    lhs_atom9,
    c_0_192 ).

fof(c_0_290,plain,
    lhs_atom5,
    c_0_193 ).

cnf(c_0_291,plain,
    lhs_atom69(X1,X2,X3,X4,X5),
    inference(split_conjunct,[status(thm)],[c_0_194]) ).

cnf(c_0_292,plain,
    lhs_atom68(X1,X2,X3,X4,X5),
    inference(split_conjunct,[status(thm)],[c_0_195]) ).

cnf(c_0_293,plain,
    lhs_atom52(X1,X2,X3,X4,X5),
    inference(split_conjunct,[status(thm)],[c_0_196]) ).

cnf(c_0_294,plain,
    lhs_atom57(X1,X2,X3,X4),
    inference(split_conjunct,[status(thm)],[c_0_197]) ).

cnf(c_0_295,plain,
    lhs_atom55(X1,X2,X3,X4),
    inference(split_conjunct,[status(thm)],[c_0_198]) ).

cnf(c_0_296,plain,
    lhs_atom54(X1,X2,X3,X4),
    inference(split_conjunct,[status(thm)],[c_0_199]) ).

cnf(c_0_297,plain,
    lhs_atom47(X1,X2,X3,X4),
    inference(split_conjunct,[status(thm)],[c_0_200]) ).

cnf(c_0_298,plain,
    lhs_atom46(X1,X2,X3,X4),
    inference(split_conjunct,[status(thm)],[c_0_201]) ).

cnf(c_0_299,plain,
    lhs_atom25(X1,X2,X3,X4),
    inference(split_conjunct,[status(thm)],[c_0_202]) ).

cnf(c_0_300,plain,
    lhs_atom17(X1,X2,X3,X4),
    inference(split_conjunct,[status(thm)],[c_0_203]) ).

cnf(c_0_301,plain,
    lhs_atom6(X1,X2,X3,X4),
    inference(split_conjunct,[status(thm)],[c_0_204]) ).

cnf(c_0_302,plain,
    lhs_atom72(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_205]) ).

cnf(c_0_303,plain,
    lhs_atom65(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_206]) ).

cnf(c_0_304,plain,
    lhs_atom62(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_207]) ).

cnf(c_0_305,plain,
    lhs_atom61(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_208]) ).

cnf(c_0_306,plain,
    lhs_atom56(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_209]) ).

cnf(c_0_307,plain,
    lhs_atom45(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_210]) ).

cnf(c_0_308,plain,
    lhs_atom42(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_211]) ).

cnf(c_0_309,plain,
    lhs_atom37(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_212]) ).

cnf(c_0_310,plain,
    lhs_atom36(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_213]) ).

cnf(c_0_311,plain,
    lhs_atom33(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_214]) ).

cnf(c_0_312,plain,
    lhs_atom20(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_215]) ).

cnf(c_0_313,plain,
    lhs_atom16(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_216]) ).

cnf(c_0_314,plain,
    lhs_atom15(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_217]) ).

cnf(c_0_315,plain,
    lhs_atom8(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_218]) ).

cnf(c_0_316,plain,
    lhs_atom7(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_219]) ).

cnf(c_0_317,plain,
    lhs_atom97(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_220]) ).

cnf(c_0_318,plain,
    lhs_atom71(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_221]) ).

cnf(c_0_319,plain,
    lhs_atom63(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_222]) ).

cnf(c_0_320,plain,
    lhs_atom59(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_223]) ).

cnf(c_0_321,plain,
    lhs_atom58(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_224]) ).

cnf(c_0_322,plain,
    lhs_atom53(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_225]) ).

cnf(c_0_323,plain,
    lhs_atom44(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_226]) ).

cnf(c_0_324,plain,
    lhs_atom39(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_227]) ).

cnf(c_0_325,plain,
    lhs_atom30(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_228]) ).

cnf(c_0_326,plain,
    lhs_atom27(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_229]) ).

cnf(c_0_327,plain,
    lhs_atom26(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_230]) ).

cnf(c_0_328,plain,
    lhs_atom24(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_231]) ).

cnf(c_0_329,plain,
    lhs_atom22(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_232]) ).

cnf(c_0_330,plain,
    lhs_atom14(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_233]) ).

cnf(c_0_331,plain,
    lhs_atom13(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_234]) ).

cnf(c_0_332,plain,
    lhs_atom12(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_235]) ).

cnf(c_0_333,plain,
    lhs_atom11(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_236]) ).

cnf(c_0_334,plain,
    lhs_atom4(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_237]) ).

cnf(c_0_335,plain,
    lhs_atom64(X1),
    inference(split_conjunct,[status(thm)],[c_0_238]) ).

cnf(c_0_336,plain,
    lhs_atom60(X1),
    inference(split_conjunct,[status(thm)],[c_0_239]) ).

cnf(c_0_337,plain,
    lhs_atom51(X1),
    inference(split_conjunct,[status(thm)],[c_0_240]) ).

cnf(c_0_338,plain,
    lhs_atom50(X1),
    inference(split_conjunct,[status(thm)],[c_0_241]) ).

cnf(c_0_339,plain,
    lhs_atom48(X1),
    inference(split_conjunct,[status(thm)],[c_0_242]) ).

cnf(c_0_340,plain,
    lhs_atom43(X1),
    inference(split_conjunct,[status(thm)],[c_0_243]) ).

cnf(c_0_341,plain,
    lhs_atom41(X1),
    inference(split_conjunct,[status(thm)],[c_0_244]) ).

cnf(c_0_342,plain,
    lhs_atom40(X1),
    inference(split_conjunct,[status(thm)],[c_0_245]) ).

cnf(c_0_343,plain,
    lhs_atom38(X1),
    inference(split_conjunct,[status(thm)],[c_0_246]) ).

cnf(c_0_344,plain,
    lhs_atom35(X1),
    inference(split_conjunct,[status(thm)],[c_0_247]) ).

cnf(c_0_345,plain,
    lhs_atom34(X1),
    inference(split_conjunct,[status(thm)],[c_0_248]) ).

cnf(c_0_346,plain,
    lhs_atom32(X1),
    inference(split_conjunct,[status(thm)],[c_0_249]) ).

cnf(c_0_347,plain,
    lhs_atom31(X1),
    inference(split_conjunct,[status(thm)],[c_0_250]) ).

cnf(c_0_348,plain,
    lhs_atom29(X1),
    inference(split_conjunct,[status(thm)],[c_0_251]) ).

cnf(c_0_349,plain,
    lhs_atom28(X1),
    inference(split_conjunct,[status(thm)],[c_0_252]) ).

cnf(c_0_350,plain,
    lhs_atom23(X1),
    inference(split_conjunct,[status(thm)],[c_0_253]) ).

cnf(c_0_351,plain,
    lhs_atom18(X1),
    inference(split_conjunct,[status(thm)],[c_0_254]) ).

cnf(c_0_352,plain,
    lhs_atom3(X1),
    inference(split_conjunct,[status(thm)],[c_0_255]) ).

cnf(c_0_353,plain,
    lhs_atom2(X1),
    inference(split_conjunct,[status(thm)],[c_0_256]) ).

cnf(c_0_354,plain,
    lhs_atom1(X1),
    inference(split_conjunct,[status(thm)],[c_0_257]) ).

cnf(c_0_355,plain,
    lhs_atom96,
    inference(split_conjunct,[status(thm)],[c_0_258]) ).

cnf(c_0_356,plain,
    lhs_atom95,
    inference(split_conjunct,[status(thm)],[c_0_259]) ).

cnf(c_0_357,plain,
    lhs_atom94,
    inference(split_conjunct,[status(thm)],[c_0_260]) ).

cnf(c_0_358,plain,
    lhs_atom93,
    inference(split_conjunct,[status(thm)],[c_0_261]) ).

cnf(c_0_359,plain,
    lhs_atom92,
    inference(split_conjunct,[status(thm)],[c_0_262]) ).

cnf(c_0_360,plain,
    lhs_atom91,
    inference(split_conjunct,[status(thm)],[c_0_263]) ).

cnf(c_0_361,plain,
    lhs_atom90,
    inference(split_conjunct,[status(thm)],[c_0_264]) ).

cnf(c_0_362,plain,
    lhs_atom89,
    inference(split_conjunct,[status(thm)],[c_0_265]) ).

cnf(c_0_363,plain,
    lhs_atom88,
    inference(split_conjunct,[status(thm)],[c_0_266]) ).

cnf(c_0_364,plain,
    lhs_atom87,
    inference(split_conjunct,[status(thm)],[c_0_267]) ).

cnf(c_0_365,plain,
    lhs_atom86,
    inference(split_conjunct,[status(thm)],[c_0_268]) ).

cnf(c_0_366,plain,
    lhs_atom85,
    inference(split_conjunct,[status(thm)],[c_0_269]) ).

cnf(c_0_367,plain,
    lhs_atom84,
    inference(split_conjunct,[status(thm)],[c_0_270]) ).

cnf(c_0_368,plain,
    lhs_atom83,
    inference(split_conjunct,[status(thm)],[c_0_271]) ).

cnf(c_0_369,plain,
    lhs_atom82,
    inference(split_conjunct,[status(thm)],[c_0_272]) ).

cnf(c_0_370,plain,
    lhs_atom81,
    inference(split_conjunct,[status(thm)],[c_0_273]) ).

cnf(c_0_371,plain,
    lhs_atom80,
    inference(split_conjunct,[status(thm)],[c_0_274]) ).

cnf(c_0_372,plain,
    lhs_atom79,
    inference(split_conjunct,[status(thm)],[c_0_275]) ).

cnf(c_0_373,plain,
    lhs_atom78,
    inference(split_conjunct,[status(thm)],[c_0_276]) ).

cnf(c_0_374,plain,
    lhs_atom77,
    inference(split_conjunct,[status(thm)],[c_0_277]) ).

cnf(c_0_375,plain,
    lhs_atom76,
    inference(split_conjunct,[status(thm)],[c_0_278]) ).

cnf(c_0_376,plain,
    lhs_atom75,
    inference(split_conjunct,[status(thm)],[c_0_279]) ).

cnf(c_0_377,plain,
    lhs_atom74,
    inference(split_conjunct,[status(thm)],[c_0_280]) ).

cnf(c_0_378,plain,
    lhs_atom73,
    inference(split_conjunct,[status(thm)],[c_0_281]) ).

cnf(c_0_379,plain,
    lhs_atom70,
    inference(split_conjunct,[status(thm)],[c_0_282]) ).

cnf(c_0_380,plain,
    lhs_atom67,
    inference(split_conjunct,[status(thm)],[c_0_283]) ).

cnf(c_0_381,plain,
    lhs_atom66,
    inference(split_conjunct,[status(thm)],[c_0_284]) ).

cnf(c_0_382,plain,
    lhs_atom49,
    inference(split_conjunct,[status(thm)],[c_0_285]) ).

cnf(c_0_383,plain,
    lhs_atom21,
    inference(split_conjunct,[status(thm)],[c_0_286]) ).

cnf(c_0_384,plain,
    lhs_atom19,
    inference(split_conjunct,[status(thm)],[c_0_287]) ).

cnf(c_0_385,plain,
    lhs_atom10,
    inference(split_conjunct,[status(thm)],[c_0_288]) ).

cnf(c_0_386,plain,
    lhs_atom9,
    inference(split_conjunct,[status(thm)],[c_0_289]) ).

cnf(c_0_387,plain,
    lhs_atom5,
    inference(split_conjunct,[status(thm)],[c_0_290]) ).

cnf(c_0_388,plain,
    lhs_atom69(X1,X2,X3,X4,X5),
    c_0_291,
    [final] ).

cnf(c_0_389,plain,
    lhs_atom68(X1,X2,X3,X4,X5),
    c_0_292,
    [final] ).

cnf(c_0_390,plain,
    lhs_atom52(X1,X2,X3,X4,X5),
    c_0_293,
    [final] ).

cnf(c_0_391,plain,
    lhs_atom57(X1,X2,X3,X4),
    c_0_294,
    [final] ).

cnf(c_0_392,plain,
    lhs_atom55(X1,X2,X3,X4),
    c_0_295,
    [final] ).

cnf(c_0_393,plain,
    lhs_atom54(X1,X2,X3,X4),
    c_0_296,
    [final] ).

cnf(c_0_394,plain,
    lhs_atom47(X1,X2,X3,X4),
    c_0_297,
    [final] ).

cnf(c_0_395,plain,
    lhs_atom46(X1,X2,X3,X4),
    c_0_298,
    [final] ).

cnf(c_0_396,plain,
    lhs_atom25(X1,X2,X3,X4),
    c_0_299,
    [final] ).

cnf(c_0_397,plain,
    lhs_atom17(X1,X2,X3,X4),
    c_0_300,
    [final] ).

cnf(c_0_398,plain,
    lhs_atom6(X1,X2,X3,X4),
    c_0_301,
    [final] ).

cnf(c_0_399,plain,
    lhs_atom72(X1,X2,X3),
    c_0_302,
    [final] ).

cnf(c_0_400,plain,
    lhs_atom65(X1,X2,X3),
    c_0_303,
    [final] ).

cnf(c_0_401,plain,
    lhs_atom62(X1,X2,X3),
    c_0_304,
    [final] ).

cnf(c_0_402,plain,
    lhs_atom61(X1,X2,X3),
    c_0_305,
    [final] ).

cnf(c_0_403,plain,
    lhs_atom56(X1,X2,X3),
    c_0_306,
    [final] ).

cnf(c_0_404,plain,
    lhs_atom45(X1,X2,X3),
    c_0_307,
    [final] ).

cnf(c_0_405,plain,
    lhs_atom42(X1,X2,X3),
    c_0_308,
    [final] ).

cnf(c_0_406,plain,
    lhs_atom37(X1,X2,X3),
    c_0_309,
    [final] ).

cnf(c_0_407,plain,
    lhs_atom36(X1,X2,X3),
    c_0_310,
    [final] ).

cnf(c_0_408,plain,
    lhs_atom33(X1,X2,X3),
    c_0_311,
    [final] ).

cnf(c_0_409,plain,
    lhs_atom20(X1,X2,X3),
    c_0_312,
    [final] ).

cnf(c_0_410,plain,
    lhs_atom16(X1,X2,X3),
    c_0_313,
    [final] ).

cnf(c_0_411,plain,
    lhs_atom15(X1,X2,X3),
    c_0_314,
    [final] ).

cnf(c_0_412,plain,
    lhs_atom8(X1,X2,X3),
    c_0_315,
    [final] ).

cnf(c_0_413,plain,
    lhs_atom7(X1,X2,X3),
    c_0_316,
    [final] ).

cnf(c_0_414,plain,
    lhs_atom97(X1,X2),
    c_0_317,
    [final] ).

cnf(c_0_415,plain,
    lhs_atom71(X1,X2),
    c_0_318,
    [final] ).

cnf(c_0_416,plain,
    lhs_atom63(X1,X2),
    c_0_319,
    [final] ).

cnf(c_0_417,plain,
    lhs_atom59(X1,X2),
    c_0_320,
    [final] ).

cnf(c_0_418,plain,
    lhs_atom58(X1,X2),
    c_0_321,
    [final] ).

cnf(c_0_419,plain,
    lhs_atom53(X1,X2),
    c_0_322,
    [final] ).

cnf(c_0_420,plain,
    lhs_atom44(X1,X2),
    c_0_323,
    [final] ).

cnf(c_0_421,plain,
    lhs_atom39(X1,X2),
    c_0_324,
    [final] ).

cnf(c_0_422,plain,
    lhs_atom30(X1,X2),
    c_0_325,
    [final] ).

cnf(c_0_423,plain,
    lhs_atom27(X1,X2),
    c_0_326,
    [final] ).

cnf(c_0_424,plain,
    lhs_atom26(X1,X2),
    c_0_327,
    [final] ).

cnf(c_0_425,plain,
    lhs_atom24(X1,X2),
    c_0_328,
    [final] ).

cnf(c_0_426,plain,
    lhs_atom22(X1,X2),
    c_0_329,
    [final] ).

cnf(c_0_427,plain,
    lhs_atom14(X1,X2),
    c_0_330,
    [final] ).

cnf(c_0_428,plain,
    lhs_atom13(X1,X2),
    c_0_331,
    [final] ).

cnf(c_0_429,plain,
    lhs_atom12(X1,X2),
    c_0_332,
    [final] ).

cnf(c_0_430,plain,
    lhs_atom11(X1,X2),
    c_0_333,
    [final] ).

cnf(c_0_431,plain,
    lhs_atom4(X1,X2),
    c_0_334,
    [final] ).

cnf(c_0_432,plain,
    lhs_atom64(X1),
    c_0_335,
    [final] ).

cnf(c_0_433,plain,
    lhs_atom60(X1),
    c_0_336,
    [final] ).

cnf(c_0_434,plain,
    lhs_atom51(X1),
    c_0_337,
    [final] ).

cnf(c_0_435,plain,
    lhs_atom50(X1),
    c_0_338,
    [final] ).

cnf(c_0_436,plain,
    lhs_atom48(X1),
    c_0_339,
    [final] ).

cnf(c_0_437,plain,
    lhs_atom43(X1),
    c_0_340,
    [final] ).

cnf(c_0_438,plain,
    lhs_atom41(X1),
    c_0_341,
    [final] ).

cnf(c_0_439,plain,
    lhs_atom40(X1),
    c_0_342,
    [final] ).

cnf(c_0_440,plain,
    lhs_atom38(X1),
    c_0_343,
    [final] ).

cnf(c_0_441,plain,
    lhs_atom35(X1),
    c_0_344,
    [final] ).

cnf(c_0_442,plain,
    lhs_atom34(X1),
    c_0_345,
    [final] ).

cnf(c_0_443,plain,
    lhs_atom32(X1),
    c_0_346,
    [final] ).

cnf(c_0_444,plain,
    lhs_atom31(X1),
    c_0_347,
    [final] ).

cnf(c_0_445,plain,
    lhs_atom29(X1),
    c_0_348,
    [final] ).

cnf(c_0_446,plain,
    lhs_atom28(X1),
    c_0_349,
    [final] ).

cnf(c_0_447,plain,
    lhs_atom23(X1),
    c_0_350,
    [final] ).

cnf(c_0_448,plain,
    lhs_atom18(X1),
    c_0_351,
    [final] ).

cnf(c_0_449,plain,
    lhs_atom3(X1),
    c_0_352,
    [final] ).

cnf(c_0_450,plain,
    lhs_atom2(X1),
    c_0_353,
    [final] ).

cnf(c_0_451,plain,
    lhs_atom1(X1),
    c_0_354,
    [final] ).

cnf(c_0_452,plain,
    lhs_atom96,
    c_0_355,
    [final] ).

cnf(c_0_453,plain,
    lhs_atom95,
    c_0_356,
    [final] ).

cnf(c_0_454,plain,
    lhs_atom94,
    c_0_357,
    [final] ).

cnf(c_0_455,plain,
    lhs_atom93,
    c_0_358,
    [final] ).

cnf(c_0_456,plain,
    lhs_atom92,
    c_0_359,
    [final] ).

cnf(c_0_457,plain,
    lhs_atom91,
    c_0_360,
    [final] ).

cnf(c_0_458,plain,
    lhs_atom90,
    c_0_361,
    [final] ).

cnf(c_0_459,plain,
    lhs_atom89,
    c_0_362,
    [final] ).

cnf(c_0_460,plain,
    lhs_atom88,
    c_0_363,
    [final] ).

cnf(c_0_461,plain,
    lhs_atom87,
    c_0_364,
    [final] ).

cnf(c_0_462,plain,
    lhs_atom86,
    c_0_365,
    [final] ).

cnf(c_0_463,plain,
    lhs_atom85,
    c_0_366,
    [final] ).

cnf(c_0_464,plain,
    lhs_atom84,
    c_0_367,
    [final] ).

cnf(c_0_465,plain,
    lhs_atom83,
    c_0_368,
    [final] ).

cnf(c_0_466,plain,
    lhs_atom82,
    c_0_369,
    [final] ).

cnf(c_0_467,plain,
    lhs_atom81,
    c_0_370,
    [final] ).

cnf(c_0_468,plain,
    lhs_atom80,
    c_0_371,
    [final] ).

cnf(c_0_469,plain,
    lhs_atom79,
    c_0_372,
    [final] ).

cnf(c_0_470,plain,
    lhs_atom78,
    c_0_373,
    [final] ).

cnf(c_0_471,plain,
    lhs_atom77,
    c_0_374,
    [final] ).

cnf(c_0_472,plain,
    lhs_atom76,
    c_0_375,
    [final] ).

cnf(c_0_473,plain,
    lhs_atom75,
    c_0_376,
    [final] ).

cnf(c_0_474,plain,
    lhs_atom74,
    c_0_377,
    [final] ).

cnf(c_0_475,plain,
    lhs_atom73,
    c_0_378,
    [final] ).

cnf(c_0_476,plain,
    lhs_atom70,
    c_0_379,
    [final] ).

cnf(c_0_477,plain,
    lhs_atom67,
    c_0_380,
    [final] ).

cnf(c_0_478,plain,
    lhs_atom66,
    c_0_381,
    [final] ).

cnf(c_0_479,plain,
    lhs_atom49,
    c_0_382,
    [final] ).

cnf(c_0_480,plain,
    lhs_atom21,
    c_0_383,
    [final] ).

cnf(c_0_481,plain,
    lhs_atom19,
    c_0_384,
    [final] ).

cnf(c_0_482,plain,
    lhs_atom10,
    c_0_385,
    [final] ).

cnf(c_0_483,plain,
    lhs_atom9,
    c_0_386,
    [final] ).

cnf(c_0_484,plain,
    lhs_atom5,
    c_0_387,
    [final] ).

% End CNF derivation
cnf(c_0_388_0,axiom,
    c_Type_Otype_Otype__case(X4,X3,hAPP(hAPP(c_Type_Otype_OFun,X2),X1),X5) = hAPP(hAPP(X3,X2),X1),
    inference(unfold_definition,[status(thm)],[c_0_388,def_lhs_atom69]) ).

cnf(c_0_389_0,axiom,
    c_Type_Otype_Otype__rec(X4,X3,hAPP(hAPP(c_Type_Otype_OFun,X2),X1),X5) = hAPP(hAPP(hAPP(hAPP(X3,X2),X1),c_Type_Otype_Otype__rec(X4,X3,X2,X5)),c_Type_Otype_Otype__rec(X4,X3,X1,X5)),
    inference(unfold_definition,[status(thm)],[c_0_389,def_lhs_atom68]) ).

cnf(c_0_390_0,axiom,
    c_Type_Oshift(c_Type_Oshift(X2,X1,X3,X5),c_HOL_Ozero__class_Ozero(tc_nat),X4,X5) = c_Type_Oshift(c_Type_Oshift(X2,c_HOL_Ozero__class_Ozero(tc_nat),X4,X5),c_Suc(X1),X3,X5),
    inference(unfold_definition,[status(thm)],[c_0_390,def_lhs_atom52]) ).

cnf(c_0_391_0,axiom,
    c_Type_Otype_Otype__rec(X3,X2,c_Type_Otype_OAtom(X1),X4) = hAPP(X3,X1),
    inference(unfold_definition,[status(thm)],[c_0_391,def_lhs_atom57]) ).

cnf(c_0_392_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_392,def_lhs_atom55]) ).

cnf(c_0_393_0,axiom,
    hAPP(c_Type_Oshift(X2,X1,X3,X4),X1) = X3,
    inference(unfold_definition,[status(thm)],[c_0_393,def_lhs_atom54]) ).

cnf(c_0_394_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_394,def_lhs_atom47]) ).

cnf(c_0_395_0,axiom,
    c_Type_Otype_Otype__case(X3,X2,c_Type_Otype_OAtom(X1),X4) = hAPP(X3,X1),
    inference(unfold_definition,[status(thm)],[c_0_395,def_lhs_atom46]) ).

cnf(c_0_396_0,axiom,
    c_Lambda_Osubst(hAPP(hAPP(c_Lambda_OdB_OApp,X2),X1),X3,X4) = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Osubst(X2,X3,X4)),c_Lambda_Osubst(X1,X3,X4)),
    inference(unfold_definition,[status(thm)],[c_0_396,def_lhs_atom25]) ).

cnf(c_0_397_0,axiom,
    c_List_Ofoldl(X1,X2,c_List_Olist_ONil(X3),X4,X3) = X2,
    inference(unfold_definition,[status(thm)],[c_0_397,def_lhs_atom17]) ).

cnf(c_0_398_0,axiom,
    c_List_Ofoldr(X1,c_List_Olist_ONil(X3),X2,X3,X4) = X2,
    inference(unfold_definition,[status(thm)],[c_0_398,def_lhs_atom6]) ).

cnf(c_0_399_0,axiom,
    c_Type_Otype_OAtom(X3) != hAPP(hAPP(c_Type_Otype_OFun,X2),X1),
    inference(unfold_definition,[status(thm)],[c_0_399,def_lhs_atom72]) ).

cnf(c_0_400_0,axiom,
    hAPP(hAPP(c_Type_Otype_OFun,X2),X1) != c_Type_Otype_OAtom(X3),
    inference(unfold_definition,[status(thm)],[c_0_400,def_lhs_atom65]) ).

cnf(c_0_401_0,axiom,
    hAPP(hAPP(c_Lambda_OdB_OApp,X3),X2) != c_Lambda_OdB_OAbs(X1),
    inference(unfold_definition,[status(thm)],[c_0_401,def_lhs_atom62]) ).

cnf(c_0_402_0,axiom,
    c_Lambda_OdB_OAbs(X1) != hAPP(hAPP(c_Lambda_OdB_OApp,X3),X2),
    inference(unfold_definition,[status(thm)],[c_0_402,def_lhs_atom61]) ).

cnf(c_0_403_0,axiom,
    c_Lambda_OdB_OVar(X1) != hAPP(hAPP(c_Lambda_OdB_OApp,X3),X2),
    inference(unfold_definition,[status(thm)],[c_0_403,def_lhs_atom56]) ).

cnf(c_0_404_0,axiom,
    hAPP(hAPP(c_Lambda_OdB_OApp,X3),X2) != c_Lambda_OdB_OVar(X1),
    inference(unfold_definition,[status(thm)],[c_0_404,def_lhs_atom45]) ).

cnf(c_0_405_0,axiom,
    c_Lambda_Osubst(c_Lambda_Olift(X1,X3),X2,X3) = X1,
    inference(unfold_definition,[status(thm)],[c_0_405,def_lhs_atom42]) ).

cnf(c_0_406_0,axiom,
    hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X3),X2),X2)),
    inference(unfold_definition,[status(thm)],[c_0_406,def_lhs_atom37]) ).

cnf(c_0_407_0,axiom,
    hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X2,X3),X1),X1)),
    inference(unfold_definition,[status(thm)],[c_0_407,def_lhs_atom36]) ).

cnf(c_0_408_0,axiom,
    c_Lambda_Olift(hAPP(hAPP(c_Lambda_OdB_OApp,X2),X1),X3) = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Olift(X2,X3)),c_Lambda_Olift(X1,X3)),
    inference(unfold_definition,[status(thm)],[c_0_408,def_lhs_atom33]) ).

cnf(c_0_409_0,axiom,
    c_Predicate_Oconversep(c_Predicate_Oconversep(X1,X3,X2),X2,X3) = X1,
    inference(unfold_definition,[status(thm)],[c_0_409,def_lhs_atom20]) ).

cnf(c_0_410_0,axiom,
    ~ c_ListOrder_Ostep1(X2,X1,c_List_Olist_ONil(X3),X3),
    inference(unfold_definition,[status(thm)],[c_0_410,def_lhs_atom16]) ).

cnf(c_0_411_0,axiom,
    ~ c_ListOrder_Ostep1(X2,c_List_Olist_ONil(X3),X1,X3),
    inference(unfold_definition,[status(thm)],[c_0_411,def_lhs_atom15]) ).

cnf(c_0_412_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_412,def_lhs_atom8]) ).

cnf(c_0_413_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_413,def_lhs_atom7]) ).

cnf(c_0_414_0,axiom,
    hBOOL(hAPP(hAPP(c_fequal(X2),X1),X1)),
    inference(unfold_definition,[status(thm)],[c_0_414,def_lhs_atom97]) ).

cnf(c_0_415_0,axiom,
    c_Type_Otyping(X2,c_Lambda_OdB_OVar(X1),hAPP(X2,X1)),
    inference(unfold_definition,[status(thm)],[c_0_415,def_lhs_atom71]) ).

cnf(c_0_416_0,axiom,
    c_Lambda_OdB_OAbs(X2) != c_Lambda_OdB_OVar(X1),
    inference(unfold_definition,[status(thm)],[c_0_416,def_lhs_atom63]) ).

cnf(c_0_417_0,axiom,
    ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OVar(X2)),X1)),
    inference(unfold_definition,[status(thm)],[c_0_417,def_lhs_atom59]) ).

cnf(c_0_418_0,axiom,
    hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X2)),X1)),c_Lambda_Osubst(X2,X1,c_HOL_Ozero__class_Ozero(tc_nat)))),
    inference(unfold_definition,[status(thm)],[c_0_418,def_lhs_atom58]) ).

cnf(c_0_419_0,axiom,
    c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OAbs(X2),
    inference(unfold_definition,[status(thm)],[c_0_419,def_lhs_atom53]) ).

cnf(c_0_420_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_420,def_lhs_atom44]) ).

cnf(c_0_421_0,axiom,
    c_Nat_Osize__class_Osize(hAPP(hAPP(c_Lambda_OdB_OApp,X2),X1),tc_Lambda_OdB) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(X2,tc_Lambda_OdB)),c_Nat_Osize__class_Osize(X1,tc_Lambda_OdB))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
    inference(unfold_definition,[status(thm)],[c_0_421,def_lhs_atom39]) ).

cnf(c_0_422_0,axiom,
    c_Type_Otype_Otype__size(hAPP(hAPP(c_Type_Otype_OFun,X2),X1)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Type_Otype_Otype__size(X2)),c_Type_Otype_Otype__size(X1))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
    inference(unfold_definition,[status(thm)],[c_0_422,def_lhs_atom30]) ).

cnf(c_0_423_0,axiom,
    c_Lambda_Osubst(c_Lambda_OdB_OVar(X2),X1,X2) = X1,
    inference(unfold_definition,[status(thm)],[c_0_423,def_lhs_atom27]) ).

cnf(c_0_424_0,axiom,
    c_Nat_Osize__class_Osize(hAPP(hAPP(c_Type_Otype_OFun,X2),X1),tc_Type_Otype) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(X2,tc_Type_Otype)),c_Nat_Osize__class_Osize(X1,tc_Type_Otype))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
    inference(unfold_definition,[status(thm)],[c_0_424,def_lhs_atom26]) ).

cnf(c_0_425_0,axiom,
    c_Lambda_OdB_OdB__size(hAPP(hAPP(c_Lambda_OdB_OApp,X2),X1)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(X2)),c_Lambda_OdB_OdB__size(X1))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
    inference(unfold_definition,[status(thm)],[c_0_425,def_lhs_atom24]) ).

cnf(c_0_426_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_426,def_lhs_atom22]) ).

cnf(c_0_427_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_427,def_lhs_atom14]) ).

cnf(c_0_428_0,axiom,
    hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(X2)),X1) = c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1)),
    inference(unfold_definition,[status(thm)],[c_0_428,def_lhs_atom13]) ).

cnf(c_0_429_0,axiom,
    hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_Suc(X1)) = c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1)),
    inference(unfold_definition,[status(thm)],[c_0_429,def_lhs_atom12]) ).

cnf(c_0_430_0,axiom,
    c_List_Olistsp(X1,c_List_Olist_ONil(X2),X2),
    inference(unfold_definition,[status(thm)],[c_0_430,def_lhs_atom11]) ).

cnf(c_0_431_0,axiom,
    hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(X2)),X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_Suc(X1)),
    inference(unfold_definition,[status(thm)],[c_0_431,def_lhs_atom4]) ).

cnf(c_0_432_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_432,def_lhs_atom64]) ).

cnf(c_0_433_0,axiom,
    c_Nat_Osize__class_Osize(c_Type_Otype_OAtom(X1),tc_Type_Otype) = c_HOL_Ozero__class_Ozero(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_433,def_lhs_atom60]) ).

cnf(c_0_434_0,axiom,
    hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(X1))),
    inference(unfold_definition,[status(thm)],[c_0_434,def_lhs_atom51]) ).

cnf(c_0_435_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_435,def_lhs_atom50]) ).

cnf(c_0_436_0,axiom,
    c_Type_Otype_Otype__size(c_Type_Otype_OAtom(X1)) = c_HOL_Ozero__class_Ozero(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_436,def_lhs_atom48]) ).

cnf(c_0_437_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_437,def_lhs_atom43]) ).

cnf(c_0_438_0,axiom,
    c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(X1),tc_Lambda_OdB) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(X1,tc_Lambda_OdB)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
    inference(unfold_definition,[status(thm)],[c_0_438,def_lhs_atom41]) ).

cnf(c_0_439_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_439,def_lhs_atom40]) ).

cnf(c_0_440_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_440,def_lhs_atom38]) ).

cnf(c_0_441_0,axiom,
    c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X1),
    inference(unfold_definition,[status(thm)],[c_0_441,def_lhs_atom35]) ).

cnf(c_0_442_0,axiom,
    c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X1),
    inference(unfold_definition,[status(thm)],[c_0_442,def_lhs_atom34]) ).

cnf(c_0_443_0,axiom,
    c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_443,def_lhs_atom32]) ).

cnf(c_0_444_0,axiom,
    c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_444,def_lhs_atom31]) ).

cnf(c_0_445_0,axiom,
    c_Suc(X1) != X1,
    inference(unfold_definition,[status(thm)],[c_0_445,def_lhs_atom29]) ).

cnf(c_0_446_0,axiom,
    X1 != c_Suc(X1),
    inference(unfold_definition,[status(thm)],[c_0_446,def_lhs_atom28]) ).

cnf(c_0_447_0,axiom,
    c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X1)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(X1)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
    inference(unfold_definition,[status(thm)],[c_0_447,def_lhs_atom23]) ).

cnf(c_0_448_0,axiom,
    c_Predicate_Oconversep(c_fequal(X1),X1,X1) = c_fequal(X1),
    inference(unfold_definition,[status(thm)],[c_0_448,def_lhs_atom18]) ).

cnf(c_0_449_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_449,def_lhs_atom3]) ).

cnf(c_0_450_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_450,def_lhs_atom2]) ).

cnf(c_0_451_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_451,def_lhs_atom1]) ).

cnf(c_0_452_0,axiom,
    class_Orderings_Oorder(tc_bool),
    inference(unfold_definition,[status(thm)],[c_0_452,def_lhs_atom96]) ).

cnf(c_0_453_0,axiom,
    class_Orderings_Opreorder(tc_bool),
    inference(unfold_definition,[status(thm)],[c_0_453,def_lhs_atom95]) ).

cnf(c_0_454_0,axiom,
    class_Power_Opower(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_454,def_lhs_atom94]) ).

cnf(c_0_455_0,axiom,
    class_Orderings_Oorder(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_455,def_lhs_atom93]) ).

cnf(c_0_456_0,axiom,
    class_Orderings_Olinorder(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_456,def_lhs_atom92]) ).

cnf(c_0_457_0,axiom,
    class_Orderings_Opreorder(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_457,def_lhs_atom91]) ).

cnf(c_0_458_0,axiom,
    class_Nat_Osemiring__char__0(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_458,def_lhs_atom90]) ).

cnf(c_0_459_0,axiom,
    class_OrderedGroup_Omonoid__add(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_459,def_lhs_atom89]) ).

cnf(c_0_460_0,axiom,
    class_OrderedGroup_Omonoid__mult(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_460,def_lhs_atom88]) ).

cnf(c_0_461_0,axiom,
    class_Ring__and__Field_Omult__zero(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_461,def_lhs_atom87]) ).

cnf(c_0_462_0,axiom,
    class_Ring__and__Field_Osemiring__0(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_462,def_lhs_atom86]) ).

cnf(c_0_463_0,axiom,
    class_Ring__and__Field_Osemiring__1(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_463,def_lhs_atom85]) ).

cnf(c_0_464_0,axiom,
    class_OrderedGroup_Osemigroup__add(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_464,def_lhs_atom84]) ).

cnf(c_0_465_0,axiom,
    class_Ring__and__Field_Ozero__neq__one(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_465,def_lhs_atom83]) ).

cnf(c_0_466_0,axiom,
    class_OrderedGroup_Ocomm__monoid__add(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_466,def_lhs_atom82]) ).

cnf(c_0_467_0,axiom,
    class_OrderedGroup_Oab__semigroup__add(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_467,def_lhs_atom81]) ).

cnf(c_0_468_0,axiom,
    class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_468,def_lhs_atom80]) ).

cnf(c_0_469_0,axiom,
    class_Ring__and__Field_Oordered__semidom(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_469,def_lhs_atom79]) ).

cnf(c_0_470_0,axiom,
    class_Ring__and__Field_Ono__zero__divisors(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_470,def_lhs_atom78]) ).

cnf(c_0_471_0,axiom,
    class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_471,def_lhs_atom77]) ).

cnf(c_0_472_0,axiom,
    class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_472,def_lhs_atom76]) ).

cnf(c_0_473_0,axiom,
    class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_473,def_lhs_atom75]) ).

cnf(c_0_474_0,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_474,def_lhs_atom74]) ).

cnf(c_0_475_0,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_475,def_lhs_atom73]) ).

cnf(c_0_476_0,axiom,
    c_Type_Otyping(v_ea____,v_s____,hAPP(hAPP(c_Type_Otype_OFun,v_Ta____),v_U____)),
    inference(unfold_definition,[status(thm)],[c_0_476,def_lhs_atom70]) ).

cnf(c_0_477_0,axiom,
    c_Type_Otyping(v_ea____,v_ta____,v_Ta____),
    inference(unfold_definition,[status(thm)],[c_0_477,def_lhs_atom67]) ).

cnf(c_0_478_0,axiom,
    hBOOL(hAPP(c_InductTermi_OIT,v_s____)),
    inference(unfold_definition,[status(thm)],[c_0_478,def_lhs_atom66]) ).

cnf(c_0_479_0,axiom,
    hBOOL(hAPP(c_InductTermi_OIT,v_ta____)),
    inference(unfold_definition,[status(thm)],[c_0_479,def_lhs_atom49]) ).

cnf(c_0_480_0,axiom,
    hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
    inference(unfold_definition,[status(thm)],[c_0_480,def_lhs_atom21]) ).

cnf(c_0_481_0,axiom,
    c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat)),
    inference(unfold_definition,[status(thm)],[c_0_481,def_lhs_atom19]) ).

cnf(c_0_482_0,axiom,
    hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat)) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
    inference(unfold_definition,[status(thm)],[c_0_482,def_lhs_atom10]) ).

cnf(c_0_483_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_483,def_lhs_atom9]) ).

cnf(c_0_484_0,axiom,
    c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
    inference(unfold_definition,[status(thm)],[c_0_484,def_lhs_atom5]) ).

% Orienting (remaining) axiom formulas using strategy ClausalAll
% CNF of (remaining) axioms:
% Start CNF derivation
fof(c_0_0_001,axiom,
    ! [X53,X40,X17,X8,X19,X50,X9] :
      ( X19 = c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__types__1__1(X9,X19,X8,X53),X9,tc_Type_Otype,tc_Type_Otype)
      | ~ c_Type_Otyping(X8,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X17),X40,tc_Lambda_OdB,tc_Lambda_OdB),X19)
      | ~ c_Type_Otypings(X8,X40,X50)
      | ~ c_Type_Otyping(X8,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X17),X40,tc_Lambda_OdB,tc_Lambda_OdB),X53,tc_Lambda_OdB,tc_Lambda_OdB),X9) ),
    file('<stdin>',cls_var__app__types_0) ).

fof(c_0_1_002,axiom,
    ! [X44,X31,X32] :
      ( X44 = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X32),c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(X32,X31,X44),tc_Lambda_OdB,tc_Lambda_OdB)
      | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X32),X31,tc_Lambda_OdB,tc_Lambda_OdB)),X44)) ),
    file('<stdin>',cls_head__Var__reduction_1) ).

fof(c_0_2_003,axiom,
    ! [X53,X40,X17,X8,X19,X50,X9] :
      ( c_Type_Otypings(X8,X53,c_Type_Osko__Type__Xvar__app__types__1__1(X9,X19,X8,X53))
      | ~ c_Type_Otyping(X8,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X17),X40,tc_Lambda_OdB,tc_Lambda_OdB),X19)
      | ~ c_Type_Otypings(X8,X40,X50)
      | ~ c_Type_Otyping(X8,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X17),X40,tc_Lambda_OdB,tc_Lambda_OdB),X53,tc_Lambda_OdB,tc_Lambda_OdB),X9) ),
    file('<stdin>',cls_var__app__types_1) ).

fof(c_0_3_004,axiom,
    ! [X44,X31,X32] :
      ( c_ListOrder_Ostep1(c_Lambda_Obeta,X31,c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(X32,X31,X44),tc_Lambda_OdB)
      | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X32),X31,tc_Lambda_OdB,tc_Lambda_OdB)),X44)) ),
    file('<stdin>',cls_head__Var__reduction_0) ).

fof(c_0_4_005,axiom,
    ! [X30,X31,X34] :
      ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,X34,X31,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X34,X30,tc_Lambda_OdB,tc_Lambda_OdB)))
      | ~ c_ListOrder_Ostep1(c_Lambda_Obeta,X31,X30,tc_Lambda_OdB) ),
    file('<stdin>',cls_apps__preserves__betas_0) ).

fof(c_0_5_006,axiom,
    ! [X30,X20,X34] :
      ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,X34,X30,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X20,X30,tc_Lambda_OdB,tc_Lambda_OdB)))
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X34),X20)) ),
    file('<stdin>',cls_apps__preserves__beta2_0) ).

fof(c_0_6_007,axiom,
    ! [X30,X20,X34] :
      ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,X34,X30,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X20,X30,tc_Lambda_OdB,tc_Lambda_OdB)))
      | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X34),X20)) ),
    file('<stdin>',cls_apps__preserves__beta_0) ).

fof(c_0_7_008,axiom,
    ! [X30,X20,X34] :
      ( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X34)),X20),X30,tc_Lambda_OdB,tc_Lambda_OdB)))
      | ~ hBOOL(hAPP(c_InductTermi_OIT,X20))
      | ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(X34,X20,c_HOL_Ozero__class_Ozero(tc_nat)),X30,tc_Lambda_OdB,tc_Lambda_OdB))) ),
    file('<stdin>',cls_Beta_0) ).

fof(c_0_8_009,axiom,
    ! [X40,X17,X8,X19,X9] :
      ( X9 = X19
      | ~ c_Type_Otyping(X8,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X17),X40,tc_Lambda_OdB,tc_Lambda_OdB),X19)
      | ~ c_Type_Otyping(X8,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X17),X40,tc_Lambda_OdB,tc_Lambda_OdB),X9) ),
    file('<stdin>',cls_var__app__type__eq_0) ).

fof(c_0_9_010,axiom,
    ! [X30,X20,X34] :
      ( ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(X34,X20,c_HOL_Ozero__class_Ozero(tc_nat)),X30,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)
      | ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X20,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(X34)),X20),X30,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB) ),
    file('<stdin>',cls_double__induction__lemma_0) ).

fof(c_0_10_011,axiom,
    ! [X40,X17,X8,X9] :
      ( c_Type_Otyping(X8,c_Lambda_OdB_OVar(X17),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__typesE__1__1(X9,X8,X17,X40),X9,tc_Type_Otype,tc_Type_Otype))
      | ~ c_Type_Otyping(X8,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X17),X40,tc_Lambda_OdB,tc_Lambda_OdB),X9) ),
    file('<stdin>',cls_var__app__typesE_0) ).

fof(c_0_11_012,axiom,
    ! [X40,X7,X8,X9] :
      ( c_Type_Otyping(X8,X7,c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeE__1__1(X9,X8,X7,X40),X9,tc_Type_Otype,tc_Type_Otype))
      | ~ c_Type_Otyping(X8,c_List_Ofoldl(c_Lambda_OdB_OApp,X7,X40,tc_Lambda_OdB,tc_Lambda_OdB),X9) ),
    file('<stdin>',cls_list__app__typeE_0) ).

fof(c_0_12_013,axiom,
    ! [X40,X7,X8,X9] :
      ( c_Type_Otyping(X8,X7,c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeD__1__1(X9,X8,X7,X40),X9,tc_Type_Otype,tc_Type_Otype))
      | ~ c_Type_Otyping(X8,c_List_Ofoldl(c_Lambda_OdB_OApp,X7,X40,tc_Lambda_OdB,tc_Lambda_OdB),X9) ),
    file('<stdin>',cls_list__app__typeD_0) ).

fof(c_0_13_014,axiom,
    ! [X40,X7,X8,X50,X9] :
      ( c_Type_Otyping(X8,c_List_Ofoldl(c_Lambda_OdB_OApp,X7,X40,tc_Lambda_OdB,tc_Lambda_OdB),X9)
      | ~ c_Type_Otypings(X8,X40,X50)
      | ~ c_Type_Otyping(X8,X7,c_List_Ofoldr(c_Type_Otype_OFun,X50,X9,tc_Type_Otype,tc_Type_Otype)) ),
    file('<stdin>',cls_list__app__typeI_0) ).

fof(c_0_14_015,axiom,
    ! [X31,X32] :
      ( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X32),X31,tc_Lambda_OdB,tc_Lambda_OdB)))
      | ~ c_List_Olistsp(c_InductTermi_OIT,X31,tc_Lambda_OdB) ),
    file('<stdin>',cls_IT_OVar_0) ).

fof(c_0_15_016,axiom,
    ! [X40,X17,X8,X9] :
      ( c_Type_Otypings(X8,X40,c_Type_Osko__Type__Xvar__app__typesE__1__1(X9,X8,X17,X40))
      | ~ c_Type_Otyping(X8,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X17),X40,tc_Lambda_OdB,tc_Lambda_OdB),X9) ),
    file('<stdin>',cls_var__app__typesE_1) ).

fof(c_0_16_017,axiom,
    ! [X40,X7,X8,X9] :
      ( c_Type_Otypings(X8,X40,c_Type_Osko__Type__Xlist__app__typeE__1__1(X9,X8,X7,X40))
      | ~ c_Type_Otyping(X8,c_List_Ofoldl(c_Lambda_OdB_OApp,X7,X40,tc_Lambda_OdB,tc_Lambda_OdB),X9) ),
    file('<stdin>',cls_list__app__typeE_1) ).

fof(c_0_17_018,axiom,
    ! [X40,X7,X8,X9] :
      ( c_Type_Otypings(X8,X40,c_Type_Osko__Type__Xlist__app__typeD__1__1(X9,X8,X7,X40))
      | ~ c_Type_Otyping(X8,c_List_Ofoldl(c_Lambda_OdB_OApp,X7,X40,tc_Lambda_OdB,tc_Lambda_OdB),X9) ),
    file('<stdin>',cls_list__app__typeD_1) ).

fof(c_0_18_019,axiom,
    ! [X30,X20,X31,X34] :
      ( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X34),X31,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X20),X30,tc_Lambda_OdB,tc_Lambda_OdB)
      | X31 = X30 ),
    file('<stdin>',cls_Abs__apps__eq__Abs__apps__conv_1) ).

fof(c_0_19_020,axiom,
    ! [X30,X20,X31,X34] :
      ( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X34),X31,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X20),X30,tc_Lambda_OdB,tc_Lambda_OdB)
      | X34 = X20 ),
    file('<stdin>',cls_Abs__apps__eq__Abs__apps__conv_0) ).

fof(c_0_20_021,axiom,
    ! [X30,X31,X32,X33] :
      ( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X33),X31,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X32),X30,tc_Lambda_OdB,tc_Lambda_OdB)
      | X31 = X30 ),
    file('<stdin>',cls_Var__apps__eq__Var__apps__conv_1) ).

fof(c_0_21_022,axiom,
    ! [X30,X31,X32,X33] :
      ( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X33),X31,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X32),X30,tc_Lambda_OdB,tc_Lambda_OdB)
      | X33 = X32 ),
    file('<stdin>',cls_Var__apps__eq__Var__apps__conv_0) ).

fof(c_0_22_023,axiom,
    ! [X56,X52,X21,X3] :
      ( ~ class_OrderedGroup_Osemigroup__add(X3)
      | c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X21),X52),X56,X3,X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X21),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),X52,X56,X3,X3)) ),
    file('<stdin>',cls_foldl__assoc_0) ).

fof(c_0_23_024,axiom,
    ! [X40,X20,X34] :
      ( c_List_Ofoldl(c_Lambda_OdB_OApp,X34,X40,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,X20,X40,tc_Lambda_OdB,tc_Lambda_OdB)
      | X34 = X20 ),
    file('<stdin>',cls_apps__eq__tail__conv_0) ).

fof(c_0_24_025,axiom,
    ! [X56,X21,X3] :
      ( ~ class_OrderedGroup_Omonoid__add(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X21),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3),X56,X3,X3)) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),X21,X56,X3,X3) ),
    file('<stdin>',cls_foldl__absorb0_0) ).

fof(c_0_25_026,axiom,
    ! [X49,X45,X3] :
      ( ~ class_OrderedGroup_Omonoid__add(X3)
      | c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),X45,X49,X3,X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X3),X49,c_HOL_Ozero__class_Ozero(X3),X3,X3)) ),
    file('<stdin>',cls_foldl__foldr1__lemma_0) ).

fof(c_0_26_027,axiom,
    ! [X49,X3] :
      ( ~ class_OrderedGroup_Omonoid__add(X3)
      | c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3),X49,X3,X3) = c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X3),X49,c_HOL_Ozero__class_Ozero(X3),X3,X3) ),
    file('<stdin>',cls_foldl__foldr1_0) ).

fof(c_0_27_028,axiom,
    ! [X49,X45,X3] :
      ( ~ class_OrderedGroup_Oab__semigroup__add(X3)
      | c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X3),X49,X45,X3,X3) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),X45,X49,X3,X3) ),
    file('<stdin>',cls_foldr__conv__foldl_0) ).

fof(c_0_28_029,axiom,
    ! [X6,X7,X8,X9] :
      ( c_Type_Otyping(X8,X7,hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__2__1(X9,X8,X7,X6)),X9))
      | ~ c_Type_Otyping(X8,hAPP(hAPP(c_Lambda_OdB_OApp,X7),X6),X9) ),
    file('<stdin>',cls_typing__elims_I2_J_0) ).

fof(c_0_29_030,axiom,
    ! [X15,X16,X12,X13,X14] :
      ( ~ hBOOL(hAPP(X14,c_Type_Otype_Otype__case(X13,X12,hAPP(hAPP(c_Type_Otype_OFun,X16),X15),t_a)))
      | hBOOL(hAPP(X14,hAPP(hAPP(X12,X16),X15))) ),
    file('<stdin>',cls_type_Osplit__asm_1) ).

fof(c_0_30_031,axiom,
    ! [X10,X11,X12,X13,X14] :
      ( ~ hBOOL(hAPP(X14,c_Type_Otype_Otype__case(X13,X12,hAPP(hAPP(c_Type_Otype_OFun,X11),X10),t_a)))
      | hBOOL(hAPP(X14,hAPP(hAPP(X12,X11),X10))) ),
    file('<stdin>',cls_type_Osplit_1) ).

fof(c_0_31_032,axiom,
    ! [X7,X20,X34] :
      ( hAPP(hAPP(c_Lambda_OdB_OApp,X34),X20) != c_List_Ofoldl(c_Lambda_OdB_OApp,X7,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)
      | hAPP(hAPP(c_Lambda_OdB_OApp,X34),X20) = X7 ),
    file('<stdin>',cls_App__eq__foldl__conv_0) ).

fof(c_0_32_033,axiom,
    ! [X30,X20,X34] :
      ( c_Lambda_OdB_OAbs(X34) != c_List_Ofoldl(c_Lambda_OdB_OApp,X20,X30,tc_Lambda_OdB,tc_Lambda_OdB)
      | c_Lambda_OdB_OAbs(X34) = X20 ),
    file('<stdin>',cls_Abs__eq__apps__conv_0) ).

fof(c_0_33_034,axiom,
    ! [X30,X20,X33] :
      ( c_Lambda_OdB_OVar(X33) != c_List_Ofoldl(c_Lambda_OdB_OApp,X20,X30,tc_Lambda_OdB,tc_Lambda_OdB)
      | c_Lambda_OdB_OVar(X33) = X20 ),
    file('<stdin>',cls_Var__eq__apps__conv_0) ).

fof(c_0_34_035,axiom,
    ! [X30,X20,X34] :
      ( c_List_Ofoldl(c_Lambda_OdB_OApp,X20,X30,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X34)
      | X20 = c_Lambda_OdB_OAbs(X34) ),
    file('<stdin>',cls_apps__eq__Abs__conv_0) ).

fof(c_0_35_036,axiom,
    ! [X30,X20,X34] :
      ( c_Lambda_OdB_OAbs(X34) != c_List_Ofoldl(c_Lambda_OdB_OApp,X20,X30,tc_Lambda_OdB,tc_Lambda_OdB)
      | X30 = c_List_Olist_ONil(tc_Lambda_OdB) ),
    file('<stdin>',cls_Abs__eq__apps__conv_1) ).

fof(c_0_36_037,axiom,
    ! [X30,X20,X34] :
      ( c_List_Ofoldl(c_Lambda_OdB_OApp,X20,X30,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X34)
      | X30 = c_List_Olist_ONil(tc_Lambda_OdB) ),
    file('<stdin>',cls_apps__eq__Abs__conv_1) ).

fof(c_0_37_038,axiom,
    ! [X30,X20,X33] :
      ( c_Lambda_OdB_OVar(X33) != c_List_Ofoldl(c_Lambda_OdB_OApp,X20,X30,tc_Lambda_OdB,tc_Lambda_OdB)
      | X30 = c_List_Olist_ONil(tc_Lambda_OdB) ),
    file('<stdin>',cls_Var__eq__apps__conv_1) ).

fof(c_0_38_039,axiom,
    ! [X52,X21,X34,X3] :
      ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X34,X3),X52),X21))
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Predicate_Oconversep(X34,X3,X3),X3),X21),X52)) ),
    file('<stdin>',cls_rtranclp__converseD_0) ).

fof(c_0_39_040,axiom,
    ! [X29,X12,X13,X14] :
      ( ~ hBOOL(hAPP(X14,c_Type_Otype_Otype__case(X13,X12,c_Type_Otype_OAtom(X29),t_a)))
      | hBOOL(hAPP(X14,hAPP(X13,X29))) ),
    file('<stdin>',cls_type_Osplit_0) ).

fof(c_0_40_041,axiom,
    ! [X46,X12,X13,X14] :
      ( ~ hBOOL(hAPP(X14,c_Type_Otype_Otype__case(X13,X12,c_Type_Otype_OAtom(X46),t_a)))
      | hBOOL(hAPP(X14,hAPP(X13,X46))) ),
    file('<stdin>',cls_type_Osplit__asm_0) ).

fof(c_0_41_042,axiom,
    ! [X52,X21,X34,X3] :
      ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Predicate_Oconversep(X34,X3,X3),X3),X21),X52))
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X34,X3),X52),X21)) ),
    file('<stdin>',cls_rtranclp__converseI_0) ).

fof(c_0_42_043,axiom,
    ! [X6,X7,X17,X8,X19,X9] :
      ( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(X7,X6,X17)))
      | ~ c_Type_Otyping(X8,X6,X19)
      | ~ hBOOL(hAPP(c_InductTermi_OIT,X6))
      | ~ c_Type_Otyping(c_Type_Oshift(X8,X17,X19,tc_Type_Otype),X7,X9)
      | ~ hBOOL(hAPP(c_InductTermi_OIT,X7)) ),
    file('<stdin>',cls_subst__type__IT_0) ).

fof(c_0_43_044,axiom,
    ! [X6,X7,X17,X47,X19,X9] :
      ( ~ c_Type_Otyping(X47,X6,X19)
      | ~ c_Type_Otyping(c_Type_Oshift(X47,X17,X19,tc_Type_Otype),X7,X9)
      | c_Type_Otyping(X47,c_Lambda_Osubst(X7,X6,X17),X9) ),
    file('<stdin>',cls_subst__lemma_0) ).

fof(c_0_44_045,axiom,
    ! [X27,X7,X43,X20] :
      ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X20),X7)),hAPP(hAPP(c_Lambda_OdB_OApp,X43),X27)))
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X7),X27))
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X20),X43)) ),
    file('<stdin>',cls_rtrancl__beta__App_0) ).

fof(c_0_45_046,axiom,
    ! [X7,X20,X34,X17] :
      ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Osubst(X7,X34,X17)),c_Lambda_Osubst(X7,X20,X17)))
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X34),X20)) ),
    file('<stdin>',cls_subst__preserves__beta2_H_0) ).

fof(c_0_46_047,axiom,
    ! [X7,X20,X34,X17] :
      ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Osubst(X34,X7,X17)),c_Lambda_Osubst(X20,X7,X17)))
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X34),X20)) ),
    file('<stdin>',cls_subst__preserves__beta_H_0) ).

fof(c_0_47_048,axiom,
    ! [X7,X18,X19,X9] :
      ( c_Type_Otyping(X18,c_Lambda_OdB_OAbs(X7),hAPP(hAPP(c_Type_Otype_OFun,X9),X19))
      | ~ c_Type_Otyping(c_Type_Oshift(X18,c_HOL_Ozero__class_Ozero(tc_nat),X9,tc_Type_Otype),X7,X19) ),
    file('<stdin>',cls_Abs_0) ).

fof(c_0_48_049,axiom,
    ! [X7,X8,X9] :
      ( c_Type_Otyping(c_Type_Oshift(X8,c_HOL_Ozero__class_Ozero(tc_nat),c_Type_Osko__Type__Xtyping__elims__3__1(X9,X8,X7),tc_Type_Otype),X7,c_Type_Osko__Type__Xtyping__elims__3__2(X9,X8,X7))
      | ~ c_Type_Otyping(X8,c_Lambda_OdB_OAbs(X7),X9) ),
    file('<stdin>',cls_typing__elims_I3_J_1) ).

fof(c_0_49_050,axiom,
    ! [X7,X20,X34,X17] :
      ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Osubst(X7,X34,X17)),c_Lambda_Osubst(X7,X20,X17)))
      | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X34),X20)) ),
    file('<stdin>',cls_subst__preserves__beta2_0) ).

fof(c_0_50_051,axiom,
    ! [X34,X48,X45,X57,X3] :
      ( hBOOL(hAPP(hAPP(X34,X48),X45))
      | ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X34,X3,X57),X45),X48)) ),
    file('<stdin>',cls_conversepD_0) ).

fof(c_0_51_052,axiom,
    ! [X34,X58,X59,X57,X3] :
      ( hBOOL(hAPP(hAPP(X34,X58),X59))
      | ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X34,X3,X57),X59),X58)) ),
    file('<stdin>',cls_conversep_Ocases_0) ).

fof(c_0_52_053,axiom,
    ! [X7,X43,X20] :
      ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X20),X7)),hAPP(hAPP(c_Lambda_OdB_OApp,X43),X7)))
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X20),X43)) ),
    file('<stdin>',cls_rtrancl__beta__AppL_0) ).

fof(c_0_53_054,axiom,
    ! [X27,X7,X20] :
      ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X20),X7)),hAPP(hAPP(c_Lambda_OdB_OApp,X20),X27)))
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X7),X27)) ),
    file('<stdin>',cls_rtrancl__beta__AppR_0) ).

fof(c_0_54_055,axiom,
    ! [X7,X20,X34,X17] :
      ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_Osubst(X34,X7,X17)),c_Lambda_Osubst(X20,X7,X17)))
      | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X34),X20)) ),
    file('<stdin>',cls_subst__preserves__beta_0) ).

fof(c_0_55_056,axiom,
    ! [X51,X52,X21,X34,X3] :
      ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X34,X3),X21),X51))
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X34,X3),X52),X51))
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X34,X3),X21),X52)) ),
    file('<stdin>',cls_rtranclp__trans_0) ).

fof(c_0_56_057,axiom,
    ! [X6,X7,X8,X9] :
      ( c_Type_Otyping(X8,X6,c_Type_Osko__Type__Xtyping__elims__2__1(X9,X8,X7,X6))
      | ~ c_Type_Otyping(X8,hAPP(hAPP(c_Lambda_OdB_OApp,X7),X6),X9) ),
    file('<stdin>',cls_typing__elims_I2_J_1) ).

fof(c_0_57_058,axiom,
    ! [X55,X54,X48,X45,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),X45),X48)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X54),X55)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),X54)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X48),X55)) ),
    file('<stdin>',cls_class__semiring_Osemiring__rules_I20_J_0) ).

fof(c_0_58_059,axiom,
    ! [X7,X8,X9] :
      ( c_Type_Otyping(c_Type_Oshift(X8,c_HOL_Ozero__class_Ozero(tc_nat),c_Type_Osko__Type__Xabs__typeE__1__1(X8,X7),tc_Type_Otype),X7,c_Type_Osko__Type__Xabs__typeE__1__2(X8,X7))
      | ~ c_Type_Otyping(X8,c_Lambda_OdB_OAbs(X7),X9) ),
    file('<stdin>',cls_abs__typeE_0) ).

fof(c_0_59_060,axiom,
    ! [X7,X17,X8,X19,X9] :
      ( c_Type_Otyping(c_Type_Oshift(X8,X17,X19,tc_Type_Otype),c_Lambda_Olift(X7,X17),X9)
      | ~ c_Type_Otyping(X8,X7,X9) ),
    file('<stdin>',cls_lift__type_0) ).

fof(c_0_60_061,axiom,
    ! [X34,X48,X45,X57,X3] :
      ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X34,X3,X57),X45),X48))
      | ~ hBOOL(hAPP(hAPP(X34,X48),X45)) ),
    file('<stdin>',cls_conversep__iff_1) ).

fof(c_0_61_062,axiom,
    ! [X34,X48,X45,X57,X3] :
      ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X34,X3,X57),X48),X45))
      | ~ hBOOL(hAPP(hAPP(X34,X45),X48)) ),
    file('<stdin>',cls_conversep_Ointros_0) ).

fof(c_0_62_063,axiom,
    ! [X6,X7,X20] :
      ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,X20),X6)),hAPP(hAPP(c_Lambda_OdB_OApp,X7),X6)))
      | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X20),X7)) ),
    file('<stdin>',cls_appL_0) ).

fof(c_0_63_064,axiom,
    ! [X6,X7,X20] :
      ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,X6),X20)),hAPP(hAPP(c_Lambda_OdB_OApp,X6),X7)))
      | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X20),X7)) ),
    file('<stdin>',cls_appR_0) ).

fof(c_0_64_065,axiom,
    ! [X32,X48,X45,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_lessequals(X45,X48,X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X48,X3)
      | ~ c_lessequals(c_Power_Opower__class_Opower(X45,c_Suc(X32),X3),c_Power_Opower__class_Opower(X48,c_Suc(X32),X3),X3) ),
    file('<stdin>',cls_power__le__imp__le__base_0) ).

fof(c_0_65_066,axiom,
    ! [X34,X54,X48,X45,X3] :
      ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X34,X3),X45),X54))
      | ~ hBOOL(hAPP(hAPP(X34,X48),X54))
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X34,X3),X45),X48)) ),
    file('<stdin>',cls_rtranclp_Ortrancl__into__rtrancl_0) ).

fof(c_0_66_067,axiom,
    ! [X34,X54,X48,X45,X3] :
      ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X34,X3),X45),X54))
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X34,X3),X48),X54))
      | ~ hBOOL(hAPP(hAPP(X34,X45),X48)) ),
    file('<stdin>',cls_converse__rtranclp__into__rtranclp_0) ).

fof(c_0_67_068,axiom,
    ! [X20,X34,X17] :
      ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Olift(X34,X17)),c_Lambda_Olift(X20,X17)))
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X34),X20)) ),
    file('<stdin>',cls_lift__preserves__beta_H_0) ).

fof(c_0_68_069,axiom,
    ! [X54,X48,X45,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),X45),X48)),X54) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),X54)),X48) ),
    file('<stdin>',cls_class__semiring_Osemiring__rules_I23_J_0) ).

fof(c_0_69_070,axiom,
    ! [X55,X54,X48,X45,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
      | c_lessequals(X45,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X48),X55),X3)
      | ~ c_lessequals(X54,X55,X3)
      | ~ c_lessequals(X45,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X48),X54),X3) ),
    file('<stdin>',cls_le__add__right__mono_0) ).

fof(c_0_70_071,axiom,
    ! [X54,X48,X45,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
      | c_lessequals(X45,X48,X3)
      | ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),X54),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X48),X54),X3) ),
    file('<stdin>',cls_add__le__cancel__right_0) ).

fof(c_0_71_072,axiom,
    ! [X54,X48,X45,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
      | c_lessequals(X45,X48,X3)
      | ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X54),X45),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X54),X48),X3) ),
    file('<stdin>',cls_add__le__cancel__left_0) ).

fof(c_0_72_073,axiom,
    ! [X32,X48,X45,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_lessequals(c_Power_Opower__class_Opower(X45,X32,X3),c_Power_Opower__class_Opower(X48,X32,X3),X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X45,X3)
      | ~ c_lessequals(X45,X48,X3) ),
    file('<stdin>',cls_power__mono_0) ).

fof(c_0_73_074,axiom,
    ! [X7,X8,X9] :
      ( X9 = hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__3__1(X9,X8,X7)),c_Type_Osko__Type__Xtyping__elims__3__2(X9,X8,X7))
      | ~ c_Type_Otyping(X8,c_Lambda_OdB_OAbs(X7),X9) ),
    file('<stdin>',cls_typing__elims_I3_J_0) ).

fof(c_0_74_075,axiom,
    ! [X43,X20] :
      ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_OdB_OAbs(X20)),c_Lambda_OdB_OAbs(X43)))
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X20),X43)) ),
    file('<stdin>',cls_rtrancl__beta__Abs_0) ).

fof(c_0_75_076,axiom,
    ! [X55,X54,X48,X45,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3)
      | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),X54),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X48),X55),X3)
      | ~ c_lessequals(X54,X55,X3)
      | ~ c_lessequals(X45,X48,X3) ),
    file('<stdin>',cls_add__mono_0) ).

fof(c_0_76_077,axiom,
    ! [X34,X48,X45,X3] :
      ( c_Wellfounded_Oaccp(X34,X48,X3)
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X34,X3),X48),X45))
      | ~ c_Wellfounded_Oaccp(X34,X45,X3) ),
    file('<stdin>',cls_accp__downwards_0) ).

fof(c_0_77_078,axiom,
    ! [X34,X48,X45,X3] :
      ( c_Wellfounded_Oaccp(X34,X48,X3)
      | ~ c_Wellfounded_Oaccp(X34,X45,X3)
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X34,X3),X48),X45)) ),
    file('<stdin>',cls_accp__downwards__aux_0) ).

fof(c_0_78_079,axiom,
    ! [X54,X48,X45,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),X45),X48)),X54) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X48),X54)) ),
    file('<stdin>',cls_class__semiring_Osemiring__rules_I21_J_0) ).

fof(c_0_79_080,axiom,
    ! [X55,X54,X45,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X54),X55)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),X54)),X55) ),
    file('<stdin>',cls_class__semiring_Osemiring__rules_I25_J_0) ).

fof(c_0_80_081,axiom,
    ! [X54,X48,X45,X3] :
      ( ~ class_OrderedGroup_Oab__semigroup__add(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),X48)),X54) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X48),X54)) ),
    file('<stdin>',cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) ).

fof(c_0_81_082,axiom,
    ! [X54,X48,X45,X3] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),X48)),X54) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X48),X54)) ),
    file('<stdin>',cls_comm__monoid__add_Omult__assoc_0) ).

fof(c_0_82_083,axiom,
    ! [X51,X52,X21,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X21),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X52),X51)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X21),X52)),X51) ),
    file('<stdin>',cls_class__semiring_Oadd__a_0) ).

fof(c_0_83_084,axiom,
    ! [X7,X20,X18,X19,X9] :
      ( c_Type_Otyping(X18,hAPP(hAPP(c_Lambda_OdB_OApp,X20),X7),X19)
      | ~ c_Type_Otyping(X18,X7,X9)
      | ~ c_Type_Otyping(X18,X20,hAPP(hAPP(c_Type_Otype_OFun,X9),X19)) ),
    file('<stdin>',cls_typing_OApp_0) ).

fof(c_0_84_085,axiom,
    ! [X27,X7,X8,X9] :
      ( c_Type_Otyping(X8,X27,X9)
      | ~ c_Type_Otyping(X8,X7,X9)
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X7),X27)) ),
    file('<stdin>',cls_subject__reduction_H_0) ).

fof(c_0_85_086,axiom,
    ! [X32,X48,X45,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_Power_Opower__class_Opower(X45,c_Suc(X32),X3) != c_Power_Opower__class_Opower(X48,c_Suc(X32),X3)
      | X45 = X48
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X48,X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X45,X3) ),
    file('<stdin>',cls_power__inject__base_0) ).

fof(c_0_86_087,axiom,
    ! [X51,X52,X21,X6,X3] :
      ( ~ class_OrderedGroup_Oab__group__add(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X21),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X52),X51)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X52),X6)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X21),X51) = X6 ),
    file('<stdin>',cls_add__cancel__21_0) ).

fof(c_0_87_088,axiom,
    ! [X48,X45,X3] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),X48),X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X48,X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X45,X3) ),
    file('<stdin>',cls_add__nonneg__nonneg_0) ).

fof(c_0_88_089,axiom,
    ! [X48,X45,X3] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
      | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),X48),c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_lessequals(X48,c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_lessequals(X45,c_HOL_Ozero__class_Ozero(X3),X3) ),
    file('<stdin>',cls_add__nonpos__nonpos_0) ).

fof(c_0_89_090,axiom,
    ! [X54,X48,X45,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
      | ~ class_OrderedGroup_Ocomm__monoid__add(X3)
      | c_lessequals(X48,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),X54),X3)
      | ~ c_lessequals(X48,X54,X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X45,X3) ),
    file('<stdin>',cls_add__increasing_0) ).

fof(c_0_90_091,axiom,
    ! [X54,X48,X45,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
      | ~ class_OrderedGroup_Ocomm__monoid__add(X3)
      | c_lessequals(X48,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),X54),X3)
      | ~ c_lessequals(X48,X45,X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X54,X3) ),
    file('<stdin>',cls_add__increasing2_0) ).

fof(c_0_91_092,axiom,
    ! [X54,X48,X45,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
      | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),X54),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X48),X54),X3)
      | ~ c_lessequals(X45,X48,X3) ),
    file('<stdin>',cls_add__le__cancel__right_1) ).

fof(c_0_92_093,axiom,
    ! [X54,X48,X45,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
      | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X54),X45),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X54),X48),X3)
      | ~ c_lessequals(X45,X48,X3) ),
    file('<stdin>',cls_add__le__cancel__left_1) ).

fof(c_0_93_094,axiom,
    ! [X54,X48,X45,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3)
      | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),X54),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X48),X54),X3)
      | ~ c_lessequals(X45,X48,X3) ),
    file('<stdin>',cls_add__right__mono_0) ).

fof(c_0_94_095,axiom,
    ! [X54,X48,X45,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3)
      | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X54),X45),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X54),X48),X3)
      | ~ c_lessequals(X45,X48,X3) ),
    file('<stdin>',cls_add__left__mono_0) ).

fof(c_0_95_096,axiom,
    ! [X20,X34,X17] :
      ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_Olift(X34,X17)),c_Lambda_Olift(X20,X17)))
      | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X34),X20)) ),
    file('<stdin>',cls_lift__preserves__beta_0) ).

fof(c_0_96_097,axiom,
    ! [X45,X3] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X3),X45,X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),X45),X3) ),
    file('<stdin>',cls_zero__le__double__add__iff__zero__le__single__add_0) ).

fof(c_0_97_098,axiom,
    ! [X45,X3] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
      | c_lessequals(X45,c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),X45),c_HOL_Ozero__class_Ozero(X3),X3) ),
    file('<stdin>',cls_double__add__le__zero__iff__single__add__le__zero_0) ).

fof(c_0_98_099,axiom,
    ! [X55,X54,X45,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X54),X55)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X54),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),X55)) ),
    file('<stdin>',cls_class__semiring_Osemiring__rules_I22_J_0) ).

fof(c_0_99_100,axiom,
    ! [X54,X48,X45,X3] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X48),X54)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X48),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),X54)) ),
    file('<stdin>',cls_comm__monoid__add_Omult__left__commute_0) ).

fof(c_0_100_101,axiom,
    ! [X51,X52,X21,X3] :
      ( ~ class_OrderedGroup_Oab__group__add(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X21),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X52),X51)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X52),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X21),X51)) ),
    file('<stdin>',cls_add__cancel__21_1) ).

fof(c_0_101_102,axiom,
    ! [X52,X21,X34,X3] :
      ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X34,X3),X21),X52))
      | ~ hBOOL(hAPP(hAPP(X34,X21),X52)) ),
    file('<stdin>',cls_r__into__rtranclp_0) ).

fof(c_0_102_103,axiom,
    ! [X34,X35,X17] :
      ( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(X34,c_Lambda_OdB_OVar(X17),X35)))
      | ~ hBOOL(hAPP(c_InductTermi_OIT,X34)) ),
    file('<stdin>',cls_subst__Var__IT_0) ).

fof(c_0_103_104,axiom,
    ! [X52,X21,X3] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X21),X52) != c_HOL_Ozero__class_Ozero(X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X52,X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X21,X3)
      | X52 = c_HOL_Ozero__class_Ozero(X3) ),
    file('<stdin>',cls_add__nonneg__eq__0__iff_1) ).

fof(c_0_104_105,axiom,
    ! [X52,X21,X3] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X21),X52) != c_HOL_Ozero__class_Ozero(X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X52,X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X21,X3)
      | X21 = c_HOL_Ozero__class_Ozero(X3) ),
    file('<stdin>',cls_add__nonneg__eq__0__iff_0) ).

fof(c_0_105_106,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_106_107,axiom,
    ! [X20,X34] :
      ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,X34),c_Lambda_Osko__Lambda__Xbeta__cases__2__1(X34,X20)))
      | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OAbs(X34)),X20)) ),
    file('<stdin>',cls_beta__cases_I2_J_1) ).

fof(c_0_107_108,axiom,
    ! [X32,X45,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_Power_Opower__class_Opower(X45,X32,X3),X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X45,X3) ),
    file('<stdin>',cls_zero__le__power_0) ).

fof(c_0_108_109,axiom,
    ! [X32,X45,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_lessequals(c_HOL_Oone__class_Oone(X3),c_Power_Opower__class_Opower(X45,X32,X3),X3)
      | ~ c_lessequals(c_HOL_Oone__class_Oone(X3),X45,X3) ),
    file('<stdin>',cls_one__le__power_0) ).

fof(c_0_109_110,axiom,
    ! [X52,X34,X45,X3] :
      ( c_Wellfounded_Oaccp(X34,X52,X3)
      | ~ hBOOL(hAPP(hAPP(X34,X52),X45))
      | ~ c_Wellfounded_Oaccp(X34,X45,X3) ),
    file('<stdin>',cls_accp_Ocases_0) ).

fof(c_0_110_111,axiom,
    ! [X34,X48,X45,X3] :
      ( c_Wellfounded_Oaccp(X34,X45,X3)
      | ~ hBOOL(hAPP(hAPP(X34,X45),X48))
      | ~ c_Wellfounded_Oaccp(X34,X48,X3) ),
    file('<stdin>',cls_accp__downward_0) ).

fof(c_0_111_112,axiom,
    ! [X45,X3] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),X45),X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X45,X3) ),
    file('<stdin>',cls_zero__le__double__add__iff__zero__le__single__add_1) ).

fof(c_0_112_113,axiom,
    ! [X45,X3] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
      | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),X45),c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_lessequals(X45,c_HOL_Ozero__class_Ozero(X3),X3) ),
    file('<stdin>',cls_double__add__le__zero__iff__single__add__le__zero_1) ).

fof(c_0_113_114,axiom,
    ! [X34] :
      ( hBOOL(hAPP(c_InductTermi_OIT,X34))
      | ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X34,tc_Lambda_OdB) ),
    file('<stdin>',cls_termi__implies__IT_0) ).

fof(c_0_114_115,axiom,
    ! [X27,X7,X8,X9] :
      ( c_Type_Otyping(X8,X27,X9)
      | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X7),X27))
      | ~ c_Type_Otyping(X8,X7,X9) ),
    file('<stdin>',cls_subject__reduction_0) ).

fof(c_0_115_116,axiom,
    ! [X32,X33,X3] :
      ( ~ class_Ring__and__Field_Osemiring__1(X3)
      | c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X33),X32),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_Nat_Osemiring__1__class_Oof__nat(X33,X3)),c_Nat_Osemiring__1__class_Oof__nat(X32,X3)) ),
    file('<stdin>',cls_of__nat__add_0) ).

fof(c_0_116_117,axiom,
    ! [X7,X17] :
      ( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,X7),c_Lambda_OdB_OVar(X17))))
      | ~ hBOOL(hAPP(c_InductTermi_OIT,X7)) ),
    file('<stdin>',cls_app__Var__IT_0) ).

fof(c_0_117_118,axiom,
    ! [X51,X52,X21,X3] :
      ( ~ class_Orderings_Oorder(X3)
      | c_lessequals(X51,X21,X3)
      | ~ c_lessequals(X51,X52,X3)
      | ~ c_lessequals(X52,X21,X3) ),
    file('<stdin>',cls_xt1_I6_J_0) ).

fof(c_0_118_119,axiom,
    ! [X51,X52,X21,X3] :
      ( ~ class_Orderings_Opreorder(X3)
      | c_lessequals(X21,X51,X3)
      | ~ c_lessequals(X52,X51,X3)
      | ~ c_lessequals(X21,X52,X3) ),
    file('<stdin>',cls_order__trans_0) ).

fof(c_0_119_120,axiom,
    ! [X7,X20] :
      ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OAbs(X20)),c_Lambda_OdB_OAbs(X7)))
      | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X20),X7)) ),
    file('<stdin>',cls_abs_0) ).

fof(c_0_120_121,axiom,
    ! [X7] :
      ( c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X7,tc_Lambda_OdB)
      | ~ hBOOL(hAPP(c_InductTermi_OIT,X7)) ),
    file('<stdin>',cls_IT__implies__termi_0) ).

fof(c_0_121_122,axiom,
    ! [X20,X34] :
      ( X20 = c_Lambda_OdB_OAbs(c_Lambda_Osko__Lambda__Xbeta__cases__2__1(X34,X20))
      | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OAbs(X34)),X20)) ),
    file('<stdin>',cls_beta__cases_I2_J_0) ).

fof(c_0_122_123,axiom,
    ! [X52,X21,X3] :
      ( ~ class_Orderings_Oorder(X3)
      | X21 = X52
      | ~ c_lessequals(X52,X21,X3)
      | ~ c_lessequals(X21,X52,X3) ),
    file('<stdin>',cls_order__eq__iff_2) ).

fof(c_0_123_124,axiom,
    ! [X52,X21,X3] :
      ( ~ class_Orderings_Oorder(X3)
      | X21 = X52
      | ~ c_lessequals(X52,X21,X3)
      | ~ c_lessequals(X21,X52,X3) ),
    file('<stdin>',cls_order__antisym_0) ).

fof(c_0_124_125,axiom,
    ! [X52,X21,X3] :
      ( ~ class_Orderings_Oorder(X3)
      | X21 = X52
      | ~ c_lessequals(X21,X52,X3)
      | ~ c_lessequals(X52,X21,X3) ),
    file('<stdin>',cls_order__antisym__conv_0) ).

fof(c_0_125_126,axiom,
    ! [X51,X52,X21,X3] :
      ( ~ class_Ring__and__Field_Oidom(X3)
      | ~ class_Int_Onumber__ring(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X21),X52) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X21),X51)
      | X52 = X51 ),
    file('<stdin>',cls_class__ringb_Oadd__cancel_0) ).

fof(c_0_126_127,axiom,
    ! [X54,X48,X45,X3] :
      ( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),X48) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),X54)
      | X48 = X54 ),
    file('<stdin>',cls_add__imp__eq_0) ).

fof(c_0_127_128,axiom,
    ! [X54,X48,X45,X3] :
      ( ~ class_OrderedGroup_Ocancel__semigroup__add(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),X48) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),X54)
      | X48 = X54 ),
    file('<stdin>',cls_add__left__cancel_0) ).

fof(c_0_128_129,axiom,
    ! [X54,X48,X45,X3] :
      ( ~ class_OrderedGroup_Ocancel__semigroup__add(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X48),X45) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X54),X45)
      | X48 = X54 ),
    file('<stdin>',cls_add__right__cancel_0) ).

fof(c_0_129_130,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_130_131,axiom,
    ! [X51,X52,X21] :
      ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X21),X52) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X21),X51)
      | X52 = X51 ),
    file('<stdin>',cls_natgb_Oadd__cancel_0) ).

fof(c_0_131_132,axiom,
    ! [X32,X33,X60] :
      ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X33),X60) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X32),X60)
      | X33 = X32 ),
    file('<stdin>',cls_nat__add__right__cancel_0) ).

fof(c_0_132_133,axiom,
    ! [X32,X33,X60] :
      ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X60),X33) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X60),X32)
      | X33 = X32 ),
    file('<stdin>',cls_nat__add__left__cancel_0) ).

fof(c_0_133_134,axiom,
    ! [X32,X45,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(X45,X32,X3) != c_HOL_Ozero__class_Ozero(X3)
      | X45 = c_HOL_Ozero__class_Ozero(X3) ),
    file('<stdin>',cls_power__eq__0__iff_0) ).

fof(c_0_134_135,axiom,
    ! [X45,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(X45,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_135_136,axiom,
    ! [X23,X24,X9,X14] :
      ( c_Type_Osko__Type__Xtype__induct__1__1(X14) != hAPP(hAPP(c_Type_Otype_OFun,X24),X23)
      | hBOOL(hAPP(X14,X9))
      | hBOOL(hAPP(X14,X23)) ),
    file('<stdin>',cls_type__induct_1) ).

fof(c_0_136_137,axiom,
    ! [X21,X22,X9,X14] :
      ( c_Type_Osko__Type__Xtype__induct__1__1(X14) != hAPP(hAPP(c_Type_Otype_OFun,X22),X21)
      | hBOOL(hAPP(X14,X9))
      | hBOOL(hAPP(X14,X22)) ),
    file('<stdin>',cls_type__induct_0) ).

fof(c_0_137_138,axiom,
    ! [X7,X17] :
      ( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Olift(X7,X17)))
      | ~ hBOOL(hAPP(c_InductTermi_OIT,X7)) ),
    file('<stdin>',cls_lift__IT_0) ).

fof(c_0_138_139,axiom,
    ! [X36,X37,X38,X39] :
      ( hAPP(hAPP(c_Lambda_OdB_OApp,X39),X37) != hAPP(hAPP(c_Lambda_OdB_OApp,X38),X36)
      | X37 = X36 ),
    file('<stdin>',cls_dB_Osimps_I2_J_1) ).

fof(c_0_139_140,axiom,
    ! [X36,X37,X38,X39] :
      ( hAPP(hAPP(c_Lambda_OdB_OApp,X39),X37) != hAPP(hAPP(c_Lambda_OdB_OApp,X38),X36)
      | X39 = X38 ),
    file('<stdin>',cls_dB_Osimps_I2_J_0) ).

fof(c_0_140_141,axiom,
    ! [X25,X10,X26,X11] :
      ( hAPP(hAPP(c_Type_Otype_OFun,X11),X10) != hAPP(hAPP(c_Type_Otype_OFun,X26),X25)
      | X11 = X26 ),
    file('<stdin>',cls_type_Osimps_I2_J_0) ).

fof(c_0_141_142,axiom,
    ! [X25,X10,X26,X11] :
      ( hAPP(hAPP(c_Type_Otype_OFun,X11),X10) != hAPP(hAPP(c_Type_Otype_OFun,X26),X25)
      | X10 = X25 ),
    file('<stdin>',cls_type_Osimps_I2_J_1) ).

fof(c_0_142_143,axiom,
    ! [X33,X3] :
      ( ~ class_Ring__and__Field_Osemiring__1(X3)
      | c_Nat_Osemiring__1__class_Oof__nat(c_Suc(X33),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Oone__class_Oone(X3)),c_Nat_Osemiring__1__class_Oof__nat(X33,X3)) ),
    file('<stdin>',cls_of__nat__Suc_0) ).

fof(c_0_143_144,axiom,
    ! [X52,X21,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_lessequals(X52,X21,X3)
      | c_lessequals(X21,X52,X3) ),
    file('<stdin>',cls_linorder__linear_0) ).

fof(c_0_144_145,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_145_146,axiom,
    ! [X54,X45,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),X54) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X54),X45) ),
    file('<stdin>',cls_class__semiring_Osemiring__rules_I24_J_0) ).

fof(c_0_146_147,axiom,
    ! [X48,X45,X3] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),X48) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X48),X45) ),
    file('<stdin>',cls_comm__monoid__add_Omult__commute_0) ).

fof(c_0_147_148,axiom,
    ! [X52,X21,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X21),X52) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X52),X21) ),
    file('<stdin>',cls_class__semiring_Oadd__c_0) ).

fof(c_0_148_149,axiom,
    ! [X17,X8,X9] :
      ( hAPP(X8,X17) = X9
      | ~ c_Type_Otyping(X8,c_Lambda_OdB_OVar(X17),X9) ),
    file('<stdin>',cls_typing__elims_I1_J_0) ).

fof(c_0_149_150,axiom,
    ! [X32,X45,X3] :
      ( ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X3)
      | c_Power_Opower__class_Opower(X45,X32,X3) != c_HOL_Ozero__class_Ozero(X3)
      | X45 = c_HOL_Ozero__class_Ozero(X3) ),
    file('<stdin>',cls_field__power__not__zero_0) ).

fof(c_0_150_151,axiom,
    ! [X21,X45,X3] :
      ( ~ class_Ring__and__Field_Oidom(X3)
      | ~ class_Int_Onumber__ring(X3)
      | X21 != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X21),X45)
      | X45 = c_HOL_Ozero__class_Ozero(X3) ),
    file('<stdin>',cls_class__ringb_Oadd__r0__iff_0) ).

fof(c_0_151_152,axiom,
    ! [X45,X3] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),X45) != c_HOL_Ozero__class_Ozero(X3)
      | X45 = c_HOL_Ozero__class_Ozero(X3) ),
    file('<stdin>',cls_double__eq__0__iff_0) ).

fof(c_0_152_153,axiom,
    ! [X32,X33] :
      ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X33),X32)
      | X32 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X33 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    file('<stdin>',cls_one__is__add_1) ).

fof(c_0_153_154,axiom,
    ! [X32,X33] :
      ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X33),X32) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X32 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X33 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    file('<stdin>',cls_add__is__1_1) ).

fof(c_0_154_155,axiom,
    ! [X9,X14] :
      ( hBOOL(hAPP(X14,X9))
      | ~ hBOOL(hAPP(X14,c_Type_Osko__Type__Xtype__induct__1__1(X14))) ),
    file('<stdin>',cls_type__induct_2) ).

fof(c_0_155_156,axiom,
    ! [X32,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),X32,X3) = c_HOL_Ozero__class_Ozero(X3)
      | X32 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('<stdin>',cls_power__eq__0__iff_2) ).

fof(c_0_156_157,axiom,
    ! [X32,X33] :
      ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X33),X32) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X32 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X32 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('<stdin>',cls_add__is__1_3) ).

fof(c_0_157_158,axiom,
    ! [X32,X33] :
      ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X33),X32) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X33 = c_HOL_Ozero__class_Ozero(tc_nat)
      | X33 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    file('<stdin>',cls_add__is__1_0) ).

fof(c_0_158_159,axiom,
    ! [X32,X33] :
      ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X33),X32)
      | X33 = c_HOL_Ozero__class_Ozero(tc_nat)
      | X33 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    file('<stdin>',cls_one__is__add_0) ).

fof(c_0_159_160,axiom,
    ! [X32,X33] :
      ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X33),X32)
      | X32 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X32 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('<stdin>',cls_one__is__add_3) ).

fof(c_0_160_161,axiom,
    ! [X32,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_Nat_Osemiring__1__class_Oof__nat(X32,X3),X3) ),
    file('<stdin>',cls_of__nat__0__le__iff_0) ).

fof(c_0_161_162,axiom,
    ! [X33,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_Nat_Osemiring__1__class_Oof__nat(X33,X3),X3) ),
    file('<stdin>',cls_zero__le__imp__of__nat_0) ).

fof(c_0_162_163,axiom,
    ! [X32,X33] :
      ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X33),X32)
      | X33 = c_HOL_Ozero__class_Ozero(tc_nat)
      | X32 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('<stdin>',cls_one__is__add_2) ).

fof(c_0_163_164,axiom,
    ! [X32,X33] :
      ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X33),X32) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X33 = c_HOL_Ozero__class_Ozero(tc_nat)
      | X32 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('<stdin>',cls_add__is__1_2) ).

fof(c_0_164_165,axiom,
    ! [X32,X3] :
      ( ~ class_Ring__and__Field_Osemiring__0(X3)
      | ~ class_Power_Opower(X3)
      | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X3),c_Suc(X32),X3) = c_HOL_Ozero__class_Ozero(X3) ),
    file('<stdin>',cls_power__0__Suc_0) ).

fof(c_0_165_166,axiom,
    ! [X32,X3] :
      ( ~ class_Ring__and__Field_Osemiring__0(X3)
      | ~ class_Power_Opower(X3)
      | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X3),X32,X3) = c_HOL_Ozero__class_Ozero(X3)
      | X32 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('<stdin>',cls_power__0__left_1) ).

fof(c_0_166_167,axiom,
    ! [X34] :
      ( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(X34)))
      | ~ hBOOL(hAPP(c_InductTermi_OIT,X34)) ),
    file('<stdin>',cls_Lambda_0) ).

fof(c_0_167_168,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_168_169,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_169_170,axiom,
    ! [X32,X33] :
      ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X33),X32) != c_HOL_Ozero__class_Ozero(tc_nat)
      | X33 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('<stdin>',cls_add__is__0_0) ).

fof(c_0_170_171,axiom,
    ! [X32,X33] :
      ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X33),X32) != c_HOL_Ozero__class_Ozero(tc_nat)
      | X32 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('<stdin>',cls_add__is__0_1) ).

fof(c_0_171_172,axiom,
    ! [X32,X33] :
      ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X33),X32) != X33
      | X32 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('<stdin>',cls_add__eq__self__zero_0) ).

fof(c_0_172_173,axiom,
    ! [X21,X45] :
      ( X21 != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X21),X45)
      | X45 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('<stdin>',cls_natgb_Oadd__r0__iff_0) ).

fof(c_0_173_174,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_174_175,axiom,
    ! [X21,X3] :
      ( ~ class_Ring__and__Field_Oidom(X3)
      | ~ class_Int_Onumber__ring(X3)
      | X21 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X21),c_HOL_Ozero__class_Ozero(X3)) ),
    file('<stdin>',cls_class__ringb_Oadd__r0__iff_1) ).

fof(c_0_175_176,axiom,
    ! [X21,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3)),X21) = X21 ),
    file('<stdin>',cls_class__semiring_Oadd__0_0) ).

fof(c_0_176_177,axiom,
    ! [X45,X3] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3)),X45) = X45 ),
    file('<stdin>',cls_comm__monoid__add_Omult__1_0) ).

fof(c_0_177_178,axiom,
    ! [X45,X3] :
      ( ~ class_OrderedGroup_Omonoid__add(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3)),X45) = X45 ),
    file('<stdin>',cls_add__0__left_0) ).

fof(c_0_178_179,axiom,
    ! [X45,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3)),X45) = X45 ),
    file('<stdin>',cls_class__semiring_Osemiring__rules_I5_J_0) ).

fof(c_0_179_180,axiom,
    ! [X32,X3] :
      ( ~ class_OrderedGroup_Omonoid__mult(X3)
      | c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X3),X32,X3) = c_HOL_Oone__class_Oone(X3) ),
    file('<stdin>',cls_power__one_0) ).

fof(c_0_180_181,axiom,
    ! [X45,X3] :
      ( ~ class_Power_Opower(X3)
      | c_Power_Opower__class_Opower(X45,c_HOL_Ozero__class_Ozero(tc_nat),X3) = c_HOL_Oone__class_Oone(X3) ),
    file('<stdin>',cls_power__0_0) ).

fof(c_0_181_182,axiom,
    ! [X21,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_Power_Opower__class_Opower(X21,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_182_183,axiom,
    ! [X45,X3] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),c_HOL_Ozero__class_Ozero(X3)) = X45 ),
    file('<stdin>',cls_comm__monoid__add_Omult__1__right_0) ).

fof(c_0_183_184,axiom,
    ! [X45,X3] :
      ( ~ class_OrderedGroup_Omonoid__add(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),c_HOL_Ozero__class_Ozero(X3)) = X45 ),
    file('<stdin>',cls_monoid__add__class_Oadd__0__right_0) ).

fof(c_0_184_185,axiom,
    ! [X45,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),c_HOL_Ozero__class_Ozero(X3)) = X45 ),
    file('<stdin>',cls_class__semiring_Osemiring__rules_I6_J_0) ).

fof(c_0_185_186,axiom,
    ! [X21,X3] :
      ( ~ class_Orderings_Oorder(X3)
      | c_lessequals(X21,X21,X3) ),
    file('<stdin>',cls_order__eq__iff_0) ).

fof(c_0_186_187,axiom,
    ! [X21,X3] :
      ( ~ class_Orderings_Opreorder(X3)
      | c_lessequals(X21,X21,X3) ),
    file('<stdin>',cls_order__eq__refl_0) ).

fof(c_0_187_188,axiom,
    ! [X32,X33,X3] :
      ( ~ class_Nat_Osemiring__char__0(X3)
      | c_Nat_Osemiring__1__class_Oof__nat(X33,X3) != c_Nat_Osemiring__1__class_Oof__nat(X32,X3)
      | X33 = X32 ),
    file('<stdin>',cls_of__nat__eq__iff_0) ).

fof(c_0_188_189,axiom,
    ! [X4,X5] :
      ( class_Orderings_Opreorder(tc_fun(X4,X5))
      | ~ class_Orderings_Opreorder(X5) ),
    file('<stdin>',clsarity_fun__Orderings_Opreorder) ).

fof(c_0_189_190,axiom,
    ! [X4,X5] :
      ( class_Orderings_Oorder(tc_fun(X4,X5))
      | ~ class_Orderings_Oorder(X5) ),
    file('<stdin>',clsarity_fun__Orderings_Oorder) ).

fof(c_0_190_191,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_191_192,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_192_193,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_193_194,axiom,
    ! [X28,X29] :
      ( c_Suc(X29) != c_Suc(X28)
      | X29 = X28 ),
    file('<stdin>',cls_nat_Oinject_0) ).

fof(c_0_194_195,axiom,
    ! [X52,X21] :
      ( c_Suc(X21) != c_Suc(X52)
      | X21 = X52 ),
    file('<stdin>',cls_Suc__inject_0) ).

fof(c_0_195_196,axiom,
    ! [X28,X29] :
      ( c_Type_Otype_OAtom(X29) != c_Type_Otype_OAtom(X28)
      | X29 = X28 ),
    file('<stdin>',cls_type_Osimps_I1_J_0) ).

fof(c_0_196_197,axiom,
    ! [X41,X42] :
      ( c_Lambda_OdB_OAbs(X42) != c_Lambda_OdB_OAbs(X41)
      | X42 = X41 ),
    file('<stdin>',cls_dB_Osimps_I3_J_0) ).

fof(c_0_197_198,axiom,
    ! [X28,X29] :
      ( c_Lambda_OdB_OVar(X29) != c_Lambda_OdB_OVar(X28)
      | X29 = X28 ),
    file('<stdin>',cls_dB_Osimps_I1_J_0) ).

fof(c_0_198_199,plain,
    ! [X53,X40,X17,X8,X19,X50,X9] :
      ( X19 = c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__types__1__1(X9,X19,X8,X53),X9,tc_Type_Otype,tc_Type_Otype)
      | ~ c_Type_Otyping(X8,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X17),X40,tc_Lambda_OdB,tc_Lambda_OdB),X19)
      | ~ c_Type_Otypings(X8,X40,X50)
      | ~ c_Type_Otyping(X8,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X17),X40,tc_Lambda_OdB,tc_Lambda_OdB),X53,tc_Lambda_OdB,tc_Lambda_OdB),X9) ),
    inference(fof_simplification,[status(thm)],[c_0_0]) ).

fof(c_0_199_200,plain,
    ! [X44,X31,X32] :
      ( X44 = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X32),c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(X32,X31,X44),tc_Lambda_OdB,tc_Lambda_OdB)
      | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X32),X31,tc_Lambda_OdB,tc_Lambda_OdB)),X44)) ),
    inference(fof_simplification,[status(thm)],[c_0_1]) ).

fof(c_0_200_201,plain,
    ! [X53,X40,X17,X8,X19,X50,X9] :
      ( c_Type_Otypings(X8,X53,c_Type_Osko__Type__Xvar__app__types__1__1(X9,X19,X8,X53))
      | ~ c_Type_Otyping(X8,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X17),X40,tc_Lambda_OdB,tc_Lambda_OdB),X19)
      | ~ c_Type_Otypings(X8,X40,X50)
      | ~ c_Type_Otyping(X8,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X17),X40,tc_Lambda_OdB,tc_Lambda_OdB),X53,tc_Lambda_OdB,tc_Lambda_OdB),X9) ),
    inference(fof_simplification,[status(thm)],[c_0_2]) ).

fof(c_0_201_202,plain,
    ! [X44,X31,X32] :
      ( c_ListOrder_Ostep1(c_Lambda_Obeta,X31,c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(X32,X31,X44),tc_Lambda_OdB)
      | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X32),X31,tc_Lambda_OdB,tc_Lambda_OdB)),X44)) ),
    inference(fof_simplification,[status(thm)],[c_0_3]) ).

fof(c_0_202_203,plain,
    ! [X30,X31,X34] :
      ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,X34,X31,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X34,X30,tc_Lambda_OdB,tc_Lambda_OdB)))
      | ~ c_ListOrder_Ostep1(c_Lambda_Obeta,X31,X30,tc_Lambda_OdB) ),
    inference(fof_simplification,[status(thm)],[c_0_4]) ).

fof(c_0_203_204,plain,
    ! [X30,X20,X34] :
      ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,X34,X30,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X20,X30,tc_Lambda_OdB,tc_Lambda_OdB)))
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X34),X20)) ),
    inference(fof_simplification,[status(thm)],[c_0_5]) ).

fof(c_0_204_205,plain,
    ! [X30,X20,X34] :
      ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,X34,X30,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X20,X30,tc_Lambda_OdB,tc_Lambda_OdB)))
      | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X34),X20)) ),
    inference(fof_simplification,[status(thm)],[c_0_6]) ).

fof(c_0_205_206,plain,
    ! [X30,X20,X34] :
      ( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X34)),X20),X30,tc_Lambda_OdB,tc_Lambda_OdB)))
      | ~ hBOOL(hAPP(c_InductTermi_OIT,X20))
      | ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(X34,X20,c_HOL_Ozero__class_Ozero(tc_nat)),X30,tc_Lambda_OdB,tc_Lambda_OdB))) ),
    inference(fof_simplification,[status(thm)],[c_0_7]) ).

fof(c_0_206_207,plain,
    ! [X40,X17,X8,X19,X9] :
      ( X9 = X19
      | ~ c_Type_Otyping(X8,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X17),X40,tc_Lambda_OdB,tc_Lambda_OdB),X19)
      | ~ c_Type_Otyping(X8,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X17),X40,tc_Lambda_OdB,tc_Lambda_OdB),X9) ),
    inference(fof_simplification,[status(thm)],[c_0_8]) ).

fof(c_0_207_208,plain,
    ! [X30,X20,X34] :
      ( ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(X34,X20,c_HOL_Ozero__class_Ozero(tc_nat)),X30,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)
      | ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X20,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(X34)),X20),X30,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB) ),
    inference(fof_simplification,[status(thm)],[c_0_9]) ).

fof(c_0_208_209,plain,
    ! [X40,X17,X8,X9] :
      ( c_Type_Otyping(X8,c_Lambda_OdB_OVar(X17),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__typesE__1__1(X9,X8,X17,X40),X9,tc_Type_Otype,tc_Type_Otype))
      | ~ c_Type_Otyping(X8,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X17),X40,tc_Lambda_OdB,tc_Lambda_OdB),X9) ),
    inference(fof_simplification,[status(thm)],[c_0_10]) ).

fof(c_0_209_210,plain,
    ! [X40,X7,X8,X9] :
      ( c_Type_Otyping(X8,X7,c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeE__1__1(X9,X8,X7,X40),X9,tc_Type_Otype,tc_Type_Otype))
      | ~ c_Type_Otyping(X8,c_List_Ofoldl(c_Lambda_OdB_OApp,X7,X40,tc_Lambda_OdB,tc_Lambda_OdB),X9) ),
    inference(fof_simplification,[status(thm)],[c_0_11]) ).

fof(c_0_210_211,plain,
    ! [X40,X7,X8,X9] :
      ( c_Type_Otyping(X8,X7,c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeD__1__1(X9,X8,X7,X40),X9,tc_Type_Otype,tc_Type_Otype))
      | ~ c_Type_Otyping(X8,c_List_Ofoldl(c_Lambda_OdB_OApp,X7,X40,tc_Lambda_OdB,tc_Lambda_OdB),X9) ),
    inference(fof_simplification,[status(thm)],[c_0_12]) ).

fof(c_0_211_212,plain,
    ! [X40,X7,X8,X50,X9] :
      ( c_Type_Otyping(X8,c_List_Ofoldl(c_Lambda_OdB_OApp,X7,X40,tc_Lambda_OdB,tc_Lambda_OdB),X9)
      | ~ c_Type_Otypings(X8,X40,X50)
      | ~ c_Type_Otyping(X8,X7,c_List_Ofoldr(c_Type_Otype_OFun,X50,X9,tc_Type_Otype,tc_Type_Otype)) ),
    inference(fof_simplification,[status(thm)],[c_0_13]) ).

fof(c_0_212_213,plain,
    ! [X31,X32] :
      ( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X32),X31,tc_Lambda_OdB,tc_Lambda_OdB)))
      | ~ c_List_Olistsp(c_InductTermi_OIT,X31,tc_Lambda_OdB) ),
    inference(fof_simplification,[status(thm)],[c_0_14]) ).

fof(c_0_213_214,plain,
    ! [X40,X17,X8,X9] :
      ( c_Type_Otypings(X8,X40,c_Type_Osko__Type__Xvar__app__typesE__1__1(X9,X8,X17,X40))
      | ~ c_Type_Otyping(X8,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X17),X40,tc_Lambda_OdB,tc_Lambda_OdB),X9) ),
    inference(fof_simplification,[status(thm)],[c_0_15]) ).

fof(c_0_214_215,plain,
    ! [X40,X7,X8,X9] :
      ( c_Type_Otypings(X8,X40,c_Type_Osko__Type__Xlist__app__typeE__1__1(X9,X8,X7,X40))
      | ~ c_Type_Otyping(X8,c_List_Ofoldl(c_Lambda_OdB_OApp,X7,X40,tc_Lambda_OdB,tc_Lambda_OdB),X9) ),
    inference(fof_simplification,[status(thm)],[c_0_16]) ).

fof(c_0_215_216,plain,
    ! [X40,X7,X8,X9] :
      ( c_Type_Otypings(X8,X40,c_Type_Osko__Type__Xlist__app__typeD__1__1(X9,X8,X7,X40))
      | ~ c_Type_Otyping(X8,c_List_Ofoldl(c_Lambda_OdB_OApp,X7,X40,tc_Lambda_OdB,tc_Lambda_OdB),X9) ),
    inference(fof_simplification,[status(thm)],[c_0_17]) ).

fof(c_0_216_217,axiom,
    ! [X30,X20,X31,X34] :
      ( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X34),X31,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X20),X30,tc_Lambda_OdB,tc_Lambda_OdB)
      | X31 = X30 ),
    c_0_18 ).

fof(c_0_217_218,axiom,
    ! [X30,X20,X31,X34] :
      ( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X34),X31,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X20),X30,tc_Lambda_OdB,tc_Lambda_OdB)
      | X34 = X20 ),
    c_0_19 ).

fof(c_0_218_219,axiom,
    ! [X30,X31,X32,X33] :
      ( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X33),X31,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X32),X30,tc_Lambda_OdB,tc_Lambda_OdB)
      | X31 = X30 ),
    c_0_20 ).

fof(c_0_219_220,axiom,
    ! [X30,X31,X32,X33] :
      ( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X33),X31,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X32),X30,tc_Lambda_OdB,tc_Lambda_OdB)
      | X33 = X32 ),
    c_0_21 ).

fof(c_0_220_221,plain,
    ! [X56,X52,X21,X3] :
      ( ~ class_OrderedGroup_Osemigroup__add(X3)
      | c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X21),X52),X56,X3,X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X21),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),X52,X56,X3,X3)) ),
    inference(fof_simplification,[status(thm)],[c_0_22]) ).

fof(c_0_221_222,axiom,
    ! [X40,X20,X34] :
      ( c_List_Ofoldl(c_Lambda_OdB_OApp,X34,X40,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,X20,X40,tc_Lambda_OdB,tc_Lambda_OdB)
      | X34 = X20 ),
    c_0_23 ).

fof(c_0_222_223,plain,
    ! [X56,X21,X3] :
      ( ~ class_OrderedGroup_Omonoid__add(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X21),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3),X56,X3,X3)) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),X21,X56,X3,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_24]) ).

fof(c_0_223_224,plain,
    ! [X49,X45,X3] :
      ( ~ class_OrderedGroup_Omonoid__add(X3)
      | c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),X45,X49,X3,X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X3),X49,c_HOL_Ozero__class_Ozero(X3),X3,X3)) ),
    inference(fof_simplification,[status(thm)],[c_0_25]) ).

fof(c_0_224_225,plain,
    ! [X49,X3] :
      ( ~ class_OrderedGroup_Omonoid__add(X3)
      | c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3),X49,X3,X3) = c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X3),X49,c_HOL_Ozero__class_Ozero(X3),X3,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_26]) ).

fof(c_0_225_226,plain,
    ! [X49,X45,X3] :
      ( ~ class_OrderedGroup_Oab__semigroup__add(X3)
      | c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X3),X49,X45,X3,X3) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),X45,X49,X3,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_27]) ).

fof(c_0_226_227,plain,
    ! [X6,X7,X8,X9] :
      ( c_Type_Otyping(X8,X7,hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__2__1(X9,X8,X7,X6)),X9))
      | ~ c_Type_Otyping(X8,hAPP(hAPP(c_Lambda_OdB_OApp,X7),X6),X9) ),
    inference(fof_simplification,[status(thm)],[c_0_28]) ).

fof(c_0_227_228,plain,
    ! [X15,X16,X12,X13,X14] :
      ( ~ hBOOL(hAPP(X14,c_Type_Otype_Otype__case(X13,X12,hAPP(hAPP(c_Type_Otype_OFun,X16),X15),t_a)))
      | hBOOL(hAPP(X14,hAPP(hAPP(X12,X16),X15))) ),
    inference(fof_simplification,[status(thm)],[c_0_29]) ).

fof(c_0_228_229,plain,
    ! [X10,X11,X12,X13,X14] :
      ( ~ hBOOL(hAPP(X14,c_Type_Otype_Otype__case(X13,X12,hAPP(hAPP(c_Type_Otype_OFun,X11),X10),t_a)))
      | hBOOL(hAPP(X14,hAPP(hAPP(X12,X11),X10))) ),
    inference(fof_simplification,[status(thm)],[c_0_30]) ).

fof(c_0_229_230,axiom,
    ! [X7,X20,X34] :
      ( hAPP(hAPP(c_Lambda_OdB_OApp,X34),X20) != c_List_Ofoldl(c_Lambda_OdB_OApp,X7,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)
      | hAPP(hAPP(c_Lambda_OdB_OApp,X34),X20) = X7 ),
    c_0_31 ).

fof(c_0_230_231,axiom,
    ! [X30,X20,X34] :
      ( c_Lambda_OdB_OAbs(X34) != c_List_Ofoldl(c_Lambda_OdB_OApp,X20,X30,tc_Lambda_OdB,tc_Lambda_OdB)
      | c_Lambda_OdB_OAbs(X34) = X20 ),
    c_0_32 ).

fof(c_0_231_232,axiom,
    ! [X30,X20,X33] :
      ( c_Lambda_OdB_OVar(X33) != c_List_Ofoldl(c_Lambda_OdB_OApp,X20,X30,tc_Lambda_OdB,tc_Lambda_OdB)
      | c_Lambda_OdB_OVar(X33) = X20 ),
    c_0_33 ).

fof(c_0_232_233,axiom,
    ! [X30,X20,X34] :
      ( c_List_Ofoldl(c_Lambda_OdB_OApp,X20,X30,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X34)
      | X20 = c_Lambda_OdB_OAbs(X34) ),
    c_0_34 ).

fof(c_0_233_234,axiom,
    ! [X30,X20,X34] :
      ( c_Lambda_OdB_OAbs(X34) != c_List_Ofoldl(c_Lambda_OdB_OApp,X20,X30,tc_Lambda_OdB,tc_Lambda_OdB)
      | X30 = c_List_Olist_ONil(tc_Lambda_OdB) ),
    c_0_35 ).

fof(c_0_234_235,axiom,
    ! [X30,X20,X34] :
      ( c_List_Ofoldl(c_Lambda_OdB_OApp,X20,X30,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X34)
      | X30 = c_List_Olist_ONil(tc_Lambda_OdB) ),
    c_0_36 ).

fof(c_0_235_236,axiom,
    ! [X30,X20,X33] :
      ( c_Lambda_OdB_OVar(X33) != c_List_Ofoldl(c_Lambda_OdB_OApp,X20,X30,tc_Lambda_OdB,tc_Lambda_OdB)
      | X30 = c_List_Olist_ONil(tc_Lambda_OdB) ),
    c_0_37 ).

fof(c_0_236_237,plain,
    ! [X52,X21,X34,X3] :
      ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X34,X3),X52),X21))
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Predicate_Oconversep(X34,X3,X3),X3),X21),X52)) ),
    inference(fof_simplification,[status(thm)],[c_0_38]) ).

fof(c_0_237_238,plain,
    ! [X29,X12,X13,X14] :
      ( ~ hBOOL(hAPP(X14,c_Type_Otype_Otype__case(X13,X12,c_Type_Otype_OAtom(X29),t_a)))
      | hBOOL(hAPP(X14,hAPP(X13,X29))) ),
    inference(fof_simplification,[status(thm)],[c_0_39]) ).

fof(c_0_238_239,plain,
    ! [X46,X12,X13,X14] :
      ( ~ hBOOL(hAPP(X14,c_Type_Otype_Otype__case(X13,X12,c_Type_Otype_OAtom(X46),t_a)))
      | hBOOL(hAPP(X14,hAPP(X13,X46))) ),
    inference(fof_simplification,[status(thm)],[c_0_40]) ).

fof(c_0_239_240,plain,
    ! [X52,X21,X34,X3] :
      ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Predicate_Oconversep(X34,X3,X3),X3),X21),X52))
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X34,X3),X52),X21)) ),
    inference(fof_simplification,[status(thm)],[c_0_41]) ).

fof(c_0_240_241,plain,
    ! [X6,X7,X17,X8,X19,X9] :
      ( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(X7,X6,X17)))
      | ~ c_Type_Otyping(X8,X6,X19)
      | ~ hBOOL(hAPP(c_InductTermi_OIT,X6))
      | ~ c_Type_Otyping(c_Type_Oshift(X8,X17,X19,tc_Type_Otype),X7,X9)
      | ~ hBOOL(hAPP(c_InductTermi_OIT,X7)) ),
    inference(fof_simplification,[status(thm)],[c_0_42]) ).

fof(c_0_241_242,plain,
    ! [X6,X7,X17,X47,X19,X9] :
      ( ~ c_Type_Otyping(X47,X6,X19)
      | ~ c_Type_Otyping(c_Type_Oshift(X47,X17,X19,tc_Type_Otype),X7,X9)
      | c_Type_Otyping(X47,c_Lambda_Osubst(X7,X6,X17),X9) ),
    inference(fof_simplification,[status(thm)],[c_0_43]) ).

fof(c_0_242_243,plain,
    ! [X27,X7,X43,X20] :
      ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X20),X7)),hAPP(hAPP(c_Lambda_OdB_OApp,X43),X27)))
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X7),X27))
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X20),X43)) ),
    inference(fof_simplification,[status(thm)],[c_0_44]) ).

fof(c_0_243_244,plain,
    ! [X7,X20,X34,X17] :
      ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Osubst(X7,X34,X17)),c_Lambda_Osubst(X7,X20,X17)))
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X34),X20)) ),
    inference(fof_simplification,[status(thm)],[c_0_45]) ).

fof(c_0_244_245,plain,
    ! [X7,X20,X34,X17] :
      ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Osubst(X34,X7,X17)),c_Lambda_Osubst(X20,X7,X17)))
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X34),X20)) ),
    inference(fof_simplification,[status(thm)],[c_0_46]) ).

fof(c_0_245_246,plain,
    ! [X7,X18,X19,X9] :
      ( c_Type_Otyping(X18,c_Lambda_OdB_OAbs(X7),hAPP(hAPP(c_Type_Otype_OFun,X9),X19))
      | ~ c_Type_Otyping(c_Type_Oshift(X18,c_HOL_Ozero__class_Ozero(tc_nat),X9,tc_Type_Otype),X7,X19) ),
    inference(fof_simplification,[status(thm)],[c_0_47]) ).

fof(c_0_246_247,plain,
    ! [X7,X8,X9] :
      ( c_Type_Otyping(c_Type_Oshift(X8,c_HOL_Ozero__class_Ozero(tc_nat),c_Type_Osko__Type__Xtyping__elims__3__1(X9,X8,X7),tc_Type_Otype),X7,c_Type_Osko__Type__Xtyping__elims__3__2(X9,X8,X7))
      | ~ c_Type_Otyping(X8,c_Lambda_OdB_OAbs(X7),X9) ),
    inference(fof_simplification,[status(thm)],[c_0_48]) ).

fof(c_0_247_248,plain,
    ! [X7,X20,X34,X17] :
      ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Osubst(X7,X34,X17)),c_Lambda_Osubst(X7,X20,X17)))
      | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X34),X20)) ),
    inference(fof_simplification,[status(thm)],[c_0_49]) ).

fof(c_0_248_249,plain,
    ! [X34,X48,X45,X57,X3] :
      ( hBOOL(hAPP(hAPP(X34,X48),X45))
      | ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X34,X3,X57),X45),X48)) ),
    inference(fof_simplification,[status(thm)],[c_0_50]) ).

fof(c_0_249_250,plain,
    ! [X34,X58,X59,X57,X3] :
      ( hBOOL(hAPP(hAPP(X34,X58),X59))
      | ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X34,X3,X57),X59),X58)) ),
    inference(fof_simplification,[status(thm)],[c_0_51]) ).

fof(c_0_250_251,plain,
    ! [X7,X43,X20] :
      ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X20),X7)),hAPP(hAPP(c_Lambda_OdB_OApp,X43),X7)))
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X20),X43)) ),
    inference(fof_simplification,[status(thm)],[c_0_52]) ).

fof(c_0_251_252,plain,
    ! [X27,X7,X20] :
      ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X20),X7)),hAPP(hAPP(c_Lambda_OdB_OApp,X20),X27)))
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X7),X27)) ),
    inference(fof_simplification,[status(thm)],[c_0_53]) ).

fof(c_0_252_253,plain,
    ! [X7,X20,X34,X17] :
      ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_Osubst(X34,X7,X17)),c_Lambda_Osubst(X20,X7,X17)))
      | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X34),X20)) ),
    inference(fof_simplification,[status(thm)],[c_0_54]) ).

fof(c_0_253_254,plain,
    ! [X51,X52,X21,X34,X3] :
      ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X34,X3),X21),X51))
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X34,X3),X52),X51))
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X34,X3),X21),X52)) ),
    inference(fof_simplification,[status(thm)],[c_0_55]) ).

fof(c_0_254_255,plain,
    ! [X6,X7,X8,X9] :
      ( c_Type_Otyping(X8,X6,c_Type_Osko__Type__Xtyping__elims__2__1(X9,X8,X7,X6))
      | ~ c_Type_Otyping(X8,hAPP(hAPP(c_Lambda_OdB_OApp,X7),X6),X9) ),
    inference(fof_simplification,[status(thm)],[c_0_56]) ).

fof(c_0_255_256,plain,
    ! [X55,X54,X48,X45,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),X45),X48)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X54),X55)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),X54)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X48),X55)) ),
    inference(fof_simplification,[status(thm)],[c_0_57]) ).

fof(c_0_256_257,plain,
    ! [X7,X8,X9] :
      ( c_Type_Otyping(c_Type_Oshift(X8,c_HOL_Ozero__class_Ozero(tc_nat),c_Type_Osko__Type__Xabs__typeE__1__1(X8,X7),tc_Type_Otype),X7,c_Type_Osko__Type__Xabs__typeE__1__2(X8,X7))
      | ~ c_Type_Otyping(X8,c_Lambda_OdB_OAbs(X7),X9) ),
    inference(fof_simplification,[status(thm)],[c_0_58]) ).

fof(c_0_257_258,plain,
    ! [X7,X17,X8,X19,X9] :
      ( c_Type_Otyping(c_Type_Oshift(X8,X17,X19,tc_Type_Otype),c_Lambda_Olift(X7,X17),X9)
      | ~ c_Type_Otyping(X8,X7,X9) ),
    inference(fof_simplification,[status(thm)],[c_0_59]) ).

fof(c_0_258_259,plain,
    ! [X34,X48,X45,X57,X3] :
      ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X34,X3,X57),X45),X48))
      | ~ hBOOL(hAPP(hAPP(X34,X48),X45)) ),
    inference(fof_simplification,[status(thm)],[c_0_60]) ).

fof(c_0_259_260,plain,
    ! [X34,X48,X45,X57,X3] :
      ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X34,X3,X57),X48),X45))
      | ~ hBOOL(hAPP(hAPP(X34,X45),X48)) ),
    inference(fof_simplification,[status(thm)],[c_0_61]) ).

fof(c_0_260_261,plain,
    ! [X6,X7,X20] :
      ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,X20),X6)),hAPP(hAPP(c_Lambda_OdB_OApp,X7),X6)))
      | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X20),X7)) ),
    inference(fof_simplification,[status(thm)],[c_0_62]) ).

fof(c_0_261_262,plain,
    ! [X6,X7,X20] :
      ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,X6),X20)),hAPP(hAPP(c_Lambda_OdB_OApp,X6),X7)))
      | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X20),X7)) ),
    inference(fof_simplification,[status(thm)],[c_0_63]) ).

fof(c_0_262_263,plain,
    ! [X32,X48,X45,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_lessequals(X45,X48,X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X48,X3)
      | ~ c_lessequals(c_Power_Opower__class_Opower(X45,c_Suc(X32),X3),c_Power_Opower__class_Opower(X48,c_Suc(X32),X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_64]) ).

fof(c_0_263_264,plain,
    ! [X34,X54,X48,X45,X3] :
      ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X34,X3),X45),X54))
      | ~ hBOOL(hAPP(hAPP(X34,X48),X54))
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X34,X3),X45),X48)) ),
    inference(fof_simplification,[status(thm)],[c_0_65]) ).

fof(c_0_264_265,plain,
    ! [X34,X54,X48,X45,X3] :
      ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X34,X3),X45),X54))
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X34,X3),X48),X54))
      | ~ hBOOL(hAPP(hAPP(X34,X45),X48)) ),
    inference(fof_simplification,[status(thm)],[c_0_66]) ).

fof(c_0_265_266,plain,
    ! [X20,X34,X17] :
      ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Olift(X34,X17)),c_Lambda_Olift(X20,X17)))
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X34),X20)) ),
    inference(fof_simplification,[status(thm)],[c_0_67]) ).

fof(c_0_266_267,plain,
    ! [X54,X48,X45,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),X45),X48)),X54) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),X54)),X48) ),
    inference(fof_simplification,[status(thm)],[c_0_68]) ).

fof(c_0_267_268,plain,
    ! [X55,X54,X48,X45,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
      | c_lessequals(X45,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X48),X55),X3)
      | ~ c_lessequals(X54,X55,X3)
      | ~ c_lessequals(X45,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X48),X54),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_69]) ).

fof(c_0_268_269,plain,
    ! [X54,X48,X45,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
      | c_lessequals(X45,X48,X3)
      | ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),X54),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X48),X54),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_70]) ).

fof(c_0_269_270,plain,
    ! [X54,X48,X45,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
      | c_lessequals(X45,X48,X3)
      | ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X54),X45),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X54),X48),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_71]) ).

fof(c_0_270_271,plain,
    ! [X32,X48,X45,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_lessequals(c_Power_Opower__class_Opower(X45,X32,X3),c_Power_Opower__class_Opower(X48,X32,X3),X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X45,X3)
      | ~ c_lessequals(X45,X48,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_72]) ).

fof(c_0_271_272,plain,
    ! [X7,X8,X9] :
      ( X9 = hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__3__1(X9,X8,X7)),c_Type_Osko__Type__Xtyping__elims__3__2(X9,X8,X7))
      | ~ c_Type_Otyping(X8,c_Lambda_OdB_OAbs(X7),X9) ),
    inference(fof_simplification,[status(thm)],[c_0_73]) ).

fof(c_0_272_273,plain,
    ! [X43,X20] :
      ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_OdB_OAbs(X20)),c_Lambda_OdB_OAbs(X43)))
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X20),X43)) ),
    inference(fof_simplification,[status(thm)],[c_0_74]) ).

fof(c_0_273_274,plain,
    ! [X55,X54,X48,X45,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3)
      | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),X54),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X48),X55),X3)
      | ~ c_lessequals(X54,X55,X3)
      | ~ c_lessequals(X45,X48,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_75]) ).

fof(c_0_274_275,plain,
    ! [X34,X48,X45,X3] :
      ( c_Wellfounded_Oaccp(X34,X48,X3)
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X34,X3),X48),X45))
      | ~ c_Wellfounded_Oaccp(X34,X45,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_76]) ).

fof(c_0_275_276,plain,
    ! [X34,X48,X45,X3] :
      ( c_Wellfounded_Oaccp(X34,X48,X3)
      | ~ c_Wellfounded_Oaccp(X34,X45,X3)
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X34,X3),X48),X45)) ),
    inference(fof_simplification,[status(thm)],[c_0_77]) ).

fof(c_0_276_277,plain,
    ! [X54,X48,X45,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),X45),X48)),X54) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X48),X54)) ),
    inference(fof_simplification,[status(thm)],[c_0_78]) ).

fof(c_0_277_278,plain,
    ! [X55,X54,X45,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X54),X55)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),X54)),X55) ),
    inference(fof_simplification,[status(thm)],[c_0_79]) ).

fof(c_0_278_279,plain,
    ! [X54,X48,X45,X3] :
      ( ~ class_OrderedGroup_Oab__semigroup__add(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),X48)),X54) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X48),X54)) ),
    inference(fof_simplification,[status(thm)],[c_0_80]) ).

fof(c_0_279_280,plain,
    ! [X54,X48,X45,X3] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),X48)),X54) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X48),X54)) ),
    inference(fof_simplification,[status(thm)],[c_0_81]) ).

fof(c_0_280_281,plain,
    ! [X51,X52,X21,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X21),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X52),X51)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X21),X52)),X51) ),
    inference(fof_simplification,[status(thm)],[c_0_82]) ).

fof(c_0_281_282,plain,
    ! [X7,X20,X18,X19,X9] :
      ( c_Type_Otyping(X18,hAPP(hAPP(c_Lambda_OdB_OApp,X20),X7),X19)
      | ~ c_Type_Otyping(X18,X7,X9)
      | ~ c_Type_Otyping(X18,X20,hAPP(hAPP(c_Type_Otype_OFun,X9),X19)) ),
    inference(fof_simplification,[status(thm)],[c_0_83]) ).

fof(c_0_282_283,plain,
    ! [X27,X7,X8,X9] :
      ( c_Type_Otyping(X8,X27,X9)
      | ~ c_Type_Otyping(X8,X7,X9)
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X7),X27)) ),
    inference(fof_simplification,[status(thm)],[c_0_84]) ).

fof(c_0_283_284,plain,
    ! [X32,X48,X45,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_Power_Opower__class_Opower(X45,c_Suc(X32),X3) != c_Power_Opower__class_Opower(X48,c_Suc(X32),X3)
      | X45 = X48
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X48,X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X45,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_85]) ).

fof(c_0_284_285,plain,
    ! [X51,X52,X21,X6,X3] :
      ( ~ class_OrderedGroup_Oab__group__add(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X21),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X52),X51)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X52),X6)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X21),X51) = X6 ),
    inference(fof_simplification,[status(thm)],[c_0_86]) ).

fof(c_0_285_286,plain,
    ! [X48,X45,X3] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),X48),X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X48,X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X45,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_87]) ).

fof(c_0_286_287,plain,
    ! [X48,X45,X3] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
      | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),X48),c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_lessequals(X48,c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_lessequals(X45,c_HOL_Ozero__class_Ozero(X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_88]) ).

fof(c_0_287_288,plain,
    ! [X54,X48,X45,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
      | ~ class_OrderedGroup_Ocomm__monoid__add(X3)
      | c_lessequals(X48,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),X54),X3)
      | ~ c_lessequals(X48,X54,X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X45,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_89]) ).

fof(c_0_288_289,plain,
    ! [X54,X48,X45,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
      | ~ class_OrderedGroup_Ocomm__monoid__add(X3)
      | c_lessequals(X48,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),X54),X3)
      | ~ c_lessequals(X48,X45,X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X54,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_90]) ).

fof(c_0_289_290,plain,
    ! [X54,X48,X45,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
      | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),X54),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X48),X54),X3)
      | ~ c_lessequals(X45,X48,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_91]) ).

fof(c_0_290_291,plain,
    ! [X54,X48,X45,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
      | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X54),X45),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X54),X48),X3)
      | ~ c_lessequals(X45,X48,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_92]) ).

fof(c_0_291_292,plain,
    ! [X54,X48,X45,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3)
      | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),X54),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X48),X54),X3)
      | ~ c_lessequals(X45,X48,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_93]) ).

fof(c_0_292_293,plain,
    ! [X54,X48,X45,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3)
      | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X54),X45),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X54),X48),X3)
      | ~ c_lessequals(X45,X48,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_94]) ).

fof(c_0_293_294,plain,
    ! [X20,X34,X17] :
      ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_Olift(X34,X17)),c_Lambda_Olift(X20,X17)))
      | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X34),X20)) ),
    inference(fof_simplification,[status(thm)],[c_0_95]) ).

fof(c_0_294_295,plain,
    ! [X45,X3] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X3),X45,X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),X45),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_96]) ).

fof(c_0_295_296,plain,
    ! [X45,X3] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
      | c_lessequals(X45,c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),X45),c_HOL_Ozero__class_Ozero(X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_97]) ).

fof(c_0_296_297,plain,
    ! [X55,X54,X45,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X54),X55)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X54),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),X55)) ),
    inference(fof_simplification,[status(thm)],[c_0_98]) ).

fof(c_0_297_298,plain,
    ! [X54,X48,X45,X3] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X48),X54)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X48),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),X54)) ),
    inference(fof_simplification,[status(thm)],[c_0_99]) ).

fof(c_0_298_299,plain,
    ! [X51,X52,X21,X3] :
      ( ~ class_OrderedGroup_Oab__group__add(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X21),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X52),X51)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X52),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X21),X51)) ),
    inference(fof_simplification,[status(thm)],[c_0_100]) ).

fof(c_0_299_300,plain,
    ! [X52,X21,X34,X3] :
      ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X34,X3),X21),X52))
      | ~ hBOOL(hAPP(hAPP(X34,X21),X52)) ),
    inference(fof_simplification,[status(thm)],[c_0_101]) ).

fof(c_0_300_301,plain,
    ! [X34,X35,X17] :
      ( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(X34,c_Lambda_OdB_OVar(X17),X35)))
      | ~ hBOOL(hAPP(c_InductTermi_OIT,X34)) ),
    inference(fof_simplification,[status(thm)],[c_0_102]) ).

fof(c_0_301_302,plain,
    ! [X52,X21,X3] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X21),X52) != c_HOL_Ozero__class_Ozero(X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X52,X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X21,X3)
      | X52 = c_HOL_Ozero__class_Ozero(X3) ),
    inference(fof_simplification,[status(thm)],[c_0_103]) ).

fof(c_0_302_303,plain,
    ! [X52,X21,X3] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X21),X52) != c_HOL_Ozero__class_Ozero(X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X52,X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X21,X3)
      | X21 = c_HOL_Ozero__class_Ozero(X3) ),
    inference(fof_simplification,[status(thm)],[c_0_104]) ).

fof(c_0_303_304,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_105]) ).

fof(c_0_304_305,plain,
    ! [X20,X34] :
      ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,X34),c_Lambda_Osko__Lambda__Xbeta__cases__2__1(X34,X20)))
      | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OAbs(X34)),X20)) ),
    inference(fof_simplification,[status(thm)],[c_0_106]) ).

fof(c_0_305_306,plain,
    ! [X32,X45,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_Power_Opower__class_Opower(X45,X32,X3),X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X45,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_107]) ).

fof(c_0_306_307,plain,
    ! [X32,X45,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_lessequals(c_HOL_Oone__class_Oone(X3),c_Power_Opower__class_Opower(X45,X32,X3),X3)
      | ~ c_lessequals(c_HOL_Oone__class_Oone(X3),X45,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_108]) ).

fof(c_0_307_308,plain,
    ! [X52,X34,X45,X3] :
      ( c_Wellfounded_Oaccp(X34,X52,X3)
      | ~ hBOOL(hAPP(hAPP(X34,X52),X45))
      | ~ c_Wellfounded_Oaccp(X34,X45,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_109]) ).

fof(c_0_308_309,plain,
    ! [X34,X48,X45,X3] :
      ( c_Wellfounded_Oaccp(X34,X45,X3)
      | ~ hBOOL(hAPP(hAPP(X34,X45),X48))
      | ~ c_Wellfounded_Oaccp(X34,X48,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_110]) ).

fof(c_0_309_310,plain,
    ! [X45,X3] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),X45),X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X45,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_111]) ).

fof(c_0_310_311,plain,
    ! [X45,X3] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
      | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),X45),c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_lessequals(X45,c_HOL_Ozero__class_Ozero(X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_112]) ).

fof(c_0_311_312,plain,
    ! [X34] :
      ( hBOOL(hAPP(c_InductTermi_OIT,X34))
      | ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X34,tc_Lambda_OdB) ),
    inference(fof_simplification,[status(thm)],[c_0_113]) ).

fof(c_0_312_313,plain,
    ! [X27,X7,X8,X9] :
      ( c_Type_Otyping(X8,X27,X9)
      | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X7),X27))
      | ~ c_Type_Otyping(X8,X7,X9) ),
    inference(fof_simplification,[status(thm)],[c_0_114]) ).

fof(c_0_313_314,plain,
    ! [X32,X33,X3] :
      ( ~ class_Ring__and__Field_Osemiring__1(X3)
      | c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X33),X32),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_Nat_Osemiring__1__class_Oof__nat(X33,X3)),c_Nat_Osemiring__1__class_Oof__nat(X32,X3)) ),
    inference(fof_simplification,[status(thm)],[c_0_115]) ).

fof(c_0_314_315,plain,
    ! [X7,X17] :
      ( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,X7),c_Lambda_OdB_OVar(X17))))
      | ~ hBOOL(hAPP(c_InductTermi_OIT,X7)) ),
    inference(fof_simplification,[status(thm)],[c_0_116]) ).

fof(c_0_315_316,plain,
    ! [X51,X52,X21,X3] :
      ( ~ class_Orderings_Oorder(X3)
      | c_lessequals(X51,X21,X3)
      | ~ c_lessequals(X51,X52,X3)
      | ~ c_lessequals(X52,X21,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_117]) ).

fof(c_0_316_317,plain,
    ! [X51,X52,X21,X3] :
      ( ~ class_Orderings_Opreorder(X3)
      | c_lessequals(X21,X51,X3)
      | ~ c_lessequals(X52,X51,X3)
      | ~ c_lessequals(X21,X52,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_118]) ).

fof(c_0_317_318,plain,
    ! [X7,X20] :
      ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OAbs(X20)),c_Lambda_OdB_OAbs(X7)))
      | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X20),X7)) ),
    inference(fof_simplification,[status(thm)],[c_0_119]) ).

fof(c_0_318_319,plain,
    ! [X7] :
      ( c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X7,tc_Lambda_OdB)
      | ~ hBOOL(hAPP(c_InductTermi_OIT,X7)) ),
    inference(fof_simplification,[status(thm)],[c_0_120]) ).

fof(c_0_319_320,plain,
    ! [X20,X34] :
      ( X20 = c_Lambda_OdB_OAbs(c_Lambda_Osko__Lambda__Xbeta__cases__2__1(X34,X20))
      | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OAbs(X34)),X20)) ),
    inference(fof_simplification,[status(thm)],[c_0_121]) ).

fof(c_0_320_321,plain,
    ! [X52,X21,X3] :
      ( ~ class_Orderings_Oorder(X3)
      | X21 = X52
      | ~ c_lessequals(X52,X21,X3)
      | ~ c_lessequals(X21,X52,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_122]) ).

fof(c_0_321_322,plain,
    ! [X52,X21,X3] :
      ( ~ class_Orderings_Oorder(X3)
      | X21 = X52
      | ~ c_lessequals(X52,X21,X3)
      | ~ c_lessequals(X21,X52,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_123]) ).

fof(c_0_322_323,plain,
    ! [X52,X21,X3] :
      ( ~ class_Orderings_Oorder(X3)
      | X21 = X52
      | ~ c_lessequals(X21,X52,X3)
      | ~ c_lessequals(X52,X21,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_124]) ).

fof(c_0_323_324,plain,
    ! [X51,X52,X21,X3] :
      ( ~ class_Ring__and__Field_Oidom(X3)
      | ~ class_Int_Onumber__ring(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X21),X52) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X21),X51)
      | X52 = X51 ),
    inference(fof_simplification,[status(thm)],[c_0_125]) ).

fof(c_0_324_325,plain,
    ! [X54,X48,X45,X3] :
      ( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),X48) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),X54)
      | X48 = X54 ),
    inference(fof_simplification,[status(thm)],[c_0_126]) ).

fof(c_0_325_326,plain,
    ! [X54,X48,X45,X3] :
      ( ~ class_OrderedGroup_Ocancel__semigroup__add(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),X48) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),X54)
      | X48 = X54 ),
    inference(fof_simplification,[status(thm)],[c_0_127]) ).

fof(c_0_326_327,plain,
    ! [X54,X48,X45,X3] :
      ( ~ class_OrderedGroup_Ocancel__semigroup__add(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X48),X45) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X54),X45)
      | X48 = X54 ),
    inference(fof_simplification,[status(thm)],[c_0_128]) ).

fof(c_0_327_328,plain,
    ! [X1,X2,X3] :
      ( X2 = X1
      | ~ hBOOL(hAPP(hAPP(c_fequal(X3),X2),X1)) ),
    inference(fof_simplification,[status(thm)],[c_0_129]) ).

fof(c_0_328_329,axiom,
    ! [X51,X52,X21] :
      ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X21),X52) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X21),X51)
      | X52 = X51 ),
    c_0_130 ).

fof(c_0_329_330,axiom,
    ! [X32,X33,X60] :
      ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X33),X60) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X32),X60)
      | X33 = X32 ),
    c_0_131 ).

fof(c_0_330_331,axiom,
    ! [X32,X33,X60] :
      ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X60),X33) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X60),X32)
      | X33 = X32 ),
    c_0_132 ).

fof(c_0_331_332,plain,
    ! [X32,X45,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(X45,X32,X3) != c_HOL_Ozero__class_Ozero(X3)
      | X45 = c_HOL_Ozero__class_Ozero(X3) ),
    inference(fof_simplification,[status(thm)],[c_0_133]) ).

fof(c_0_332_333,plain,
    ! [X45,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(X45,c_HOL_Ozero__class_Ozero(tc_nat),X3) != c_HOL_Ozero__class_Ozero(X3) ),
    inference(fof_simplification,[status(thm)],[c_0_134]) ).

fof(c_0_333_334,axiom,
    ! [X23,X24,X9,X14] :
      ( c_Type_Osko__Type__Xtype__induct__1__1(X14) != hAPP(hAPP(c_Type_Otype_OFun,X24),X23)
      | hBOOL(hAPP(X14,X9))
      | hBOOL(hAPP(X14,X23)) ),
    c_0_135 ).

fof(c_0_334_335,axiom,
    ! [X21,X22,X9,X14] :
      ( c_Type_Osko__Type__Xtype__induct__1__1(X14) != hAPP(hAPP(c_Type_Otype_OFun,X22),X21)
      | hBOOL(hAPP(X14,X9))
      | hBOOL(hAPP(X14,X22)) ),
    c_0_136 ).

fof(c_0_335_336,plain,
    ! [X7,X17] :
      ( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Olift(X7,X17)))
      | ~ hBOOL(hAPP(c_InductTermi_OIT,X7)) ),
    inference(fof_simplification,[status(thm)],[c_0_137]) ).

fof(c_0_336_337,axiom,
    ! [X36,X37,X38,X39] :
      ( hAPP(hAPP(c_Lambda_OdB_OApp,X39),X37) != hAPP(hAPP(c_Lambda_OdB_OApp,X38),X36)
      | X37 = X36 ),
    c_0_138 ).

fof(c_0_337_338,axiom,
    ! [X36,X37,X38,X39] :
      ( hAPP(hAPP(c_Lambda_OdB_OApp,X39),X37) != hAPP(hAPP(c_Lambda_OdB_OApp,X38),X36)
      | X39 = X38 ),
    c_0_139 ).

fof(c_0_338_339,axiom,
    ! [X25,X10,X26,X11] :
      ( hAPP(hAPP(c_Type_Otype_OFun,X11),X10) != hAPP(hAPP(c_Type_Otype_OFun,X26),X25)
      | X11 = X26 ),
    c_0_140 ).

fof(c_0_339_340,axiom,
    ! [X25,X10,X26,X11] :
      ( hAPP(hAPP(c_Type_Otype_OFun,X11),X10) != hAPP(hAPP(c_Type_Otype_OFun,X26),X25)
      | X10 = X25 ),
    c_0_141 ).

fof(c_0_340_341,plain,
    ! [X33,X3] :
      ( ~ class_Ring__and__Field_Osemiring__1(X3)
      | c_Nat_Osemiring__1__class_Oof__nat(c_Suc(X33),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Oone__class_Oone(X3)),c_Nat_Osemiring__1__class_Oof__nat(X33,X3)) ),
    inference(fof_simplification,[status(thm)],[c_0_142]) ).

fof(c_0_341_342,plain,
    ! [X52,X21,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_lessequals(X52,X21,X3)
      | c_lessequals(X21,X52,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_143]) ).

fof(c_0_342_343,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_144]) ).

fof(c_0_343_344,plain,
    ! [X54,X45,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),X54) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X54),X45) ),
    inference(fof_simplification,[status(thm)],[c_0_145]) ).

fof(c_0_344_345,plain,
    ! [X48,X45,X3] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),X48) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X48),X45) ),
    inference(fof_simplification,[status(thm)],[c_0_146]) ).

fof(c_0_345_346,plain,
    ! [X52,X21,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X21),X52) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X52),X21) ),
    inference(fof_simplification,[status(thm)],[c_0_147]) ).

fof(c_0_346_347,plain,
    ! [X17,X8,X9] :
      ( hAPP(X8,X17) = X9
      | ~ c_Type_Otyping(X8,c_Lambda_OdB_OVar(X17),X9) ),
    inference(fof_simplification,[status(thm)],[c_0_148]) ).

fof(c_0_347_348,plain,
    ! [X32,X45,X3] :
      ( ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X3)
      | c_Power_Opower__class_Opower(X45,X32,X3) != c_HOL_Ozero__class_Ozero(X3)
      | X45 = c_HOL_Ozero__class_Ozero(X3) ),
    inference(fof_simplification,[status(thm)],[c_0_149]) ).

fof(c_0_348_349,plain,
    ! [X21,X45,X3] :
      ( ~ class_Ring__and__Field_Oidom(X3)
      | ~ class_Int_Onumber__ring(X3)
      | X21 != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X21),X45)
      | X45 = c_HOL_Ozero__class_Ozero(X3) ),
    inference(fof_simplification,[status(thm)],[c_0_150]) ).

fof(c_0_349_350,plain,
    ! [X45,X3] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),X45) != c_HOL_Ozero__class_Ozero(X3)
      | X45 = c_HOL_Ozero__class_Ozero(X3) ),
    inference(fof_simplification,[status(thm)],[c_0_151]) ).

fof(c_0_350_351,axiom,
    ! [X32,X33] :
      ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X33),X32)
      | X32 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X33 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    c_0_152 ).

fof(c_0_351_352,axiom,
    ! [X32,X33] :
      ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X33),X32) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X32 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X33 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    c_0_153 ).

fof(c_0_352_353,plain,
    ! [X9,X14] :
      ( hBOOL(hAPP(X14,X9))
      | ~ hBOOL(hAPP(X14,c_Type_Osko__Type__Xtype__induct__1__1(X14))) ),
    inference(fof_simplification,[status(thm)],[c_0_154]) ).

fof(c_0_353_354,plain,
    ! [X32,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),X32,X3) = c_HOL_Ozero__class_Ozero(X3)
      | X32 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_155]) ).

fof(c_0_354_355,axiom,
    ! [X32,X33] :
      ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X33),X32) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X32 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X32 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    c_0_156 ).

fof(c_0_355_356,axiom,
    ! [X32,X33] :
      ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X33),X32) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X33 = c_HOL_Ozero__class_Ozero(tc_nat)
      | X33 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    c_0_157 ).

fof(c_0_356_357,axiom,
    ! [X32,X33] :
      ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X33),X32)
      | X33 = c_HOL_Ozero__class_Ozero(tc_nat)
      | X33 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    c_0_158 ).

fof(c_0_357_358,axiom,
    ! [X32,X33] :
      ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X33),X32)
      | X32 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X32 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    c_0_159 ).

fof(c_0_358_359,plain,
    ! [X32,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_Nat_Osemiring__1__class_Oof__nat(X32,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_160]) ).

fof(c_0_359_360,plain,
    ! [X33,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_Nat_Osemiring__1__class_Oof__nat(X33,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_161]) ).

fof(c_0_360_361,axiom,
    ! [X32,X33] :
      ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X33),X32)
      | X33 = c_HOL_Ozero__class_Ozero(tc_nat)
      | X32 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    c_0_162 ).

fof(c_0_361_362,axiom,
    ! [X32,X33] :
      ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X33),X32) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X33 = c_HOL_Ozero__class_Ozero(tc_nat)
      | X32 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    c_0_163 ).

fof(c_0_362_363,plain,
    ! [X32,X3] :
      ( ~ class_Ring__and__Field_Osemiring__0(X3)
      | ~ class_Power_Opower(X3)
      | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X3),c_Suc(X32),X3) = c_HOL_Ozero__class_Ozero(X3) ),
    inference(fof_simplification,[status(thm)],[c_0_164]) ).

fof(c_0_363_364,plain,
    ! [X32,X3] :
      ( ~ class_Ring__and__Field_Osemiring__0(X3)
      | ~ class_Power_Opower(X3)
      | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X3),X32,X3) = c_HOL_Ozero__class_Ozero(X3)
      | X32 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_165]) ).

fof(c_0_364_365,plain,
    ! [X34] :
      ( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(X34)))
      | ~ hBOOL(hAPP(c_InductTermi_OIT,X34)) ),
    inference(fof_simplification,[status(thm)],[c_0_166]) ).

fof(c_0_365_366,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_167]) ).

fof(c_0_366_367,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_168]) ).

fof(c_0_367_368,axiom,
    ! [X32,X33] :
      ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X33),X32) != c_HOL_Ozero__class_Ozero(tc_nat)
      | X33 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    c_0_169 ).

fof(c_0_368_369,axiom,
    ! [X32,X33] :
      ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X33),X32) != c_HOL_Ozero__class_Ozero(tc_nat)
      | X32 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    c_0_170 ).

fof(c_0_369_370,axiom,
    ! [X32,X33] :
      ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X33),X32) != X33
      | X32 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    c_0_171 ).

fof(c_0_370_371,axiom,
    ! [X21,X45] :
      ( X21 != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X21),X45)
      | X45 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    c_0_172 ).

fof(c_0_371_372,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_173]) ).

fof(c_0_372_373,plain,
    ! [X21,X3] :
      ( ~ class_Ring__and__Field_Oidom(X3)
      | ~ class_Int_Onumber__ring(X3)
      | X21 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X21),c_HOL_Ozero__class_Ozero(X3)) ),
    inference(fof_simplification,[status(thm)],[c_0_174]) ).

fof(c_0_373_374,plain,
    ! [X21,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3)),X21) = X21 ),
    inference(fof_simplification,[status(thm)],[c_0_175]) ).

fof(c_0_374_375,plain,
    ! [X45,X3] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3)),X45) = X45 ),
    inference(fof_simplification,[status(thm)],[c_0_176]) ).

fof(c_0_375_376,plain,
    ! [X45,X3] :
      ( ~ class_OrderedGroup_Omonoid__add(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3)),X45) = X45 ),
    inference(fof_simplification,[status(thm)],[c_0_177]) ).

fof(c_0_376_377,plain,
    ! [X45,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3)),X45) = X45 ),
    inference(fof_simplification,[status(thm)],[c_0_178]) ).

fof(c_0_377_378,plain,
    ! [X32,X3] :
      ( ~ class_OrderedGroup_Omonoid__mult(X3)
      | c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X3),X32,X3) = c_HOL_Oone__class_Oone(X3) ),
    inference(fof_simplification,[status(thm)],[c_0_179]) ).

fof(c_0_378_379,plain,
    ! [X45,X3] :
      ( ~ class_Power_Opower(X3)
      | c_Power_Opower__class_Opower(X45,c_HOL_Ozero__class_Ozero(tc_nat),X3) = c_HOL_Oone__class_Oone(X3) ),
    inference(fof_simplification,[status(thm)],[c_0_180]) ).

fof(c_0_379_380,plain,
    ! [X21,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_Power_Opower__class_Opower(X21,c_HOL_Ozero__class_Ozero(tc_nat),X3) = c_HOL_Oone__class_Oone(X3) ),
    inference(fof_simplification,[status(thm)],[c_0_181]) ).

fof(c_0_380_381,plain,
    ! [X45,X3] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),c_HOL_Ozero__class_Ozero(X3)) = X45 ),
    inference(fof_simplification,[status(thm)],[c_0_182]) ).

fof(c_0_381_382,plain,
    ! [X45,X3] :
      ( ~ class_OrderedGroup_Omonoid__add(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),c_HOL_Ozero__class_Ozero(X3)) = X45 ),
    inference(fof_simplification,[status(thm)],[c_0_183]) ).

fof(c_0_382_383,plain,
    ! [X45,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),c_HOL_Ozero__class_Ozero(X3)) = X45 ),
    inference(fof_simplification,[status(thm)],[c_0_184]) ).

fof(c_0_383_384,plain,
    ! [X21,X3] :
      ( ~ class_Orderings_Oorder(X3)
      | c_lessequals(X21,X21,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_185]) ).

fof(c_0_384_385,plain,
    ! [X21,X3] :
      ( ~ class_Orderings_Opreorder(X3)
      | c_lessequals(X21,X21,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_186]) ).

fof(c_0_385_386,plain,
    ! [X32,X33,X3] :
      ( ~ class_Nat_Osemiring__char__0(X3)
      | c_Nat_Osemiring__1__class_Oof__nat(X33,X3) != c_Nat_Osemiring__1__class_Oof__nat(X32,X3)
      | X33 = X32 ),
    inference(fof_simplification,[status(thm)],[c_0_187]) ).

fof(c_0_386_387,plain,
    ! [X4,X5] :
      ( class_Orderings_Opreorder(tc_fun(X4,X5))
      | ~ class_Orderings_Opreorder(X5) ),
    inference(fof_simplification,[status(thm)],[c_0_188]) ).

fof(c_0_387_388,plain,
    ! [X4,X5] :
      ( class_Orderings_Oorder(tc_fun(X4,X5))
      | ~ class_Orderings_Oorder(X5) ),
    inference(fof_simplification,[status(thm)],[c_0_189]) ).

fof(c_0_388_389,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_190]) ).

fof(c_0_389_390,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_191]) ).

fof(c_0_390_391,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_192]) ).

fof(c_0_391_392,axiom,
    ! [X28,X29] :
      ( c_Suc(X29) != c_Suc(X28)
      | X29 = X28 ),
    c_0_193 ).

fof(c_0_392_393,axiom,
    ! [X52,X21] :
      ( c_Suc(X21) != c_Suc(X52)
      | X21 = X52 ),
    c_0_194 ).

fof(c_0_393_394,axiom,
    ! [X28,X29] :
      ( c_Type_Otype_OAtom(X29) != c_Type_Otype_OAtom(X28)
      | X29 = X28 ),
    c_0_195 ).

fof(c_0_394_395,axiom,
    ! [X41,X42] :
      ( c_Lambda_OdB_OAbs(X42) != c_Lambda_OdB_OAbs(X41)
      | X42 = X41 ),
    c_0_196 ).

fof(c_0_395_396,axiom,
    ! [X28,X29] :
      ( c_Lambda_OdB_OVar(X29) != c_Lambda_OdB_OVar(X28)
      | X29 = X28 ),
    c_0_197 ).

fof(c_0_396_397,plain,
    ! [X54,X55,X56,X57,X58,X59,X60] :
      ( X58 = c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__types__1__1(X60,X58,X57,X54),X60,tc_Type_Otype,tc_Type_Otype)
      | ~ c_Type_Otyping(X57,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X56),X55,tc_Lambda_OdB,tc_Lambda_OdB),X58)
      | ~ c_Type_Otypings(X57,X55,X59)
      | ~ c_Type_Otyping(X57,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X56),X55,tc_Lambda_OdB,tc_Lambda_OdB),X54,tc_Lambda_OdB,tc_Lambda_OdB),X60) ),
    inference(variable_rename,[status(thm)],[c_0_198]) ).

fof(c_0_397_398,plain,
    ! [X45,X46,X47] :
      ( X45 = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X47),c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(X47,X46,X45),tc_Lambda_OdB,tc_Lambda_OdB)
      | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X47),X46,tc_Lambda_OdB,tc_Lambda_OdB)),X45)) ),
    inference(variable_rename,[status(thm)],[c_0_199]) ).

fof(c_0_398_399,plain,
    ! [X54,X55,X56,X57,X58,X59,X60] :
      ( c_Type_Otypings(X57,X54,c_Type_Osko__Type__Xvar__app__types__1__1(X60,X58,X57,X54))
      | ~ c_Type_Otyping(X57,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X56),X55,tc_Lambda_OdB,tc_Lambda_OdB),X58)
      | ~ c_Type_Otypings(X57,X55,X59)
      | ~ c_Type_Otyping(X57,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X56),X55,tc_Lambda_OdB,tc_Lambda_OdB),X54,tc_Lambda_OdB,tc_Lambda_OdB),X60) ),
    inference(variable_rename,[status(thm)],[c_0_200]) ).

fof(c_0_399_400,plain,
    ! [X45,X46,X47] :
      ( c_ListOrder_Ostep1(c_Lambda_Obeta,X46,c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(X47,X46,X45),tc_Lambda_OdB)
      | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X47),X46,tc_Lambda_OdB,tc_Lambda_OdB)),X45)) ),
    inference(variable_rename,[status(thm)],[c_0_201]) ).

fof(c_0_400_401,plain,
    ! [X35,X36,X37] :
      ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,X37,X36,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X37,X35,tc_Lambda_OdB,tc_Lambda_OdB)))
      | ~ c_ListOrder_Ostep1(c_Lambda_Obeta,X36,X35,tc_Lambda_OdB) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_202])])]) ).

fof(c_0_401_402,plain,
    ! [X35,X36,X37] :
      ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,X37,X35,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X36,X35,tc_Lambda_OdB,tc_Lambda_OdB)))
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X37),X36)) ),
    inference(variable_rename,[status(thm)],[c_0_203]) ).

fof(c_0_402_403,plain,
    ! [X35,X36,X37] :
      ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,X37,X35,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X36,X35,tc_Lambda_OdB,tc_Lambda_OdB)))
      | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X37),X36)) ),
    inference(variable_rename,[status(thm)],[c_0_204]) ).

fof(c_0_403_404,plain,
    ! [X35,X36,X37] :
      ( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X37)),X36),X35,tc_Lambda_OdB,tc_Lambda_OdB)))
      | ~ hBOOL(hAPP(c_InductTermi_OIT,X36))
      | ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(X37,X36,c_HOL_Ozero__class_Ozero(tc_nat)),X35,tc_Lambda_OdB,tc_Lambda_OdB))) ),
    inference(variable_rename,[status(thm)],[c_0_205]) ).

fof(c_0_404_405,plain,
    ! [X41,X42,X43,X44,X45] :
      ( X45 = X44
      | ~ c_Type_Otyping(X43,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X42),X41,tc_Lambda_OdB,tc_Lambda_OdB),X44)
      | ~ c_Type_Otyping(X43,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X42),X41,tc_Lambda_OdB,tc_Lambda_OdB),X45) ),
    inference(variable_rename,[status(thm)],[c_0_206]) ).

fof(c_0_405_406,plain,
    ! [X35,X36,X37] :
      ( ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(X37,X36,c_HOL_Ozero__class_Ozero(tc_nat)),X35,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)
      | ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X36,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(X37)),X36),X35,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB) ),
    inference(variable_rename,[status(thm)],[c_0_207]) ).

fof(c_0_406_407,plain,
    ! [X41,X42,X43,X44] :
      ( c_Type_Otyping(X43,c_Lambda_OdB_OVar(X42),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__typesE__1__1(X44,X43,X42,X41),X44,tc_Type_Otype,tc_Type_Otype))
      | ~ c_Type_Otyping(X43,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X42),X41,tc_Lambda_OdB,tc_Lambda_OdB),X44) ),
    inference(variable_rename,[status(thm)],[c_0_208]) ).

fof(c_0_407_408,plain,
    ! [X41,X42,X43,X44] :
      ( c_Type_Otyping(X43,X42,c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeE__1__1(X44,X43,X42,X41),X44,tc_Type_Otype,tc_Type_Otype))
      | ~ c_Type_Otyping(X43,c_List_Ofoldl(c_Lambda_OdB_OApp,X42,X41,tc_Lambda_OdB,tc_Lambda_OdB),X44) ),
    inference(variable_rename,[status(thm)],[c_0_209]) ).

fof(c_0_408_409,plain,
    ! [X41,X42,X43,X44] :
      ( c_Type_Otyping(X43,X42,c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeD__1__1(X44,X43,X42,X41),X44,tc_Type_Otype,tc_Type_Otype))
      | ~ c_Type_Otyping(X43,c_List_Ofoldl(c_Lambda_OdB_OApp,X42,X41,tc_Lambda_OdB,tc_Lambda_OdB),X44) ),
    inference(variable_rename,[status(thm)],[c_0_210]) ).

fof(c_0_409_410,plain,
    ! [X51,X52,X53,X54,X55] :
      ( c_Type_Otyping(X53,c_List_Ofoldl(c_Lambda_OdB_OApp,X52,X51,tc_Lambda_OdB,tc_Lambda_OdB),X55)
      | ~ c_Type_Otypings(X53,X51,X54)
      | ~ c_Type_Otyping(X53,X52,c_List_Ofoldr(c_Type_Otype_OFun,X54,X55,tc_Type_Otype,tc_Type_Otype)) ),
    inference(variable_rename,[status(thm)],[c_0_211]) ).

fof(c_0_410_411,plain,
    ! [X33,X34] :
      ( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X34),X33,tc_Lambda_OdB,tc_Lambda_OdB)))
      | ~ c_List_Olistsp(c_InductTermi_OIT,X33,tc_Lambda_OdB) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_212])])]) ).

fof(c_0_411_412,plain,
    ! [X41,X42,X43,X44] :
      ( c_Type_Otypings(X43,X41,c_Type_Osko__Type__Xvar__app__typesE__1__1(X44,X43,X42,X41))
      | ~ c_Type_Otyping(X43,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X42),X41,tc_Lambda_OdB,tc_Lambda_OdB),X44) ),
    inference(variable_rename,[status(thm)],[c_0_213]) ).

fof(c_0_412_413,plain,
    ! [X41,X42,X43,X44] :
      ( c_Type_Otypings(X43,X41,c_Type_Osko__Type__Xlist__app__typeE__1__1(X44,X43,X42,X41))
      | ~ c_Type_Otyping(X43,c_List_Ofoldl(c_Lambda_OdB_OApp,X42,X41,tc_Lambda_OdB,tc_Lambda_OdB),X44) ),
    inference(variable_rename,[status(thm)],[c_0_214]) ).

fof(c_0_413_414,plain,
    ! [X41,X42,X43,X44] :
      ( c_Type_Otypings(X43,X41,c_Type_Osko__Type__Xlist__app__typeD__1__1(X44,X43,X42,X41))
      | ~ c_Type_Otyping(X43,c_List_Ofoldl(c_Lambda_OdB_OApp,X42,X41,tc_Lambda_OdB,tc_Lambda_OdB),X44) ),
    inference(variable_rename,[status(thm)],[c_0_215]) ).

fof(c_0_414_415,plain,
    ! [X35,X36,X37,X38] :
      ( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X38),X37,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X36),X35,tc_Lambda_OdB,tc_Lambda_OdB)
      | X37 = X35 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_216])])]) ).

fof(c_0_415_416,plain,
    ! [X35,X36,X37,X38] :
      ( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X38),X37,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X36),X35,tc_Lambda_OdB,tc_Lambda_OdB)
      | X38 = X36 ),
    inference(variable_rename,[status(thm)],[c_0_217]) ).

fof(c_0_416_417,plain,
    ! [X34,X35,X36,X37] :
      ( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X37),X35,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X36),X34,tc_Lambda_OdB,tc_Lambda_OdB)
      | X35 = X34 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_218])])]) ).

fof(c_0_417_418,plain,
    ! [X34,X35,X36,X37] :
      ( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X37),X35,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X36),X34,tc_Lambda_OdB,tc_Lambda_OdB)
      | X37 = X36 ),
    inference(variable_rename,[status(thm)],[c_0_219]) ).

fof(c_0_418_419,plain,
    ! [X57,X58,X59,X60] :
      ( ~ class_OrderedGroup_Osemigroup__add(X60)
      | c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X60),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X60),X59),X58),X57,X60,X60) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X60),X59),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X60),X58,X57,X60,X60)) ),
    inference(variable_rename,[status(thm)],[c_0_220]) ).

fof(c_0_419_420,plain,
    ! [X41,X42,X43] :
      ( c_List_Ofoldl(c_Lambda_OdB_OApp,X43,X41,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,X42,X41,tc_Lambda_OdB,tc_Lambda_OdB)
      | X43 = X42 ),
    inference(variable_rename,[status(thm)],[c_0_221]) ).

fof(c_0_420_421,plain,
    ! [X57,X58,X59] :
      ( ~ class_OrderedGroup_Omonoid__add(X59)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X59),X58),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X59),c_HOL_Ozero__class_Ozero(X59),X57,X59,X59)) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X59),X58,X57,X59,X59) ),
    inference(variable_rename,[status(thm)],[c_0_222]) ).

fof(c_0_421_422,plain,
    ! [X50,X51,X52] :
      ( ~ class_OrderedGroup_Omonoid__add(X52)
      | c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X52),X51,X50,X52,X52) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X52),X51),c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X52),X50,c_HOL_Ozero__class_Ozero(X52),X52,X52)) ),
    inference(variable_rename,[status(thm)],[c_0_223]) ).

fof(c_0_422_423,plain,
    ! [X50,X51] :
      ( ~ class_OrderedGroup_Omonoid__add(X51)
      | c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X51),c_HOL_Ozero__class_Ozero(X51),X50,X51,X51) = c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X51),X50,c_HOL_Ozero__class_Ozero(X51),X51,X51) ),
    inference(variable_rename,[status(thm)],[c_0_224]) ).

fof(c_0_423_424,plain,
    ! [X50,X51,X52] :
      ( ~ class_OrderedGroup_Oab__semigroup__add(X52)
      | c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X52),X50,X51,X52,X52) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X52),X51,X50,X52,X52) ),
    inference(variable_rename,[status(thm)],[c_0_225]) ).

fof(c_0_424_425,plain,
    ! [X10,X11,X12,X13] :
      ( c_Type_Otyping(X12,X11,hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__2__1(X13,X12,X11,X10)),X13))
      | ~ c_Type_Otyping(X12,hAPP(hAPP(c_Lambda_OdB_OApp,X11),X10),X13) ),
    inference(variable_rename,[status(thm)],[c_0_226]) ).

fof(c_0_425_426,plain,
    ! [X17,X18,X19,X20,X21] :
      ( ~ hBOOL(hAPP(X21,c_Type_Otype_Otype__case(X20,X19,hAPP(hAPP(c_Type_Otype_OFun,X18),X17),t_a)))
      | hBOOL(hAPP(X21,hAPP(hAPP(X19,X18),X17))) ),
    inference(variable_rename,[status(thm)],[c_0_227]) ).

fof(c_0_426_427,plain,
    ! [X15,X16,X17,X18,X19] :
      ( ~ hBOOL(hAPP(X19,c_Type_Otype_Otype__case(X18,X17,hAPP(hAPP(c_Type_Otype_OFun,X16),X15),t_a)))
      | hBOOL(hAPP(X19,hAPP(hAPP(X17,X16),X15))) ),
    inference(variable_rename,[status(thm)],[c_0_228]) ).

fof(c_0_427_428,plain,
    ! [X35,X36,X37] :
      ( hAPP(hAPP(c_Lambda_OdB_OApp,X37),X36) != c_List_Ofoldl(c_Lambda_OdB_OApp,X35,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)
      | hAPP(hAPP(c_Lambda_OdB_OApp,X37),X36) = X35 ),
    inference(variable_rename,[status(thm)],[c_0_229]) ).

fof(c_0_428_429,plain,
    ! [X35,X36,X37] :
      ( c_Lambda_OdB_OAbs(X37) != c_List_Ofoldl(c_Lambda_OdB_OApp,X36,X35,tc_Lambda_OdB,tc_Lambda_OdB)
      | c_Lambda_OdB_OAbs(X37) = X36 ),
    inference(variable_rename,[status(thm)],[c_0_230]) ).

fof(c_0_429_430,plain,
    ! [X34,X35,X36] :
      ( c_Lambda_OdB_OVar(X36) != c_List_Ofoldl(c_Lambda_OdB_OApp,X35,X34,tc_Lambda_OdB,tc_Lambda_OdB)
      | c_Lambda_OdB_OVar(X36) = X35 ),
    inference(variable_rename,[status(thm)],[c_0_231]) ).

fof(c_0_430_431,plain,
    ! [X35,X36,X37] :
      ( c_List_Ofoldl(c_Lambda_OdB_OApp,X36,X35,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X37)
      | X36 = c_Lambda_OdB_OAbs(X37) ),
    inference(variable_rename,[status(thm)],[c_0_232]) ).

fof(c_0_431_432,plain,
    ! [X35,X36,X37] :
      ( c_Lambda_OdB_OAbs(X37) != c_List_Ofoldl(c_Lambda_OdB_OApp,X36,X35,tc_Lambda_OdB,tc_Lambda_OdB)
      | X35 = c_List_Olist_ONil(tc_Lambda_OdB) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_233])])]) ).

fof(c_0_432_433,plain,
    ! [X35,X36,X37] :
      ( c_List_Ofoldl(c_Lambda_OdB_OApp,X36,X35,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X37)
      | X35 = c_List_Olist_ONil(tc_Lambda_OdB) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_234])])]) ).

fof(c_0_433_434,plain,
    ! [X34,X35,X36] :
      ( c_Lambda_OdB_OVar(X36) != c_List_Ofoldl(c_Lambda_OdB_OApp,X35,X34,tc_Lambda_OdB,tc_Lambda_OdB)
      | X34 = c_List_Olist_ONil(tc_Lambda_OdB) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_235])])]) ).

fof(c_0_434_435,plain,
    ! [X53,X54,X55,X56] :
      ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X55,X56),X53),X54))
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Predicate_Oconversep(X55,X56,X56),X56),X54),X53)) ),
    inference(variable_rename,[status(thm)],[c_0_236]) ).

fof(c_0_435_436,plain,
    ! [X30,X31,X32,X33] :
      ( ~ hBOOL(hAPP(X33,c_Type_Otype_Otype__case(X32,X31,c_Type_Otype_OAtom(X30),t_a)))
      | hBOOL(hAPP(X33,hAPP(X32,X30))) ),
    inference(variable_rename,[status(thm)],[c_0_237]) ).

fof(c_0_436_437,plain,
    ! [X47,X48,X49,X50] :
      ( ~ hBOOL(hAPP(X50,c_Type_Otype_Otype__case(X49,X48,c_Type_Otype_OAtom(X47),t_a)))
      | hBOOL(hAPP(X50,hAPP(X49,X47))) ),
    inference(variable_rename,[status(thm)],[c_0_238]) ).

fof(c_0_437_438,plain,
    ! [X53,X54,X55,X56] :
      ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Predicate_Oconversep(X55,X56,X56),X56),X54),X53))
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X55,X56),X53),X54)) ),
    inference(variable_rename,[status(thm)],[c_0_239]) ).

fof(c_0_438_439,plain,
    ! [X20,X21,X22,X23,X24,X25] :
      ( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(X21,X20,X22)))
      | ~ c_Type_Otyping(X23,X20,X24)
      | ~ hBOOL(hAPP(c_InductTermi_OIT,X20))
      | ~ c_Type_Otyping(c_Type_Oshift(X23,X22,X24,tc_Type_Otype),X21,X25)
      | ~ hBOOL(hAPP(c_InductTermi_OIT,X21)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_240])])]) ).

fof(c_0_439_440,plain,
    ! [X48,X49,X50,X51,X52,X53] :
      ( ~ c_Type_Otyping(X51,X48,X52)
      | ~ c_Type_Otyping(c_Type_Oshift(X51,X50,X52,tc_Type_Otype),X49,X53)
      | c_Type_Otyping(X51,c_Lambda_Osubst(X49,X48,X50),X53) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_241])])]) ).

fof(c_0_440_441,plain,
    ! [X44,X45,X46,X47] :
      ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X47),X45)),hAPP(hAPP(c_Lambda_OdB_OApp,X46),X44)))
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X45),X44))
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X47),X46)) ),
    inference(variable_rename,[status(thm)],[c_0_242]) ).

fof(c_0_441_442,plain,
    ! [X35,X36,X37,X38] :
      ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Osubst(X35,X37,X38)),c_Lambda_Osubst(X35,X36,X38)))
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X37),X36)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_243])])]) ).

fof(c_0_442_443,plain,
    ! [X35,X36,X37,X38] :
      ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Osubst(X37,X35,X38)),c_Lambda_Osubst(X36,X35,X38)))
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X37),X36)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_244])])]) ).

fof(c_0_443_444,plain,
    ! [X20,X21,X22,X23] :
      ( c_Type_Otyping(X21,c_Lambda_OdB_OAbs(X20),hAPP(hAPP(c_Type_Otype_OFun,X23),X22))
      | ~ c_Type_Otyping(c_Type_Oshift(X21,c_HOL_Ozero__class_Ozero(tc_nat),X23,tc_Type_Otype),X20,X22) ),
    inference(variable_rename,[status(thm)],[c_0_245]) ).

fof(c_0_444_445,plain,
    ! [X10,X11,X12] :
      ( c_Type_Otyping(c_Type_Oshift(X11,c_HOL_Ozero__class_Ozero(tc_nat),c_Type_Osko__Type__Xtyping__elims__3__1(X12,X11,X10),tc_Type_Otype),X10,c_Type_Osko__Type__Xtyping__elims__3__2(X12,X11,X10))
      | ~ c_Type_Otyping(X11,c_Lambda_OdB_OAbs(X10),X12) ),
    inference(variable_rename,[status(thm)],[c_0_246]) ).

fof(c_0_445_446,plain,
    ! [X35,X36,X37,X38] :
      ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Osubst(X35,X37,X38)),c_Lambda_Osubst(X35,X36,X38)))
      | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X37),X36)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_247])])]) ).

fof(c_0_446_447,plain,
    ! [X58,X59,X60,X61,X62] :
      ( hBOOL(hAPP(hAPP(X58,X59),X60))
      | ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X58,X62,X61),X60),X59)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_248])])]) ).

fof(c_0_447_448,plain,
    ! [X60,X61,X62,X63,X64] :
      ( hBOOL(hAPP(hAPP(X60,X61),X62))
      | ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X60,X64,X63),X62),X61)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_249])])]) ).

fof(c_0_448_449,plain,
    ! [X44,X45,X46] :
      ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X46),X44)),hAPP(hAPP(c_Lambda_OdB_OApp,X45),X44)))
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X46),X45)) ),
    inference(variable_rename,[status(thm)],[c_0_250]) ).

fof(c_0_449_450,plain,
    ! [X28,X29,X30] :
      ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X30),X29)),hAPP(hAPP(c_Lambda_OdB_OApp,X30),X28)))
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X29),X28)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_251])])]) ).

fof(c_0_450_451,plain,
    ! [X35,X36,X37,X38] :
      ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_Osubst(X37,X35,X38)),c_Lambda_Osubst(X36,X35,X38)))
      | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X37),X36)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_252])])]) ).

fof(c_0_451_452,plain,
    ! [X53,X54,X55,X56,X57] :
      ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X56,X57),X55),X53))
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X56,X57),X54),X53))
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X56,X57),X55),X54)) ),
    inference(variable_rename,[status(thm)],[c_0_253]) ).

fof(c_0_452_453,plain,
    ! [X10,X11,X12,X13] :
      ( c_Type_Otyping(X12,X10,c_Type_Osko__Type__Xtyping__elims__2__1(X13,X12,X11,X10))
      | ~ c_Type_Otyping(X12,hAPP(hAPP(c_Lambda_OdB_OApp,X11),X10),X13) ),
    inference(variable_rename,[status(thm)],[c_0_254]) ).

fof(c_0_453_454,plain,
    ! [X56,X57,X58,X59,X60] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X60)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X60),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X60),X59),X58)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X60),X57),X56)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X60),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X60),X59),X57)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X60),X58),X56)) ),
    inference(variable_rename,[status(thm)],[c_0_255]) ).

fof(c_0_454_455,plain,
    ! [X10,X11,X12] :
      ( c_Type_Otyping(c_Type_Oshift(X11,c_HOL_Ozero__class_Ozero(tc_nat),c_Type_Osko__Type__Xabs__typeE__1__1(X11,X10),tc_Type_Otype),X10,c_Type_Osko__Type__Xabs__typeE__1__2(X11,X10))
      | ~ c_Type_Otyping(X11,c_Lambda_OdB_OAbs(X10),X12) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_256])])]) ).

fof(c_0_455_456,plain,
    ! [X20,X21,X22,X23,X24] :
      ( c_Type_Otyping(c_Type_Oshift(X22,X21,X23,tc_Type_Otype),c_Lambda_Olift(X20,X21),X24)
      | ~ c_Type_Otyping(X22,X20,X24) ),
    inference(variable_rename,[status(thm)],[c_0_257]) ).

fof(c_0_456_457,plain,
    ! [X58,X59,X60,X61,X62] :
      ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X58,X62,X61),X60),X59))
      | ~ hBOOL(hAPP(hAPP(X58,X59),X60)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_258])])]) ).

fof(c_0_457_458,plain,
    ! [X58,X59,X60,X61,X62] :
      ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X58,X62,X61),X59),X60))
      | ~ hBOOL(hAPP(hAPP(X58,X60),X59)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_259])])]) ).

fof(c_0_458_459,plain,
    ! [X21,X22,X23] :
      ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,X23),X21)),hAPP(hAPP(c_Lambda_OdB_OApp,X22),X21)))
      | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X23),X22)) ),
    inference(variable_rename,[status(thm)],[c_0_260]) ).

fof(c_0_459_460,plain,
    ! [X21,X22,X23] :
      ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,X21),X23)),hAPP(hAPP(c_Lambda_OdB_OApp,X21),X22)))
      | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X23),X22)) ),
    inference(variable_rename,[status(thm)],[c_0_261]) ).

fof(c_0_460_461,plain,
    ! [X49,X50,X51,X52] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X52)
      | c_lessequals(X51,X50,X52)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X52),X50,X52)
      | ~ c_lessequals(c_Power_Opower__class_Opower(X51,c_Suc(X49),X52),c_Power_Opower__class_Opower(X50,c_Suc(X49),X52),X52) ),
    inference(variable_rename,[status(thm)],[c_0_262]) ).

fof(c_0_461_462,plain,
    ! [X55,X56,X57,X58,X59] :
      ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X55,X59),X58),X56))
      | ~ hBOOL(hAPP(hAPP(X55,X57),X56))
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X55,X59),X58),X57)) ),
    inference(variable_rename,[status(thm)],[c_0_263]) ).

fof(c_0_462_463,plain,
    ! [X55,X56,X57,X58,X59] :
      ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X55,X59),X58),X56))
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X55,X59),X57),X56))
      | ~ hBOOL(hAPP(hAPP(X55,X58),X57)) ),
    inference(variable_rename,[status(thm)],[c_0_264]) ).

fof(c_0_463_464,plain,
    ! [X35,X36,X37] :
      ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Olift(X36,X37)),c_Lambda_Olift(X35,X37)))
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X36),X35)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_265])])]) ).

fof(c_0_464_465,plain,
    ! [X55,X56,X57,X58] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X58)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X58),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X58),X57),X56)),X55) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X58),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X58),X57),X55)),X56) ),
    inference(variable_rename,[status(thm)],[c_0_266]) ).

fof(c_0_465_466,plain,
    ! [X56,X57,X58,X59,X60] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X60)
      | c_lessequals(X59,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X60),X58),X56),X60)
      | ~ c_lessequals(X57,X56,X60)
      | ~ c_lessequals(X59,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X60),X58),X57),X60) ),
    inference(variable_rename,[status(thm)],[c_0_267]) ).

fof(c_0_466_467,plain,
    ! [X55,X56,X57,X58] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X58)
      | c_lessequals(X57,X56,X58)
      | ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X58),X57),X55),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X58),X56),X55),X58) ),
    inference(variable_rename,[status(thm)],[c_0_268]) ).

fof(c_0_467_468,plain,
    ! [X55,X56,X57,X58] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X58)
      | c_lessequals(X57,X56,X58)
      | ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X58),X55),X57),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X58),X55),X56),X58) ),
    inference(variable_rename,[status(thm)],[c_0_269]) ).

fof(c_0_468_469,plain,
    ! [X49,X50,X51,X52] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X52)
      | c_lessequals(c_Power_Opower__class_Opower(X51,X49,X52),c_Power_Opower__class_Opower(X50,X49,X52),X52)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X52),X51,X52)
      | ~ c_lessequals(X51,X50,X52) ),
    inference(variable_rename,[status(thm)],[c_0_270]) ).

fof(c_0_469_470,plain,
    ! [X10,X11,X12] :
      ( X12 = hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__3__1(X12,X11,X10)),c_Type_Osko__Type__Xtyping__elims__3__2(X12,X11,X10))
      | ~ c_Type_Otyping(X11,c_Lambda_OdB_OAbs(X10),X12) ),
    inference(variable_rename,[status(thm)],[c_0_271]) ).

fof(c_0_470_471,plain,
    ! [X44,X45] :
      ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_OdB_OAbs(X45)),c_Lambda_OdB_OAbs(X44)))
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X45),X44)) ),
    inference(variable_rename,[status(thm)],[c_0_272]) ).

fof(c_0_471_472,plain,
    ! [X56,X57,X58,X59,X60] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X60)
      | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X60),X59),X57),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X60),X58),X56),X60)
      | ~ c_lessequals(X57,X56,X60)
      | ~ c_lessequals(X59,X58,X60) ),
    inference(variable_rename,[status(thm)],[c_0_273]) ).

fof(c_0_472_473,plain,
    ! [X49,X50,X51,X52] :
      ( c_Wellfounded_Oaccp(X49,X50,X52)
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X49,X52),X50),X51))
      | ~ c_Wellfounded_Oaccp(X49,X51,X52) ),
    inference(variable_rename,[status(thm)],[c_0_274]) ).

fof(c_0_473_474,plain,
    ! [X49,X50,X51,X52] :
      ( c_Wellfounded_Oaccp(X49,X50,X52)
      | ~ c_Wellfounded_Oaccp(X49,X51,X52)
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X49,X52),X50),X51)) ),
    inference(variable_rename,[status(thm)],[c_0_275]) ).

fof(c_0_474_475,plain,
    ! [X55,X56,X57,X58] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X58)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X58),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X58),X57),X56)),X55) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X58),X57),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X58),X56),X55)) ),
    inference(variable_rename,[status(thm)],[c_0_276]) ).

fof(c_0_475_476,plain,
    ! [X56,X57,X58,X59] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X59)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X59),X58),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X59),X57),X56)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X59),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X59),X58),X57)),X56) ),
    inference(variable_rename,[status(thm)],[c_0_277]) ).

fof(c_0_476_477,plain,
    ! [X55,X56,X57,X58] :
      ( ~ class_OrderedGroup_Oab__semigroup__add(X58)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X58),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X58),X57),X56)),X55) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X58),X57),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X58),X56),X55)) ),
    inference(variable_rename,[status(thm)],[c_0_278]) ).

fof(c_0_477_478,plain,
    ! [X55,X56,X57,X58] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X58)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X58),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X58),X57),X56)),X55) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X58),X57),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X58),X56),X55)) ),
    inference(variable_rename,[status(thm)],[c_0_279]) ).

fof(c_0_478_479,plain,
    ! [X53,X54,X55,X56] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X56)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X56),X55),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X56),X54),X53)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X56),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X56),X55),X54)),X53) ),
    inference(variable_rename,[status(thm)],[c_0_280]) ).

fof(c_0_479_480,plain,
    ! [X21,X22,X23,X24,X25] :
      ( c_Type_Otyping(X23,hAPP(hAPP(c_Lambda_OdB_OApp,X22),X21),X24)
      | ~ c_Type_Otyping(X23,X21,X25)
      | ~ c_Type_Otyping(X23,X22,hAPP(hAPP(c_Type_Otype_OFun,X25),X24)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_281])])]) ).

fof(c_0_480_481,plain,
    ! [X28,X29,X30,X31] :
      ( c_Type_Otyping(X30,X28,X31)
      | ~ c_Type_Otyping(X30,X29,X31)
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X29),X28)) ),
    inference(variable_rename,[status(thm)],[c_0_282]) ).

fof(c_0_481_482,plain,
    ! [X49,X50,X51,X52] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X52)
      | c_Power_Opower__class_Opower(X51,c_Suc(X49),X52) != c_Power_Opower__class_Opower(X50,c_Suc(X49),X52)
      | X51 = X50
      | ~ 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_283]) ).

fof(c_0_482_483,plain,
    ! [X53,X54,X55,X56,X57] :
      ( ~ class_OrderedGroup_Oab__group__add(X57)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X57),X55),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X57),X54),X53)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X57),X54),X56)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X57),X55),X53) = X56 ),
    inference(variable_rename,[status(thm)],[c_0_284]) ).

fof(c_0_483_484,plain,
    ! [X49,X50,X51] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X51)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X51),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X51),X50),X49),X51)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X51),X49,X51)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X51),X50,X51) ),
    inference(variable_rename,[status(thm)],[c_0_285]) ).

fof(c_0_484_485,plain,
    ! [X49,X50,X51] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X51)
      | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X51),X50),X49),c_HOL_Ozero__class_Ozero(X51),X51)
      | ~ c_lessequals(X49,c_HOL_Ozero__class_Ozero(X51),X51)
      | ~ c_lessequals(X50,c_HOL_Ozero__class_Ozero(X51),X51) ),
    inference(variable_rename,[status(thm)],[c_0_286]) ).

fof(c_0_485,plain,
    ! [X55,X56,X57,X58] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X58)
      | ~ class_OrderedGroup_Ocomm__monoid__add(X58)
      | c_lessequals(X56,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X58),X57),X55),X58)
      | ~ c_lessequals(X56,X55,X58)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X58),X57,X58) ),
    inference(variable_rename,[status(thm)],[c_0_287]) ).

fof(c_0_486,plain,
    ! [X55,X56,X57,X58] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X58)
      | ~ class_OrderedGroup_Ocomm__monoid__add(X58)
      | c_lessequals(X56,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X58),X57),X55),X58)
      | ~ c_lessequals(X56,X57,X58)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X58),X55,X58) ),
    inference(variable_rename,[status(thm)],[c_0_288]) ).

fof(c_0_487,plain,
    ! [X55,X56,X57,X58] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X58)
      | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X58),X57),X55),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X58),X56),X55),X58)
      | ~ c_lessequals(X57,X56,X58) ),
    inference(variable_rename,[status(thm)],[c_0_289]) ).

fof(c_0_488,plain,
    ! [X55,X56,X57,X58] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X58)
      | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X58),X55),X57),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X58),X55),X56),X58)
      | ~ c_lessequals(X57,X56,X58) ),
    inference(variable_rename,[status(thm)],[c_0_290]) ).

fof(c_0_489,plain,
    ! [X55,X56,X57,X58] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X58)
      | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X58),X57),X55),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X58),X56),X55),X58)
      | ~ c_lessequals(X57,X56,X58) ),
    inference(variable_rename,[status(thm)],[c_0_291]) ).

fof(c_0_490,plain,
    ! [X55,X56,X57,X58] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X58)
      | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X58),X55),X57),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X58),X55),X56),X58)
      | ~ c_lessequals(X57,X56,X58) ),
    inference(variable_rename,[status(thm)],[c_0_292]) ).

fof(c_0_491,plain,
    ! [X35,X36,X37] :
      ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_Olift(X36,X37)),c_Lambda_Olift(X35,X37)))
      | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X36),X35)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_293])])]) ).

fof(c_0_492,plain,
    ! [X46,X47] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X47)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X47),X46,X47)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X47),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X47),X46),X46),X47) ),
    inference(variable_rename,[status(thm)],[c_0_294]) ).

fof(c_0_493,plain,
    ! [X46,X47] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X47)
      | c_lessequals(X46,c_HOL_Ozero__class_Ozero(X47),X47)
      | ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X47),X46),X46),c_HOL_Ozero__class_Ozero(X47),X47) ),
    inference(variable_rename,[status(thm)],[c_0_295]) ).

fof(c_0_494,plain,
    ! [X56,X57,X58,X59] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X59)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X59),X58),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X59),X57),X56)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X59),X57),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X59),X58),X56)) ),
    inference(variable_rename,[status(thm)],[c_0_296]) ).

fof(c_0_495,plain,
    ! [X55,X56,X57,X58] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X58)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X58),X57),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X58),X56),X55)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X58),X56),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X58),X57),X55)) ),
    inference(variable_rename,[status(thm)],[c_0_297]) ).

fof(c_0_496,plain,
    ! [X53,X54,X55,X56] :
      ( ~ class_OrderedGroup_Oab__group__add(X56)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X56),X55),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X56),X54),X53)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X56),X54),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X56),X55),X53)) ),
    inference(variable_rename,[status(thm)],[c_0_298]) ).

fof(c_0_497,plain,
    ! [X53,X54,X55,X56] :
      ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X55,X56),X54),X53))
      | ~ hBOOL(hAPP(hAPP(X55,X54),X53)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_299])])]) ).

fof(c_0_498,plain,
    ! [X36,X37,X38] :
      ( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(X36,c_Lambda_OdB_OVar(X38),X37)))
      | ~ hBOOL(hAPP(c_InductTermi_OIT,X36)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_300])])]) ).

fof(c_0_499,plain,
    ! [X53,X54,X55] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X55)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X55),X54),X53) != c_HOL_Ozero__class_Ozero(X55)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X55),X53,X55)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X55),X54,X55)
      | X53 = c_HOL_Ozero__class_Ozero(X55) ),
    inference(variable_rename,[status(thm)],[c_0_301]) ).

fof(c_0_500,plain,
    ! [X53,X54,X55] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X55)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X55),X54),X53) != c_HOL_Ozero__class_Ozero(X55)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X55),X53,X55)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X55),X54,X55)
      | X54 = c_HOL_Ozero__class_Ozero(X55) ),
    inference(variable_rename,[status(thm)],[c_0_302]) ).

fof(c_0_501,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_303]) ).

fof(c_0_502,plain,
    ! [X35,X36] :
      ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,X36),c_Lambda_Osko__Lambda__Xbeta__cases__2__1(X36,X35)))
      | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OAbs(X36)),X35)) ),
    inference(variable_rename,[status(thm)],[c_0_304]) ).

fof(c_0_503,plain,
    ! [X46,X47,X48] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X48)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X48),c_Power_Opower__class_Opower(X47,X46,X48),X48)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X48),X47,X48) ),
    inference(variable_rename,[status(thm)],[c_0_305]) ).

fof(c_0_504,plain,
    ! [X46,X47,X48] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X48)
      | c_lessequals(c_HOL_Oone__class_Oone(X48),c_Power_Opower__class_Opower(X47,X46,X48),X48)
      | ~ c_lessequals(c_HOL_Oone__class_Oone(X48),X47,X48) ),
    inference(variable_rename,[status(thm)],[c_0_306]) ).

fof(c_0_505,plain,
    ! [X53,X54,X55,X56] :
      ( c_Wellfounded_Oaccp(X54,X53,X56)
      | ~ hBOOL(hAPP(hAPP(X54,X53),X55))
      | ~ c_Wellfounded_Oaccp(X54,X55,X56) ),
    inference(variable_rename,[status(thm)],[c_0_307]) ).

fof(c_0_506,plain,
    ! [X49,X50,X51,X52] :
      ( c_Wellfounded_Oaccp(X49,X51,X52)
      | ~ hBOOL(hAPP(hAPP(X49,X51),X50))
      | ~ c_Wellfounded_Oaccp(X49,X50,X52) ),
    inference(variable_rename,[status(thm)],[c_0_308]) ).

fof(c_0_507,plain,
    ! [X46,X47] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X47)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X47),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X47),X46),X46),X47)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X47),X46,X47) ),
    inference(variable_rename,[status(thm)],[c_0_309]) ).

fof(c_0_508,plain,
    ! [X46,X47] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X47)
      | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X47),X46),X46),c_HOL_Ozero__class_Ozero(X47),X47)
      | ~ c_lessequals(X46,c_HOL_Ozero__class_Ozero(X47),X47) ),
    inference(variable_rename,[status(thm)],[c_0_310]) ).

fof(c_0_509,plain,
    ! [X35] :
      ( hBOOL(hAPP(c_InductTermi_OIT,X35))
      | ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X35,tc_Lambda_OdB) ),
    inference(variable_rename,[status(thm)],[c_0_311]) ).

fof(c_0_510,plain,
    ! [X28,X29,X30,X31] :
      ( c_Type_Otyping(X30,X28,X31)
      | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X29),X28))
      | ~ c_Type_Otyping(X30,X29,X31) ),
    inference(variable_rename,[status(thm)],[c_0_312]) ).

fof(c_0_511,plain,
    ! [X34,X35,X36] :
      ( ~ class_Ring__and__Field_Osemiring__1(X36)
      | c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X35),X34),X36) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X36),c_Nat_Osemiring__1__class_Oof__nat(X35,X36)),c_Nat_Osemiring__1__class_Oof__nat(X34,X36)) ),
    inference(variable_rename,[status(thm)],[c_0_313]) ).

fof(c_0_512,plain,
    ! [X18,X19] :
      ( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,X18),c_Lambda_OdB_OVar(X19))))
      | ~ hBOOL(hAPP(c_InductTermi_OIT,X18)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_314])])]) ).

fof(c_0_513,plain,
    ! [X53,X54,X55,X56] :
      ( ~ class_Orderings_Oorder(X56)
      | c_lessequals(X53,X55,X56)
      | ~ c_lessequals(X53,X54,X56)
      | ~ c_lessequals(X54,X55,X56) ),
    inference(variable_rename,[status(thm)],[c_0_315]) ).

fof(c_0_514,plain,
    ! [X53,X54,X55,X56] :
      ( ~ class_Orderings_Opreorder(X56)
      | c_lessequals(X55,X53,X56)
      | ~ c_lessequals(X54,X53,X56)
      | ~ c_lessequals(X55,X54,X56) ),
    inference(variable_rename,[status(thm)],[c_0_316]) ).

fof(c_0_515,plain,
    ! [X21,X22] :
      ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OAbs(X22)),c_Lambda_OdB_OAbs(X21)))
      | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X22),X21)) ),
    inference(variable_rename,[status(thm)],[c_0_317]) ).

fof(c_0_516,plain,
    ! [X8] :
      ( c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X8,tc_Lambda_OdB)
      | ~ hBOOL(hAPP(c_InductTermi_OIT,X8)) ),
    inference(variable_rename,[status(thm)],[c_0_318]) ).

fof(c_0_517,plain,
    ! [X35,X36] :
      ( X35 = c_Lambda_OdB_OAbs(c_Lambda_Osko__Lambda__Xbeta__cases__2__1(X36,X35))
      | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OAbs(X36)),X35)) ),
    inference(variable_rename,[status(thm)],[c_0_319]) ).

fof(c_0_518,plain,
    ! [X53,X54,X55] :
      ( ~ class_Orderings_Oorder(X55)
      | X54 = X53
      | ~ c_lessequals(X53,X54,X55)
      | ~ c_lessequals(X54,X53,X55) ),
    inference(variable_rename,[status(thm)],[c_0_320]) ).

fof(c_0_519,plain,
    ! [X53,X54,X55] :
      ( ~ class_Orderings_Oorder(X55)
      | X54 = X53
      | ~ c_lessequals(X53,X54,X55)
      | ~ c_lessequals(X54,X53,X55) ),
    inference(variable_rename,[status(thm)],[c_0_321]) ).

fof(c_0_520,plain,
    ! [X53,X54,X55] :
      ( ~ class_Orderings_Oorder(X55)
      | X54 = X53
      | ~ c_lessequals(X54,X53,X55)
      | ~ c_lessequals(X53,X54,X55) ),
    inference(variable_rename,[status(thm)],[c_0_322]) ).

fof(c_0_521,plain,
    ! [X53,X54,X55,X56] :
      ( ~ class_Ring__and__Field_Oidom(X56)
      | ~ class_Int_Onumber__ring(X56)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X56),X55),X54) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X56),X55),X53)
      | X54 = X53 ),
    inference(variable_rename,[status(thm)],[c_0_323]) ).

fof(c_0_522,plain,
    ! [X55,X56,X57,X58] :
      ( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X58)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X58),X57),X56) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X58),X57),X55)
      | X56 = X55 ),
    inference(variable_rename,[status(thm)],[c_0_324]) ).

fof(c_0_523,plain,
    ! [X55,X56,X57,X58] :
      ( ~ class_OrderedGroup_Ocancel__semigroup__add(X58)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X58),X57),X56) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X58),X57),X55)
      | X56 = X55 ),
    inference(variable_rename,[status(thm)],[c_0_325]) ).

fof(c_0_524,plain,
    ! [X55,X56,X57,X58] :
      ( ~ class_OrderedGroup_Ocancel__semigroup__add(X58)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X58),X56),X57) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X58),X55),X57)
      | X56 = X55 ),
    inference(variable_rename,[status(thm)],[c_0_326]) ).

fof(c_0_525,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_327])])]) ).

fof(c_0_526,plain,
    ! [X53,X54,X55] :
      ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X55),X54) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X55),X53)
      | X54 = X53 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_328])])]) ).

fof(c_0_527,plain,
    ! [X61,X62,X63] :
      ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X62),X63) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X61),X63)
      | X62 = X61 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_329])])]) ).

fof(c_0_528,plain,
    ! [X61,X62,X63] :
      ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X63),X62) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X63),X61)
      | X62 = X61 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_330])])]) ).

fof(c_0_529,plain,
    ! [X46,X47,X48] :
      ( ~ class_Ring__and__Field_Ozero__neq__one(X48)
      | ~ class_Ring__and__Field_Ono__zero__divisors(X48)
      | ~ class_Ring__and__Field_Omult__zero(X48)
      | ~ class_Power_Opower(X48)
      | c_Power_Opower__class_Opower(X47,X46,X48) != c_HOL_Ozero__class_Ozero(X48)
      | X47 = c_HOL_Ozero__class_Ozero(X48) ),
    inference(variable_rename,[status(thm)],[c_0_331]) ).

fof(c_0_530,plain,
    ! [X46,X47] :
      ( ~ class_Ring__and__Field_Ozero__neq__one(X47)
      | ~ class_Ring__and__Field_Ono__zero__divisors(X47)
      | ~ class_Ring__and__Field_Omult__zero(X47)
      | ~ class_Power_Opower(X47)
      | c_Power_Opower__class_Opower(X46,c_HOL_Ozero__class_Ozero(tc_nat),X47) != c_HOL_Ozero__class_Ozero(X47) ),
    inference(variable_rename,[status(thm)],[c_0_332]) ).

fof(c_0_531,plain,
    ! [X25,X26,X27,X28] :
      ( c_Type_Osko__Type__Xtype__induct__1__1(X28) != hAPP(hAPP(c_Type_Otype_OFun,X26),X25)
      | hBOOL(hAPP(X28,X27))
      | hBOOL(hAPP(X28,X25)) ),
    inference(variable_rename,[status(thm)],[c_0_333]) ).

fof(c_0_532,plain,
    ! [X23,X24,X25,X26] :
      ( c_Type_Osko__Type__Xtype__induct__1__1(X26) != hAPP(hAPP(c_Type_Otype_OFun,X24),X23)
      | hBOOL(hAPP(X26,X25))
      | hBOOL(hAPP(X26,X24)) ),
    inference(variable_rename,[status(thm)],[c_0_334]) ).

fof(c_0_533,plain,
    ! [X18,X19] :
      ( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Olift(X18,X19)))
      | ~ hBOOL(hAPP(c_InductTermi_OIT,X18)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_335])])]) ).

fof(c_0_534,plain,
    ! [X40,X41,X42,X43] :
      ( hAPP(hAPP(c_Lambda_OdB_OApp,X43),X41) != hAPP(hAPP(c_Lambda_OdB_OApp,X42),X40)
      | X41 = X40 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_336])])]) ).

fof(c_0_535,plain,
    ! [X40,X41,X42,X43] :
      ( hAPP(hAPP(c_Lambda_OdB_OApp,X43),X41) != hAPP(hAPP(c_Lambda_OdB_OApp,X42),X40)
      | X43 = X42 ),
    inference(variable_rename,[status(thm)],[c_0_337]) ).

fof(c_0_536,plain,
    ! [X27,X28,X29,X30] :
      ( hAPP(hAPP(c_Type_Otype_OFun,X30),X28) != hAPP(hAPP(c_Type_Otype_OFun,X29),X27)
      | X30 = X29 ),
    inference(variable_rename,[status(thm)],[c_0_338]) ).

fof(c_0_537,plain,
    ! [X27,X28,X29,X30] :
      ( hAPP(hAPP(c_Type_Otype_OFun,X30),X28) != hAPP(hAPP(c_Type_Otype_OFun,X29),X27)
      | X28 = X27 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_339])])]) ).

fof(c_0_538,plain,
    ! [X34,X35] :
      ( ~ class_Ring__and__Field_Osemiring__1(X35)
      | c_Nat_Osemiring__1__class_Oof__nat(c_Suc(X34),X35) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X35),c_HOL_Oone__class_Oone(X35)),c_Nat_Osemiring__1__class_Oof__nat(X34,X35)) ),
    inference(variable_rename,[status(thm)],[c_0_340]) ).

fof(c_0_539,plain,
    ! [X53,X54,X55] :
      ( ~ class_Orderings_Olinorder(X55)
      | c_lessequals(X53,X54,X55)
      | c_lessequals(X54,X53,X55) ),
    inference(variable_rename,[status(thm)],[c_0_341]) ).

fof(c_0_540,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_342]) ).

fof(c_0_541,plain,
    ! [X55,X56,X57] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X57)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X57),X56),X55) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X57),X55),X56) ),
    inference(variable_rename,[status(thm)],[c_0_343]) ).

fof(c_0_542,plain,
    ! [X49,X50,X51] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X51)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X51),X50),X49) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X51),X49),X50) ),
    inference(variable_rename,[status(thm)],[c_0_344]) ).

fof(c_0_543,plain,
    ! [X53,X54,X55] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X55)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X55),X54),X53) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X55),X53),X54) ),
    inference(variable_rename,[status(thm)],[c_0_345]) ).

fof(c_0_544,plain,
    ! [X18,X19,X20] :
      ( hAPP(X19,X18) = X20
      | ~ c_Type_Otyping(X19,c_Lambda_OdB_OVar(X18),X20) ),
    inference(variable_rename,[status(thm)],[c_0_346]) ).

fof(c_0_545,plain,
    ! [X46,X47,X48] :
      ( ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X48)
      | c_Power_Opower__class_Opower(X47,X46,X48) != c_HOL_Ozero__class_Ozero(X48)
      | X47 = c_HOL_Ozero__class_Ozero(X48) ),
    inference(variable_rename,[status(thm)],[c_0_347]) ).

fof(c_0_546,plain,
    ! [X46,X47,X48] :
      ( ~ class_Ring__and__Field_Oidom(X48)
      | ~ class_Int_Onumber__ring(X48)
      | X46 != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X48),X46),X47)
      | X47 = c_HOL_Ozero__class_Ozero(X48) ),
    inference(variable_rename,[status(thm)],[c_0_348]) ).

fof(c_0_547,plain,
    ! [X46,X47] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X47)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X47),X46),X46) != c_HOL_Ozero__class_Ozero(X47)
      | X46 = c_HOL_Ozero__class_Ozero(X47) ),
    inference(variable_rename,[status(thm)],[c_0_349]) ).

fof(c_0_548,plain,
    ! [X34,X35] :
      ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X35),X34)
      | X34 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X35 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    inference(variable_rename,[status(thm)],[c_0_350]) ).

fof(c_0_549,plain,
    ! [X34,X35] :
      ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X35),X34) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X34 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X35 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    inference(variable_rename,[status(thm)],[c_0_351]) ).

fof(c_0_550,plain,
    ! [X15,X16] :
      ( hBOOL(hAPP(X16,X15))
      | ~ hBOOL(hAPP(X16,c_Type_Osko__Type__Xtype__induct__1__1(X16))) ),
    inference(variable_rename,[status(thm)],[c_0_352]) ).

fof(c_0_551,plain,
    ! [X33,X34] :
      ( ~ class_Ring__and__Field_Ozero__neq__one(X34)
      | ~ class_Ring__and__Field_Ono__zero__divisors(X34)
      | ~ class_Ring__and__Field_Omult__zero(X34)
      | ~ class_Power_Opower(X34)
      | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X34),X33,X34) = c_HOL_Ozero__class_Ozero(X34)
      | X33 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_353]) ).

fof(c_0_552,plain,
    ! [X34,X35] :
      ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X35),X34) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X34 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X34 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_354])])]) ).

fof(c_0_553,plain,
    ! [X34,X35] :
      ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X35),X34) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X35 = c_HOL_Ozero__class_Ozero(tc_nat)
      | X35 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    inference(variable_rename,[status(thm)],[c_0_355]) ).

fof(c_0_554,plain,
    ! [X34,X35] :
      ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X35),X34)
      | X35 = c_HOL_Ozero__class_Ozero(tc_nat)
      | X35 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    inference(variable_rename,[status(thm)],[c_0_356]) ).

fof(c_0_555,plain,
    ! [X34,X35] :
      ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X35),X34)
      | X34 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X34 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_357])])]) ).

fof(c_0_556,plain,
    ! [X33,X34] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X34)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X34),c_Nat_Osemiring__1__class_Oof__nat(X33,X34),X34) ),
    inference(variable_rename,[status(thm)],[c_0_358]) ).

fof(c_0_557,plain,
    ! [X34,X35] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X35)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X35),c_Nat_Osemiring__1__class_Oof__nat(X34,X35),X35) ),
    inference(variable_rename,[status(thm)],[c_0_359]) ).

fof(c_0_558,plain,
    ! [X34,X35] :
      ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X35),X34)
      | X35 = c_HOL_Ozero__class_Ozero(tc_nat)
      | X34 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_360]) ).

fof(c_0_559,plain,
    ! [X34,X35] :
      ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X35),X34) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X35 = c_HOL_Ozero__class_Ozero(tc_nat)
      | X34 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_361]) ).

fof(c_0_560,plain,
    ! [X33,X34] :
      ( ~ class_Ring__and__Field_Osemiring__0(X34)
      | ~ class_Power_Opower(X34)
      | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X34),c_Suc(X33),X34) = c_HOL_Ozero__class_Ozero(X34) ),
    inference(variable_rename,[status(thm)],[c_0_362]) ).

fof(c_0_561,plain,
    ! [X33,X34] :
      ( ~ class_Ring__and__Field_Osemiring__0(X34)
      | ~ class_Power_Opower(X34)
      | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X34),X33,X34) = c_HOL_Ozero__class_Ozero(X34)
      | X33 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_363]) ).

fof(c_0_562,plain,
    ! [X35] :
      ( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(X35)))
      | ~ hBOOL(hAPP(c_InductTermi_OIT,X35)) ),
    inference(variable_rename,[status(thm)],[c_0_364]) ).

fof(c_0_563,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_365]) ).

fof(c_0_564,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_366]) ).

fof(c_0_565,plain,
    ! [X34,X35] :
      ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X35),X34) != c_HOL_Ozero__class_Ozero(tc_nat)
      | X35 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_367]) ).

fof(c_0_566,plain,
    ! [X34,X35] :
      ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X35),X34) != c_HOL_Ozero__class_Ozero(tc_nat)
      | X34 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_368])])]) ).

fof(c_0_567,plain,
    ! [X34,X35] :
      ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X35),X34) != X35
      | X34 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_369])])]) ).

fof(c_0_568,plain,
    ! [X46,X47] :
      ( X46 != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X46),X47)
      | X47 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_370]) ).

fof(c_0_569,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_371]) ).

fof(c_0_570,plain,
    ! [X22,X23] :
      ( ~ class_Ring__and__Field_Oidom(X23)
      | ~ class_Int_Onumber__ring(X23)
      | X22 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X23),X22),c_HOL_Ozero__class_Ozero(X23)) ),
    inference(variable_rename,[status(thm)],[c_0_372]) ).

fof(c_0_571,plain,
    ! [X22,X23] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X23)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X23),c_HOL_Ozero__class_Ozero(X23)),X22) = X22 ),
    inference(variable_rename,[status(thm)],[c_0_373]) ).

fof(c_0_572,plain,
    ! [X46,X47] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X47)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X47),c_HOL_Ozero__class_Ozero(X47)),X46) = X46 ),
    inference(variable_rename,[status(thm)],[c_0_374]) ).

fof(c_0_573,plain,
    ! [X46,X47] :
      ( ~ class_OrderedGroup_Omonoid__add(X47)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X47),c_HOL_Ozero__class_Ozero(X47)),X46) = X46 ),
    inference(variable_rename,[status(thm)],[c_0_375]) ).

fof(c_0_574,plain,
    ! [X46,X47] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X47)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X47),c_HOL_Ozero__class_Ozero(X47)),X46) = X46 ),
    inference(variable_rename,[status(thm)],[c_0_376]) ).

fof(c_0_575,plain,
    ! [X33,X34] :
      ( ~ class_OrderedGroup_Omonoid__mult(X34)
      | c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X34),X33,X34) = c_HOL_Oone__class_Oone(X34) ),
    inference(variable_rename,[status(thm)],[c_0_377]) ).

fof(c_0_576,plain,
    ! [X46,X47] :
      ( ~ class_Power_Opower(X47)
      | c_Power_Opower__class_Opower(X46,c_HOL_Ozero__class_Ozero(tc_nat),X47) = c_HOL_Oone__class_Oone(X47) ),
    inference(variable_rename,[status(thm)],[c_0_378]) ).

fof(c_0_577,plain,
    ! [X22,X23] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X23)
      | c_Power_Opower__class_Opower(X22,c_HOL_Ozero__class_Ozero(tc_nat),X23) = c_HOL_Oone__class_Oone(X23) ),
    inference(variable_rename,[status(thm)],[c_0_379]) ).

fof(c_0_578,plain,
    ! [X46,X47] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X47)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X47),X46),c_HOL_Ozero__class_Ozero(X47)) = X46 ),
    inference(variable_rename,[status(thm)],[c_0_380]) ).

fof(c_0_579,plain,
    ! [X46,X47] :
      ( ~ class_OrderedGroup_Omonoid__add(X47)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X47),X46),c_HOL_Ozero__class_Ozero(X47)) = X46 ),
    inference(variable_rename,[status(thm)],[c_0_381]) ).

fof(c_0_580,plain,
    ! [X46,X47] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X47)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X47),X46),c_HOL_Ozero__class_Ozero(X47)) = X46 ),
    inference(variable_rename,[status(thm)],[c_0_382]) ).

fof(c_0_581,plain,
    ! [X22,X23] :
      ( ~ class_Orderings_Oorder(X23)
      | c_lessequals(X22,X22,X23) ),
    inference(variable_rename,[status(thm)],[c_0_383]) ).

fof(c_0_582,plain,
    ! [X22,X23] :
      ( ~ class_Orderings_Opreorder(X23)
      | c_lessequals(X22,X22,X23) ),
    inference(variable_rename,[status(thm)],[c_0_384]) ).

fof(c_0_583,plain,
    ! [X34,X35,X36] :
      ( ~ class_Nat_Osemiring__char__0(X36)
      | c_Nat_Osemiring__1__class_Oof__nat(X35,X36) != c_Nat_Osemiring__1__class_Oof__nat(X34,X36)
      | X35 = X34 ),
    inference(variable_rename,[status(thm)],[c_0_385]) ).

fof(c_0_584,plain,
    ! [X6,X7] :
      ( class_Orderings_Opreorder(tc_fun(X6,X7))
      | ~ class_Orderings_Opreorder(X7) ),
    inference(variable_rename,[status(thm)],[c_0_386]) ).

fof(c_0_585,plain,
    ! [X6,X7] :
      ( class_Orderings_Oorder(tc_fun(X6,X7))
      | ~ class_Orderings_Oorder(X7) ),
    inference(variable_rename,[status(thm)],[c_0_387]) ).

fof(c_0_586,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_388]) ).

fof(c_0_587,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_389]) ).

fof(c_0_588,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_390]) ).

fof(c_0_589,plain,
    ! [X30,X31] :
      ( c_Suc(X31) != c_Suc(X30)
      | X31 = X30 ),
    inference(variable_rename,[status(thm)],[c_0_391]) ).

fof(c_0_590,plain,
    ! [X53,X54] :
      ( c_Suc(X54) != c_Suc(X53)
      | X54 = X53 ),
    inference(variable_rename,[status(thm)],[c_0_392]) ).

fof(c_0_591,plain,
    ! [X30,X31] :
      ( c_Type_Otype_OAtom(X31) != c_Type_Otype_OAtom(X30)
      | X31 = X30 ),
    inference(variable_rename,[status(thm)],[c_0_393]) ).

fof(c_0_592,plain,
    ! [X43,X44] :
      ( c_Lambda_OdB_OAbs(X44) != c_Lambda_OdB_OAbs(X43)
      | X44 = X43 ),
    inference(variable_rename,[status(thm)],[c_0_394]) ).

fof(c_0_593,plain,
    ! [X30,X31] :
      ( c_Lambda_OdB_OVar(X31) != c_Lambda_OdB_OVar(X30)
      | X31 = X30 ),
    inference(variable_rename,[status(thm)],[c_0_395]) ).

cnf(c_0_594,plain,
    ( X7 = c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__types__1__1(X5,X7,X1,X4),X5,tc_Type_Otype,tc_Type_Otype)
    | ~ 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_396]) ).

cnf(c_0_595,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_397]) ).

cnf(c_0_596,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_398]) ).

cnf(c_0_597,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_399]) ).

cnf(c_0_598,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_400]) ).

cnf(c_0_599,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_401]) ).

cnf(c_0_600,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_402]) ).

cnf(c_0_601,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,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_403]) ).

cnf(c_0_602,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_404]) ).

cnf(c_0_603,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,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_405]) ).

cnf(c_0_604,plain,
    ( c_Type_Otyping(X1,c_Lambda_OdB_OVar(X2),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__typesE__1__1(X4,X1,X2,X3),X4,tc_Type_Otype,tc_Type_Otype))
    | ~ 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_406]) ).

cnf(c_0_605,plain,
    ( c_Type_Otyping(X1,X2,c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeE__1__1(X4,X1,X2,X3),X4,tc_Type_Otype,tc_Type_Otype))
    | ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB),X4) ),
    inference(split_conjunct,[status(thm)],[c_0_407]) ).

cnf(c_0_606,plain,
    ( c_Type_Otyping(X1,X2,c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeD__1__1(X4,X1,X2,X3),X4,tc_Type_Otype,tc_Type_Otype))
    | ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB),X4) ),
    inference(split_conjunct,[status(thm)],[c_0_408]) ).

cnf(c_0_607,plain,
    ( c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X5,tc_Lambda_OdB,tc_Lambda_OdB),X4)
    | ~ c_Type_Otyping(X1,X2,c_List_Ofoldr(c_Type_Otype_OFun,X3,X4,tc_Type_Otype,tc_Type_Otype))
    | ~ c_Type_Otypings(X1,X5,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_409]) ).

cnf(c_0_608,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_410]) ).

cnf(c_0_609,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_411]) ).

cnf(c_0_610,plain,
    ( c_Type_Otypings(X1,X3,c_Type_Osko__Type__Xlist__app__typeE__1__1(X4,X1,X2,X3))
    | ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB),X4) ),
    inference(split_conjunct,[status(thm)],[c_0_412]) ).

cnf(c_0_611,plain,
    ( c_Type_Otypings(X1,X3,c_Type_Osko__Type__Xlist__app__typeD__1__1(X4,X1,X2,X3))
    | ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB),X4) ),
    inference(split_conjunct,[status(thm)],[c_0_413]) ).

cnf(c_0_612,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_414]) ).

cnf(c_0_613,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_415]) ).

cnf(c_0_614,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_416]) ).

cnf(c_0_615,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_417]) ).

cnf(c_0_616,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_418]) ).

cnf(c_0_617,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_419]) ).

cnf(c_0_618,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_420]) ).

cnf(c_0_619,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_421]) ).

cnf(c_0_620,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_422]) ).

cnf(c_0_621,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_423]) ).

cnf(c_0_622,plain,
    ( c_Type_Otyping(X1,X2,hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__2__1(X4,X1,X2,X3)),X4))
    | ~ c_Type_Otyping(X1,hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3),X4) ),
    inference(split_conjunct,[status(thm)],[c_0_424]) ).

cnf(c_0_623,plain,
    ( hBOOL(hAPP(X1,hAPP(hAPP(X2,X3),X4)))
    | ~ hBOOL(hAPP(X1,c_Type_Otype_Otype__case(X5,X2,hAPP(hAPP(c_Type_Otype_OFun,X3),X4),t_a))) ),
    inference(split_conjunct,[status(thm)],[c_0_425]) ).

cnf(c_0_624,plain,
    ( hBOOL(hAPP(X1,hAPP(hAPP(X2,X3),X4)))
    | ~ hBOOL(hAPP(X1,c_Type_Otype_Otype__case(X5,X2,hAPP(hAPP(c_Type_Otype_OFun,X3),X4),t_a))) ),
    inference(split_conjunct,[status(thm)],[c_0_426]) ).

cnf(c_0_625,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_427]) ).

cnf(c_0_626,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_428]) ).

cnf(c_0_627,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_429]) ).

cnf(c_0_628,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_430]) ).

cnf(c_0_629,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_431]) ).

cnf(c_0_630,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_432]) ).

cnf(c_0_631,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_433]) ).

cnf(c_0_632,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_434]) ).

cnf(c_0_633,plain,
    ( hBOOL(hAPP(X1,hAPP(X2,X3)))
    | ~ hBOOL(hAPP(X1,c_Type_Otype_Otype__case(X2,X4,c_Type_Otype_OAtom(X3),t_a))) ),
    inference(split_conjunct,[status(thm)],[c_0_435]) ).

cnf(c_0_634,plain,
    ( hBOOL(hAPP(X1,hAPP(X2,X3)))
    | ~ hBOOL(hAPP(X1,c_Type_Otype_Otype__case(X2,X4,c_Type_Otype_OAtom(X3),t_a))) ),
    inference(split_conjunct,[status(thm)],[c_0_436]) ).

cnf(c_0_635,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_437]) ).

cnf(c_0_636,plain,
    ( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(X1,X6,X3)))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
    | ~ c_Type_Otyping(c_Type_Oshift(X2,X3,X4,tc_Type_Otype),X1,X5)
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X6))
    | ~ c_Type_Otyping(X2,X6,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_438]) ).

cnf(c_0_637,plain,
    ( c_Type_Otyping(X1,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_439]) ).

cnf(c_0_638,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_440]) ).

cnf(c_0_639,plain,
    ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Osubst(X3,X1,X4)),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_441]) ).

cnf(c_0_640,plain,
    ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Osubst(X1,X3,X4)),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_442]) ).

cnf(c_0_641,plain,
    ( c_Type_Otyping(X1,c_Lambda_OdB_OAbs(X3),hAPP(hAPP(c_Type_Otype_OFun,X2),X4))
    | ~ c_Type_Otyping(c_Type_Oshift(X1,c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_Type_Otype),X3,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_443]) ).

cnf(c_0_642,plain,
    ( c_Type_Otyping(c_Type_Oshift(X1,c_HOL_Ozero__class_Ozero(tc_nat),c_Type_Osko__Type__Xtyping__elims__3__1(X3,X1,X2),tc_Type_Otype),X2,c_Type_Osko__Type__Xtyping__elims__3__2(X3,X1,X2))
    | ~ c_Type_Otyping(X1,c_Lambda_OdB_OAbs(X2),X3) ),
    inference(split_conjunct,[status(thm)],[c_0_444]) ).

cnf(c_0_643,plain,
    ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Osubst(X3,X1,X4)),c_Lambda_Osubst(X3,X2,X4)))
    | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_445]) ).

cnf(c_0_644,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_446]) ).

cnf(c_0_645,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_447]) ).

cnf(c_0_646,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_448]) ).

cnf(c_0_647,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_449]) ).

cnf(c_0_648,plain,
    ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_Osubst(X1,X3,X4)),c_Lambda_Osubst(X2,X3,X4)))
    | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_450]) ).

cnf(c_0_649,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_451]) ).

cnf(c_0_650,plain,
    ( c_Type_Otyping(X1,X3,c_Type_Osko__Type__Xtyping__elims__2__1(X4,X1,X2,X3))
    | ~ c_Type_Otyping(X1,hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3),X4) ),
    inference(split_conjunct,[status(thm)],[c_0_452]) ).

cnf(c_0_651,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_453]) ).

cnf(c_0_652,plain,
    ( c_Type_Otyping(c_Type_Oshift(X1,c_HOL_Ozero__class_Ozero(tc_nat),c_Type_Osko__Type__Xabs__typeE__1__1(X1,X2),tc_Type_Otype),X2,c_Type_Osko__Type__Xabs__typeE__1__2(X1,X2))
    | ~ c_Type_Otyping(X1,c_Lambda_OdB_OAbs(X2),X3) ),
    inference(split_conjunct,[status(thm)],[c_0_454]) ).

cnf(c_0_653,plain,
    ( c_Type_Otyping(c_Type_Oshift(X1,X4,X5,tc_Type_Otype),c_Lambda_Olift(X2,X4),X3)
    | ~ c_Type_Otyping(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_455]) ).

cnf(c_0_654,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_456]) ).

cnf(c_0_655,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_457]) ).

cnf(c_0_656,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_458]) ).

cnf(c_0_657,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_459]) ).

cnf(c_0_658,plain,
    ( c_lessequals(X1,X4,X3)
    | ~ c_lessequals(c_Power_Opower__class_Opower(X1,c_Suc(X2),X3),c_Power_Opower__class_Opower(X4,c_Suc(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_460]) ).

cnf(c_0_659,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_461]) ).

cnf(c_0_660,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_462]) ).

cnf(c_0_661,plain,
    ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Olift(X1,X3)),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_463]) ).

cnf(c_0_662,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_464]) ).

cnf(c_0_663,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_465]) ).

cnf(c_0_664,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_466]) ).

cnf(c_0_665,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_467]) ).

cnf(c_0_666,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_468]) ).

cnf(c_0_667,plain,
    ( X3 = hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__3__1(X3,X1,X2)),c_Type_Osko__Type__Xtyping__elims__3__2(X3,X1,X2))
    | ~ c_Type_Otyping(X1,c_Lambda_OdB_OAbs(X2),X3) ),
    inference(split_conjunct,[status(thm)],[c_0_469]) ).

cnf(c_0_668,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_470]) ).

cnf(c_0_669,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_471]) ).

cnf(c_0_670,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_472]) ).

cnf(c_0_671,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_473]) ).

cnf(c_0_672,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_474]) ).

cnf(c_0_673,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_475]) ).

cnf(c_0_674,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_476]) ).

cnf(c_0_675,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_477]) ).

cnf(c_0_676,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_478]) ).

cnf(c_0_677,plain,
    ( c_Type_Otyping(X1,hAPP(hAPP(c_Lambda_OdB_OApp,X2),X5),X4)
    | ~ c_Type_Otyping(X1,X2,hAPP(hAPP(c_Type_Otype_OFun,X3),X4))
    | ~ c_Type_Otyping(X1,X5,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_479]) ).

cnf(c_0_678,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_480]) ).

cnf(c_0_679,plain,
    ( X2 = X3
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | c_Power_Opower__class_Opower(X2,c_Suc(X4),X1) != c_Power_Opower__class_Opower(X3,c_Suc(X4),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_481]) ).

cnf(c_0_680,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_482]) ).

cnf(c_0_681,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_483]) ).

cnf(c_0_682,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_484]) ).

cnf(c_0_683,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_485]) ).

cnf(c_0_684,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_486]) ).

cnf(c_0_685,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_487]) ).

cnf(c_0_686,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_488]) ).

cnf(c_0_687,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_489]) ).

cnf(c_0_688,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_490]) ).

cnf(c_0_689,plain,
    ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_Olift(X1,X3)),c_Lambda_Olift(X2,X3)))
    | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_491]) ).

cnf(c_0_690,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_492]) ).

cnf(c_0_691,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_493]) ).

cnf(c_0_692,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_494]) ).

cnf(c_0_693,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_495]) ).

cnf(c_0_694,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_496]) ).

cnf(c_0_695,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_497]) ).

cnf(c_0_696,plain,
    ( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(X1,c_Lambda_OdB_OVar(X2),X3)))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_498]) ).

cnf(c_0_697,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_499]) ).

cnf(c_0_698,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_500]) ).

cnf(c_0_699,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_501]) ).

cnf(c_0_700,plain,
    ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),c_Lambda_Osko__Lambda__Xbeta__cases__2__1(X1,X2)))
    | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OAbs(X1)),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_502]) ).

cnf(c_0_701,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_503]) ).

cnf(c_0_702,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_504]) ).

cnf(c_0_703,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_505]) ).

cnf(c_0_704,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_506]) ).

cnf(c_0_705,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_507]) ).

cnf(c_0_706,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_508]) ).

cnf(c_0_707,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_509]) ).

cnf(c_0_708,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_510]) ).

cnf(c_0_709,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_511]) ).

cnf(c_0_710,plain,
    ( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,X1),c_Lambda_OdB_OVar(X2))))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_512]) ).

cnf(c_0_711,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_513]) ).

cnf(c_0_712,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_514]) ).

cnf(c_0_713,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_515]) ).

cnf(c_0_714,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_516]) ).

cnf(c_0_715,plain,
    ( X2 = c_Lambda_OdB_OAbs(c_Lambda_Osko__Lambda__Xbeta__cases__2__1(X1,X2))
    | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OAbs(X1)),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_517]) ).

cnf(c_0_716,plain,
    ( X1 = X2
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_lessequals(X2,X1,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_518]) ).

cnf(c_0_717,plain,
    ( X1 = X2
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_lessequals(X2,X1,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_519]) ).

cnf(c_0_718,plain,
    ( X2 = X1
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_lessequals(X2,X1,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_520]) ).

cnf(c_0_719,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_521]) ).

cnf(c_0_720,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_522]) ).

cnf(c_0_721,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_523]) ).

cnf(c_0_722,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_524]) ).

cnf(c_0_723,plain,
    ( X2 = X3
    | ~ hBOOL(hAPP(hAPP(c_fequal(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_525]) ).

cnf(c_0_724,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_526]) ).

cnf(c_0_725,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_527]) ).

cnf(c_0_726,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_528]) ).

cnf(c_0_727,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_529]) ).

cnf(c_0_728,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_530]) ).

cnf(c_0_729,plain,
    ( hBOOL(hAPP(X1,X2))
    | hBOOL(hAPP(X1,X3))
    | c_Type_Osko__Type__Xtype__induct__1__1(X1) != hAPP(hAPP(c_Type_Otype_OFun,X4),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_531]) ).

cnf(c_0_730,plain,
    ( hBOOL(hAPP(X1,X2))
    | hBOOL(hAPP(X1,X3))
    | c_Type_Osko__Type__Xtype__induct__1__1(X1) != hAPP(hAPP(c_Type_Otype_OFun,X2),X4) ),
    inference(split_conjunct,[status(thm)],[c_0_532]) ).

cnf(c_0_731,plain,
    ( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Olift(X1,X2)))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_533]) ).

cnf(c_0_732,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_534]) ).

cnf(c_0_733,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_535]) ).

cnf(c_0_734,plain,
    ( X1 = X2
    | hAPP(hAPP(c_Type_Otype_OFun,X1),X3) != hAPP(hAPP(c_Type_Otype_OFun,X2),X4) ),
    inference(split_conjunct,[status(thm)],[c_0_536]) ).

cnf(c_0_735,plain,
    ( X1 = X2
    | hAPP(hAPP(c_Type_Otype_OFun,X3),X1) != hAPP(hAPP(c_Type_Otype_OFun,X4),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_537]) ).

cnf(c_0_736,plain,
    ( c_Nat_Osemiring__1__class_Oof__nat(c_Suc(X1),X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_HOL_Oone__class_Oone(X2)),c_Nat_Osemiring__1__class_Oof__nat(X1,X2))
    | ~ class_Ring__and__Field_Osemiring__1(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_538]) ).

cnf(c_0_737,plain,
    ( c_lessequals(X1,X2,X3)
    | c_lessequals(X2,X1,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_539]) ).

cnf(c_0_738,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_540]) ).

cnf(c_0_739,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_541]) ).

cnf(c_0_740,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_542]) ).

cnf(c_0_741,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_543]) ).

cnf(c_0_742,plain,
    ( hAPP(X1,X2) = X3
    | ~ c_Type_Otyping(X1,c_Lambda_OdB_OVar(X2),X3) ),
    inference(split_conjunct,[status(thm)],[c_0_544]) ).

cnf(c_0_743,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_545]) ).

cnf(c_0_744,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_546]) ).

cnf(c_0_745,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_547]) ).

cnf(c_0_746,plain,
    ( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_548]) ).

cnf(c_0_747,plain,
    ( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    inference(split_conjunct,[status(thm)],[c_0_549]) ).

cnf(c_0_748,plain,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,c_Type_Osko__Type__Xtype__induct__1__1(X1))) ),
    inference(split_conjunct,[status(thm)],[c_0_550]) ).

cnf(c_0_749,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_551]) ).

cnf(c_0_750,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    inference(split_conjunct,[status(thm)],[c_0_552]) ).

cnf(c_0_751,plain,
    ( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    inference(split_conjunct,[status(thm)],[c_0_553]) ).

cnf(c_0_752,plain,
    ( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_554]) ).

cnf(c_0_753,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) ),
    inference(split_conjunct,[status(thm)],[c_0_555]) ).

cnf(c_0_754,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_556]) ).

cnf(c_0_755,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_557]) ).

cnf(c_0_756,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X2 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) ),
    inference(split_conjunct,[status(thm)],[c_0_558]) ).

cnf(c_0_757,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X2 = c_HOL_Ozero__class_Ozero(tc_nat)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    inference(split_conjunct,[status(thm)],[c_0_559]) ).

cnf(c_0_758,plain,
    ( c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),c_Suc(X2),X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Power_Opower(X1)
    | ~ class_Ring__and__Field_Osemiring__0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_560]) ).

cnf(c_0_759,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_561]) ).

cnf(c_0_760,plain,
    ( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(X1)))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_562]) ).

cnf(c_0_761,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_563]) ).

cnf(c_0_762,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_564]) ).

cnf(c_0_763,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_565]) ).

cnf(c_0_764,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_566]) ).

cnf(c_0_765,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_567]) ).

cnf(c_0_766,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_568]) ).

cnf(c_0_767,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_569]) ).

cnf(c_0_768,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_570]) ).

cnf(c_0_769,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_571]) ).

cnf(c_0_770,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_572]) ).

cnf(c_0_771,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_573]) ).

cnf(c_0_772,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_574]) ).

cnf(c_0_773,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_575]) ).

cnf(c_0_774,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_576]) ).

cnf(c_0_775,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_577]) ).

cnf(c_0_776,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_578]) ).

cnf(c_0_777,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_579]) ).

cnf(c_0_778,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_580]) ).

cnf(c_0_779,plain,
    ( c_lessequals(X1,X1,X2)
    | ~ class_Orderings_Oorder(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_581]) ).

cnf(c_0_780,plain,
    ( c_lessequals(X1,X1,X2)
    | ~ class_Orderings_Opreorder(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_582]) ).

cnf(c_0_781,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_583]) ).

cnf(c_0_782,plain,
    ( class_Orderings_Opreorder(tc_fun(X2,X1))
    | ~ class_Orderings_Opreorder(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_584]) ).

cnf(c_0_783,plain,
    ( class_Orderings_Oorder(tc_fun(X2,X1))
    | ~ class_Orderings_Oorder(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_585]) ).

cnf(c_0_784,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_586]) ).

cnf(c_0_785,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_587]) ).

cnf(c_0_786,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_588]) ).

cnf(c_0_787,plain,
    ( X1 = X2
    | c_Suc(X1) != c_Suc(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_589]) ).

cnf(c_0_788,plain,
    ( X1 = X2
    | c_Suc(X1) != c_Suc(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_590]) ).

cnf(c_0_789,plain,
    ( X1 = X2
    | c_Type_Otype_OAtom(X1) != c_Type_Otype_OAtom(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_591]) ).

cnf(c_0_790,plain,
    ( X1 = X2
    | c_Lambda_OdB_OAbs(X1) != c_Lambda_OdB_OAbs(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_592]) ).

cnf(c_0_791,plain,
    ( X1 = X2
    | c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OVar(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_593]) ).

cnf(c_0_792,plain,
    ( c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__types__1__1(X5,X7,X1,X4),X5,tc_Type_Otype,tc_Type_Otype) = X7
    | ~ 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_594,
    [final] ).

cnf(c_0_793,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_595,
    [final] ).

cnf(c_0_794,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_596,
    [final] ).

cnf(c_0_795,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_597,
    [final] ).

cnf(c_0_796,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_598,
    [final] ).

cnf(c_0_797,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_599,
    [final] ).

cnf(c_0_798,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_600,
    [final] ).

cnf(c_0_799,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,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_601,
    [final] ).

cnf(c_0_800,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_602,
    [final] ).

cnf(c_0_801,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,c_Lambda_Osubst(X1,X2,c_HOL_Ozero__class_Ozero(tc_nat)),X3,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB) ),
    c_0_603,
    [final] ).

cnf(c_0_802,plain,
    ( c_Type_Otyping(X1,c_Lambda_OdB_OVar(X2),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__typesE__1__1(X4,X1,X2,X3),X4,tc_Type_Otype,tc_Type_Otype))
    | ~ 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_604,
    [final] ).

cnf(c_0_803,plain,
    ( c_Type_Otyping(X1,X2,c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeE__1__1(X4,X1,X2,X3),X4,tc_Type_Otype,tc_Type_Otype))
    | ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB),X4) ),
    c_0_605,
    [final] ).

cnf(c_0_804,plain,
    ( c_Type_Otyping(X1,X2,c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeD__1__1(X4,X1,X2,X3),X4,tc_Type_Otype,tc_Type_Otype))
    | ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB),X4) ),
    c_0_606,
    [final] ).

cnf(c_0_805,plain,
    ( c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X5,tc_Lambda_OdB,tc_Lambda_OdB),X4)
    | ~ c_Type_Otyping(X1,X2,c_List_Ofoldr(c_Type_Otype_OFun,X3,X4,tc_Type_Otype,tc_Type_Otype))
    | ~ c_Type_Otypings(X1,X5,X3) ),
    c_0_607,
    [final] ).

cnf(c_0_806,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_608,
    [final] ).

cnf(c_0_807,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_609,
    [final] ).

cnf(c_0_808,plain,
    ( c_Type_Otypings(X1,X3,c_Type_Osko__Type__Xlist__app__typeE__1__1(X4,X1,X2,X3))
    | ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB),X4) ),
    c_0_610,
    [final] ).

cnf(c_0_809,plain,
    ( c_Type_Otypings(X1,X3,c_Type_Osko__Type__Xlist__app__typeD__1__1(X4,X1,X2,X3))
    | ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB),X4) ),
    c_0_611,
    [final] ).

cnf(c_0_810,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_612,
    [final] ).

cnf(c_0_811,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_613,
    [final] ).

cnf(c_0_812,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_614,
    [final] ).

cnf(c_0_813,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_615,
    [final] ).

cnf(c_0_814,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_616,
    [final] ).

cnf(c_0_815,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_617,
    [final] ).

cnf(c_0_816,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_618,
    [final] ).

cnf(c_0_817,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_619,
    [final] ).

cnf(c_0_818,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_620,
    [final] ).

cnf(c_0_819,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_621,
    [final] ).

cnf(c_0_820,plain,
    ( c_Type_Otyping(X1,X2,hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__2__1(X4,X1,X2,X3)),X4))
    | ~ c_Type_Otyping(X1,hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3),X4) ),
    c_0_622,
    [final] ).

cnf(c_0_821,plain,
    ( hBOOL(hAPP(X1,hAPP(hAPP(X2,X3),X4)))
    | ~ hBOOL(hAPP(X1,c_Type_Otype_Otype__case(X5,X2,hAPP(hAPP(c_Type_Otype_OFun,X3),X4),t_a))) ),
    c_0_623,
    [final] ).

cnf(c_0_822,plain,
    ( hBOOL(hAPP(X1,hAPP(hAPP(X2,X3),X4)))
    | ~ hBOOL(hAPP(X1,c_Type_Otype_Otype__case(X5,X2,hAPP(hAPP(c_Type_Otype_OFun,X3),X4),t_a))) ),
    c_0_624,
    [final] ).

cnf(c_0_823,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_625,
    [final] ).

cnf(c_0_824,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_626,
    [final] ).

cnf(c_0_825,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_627,
    [final] ).

cnf(c_0_826,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_628,
    [final] ).

cnf(c_0_827,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_629,
    [final] ).

cnf(c_0_828,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_630,
    [final] ).

cnf(c_0_829,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_631,
    [final] ).

cnf(c_0_830,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_632,
    [final] ).

cnf(c_0_831,plain,
    ( hBOOL(hAPP(X1,hAPP(X2,X3)))
    | ~ hBOOL(hAPP(X1,c_Type_Otype_Otype__case(X2,X4,c_Type_Otype_OAtom(X3),t_a))) ),
    c_0_633,
    [final] ).

cnf(c_0_832,plain,
    ( hBOOL(hAPP(X1,hAPP(X2,X3)))
    | ~ hBOOL(hAPP(X1,c_Type_Otype_Otype__case(X2,X4,c_Type_Otype_OAtom(X3),t_a))) ),
    c_0_634,
    [final] ).

cnf(c_0_833,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_635,
    [final] ).

cnf(c_0_834,plain,
    ( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(X1,X6,X3)))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
    | ~ c_Type_Otyping(c_Type_Oshift(X2,X3,X4,tc_Type_Otype),X1,X5)
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X6))
    | ~ c_Type_Otyping(X2,X6,X4) ),
    c_0_636,
    [final] ).

cnf(c_0_835,plain,
    ( c_Type_Otyping(X1,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_637,
    [final] ).

cnf(c_0_836,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_638,
    [final] ).

cnf(c_0_837,plain,
    ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Osubst(X3,X1,X4)),c_Lambda_Osubst(X3,X2,X4)))
    | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2)) ),
    c_0_639,
    [final] ).

cnf(c_0_838,plain,
    ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Osubst(X1,X3,X4)),c_Lambda_Osubst(X2,X3,X4)))
    | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2)) ),
    c_0_640,
    [final] ).

cnf(c_0_839,plain,
    ( c_Type_Otyping(X1,c_Lambda_OdB_OAbs(X3),hAPP(hAPP(c_Type_Otype_OFun,X2),X4))
    | ~ c_Type_Otyping(c_Type_Oshift(X1,c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_Type_Otype),X3,X4) ),
    c_0_641,
    [final] ).

cnf(c_0_840,plain,
    ( c_Type_Otyping(c_Type_Oshift(X1,c_HOL_Ozero__class_Ozero(tc_nat),c_Type_Osko__Type__Xtyping__elims__3__1(X3,X1,X2),tc_Type_Otype),X2,c_Type_Osko__Type__Xtyping__elims__3__2(X3,X1,X2))
    | ~ c_Type_Otyping(X1,c_Lambda_OdB_OAbs(X2),X3) ),
    c_0_642,
    [final] ).

cnf(c_0_841,plain,
    ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Osubst(X3,X1,X4)),c_Lambda_Osubst(X3,X2,X4)))
    | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2)) ),
    c_0_643,
    [final] ).

cnf(c_0_842,plain,
    ( hBOOL(hAPP(hAPP(X1,X5),X4))
    | ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X2,X3),X4),X5)) ),
    c_0_644,
    [final] ).

cnf(c_0_843,plain,
    ( hBOOL(hAPP(hAPP(X1,X5),X4))
    | ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X2,X3),X4),X5)) ),
    c_0_645,
    [final] ).

cnf(c_0_844,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_646,
    [final] ).

cnf(c_0_845,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_647,
    [final] ).

cnf(c_0_846,plain,
    ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_Osubst(X1,X3,X4)),c_Lambda_Osubst(X2,X3,X4)))
    | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2)) ),
    c_0_648,
    [final] ).

cnf(c_0_847,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_649,
    [final] ).

cnf(c_0_848,plain,
    ( c_Type_Otyping(X1,X3,c_Type_Osko__Type__Xtyping__elims__2__1(X4,X1,X2,X3))
    | ~ c_Type_Otyping(X1,hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3),X4) ),
    c_0_650,
    [final] ).

cnf(c_0_849,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_651,
    [final] ).

cnf(c_0_850,plain,
    ( c_Type_Otyping(c_Type_Oshift(X1,c_HOL_Ozero__class_Ozero(tc_nat),c_Type_Osko__Type__Xabs__typeE__1__1(X1,X2),tc_Type_Otype),X2,c_Type_Osko__Type__Xabs__typeE__1__2(X1,X2))
    | ~ c_Type_Otyping(X1,c_Lambda_OdB_OAbs(X2),X3) ),
    c_0_652,
    [final] ).

cnf(c_0_851,plain,
    ( c_Type_Otyping(c_Type_Oshift(X1,X4,X5,tc_Type_Otype),c_Lambda_Olift(X2,X4),X3)
    | ~ c_Type_Otyping(X1,X2,X3) ),
    c_0_653,
    [final] ).

cnf(c_0_852,plain,
    ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X4,X5),X3),X2))
    | ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
    c_0_654,
    [final] ).

cnf(c_0_853,plain,
    ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X4,X5),X3),X2))
    | ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
    c_0_655,
    [final] ).

cnf(c_0_854,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_656,
    [final] ).

cnf(c_0_855,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_657,
    [final] ).

cnf(c_0_856,plain,
    ( c_lessequals(X1,X4,X3)
    | ~ c_lessequals(c_Power_Opower__class_Opower(X1,c_Suc(X2),X3),c_Power_Opower__class_Opower(X4,c_Suc(X2),X3),X3)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
    | ~ class_Ring__and__Field_Oordered__semidom(X3) ),
    c_0_658,
    [final] ).

cnf(c_0_857,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_659,
    [final] ).

cnf(c_0_858,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_660,
    [final] ).

cnf(c_0_859,plain,
    ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Olift(X1,X3)),c_Lambda_Olift(X2,X3)))
    | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2)) ),
    c_0_661,
    [final] ).

cnf(c_0_860,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_662,
    [final] ).

cnf(c_0_861,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_663,
    [final] ).

cnf(c_0_862,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_664,
    [final] ).

cnf(c_0_863,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_665,
    [final] ).

cnf(c_0_864,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_666,
    [final] ).

cnf(c_0_865,plain,
    ( hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__3__1(X3,X1,X2)),c_Type_Osko__Type__Xtyping__elims__3__2(X3,X1,X2)) = X3
    | ~ c_Type_Otyping(X1,c_Lambda_OdB_OAbs(X2),X3) ),
    c_0_667,
    [final] ).

cnf(c_0_866,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_668,
    [final] ).

cnf(c_0_867,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_669,
    [final] ).

cnf(c_0_868,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_670,
    [final] ).

cnf(c_0_869,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_671,
    [final] ).

cnf(c_0_870,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_672,
    [final] ).

cnf(c_0_871,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_673,
    [final] ).

cnf(c_0_872,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_674,
    [final] ).

cnf(c_0_873,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_675,
    [final] ).

cnf(c_0_874,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_676,
    [final] ).

cnf(c_0_875,plain,
    ( c_Type_Otyping(X1,hAPP(hAPP(c_Lambda_OdB_OApp,X2),X5),X4)
    | ~ c_Type_Otyping(X1,X2,hAPP(hAPP(c_Type_Otype_OFun,X3),X4))
    | ~ c_Type_Otyping(X1,X5,X3) ),
    c_0_677,
    [final] ).

cnf(c_0_876,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_678,
    [final] ).

cnf(c_0_877,plain,
    ( X2 = X3
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | c_Power_Opower__class_Opower(X2,c_Suc(X4),X1) != c_Power_Opower__class_Opower(X3,c_Suc(X4),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_679,
    [final] ).

cnf(c_0_878,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_680,
    [final] ).

cnf(c_0_879,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_681,
    [final] ).

cnf(c_0_880,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_682,
    [final] ).

cnf(c_0_881,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_683,
    [final] ).

cnf(c_0_882,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_684,
    [final] ).

cnf(c_0_883,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_685,
    [final] ).

cnf(c_0_884,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_686,
    [final] ).

cnf(c_0_885,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_687,
    [final] ).

cnf(c_0_886,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_688,
    [final] ).

cnf(c_0_887,plain,
    ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_Olift(X1,X3)),c_Lambda_Olift(X2,X3)))
    | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2)) ),
    c_0_689,
    [final] ).

cnf(c_0_888,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_690,
    [final] ).

cnf(c_0_889,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_691,
    [final] ).

cnf(c_0_890,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_692,
    [final] ).

cnf(c_0_891,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_693,
    [final] ).

cnf(c_0_892,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_694,
    [final] ).

cnf(c_0_893,plain,
    ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X4),X2),X3))
    | ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
    c_0_695,
    [final] ).

cnf(c_0_894,plain,
    ( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(X1,c_Lambda_OdB_OVar(X2),X3)))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
    c_0_696,
    [final] ).

cnf(c_0_895,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_697,
    [final] ).

cnf(c_0_896,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_698,
    [final] ).

cnf(c_0_897,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_699,
    [final] ).

cnf(c_0_898,plain,
    ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),c_Lambda_Osko__Lambda__Xbeta__cases__2__1(X1,X2)))
    | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OAbs(X1)),X2)) ),
    c_0_700,
    [final] ).

cnf(c_0_899,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_701,
    [final] ).

cnf(c_0_900,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_702,
    [final] ).

cnf(c_0_901,plain,
    ( c_Wellfounded_Oaccp(X1,X4,X3)
    | ~ c_Wellfounded_Oaccp(X1,X2,X3)
    | ~ hBOOL(hAPP(hAPP(X1,X4),X2)) ),
    c_0_703,
    [final] ).

cnf(c_0_902,plain,
    ( c_Wellfounded_Oaccp(X1,X4,X3)
    | ~ c_Wellfounded_Oaccp(X1,X2,X3)
    | ~ hBOOL(hAPP(hAPP(X1,X4),X2)) ),
    c_0_704,
    [final] ).

cnf(c_0_903,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_705,
    [final] ).

cnf(c_0_904,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_706,
    [final] ).

cnf(c_0_905,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_707,
    [final] ).

cnf(c_0_906,plain,
    ( c_Type_Otyping(X1,X4,X3)
    | ~ c_Type_Otyping(X1,X2,X3)
    | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X2),X4)) ),
    c_0_708,
    [final] ).

cnf(c_0_907,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_709,
    [final] ).

cnf(c_0_908,plain,
    ( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,X1),c_Lambda_OdB_OVar(X2))))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
    c_0_710,
    [final] ).

cnf(c_0_909,plain,
    ( c_lessequals(X4,X2,X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_lessequals(X4,X1,X3)
    | ~ class_Orderings_Oorder(X3) ),
    c_0_711,
    [final] ).

cnf(c_0_910,plain,
    ( c_lessequals(X1,X4,X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_lessequals(X2,X4,X3)
    | ~ class_Orderings_Opreorder(X3) ),
    c_0_712,
    [final] ).

cnf(c_0_911,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_713,
    [final] ).

cnf(c_0_912,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_714,
    [final] ).

cnf(c_0_913,plain,
    ( c_Lambda_OdB_OAbs(c_Lambda_Osko__Lambda__Xbeta__cases__2__1(X1,X2)) = X2
    | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OAbs(X1)),X2)) ),
    c_0_715,
    [final] ).

cnf(c_0_914,plain,
    ( X1 = X2
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_lessequals(X2,X1,X3)
    | ~ class_Orderings_Oorder(X3) ),
    c_0_716,
    [final] ).

cnf(c_0_915,plain,
    ( X1 = X2
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_lessequals(X2,X1,X3)
    | ~ class_Orderings_Oorder(X3) ),
    c_0_717,
    [final] ).

cnf(c_0_916,plain,
    ( X2 = X1
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_lessequals(X2,X1,X3)
    | ~ class_Orderings_Oorder(X3) ),
    c_0_718,
    [final] ).

cnf(c_0_917,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_719,
    [final] ).

cnf(c_0_918,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_720,
    [final] ).

cnf(c_0_919,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_721,
    [final] ).

cnf(c_0_920,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_722,
    [final] ).

cnf(c_0_921,plain,
    ( X2 = X3
    | ~ hBOOL(hAPP(hAPP(c_fequal(X1),X2),X3)) ),
    c_0_723,
    [final] ).

cnf(c_0_922,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_724,
    [final] ).

cnf(c_0_923,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_725,
    [final] ).

cnf(c_0_924,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_726,
    [final] ).

cnf(c_0_925,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_727,
    [final] ).

cnf(c_0_926,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_728,
    [final] ).

cnf(c_0_927,plain,
    ( hBOOL(hAPP(X1,X2))
    | hBOOL(hAPP(X1,X3))
    | c_Type_Osko__Type__Xtype__induct__1__1(X1) != hAPP(hAPP(c_Type_Otype_OFun,X4),X2) ),
    c_0_729,
    [final] ).

cnf(c_0_928,plain,
    ( hBOOL(hAPP(X1,X2))
    | hBOOL(hAPP(X1,X3))
    | c_Type_Osko__Type__Xtype__induct__1__1(X1) != hAPP(hAPP(c_Type_Otype_OFun,X2),X4) ),
    c_0_730,
    [final] ).

cnf(c_0_929,plain,
    ( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Olift(X1,X2)))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
    c_0_731,
    [final] ).

cnf(c_0_930,plain,
    ( X1 = X2
    | hAPP(hAPP(c_Lambda_OdB_OApp,X3),X1) != hAPP(hAPP(c_Lambda_OdB_OApp,X4),X2) ),
    c_0_732,
    [final] ).

cnf(c_0_931,plain,
    ( X1 = X2
    | hAPP(hAPP(c_Lambda_OdB_OApp,X1),X3) != hAPP(hAPP(c_Lambda_OdB_OApp,X2),X4) ),
    c_0_733,
    [final] ).

cnf(c_0_932,plain,
    ( X1 = X2
    | hAPP(hAPP(c_Type_Otype_OFun,X1),X3) != hAPP(hAPP(c_Type_Otype_OFun,X2),X4) ),
    c_0_734,
    [final] ).

cnf(c_0_933,plain,
    ( X1 = X2
    | hAPP(hAPP(c_Type_Otype_OFun,X3),X1) != hAPP(hAPP(c_Type_Otype_OFun,X4),X2) ),
    c_0_735,
    [final] ).

cnf(c_0_934,plain,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_HOL_Oone__class_Oone(X2)),c_Nat_Osemiring__1__class_Oof__nat(X1,X2)) = c_Nat_Osemiring__1__class_Oof__nat(c_Suc(X1),X2)
    | ~ class_Ring__and__Field_Osemiring__1(X2) ),
    c_0_736,
    [final] ).

cnf(c_0_935,plain,
    ( c_lessequals(X1,X2,X3)
    | c_lessequals(X2,X1,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_737,
    [final] ).

cnf(c_0_936,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_738,
    [final] ).

cnf(c_0_937,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_739,
    [final] ).

cnf(c_0_938,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_740,
    [final] ).

cnf(c_0_939,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_741,
    [final] ).

cnf(c_0_940,plain,
    ( hAPP(X1,X2) = X3
    | ~ c_Type_Otyping(X1,c_Lambda_OdB_OVar(X2),X3) ),
    c_0_742,
    [final] ).

cnf(c_0_941,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_743,
    [final] ).

cnf(c_0_942,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_744,
    [final] ).

cnf(c_0_943,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_745,
    [final] ).

cnf(c_0_944,plain,
    ( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    c_0_746,
    [final] ).

cnf(c_0_945,plain,
    ( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    c_0_747,
    [final] ).

cnf(c_0_946,plain,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,c_Type_Osko__Type__Xtype__induct__1__1(X1))) ),
    c_0_748,
    [final] ).

cnf(c_0_947,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_749,
    [final] ).

cnf(c_0_948,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    c_0_750,
    [final] ).

cnf(c_0_949,plain,
    ( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    c_0_751,
    [final] ).

cnf(c_0_950,plain,
    ( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    c_0_752,
    [final] ).

cnf(c_0_951,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    c_0_753,
    [final] ).

cnf(c_0_952,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_754,
    [final] ).

cnf(c_0_953,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_755,
    [final] ).

cnf(c_0_954,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X2 = c_HOL_Ozero__class_Ozero(tc_nat)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    c_0_756,
    [final] ).

cnf(c_0_955,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X2 = c_HOL_Ozero__class_Ozero(tc_nat)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    c_0_757,
    [final] ).

cnf(c_0_956,plain,
    ( c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),c_Suc(X2),X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Power_Opower(X1)
    | ~ class_Ring__and__Field_Osemiring__0(X1) ),
    c_0_758,
    [final] ).

cnf(c_0_957,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_759,
    [final] ).

cnf(c_0_958,plain,
    ( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(X1)))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
    c_0_760,
    [final] ).

cnf(c_0_959,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_761,
    [final] ).

cnf(c_0_960,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_762,
    [final] ).

cnf(c_0_961,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_763,
    [final] ).

cnf(c_0_962,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_764,
    [final] ).

cnf(c_0_963,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != X2 ),
    c_0_765,
    [final] ).

cnf(c_0_964,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != X2 ),
    c_0_766,
    [final] ).

cnf(c_0_965,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_767,
    [final] ).

cnf(c_0_966,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_768,
    [final] ).

cnf(c_0_967,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_769,
    [final] ).

cnf(c_0_968,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_770,
    [final] ).

cnf(c_0_969,plain,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
    | ~ class_OrderedGroup_Omonoid__add(X1) ),
    c_0_771,
    [final] ).

cnf(c_0_970,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_772,
    [final] ).

cnf(c_0_971,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_773,
    [final] ).

cnf(c_0_972,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_774,
    [final] ).

cnf(c_0_973,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_775,
    [final] ).

cnf(c_0_974,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_776,
    [final] ).

cnf(c_0_975,plain,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = X2
    | ~ class_OrderedGroup_Omonoid__add(X1) ),
    c_0_777,
    [final] ).

cnf(c_0_976,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_778,
    [final] ).

cnf(c_0_977,plain,
    ( c_lessequals(X1,X1,X2)
    | ~ class_Orderings_Oorder(X2) ),
    c_0_779,
    [final] ).

cnf(c_0_978,plain,
    ( c_lessequals(X1,X1,X2)
    | ~ class_Orderings_Opreorder(X2) ),
    c_0_780,
    [final] ).

cnf(c_0_979,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_781,
    [final] ).

cnf(c_0_980,plain,
    ( class_Orderings_Opreorder(tc_fun(X2,X1))
    | ~ class_Orderings_Opreorder(X1) ),
    c_0_782,
    [final] ).

cnf(c_0_981,plain,
    ( class_Orderings_Oorder(tc_fun(X2,X1))
    | ~ class_Orderings_Oorder(X1) ),
    c_0_783,
    [final] ).

cnf(c_0_982,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_784,
    [final] ).

cnf(c_0_983,plain,
    ( c_HOL_Oone__class_Oone(X1) != c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Ozero__neq__one(X1) ),
    c_0_785,
    [final] ).

cnf(c_0_984,plain,
    ( c_HOL_Oone__class_Oone(X1) != c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Ozero__neq__one(X1) ),
    c_0_786,
    [final] ).

cnf(c_0_985,plain,
    ( X1 = X2
    | c_Suc(X1) != c_Suc(X2) ),
    c_0_787,
    [final] ).

cnf(c_0_986,plain,
    ( X1 = X2
    | c_Suc(X1) != c_Suc(X2) ),
    c_0_788,
    [final] ).

cnf(c_0_987,plain,
    ( X1 = X2
    | c_Type_Otype_OAtom(X1) != c_Type_Otype_OAtom(X2) ),
    c_0_789,
    [final] ).

cnf(c_0_988,plain,
    ( X1 = X2
    | c_Lambda_OdB_OAbs(X1) != c_Lambda_OdB_OAbs(X2) ),
    c_0_790,
    [final] ).

cnf(c_0_989,plain,
    ( X1 = X2
    | c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OVar(X2) ),
    c_0_791,
    [final] ).

% End CNF derivation
% Generating one_way clauses for all literals in the CNF.
cnf(c_0_792_0,axiom,
    ( c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__types__1__1(X5,X7,X1,X4),X5,tc_Type_Otype,tc_Type_Otype) = X7
    | ~ 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_792]) ).

cnf(c_0_792_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_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__types__1__1(X5,X7,X1,X4),X5,tc_Type_Otype,tc_Type_Otype) = X7
    | ~ 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_792]) ).

cnf(c_0_792_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_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__types__1__1(X5,X7,X1,X4),X5,tc_Type_Otype,tc_Type_Otype) = X7
    | ~ 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_792]) ).

cnf(c_0_792_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_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__types__1__1(X5,X7,X1,X4),X5,tc_Type_Otype,tc_Type_Otype) = X7 ),
    inference(literals_permutation,[status(thm)],[c_0_792]) ).

cnf(c_0_793_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_793]) ).

cnf(c_0_793_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_793]) ).

cnf(c_0_794_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_794]) ).

cnf(c_0_794_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_794]) ).

cnf(c_0_794_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_794]) ).

cnf(c_0_794_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_794]) ).

cnf(c_0_795_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_795]) ).

cnf(c_0_795_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_795]) ).

cnf(c_0_796_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_796]) ).

cnf(c_0_796_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_796]) ).

cnf(c_0_797_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_797]) ).

cnf(c_0_797_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_797]) ).

cnf(c_0_798_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_798]) ).

cnf(c_0_798_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_798]) ).

cnf(c_0_799_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,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_799]) ).

cnf(c_0_799_1,axiom,
    ( ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,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_799]) ).

cnf(c_0_799_2,axiom,
    ( ~ hBOOL(hAPP(c_InductTermi_OIT,X2))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,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_799]) ).

cnf(c_0_800_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_800]) ).

cnf(c_0_800_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_800]) ).

cnf(c_0_800_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_800]) ).

cnf(c_0_801_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,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_801]) ).

cnf(c_0_801_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,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_801]) ).

cnf(c_0_801_2,axiom,
    ( ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,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_801]) ).

cnf(c_0_802_0,axiom,
    ( c_Type_Otyping(X1,c_Lambda_OdB_OVar(X2),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__typesE__1__1(X4,X1,X2,X3),X4,tc_Type_Otype,tc_Type_Otype))
    | ~ 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_802]) ).

cnf(c_0_802_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_Otyping(X1,c_Lambda_OdB_OVar(X2),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__typesE__1__1(X4,X1,X2,X3),X4,tc_Type_Otype,tc_Type_Otype)) ),
    inference(literals_permutation,[status(thm)],[c_0_802]) ).

cnf(c_0_803_0,axiom,
    ( c_Type_Otyping(X1,X2,c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeE__1__1(X4,X1,X2,X3),X4,tc_Type_Otype,tc_Type_Otype))
    | ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_803]) ).

cnf(c_0_803_1,axiom,
    ( ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB),X4)
    | c_Type_Otyping(X1,X2,c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeE__1__1(X4,X1,X2,X3),X4,tc_Type_Otype,tc_Type_Otype)) ),
    inference(literals_permutation,[status(thm)],[c_0_803]) ).

cnf(c_0_804_0,axiom,
    ( c_Type_Otyping(X1,X2,c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeD__1__1(X4,X1,X2,X3),X4,tc_Type_Otype,tc_Type_Otype))
    | ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_804]) ).

cnf(c_0_804_1,axiom,
    ( ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB),X4)
    | c_Type_Otyping(X1,X2,c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeD__1__1(X4,X1,X2,X3),X4,tc_Type_Otype,tc_Type_Otype)) ),
    inference(literals_permutation,[status(thm)],[c_0_804]) ).

cnf(c_0_805_0,axiom,
    ( c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X5,tc_Lambda_OdB,tc_Lambda_OdB),X4)
    | ~ c_Type_Otyping(X1,X2,c_List_Ofoldr(c_Type_Otype_OFun,X3,X4,tc_Type_Otype,tc_Type_Otype))
    | ~ c_Type_Otypings(X1,X5,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_805]) ).

cnf(c_0_805_1,axiom,
    ( ~ c_Type_Otyping(X1,X2,c_List_Ofoldr(c_Type_Otype_OFun,X3,X4,tc_Type_Otype,tc_Type_Otype))
    | c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X5,tc_Lambda_OdB,tc_Lambda_OdB),X4)
    | ~ c_Type_Otypings(X1,X5,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_805]) ).

cnf(c_0_805_2,axiom,
    ( ~ c_Type_Otypings(X1,X5,X3)
    | ~ c_Type_Otyping(X1,X2,c_List_Ofoldr(c_Type_Otype_OFun,X3,X4,tc_Type_Otype,tc_Type_Otype))
    | c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X5,tc_Lambda_OdB,tc_Lambda_OdB),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_805]) ).

cnf(c_0_806_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_806]) ).

cnf(c_0_806_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_806]) ).

cnf(c_0_807_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_807]) ).

cnf(c_0_807_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_807]) ).

cnf(c_0_808_0,axiom,
    ( c_Type_Otypings(X1,X3,c_Type_Osko__Type__Xlist__app__typeE__1__1(X4,X1,X2,X3))
    | ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_808]) ).

cnf(c_0_808_1,axiom,
    ( ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB),X4)
    | c_Type_Otypings(X1,X3,c_Type_Osko__Type__Xlist__app__typeE__1__1(X4,X1,X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_808]) ).

cnf(c_0_809_0,axiom,
    ( c_Type_Otypings(X1,X3,c_Type_Osko__Type__Xlist__app__typeD__1__1(X4,X1,X2,X3))
    | ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_809]) ).

cnf(c_0_809_1,axiom,
    ( ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB),X4)
    | c_Type_Otypings(X1,X3,c_Type_Osko__Type__Xlist__app__typeD__1__1(X4,X1,X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_809]) ).

cnf(c_0_810_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_810]) ).

cnf(c_0_810_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_810]) ).

cnf(c_0_811_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_811]) ).

cnf(c_0_811_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_811]) ).

cnf(c_0_812_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_812]) ).

cnf(c_0_812_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_812]) ).

cnf(c_0_813_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_813]) ).

cnf(c_0_813_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_813]) ).

cnf(c_0_814_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_814]) ).

cnf(c_0_814_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_814]) ).

cnf(c_0_815_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_815]) ).

cnf(c_0_815_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_815]) ).

cnf(c_0_816_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_816]) ).

cnf(c_0_816_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_816]) ).

cnf(c_0_817_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_817]) ).

cnf(c_0_817_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_817]) ).

cnf(c_0_818_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_818]) ).

cnf(c_0_818_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_818]) ).

cnf(c_0_819_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_819]) ).

cnf(c_0_819_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_819]) ).

cnf(c_0_820_0,axiom,
    ( c_Type_Otyping(X1,X2,hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__2__1(X4,X1,X2,X3)),X4))
    | ~ c_Type_Otyping(X1,hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_820]) ).

cnf(c_0_820_1,axiom,
    ( ~ c_Type_Otyping(X1,hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3),X4)
    | c_Type_Otyping(X1,X2,hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__2__1(X4,X1,X2,X3)),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_820]) ).

cnf(c_0_821_0,axiom,
    ( hBOOL(hAPP(X1,hAPP(hAPP(X2,X3),X4)))
    | ~ hBOOL(hAPP(X1,c_Type_Otype_Otype__case(X5,X2,hAPP(hAPP(c_Type_Otype_OFun,X3),X4),t_a))) ),
    inference(literals_permutation,[status(thm)],[c_0_821]) ).

cnf(c_0_821_1,axiom,
    ( ~ hBOOL(hAPP(X1,c_Type_Otype_Otype__case(X5,X2,hAPP(hAPP(c_Type_Otype_OFun,X3),X4),t_a)))
    | hBOOL(hAPP(X1,hAPP(hAPP(X2,X3),X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_821]) ).

cnf(c_0_822_0,axiom,
    ( hBOOL(hAPP(X1,hAPP(hAPP(X2,X3),X4)))
    | ~ hBOOL(hAPP(X1,c_Type_Otype_Otype__case(X5,X2,hAPP(hAPP(c_Type_Otype_OFun,X3),X4),t_a))) ),
    inference(literals_permutation,[status(thm)],[c_0_822]) ).

cnf(c_0_822_1,axiom,
    ( ~ hBOOL(hAPP(X1,c_Type_Otype_Otype__case(X5,X2,hAPP(hAPP(c_Type_Otype_OFun,X3),X4),t_a)))
    | hBOOL(hAPP(X1,hAPP(hAPP(X2,X3),X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_822]) ).

cnf(c_0_823_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_823]) ).

cnf(c_0_823_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_823]) ).

cnf(c_0_824_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_824]) ).

cnf(c_0_824_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_824]) ).

cnf(c_0_825_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_825]) ).

cnf(c_0_825_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_825]) ).

cnf(c_0_826_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_826]) ).

cnf(c_0_826_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_826]) ).

cnf(c_0_827_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_827]) ).

cnf(c_0_827_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_827]) ).

cnf(c_0_828_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_828]) ).

cnf(c_0_828_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_828]) ).

cnf(c_0_829_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_829]) ).

cnf(c_0_829_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_829]) ).

cnf(c_0_830_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_830]) ).

cnf(c_0_830_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_830]) ).

cnf(c_0_831_0,axiom,
    ( hBOOL(hAPP(X1,hAPP(X2,X3)))
    | ~ hBOOL(hAPP(X1,c_Type_Otype_Otype__case(X2,X4,c_Type_Otype_OAtom(X3),t_a))) ),
    inference(literals_permutation,[status(thm)],[c_0_831]) ).

cnf(c_0_831_1,axiom,
    ( ~ hBOOL(hAPP(X1,c_Type_Otype_Otype__case(X2,X4,c_Type_Otype_OAtom(X3),t_a)))
    | hBOOL(hAPP(X1,hAPP(X2,X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_831]) ).

cnf(c_0_832_0,axiom,
    ( hBOOL(hAPP(X1,hAPP(X2,X3)))
    | ~ hBOOL(hAPP(X1,c_Type_Otype_Otype__case(X2,X4,c_Type_Otype_OAtom(X3),t_a))) ),
    inference(literals_permutation,[status(thm)],[c_0_832]) ).

cnf(c_0_832_1,axiom,
    ( ~ hBOOL(hAPP(X1,c_Type_Otype_Otype__case(X2,X4,c_Type_Otype_OAtom(X3),t_a)))
    | hBOOL(hAPP(X1,hAPP(X2,X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_832]) ).

cnf(c_0_833_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_833]) ).

cnf(c_0_833_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_833]) ).

cnf(c_0_834_0,axiom,
    ( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(X1,X6,X3)))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
    | ~ c_Type_Otyping(c_Type_Oshift(X2,X3,X4,tc_Type_Otype),X1,X5)
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X6))
    | ~ c_Type_Otyping(X2,X6,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_834]) ).

cnf(c_0_834_1,axiom,
    ( ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
    | hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(X1,X6,X3)))
    | ~ c_Type_Otyping(c_Type_Oshift(X2,X3,X4,tc_Type_Otype),X1,X5)
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X6))
    | ~ c_Type_Otyping(X2,X6,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_834]) ).

cnf(c_0_834_2,axiom,
    ( ~ c_Type_Otyping(c_Type_Oshift(X2,X3,X4,tc_Type_Otype),X1,X5)
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
    | hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(X1,X6,X3)))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X6))
    | ~ c_Type_Otyping(X2,X6,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_834]) ).

cnf(c_0_834_3,axiom,
    ( ~ hBOOL(hAPP(c_InductTermi_OIT,X6))
    | ~ c_Type_Otyping(c_Type_Oshift(X2,X3,X4,tc_Type_Otype),X1,X5)
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
    | hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(X1,X6,X3)))
    | ~ c_Type_Otyping(X2,X6,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_834]) ).

cnf(c_0_834_4,axiom,
    ( ~ c_Type_Otyping(X2,X6,X4)
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X6))
    | ~ c_Type_Otyping(c_Type_Oshift(X2,X3,X4,tc_Type_Otype),X1,X5)
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
    | hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(X1,X6,X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_834]) ).

cnf(c_0_835_0,axiom,
    ( c_Type_Otyping(X1,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_835]) ).

cnf(c_0_835_1,axiom,
    ( ~ c_Type_Otyping(c_Type_Oshift(X1,X4,X6,tc_Type_Otype),X2,X5)
    | c_Type_Otyping(X1,c_Lambda_Osubst(X2,X3,X4),X5)
    | ~ c_Type_Otyping(X1,X3,X6) ),
    inference(literals_permutation,[status(thm)],[c_0_835]) ).

cnf(c_0_835_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,c_Lambda_Osubst(X2,X3,X4),X5) ),
    inference(literals_permutation,[status(thm)],[c_0_835]) ).

cnf(c_0_836_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_836]) ).

cnf(c_0_836_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_836]) ).

cnf(c_0_836_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_836]) ).

cnf(c_0_837_0,axiom,
    ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Osubst(X3,X1,X4)),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_837]) ).

cnf(c_0_837_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_Osubst(X3,X1,X4)),c_Lambda_Osubst(X3,X2,X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_837]) ).

cnf(c_0_838_0,axiom,
    ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Osubst(X1,X3,X4)),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_838]) ).

cnf(c_0_838_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_Osubst(X1,X3,X4)),c_Lambda_Osubst(X2,X3,X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_838]) ).

cnf(c_0_839_0,axiom,
    ( c_Type_Otyping(X1,c_Lambda_OdB_OAbs(X3),hAPP(hAPP(c_Type_Otype_OFun,X2),X4))
    | ~ c_Type_Otyping(c_Type_Oshift(X1,c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_Type_Otype),X3,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_839]) ).

cnf(c_0_839_1,axiom,
    ( ~ c_Type_Otyping(c_Type_Oshift(X1,c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_Type_Otype),X3,X4)
    | c_Type_Otyping(X1,c_Lambda_OdB_OAbs(X3),hAPP(hAPP(c_Type_Otype_OFun,X2),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_839]) ).

cnf(c_0_840_0,axiom,
    ( c_Type_Otyping(c_Type_Oshift(X1,c_HOL_Ozero__class_Ozero(tc_nat),c_Type_Osko__Type__Xtyping__elims__3__1(X3,X1,X2),tc_Type_Otype),X2,c_Type_Osko__Type__Xtyping__elims__3__2(X3,X1,X2))
    | ~ c_Type_Otyping(X1,c_Lambda_OdB_OAbs(X2),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_840]) ).

cnf(c_0_840_1,axiom,
    ( ~ c_Type_Otyping(X1,c_Lambda_OdB_OAbs(X2),X3)
    | c_Type_Otyping(c_Type_Oshift(X1,c_HOL_Ozero__class_Ozero(tc_nat),c_Type_Osko__Type__Xtyping__elims__3__1(X3,X1,X2),tc_Type_Otype),X2,c_Type_Osko__Type__Xtyping__elims__3__2(X3,X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_840]) ).

cnf(c_0_841_0,axiom,
    ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Osubst(X3,X1,X4)),c_Lambda_Osubst(X3,X2,X4)))
    | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_841]) ).

cnf(c_0_841_1,axiom,
    ( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2))
    | hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Osubst(X3,X1,X4)),c_Lambda_Osubst(X3,X2,X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_841]) ).

cnf(c_0_842_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_842]) ).

cnf(c_0_842_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_842]) ).

cnf(c_0_843_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_843]) ).

cnf(c_0_843_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_843]) ).

cnf(c_0_844_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_844]) ).

cnf(c_0_844_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_844]) ).

cnf(c_0_845_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_845]) ).

cnf(c_0_845_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_845]) ).

cnf(c_0_846_0,axiom,
    ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_Osubst(X1,X3,X4)),c_Lambda_Osubst(X2,X3,X4)))
    | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_846]) ).

cnf(c_0_846_1,axiom,
    ( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2))
    | hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_Osubst(X1,X3,X4)),c_Lambda_Osubst(X2,X3,X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_846]) ).

cnf(c_0_847_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_847]) ).

cnf(c_0_847_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_847]) ).

cnf(c_0_847_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_847]) ).

cnf(c_0_848_0,axiom,
    ( c_Type_Otyping(X1,X3,c_Type_Osko__Type__Xtyping__elims__2__1(X4,X1,X2,X3))
    | ~ c_Type_Otyping(X1,hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_848]) ).

cnf(c_0_848_1,axiom,
    ( ~ c_Type_Otyping(X1,hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3),X4)
    | c_Type_Otyping(X1,X3,c_Type_Osko__Type__Xtyping__elims__2__1(X4,X1,X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_848]) ).

cnf(c_0_849_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_849]) ).

cnf(c_0_849_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_849]) ).

cnf(c_0_850_0,axiom,
    ( c_Type_Otyping(c_Type_Oshift(X1,c_HOL_Ozero__class_Ozero(tc_nat),c_Type_Osko__Type__Xabs__typeE__1__1(X1,X2),tc_Type_Otype),X2,c_Type_Osko__Type__Xabs__typeE__1__2(X1,X2))
    | ~ c_Type_Otyping(X1,c_Lambda_OdB_OAbs(X2),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_850]) ).

cnf(c_0_850_1,axiom,
    ( ~ c_Type_Otyping(X1,c_Lambda_OdB_OAbs(X2),X3)
    | c_Type_Otyping(c_Type_Oshift(X1,c_HOL_Ozero__class_Ozero(tc_nat),c_Type_Osko__Type__Xabs__typeE__1__1(X1,X2),tc_Type_Otype),X2,c_Type_Osko__Type__Xabs__typeE__1__2(X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_850]) ).

cnf(c_0_851_0,axiom,
    ( c_Type_Otyping(c_Type_Oshift(X1,X4,X5,tc_Type_Otype),c_Lambda_Olift(X2,X4),X3)
    | ~ c_Type_Otyping(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_851]) ).

cnf(c_0_851_1,axiom,
    ( ~ c_Type_Otyping(X1,X2,X3)
    | c_Type_Otyping(c_Type_Oshift(X1,X4,X5,tc_Type_Otype),c_Lambda_Olift(X2,X4),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_851]) ).

cnf(c_0_852_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_852]) ).

cnf(c_0_852_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_852]) ).

cnf(c_0_853_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_853]) ).

cnf(c_0_853_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_853]) ).

cnf(c_0_854_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_854]) ).

cnf(c_0_854_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_854]) ).

cnf(c_0_855_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_855]) ).

cnf(c_0_855_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_855]) ).

cnf(c_0_856_0,axiom,
    ( c_lessequals(X1,X4,X3)
    | ~ c_lessequals(c_Power_Opower__class_Opower(X1,c_Suc(X2),X3),c_Power_Opower__class_Opower(X4,c_Suc(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_856]) ).

cnf(c_0_856_1,axiom,
    ( ~ c_lessequals(c_Power_Opower__class_Opower(X1,c_Suc(X2),X3),c_Power_Opower__class_Opower(X4,c_Suc(X2),X3),X3)
    | c_lessequals(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_856]) ).

cnf(c_0_856_2,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
    | ~ c_lessequals(c_Power_Opower__class_Opower(X1,c_Suc(X2),X3),c_Power_Opower__class_Opower(X4,c_Suc(X2),X3),X3)
    | c_lessequals(X1,X4,X3)
    | ~ class_Ring__and__Field_Oordered__semidom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_856]) ).

cnf(c_0_856_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X3)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
    | ~ c_lessequals(c_Power_Opower__class_Opower(X1,c_Suc(X2),X3),c_Power_Opower__class_Opower(X4,c_Suc(X2),X3),X3)
    | c_lessequals(X1,X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_856]) ).

cnf(c_0_857_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_857]) ).

cnf(c_0_857_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_857]) ).

cnf(c_0_857_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_857]) ).

cnf(c_0_858_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_858]) ).

cnf(c_0_858_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_858]) ).

cnf(c_0_858_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_858]) ).

cnf(c_0_859_0,axiom,
    ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Olift(X1,X3)),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_859]) ).

cnf(c_0_859_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_Olift(X1,X3)),c_Lambda_Olift(X2,X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_859]) ).

cnf(c_0_860_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_860]) ).

cnf(c_0_860_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_860]) ).

cnf(c_0_861_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_861]) ).

cnf(c_0_861_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_861]) ).

cnf(c_0_861_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_861]) ).

cnf(c_0_861_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_861]) ).

cnf(c_0_862_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_862]) ).

cnf(c_0_862_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_862]) ).

cnf(c_0_862_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_862]) ).

cnf(c_0_863_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_863]) ).

cnf(c_0_863_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_863]) ).

cnf(c_0_863_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_863]) ).

cnf(c_0_864_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_864]) ).

cnf(c_0_864_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_864]) ).

cnf(c_0_864_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_864]) ).

cnf(c_0_864_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_864]) ).

cnf(c_0_865_0,axiom,
    ( hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__3__1(X3,X1,X2)),c_Type_Osko__Type__Xtyping__elims__3__2(X3,X1,X2)) = X3
    | ~ c_Type_Otyping(X1,c_Lambda_OdB_OAbs(X2),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_865]) ).

cnf(c_0_865_1,axiom,
    ( ~ c_Type_Otyping(X1,c_Lambda_OdB_OAbs(X2),X3)
    | hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__3__1(X3,X1,X2)),c_Type_Osko__Type__Xtyping__elims__3__2(X3,X1,X2)) = X3 ),
    inference(literals_permutation,[status(thm)],[c_0_865]) ).

cnf(c_0_866_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_866]) ).

cnf(c_0_866_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_866]) ).

cnf(c_0_867_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_867]) ).

cnf(c_0_867_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_867]) ).

cnf(c_0_867_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_867]) ).

cnf(c_0_867_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_867]) ).

cnf(c_0_868_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_868]) ).

cnf(c_0_868_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_868]) ).

cnf(c_0_868_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_868]) ).

cnf(c_0_869_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_869]) ).

cnf(c_0_869_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_869]) ).

cnf(c_0_869_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_869]) ).

cnf(c_0_870_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_870]) ).

cnf(c_0_870_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_870]) ).

cnf(c_0_871_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_871]) ).

cnf(c_0_871_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_871]) ).

cnf(c_0_872_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_872]) ).

cnf(c_0_872_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_872]) ).

cnf(c_0_873_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_873]) ).

cnf(c_0_873_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_873]) ).

cnf(c_0_874_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_874]) ).

cnf(c_0_874_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_874]) ).

cnf(c_0_875_0,axiom,
    ( c_Type_Otyping(X1,hAPP(hAPP(c_Lambda_OdB_OApp,X2),X5),X4)
    | ~ c_Type_Otyping(X1,X2,hAPP(hAPP(c_Type_Otype_OFun,X3),X4))
    | ~ c_Type_Otyping(X1,X5,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_875]) ).

cnf(c_0_875_1,axiom,
    ( ~ c_Type_Otyping(X1,X2,hAPP(hAPP(c_Type_Otype_OFun,X3),X4))
    | c_Type_Otyping(X1,hAPP(hAPP(c_Lambda_OdB_OApp,X2),X5),X4)
    | ~ c_Type_Otyping(X1,X5,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_875]) ).

cnf(c_0_875_2,axiom,
    ( ~ c_Type_Otyping(X1,X5,X3)
    | ~ c_Type_Otyping(X1,X2,hAPP(hAPP(c_Type_Otype_OFun,X3),X4))
    | c_Type_Otyping(X1,hAPP(hAPP(c_Lambda_OdB_OApp,X2),X5),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_875]) ).

cnf(c_0_876_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_876]) ).

cnf(c_0_876_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_876]) ).

cnf(c_0_876_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_876]) ).

cnf(c_0_877_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_Power_Opower__class_Opower(X2,c_Suc(X4),X1) != c_Power_Opower__class_Opower(X3,c_Suc(X4),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_877]) ).

cnf(c_0_877_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_Power_Opower__class_Opower(X2,c_Suc(X4),X1) != c_Power_Opower__class_Opower(X3,c_Suc(X4),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_877]) ).

cnf(c_0_877_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_Power_Opower__class_Opower(X2,c_Suc(X4),X1) != c_Power_Opower__class_Opower(X3,c_Suc(X4),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_877]) ).

cnf(c_0_877_3,axiom,
    ( c_Power_Opower__class_Opower(X2,c_Suc(X4),X1) != c_Power_Opower__class_Opower(X3,c_Suc(X4),X1)
    | ~ 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_877]) ).

cnf(c_0_877_4,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | c_Power_Opower__class_Opower(X2,c_Suc(X4),X1) != c_Power_Opower__class_Opower(X3,c_Suc(X4),X1)
    | ~ 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_877]) ).

cnf(c_0_878_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_878]) ).

cnf(c_0_878_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_878]) ).

cnf(c_0_878_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_878]) ).

cnf(c_0_879_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_879]) ).

cnf(c_0_879_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_879]) ).

cnf(c_0_879_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_879]) ).

cnf(c_0_879_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_879]) ).

cnf(c_0_880_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_880]) ).

cnf(c_0_880_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_880]) ).

cnf(c_0_880_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_880]) ).

cnf(c_0_880_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_880]) ).

cnf(c_0_881_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_881]) ).

cnf(c_0_881_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_881]) ).

cnf(c_0_881_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_881]) ).

cnf(c_0_881_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_881]) ).

cnf(c_0_881_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_881]) ).

cnf(c_0_882_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_882]) ).

cnf(c_0_882_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_882]) ).

cnf(c_0_882_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_882]) ).

cnf(c_0_882_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_882]) ).

cnf(c_0_882_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_882]) ).

cnf(c_0_883_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_883]) ).

cnf(c_0_883_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_883]) ).

cnf(c_0_883_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_883]) ).

cnf(c_0_884_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_884]) ).

cnf(c_0_884_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_884]) ).

cnf(c_0_884_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_884]) ).

cnf(c_0_885_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_885]) ).

cnf(c_0_885_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_885]) ).

cnf(c_0_885_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_885]) ).

cnf(c_0_886_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_886]) ).

cnf(c_0_886_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_886]) ).

cnf(c_0_886_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_886]) ).

cnf(c_0_887_0,axiom,
    ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_Olift(X1,X3)),c_Lambda_Olift(X2,X3)))
    | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_887]) ).

cnf(c_0_887_1,axiom,
    ( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2))
    | hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_Olift(X1,X3)),c_Lambda_Olift(X2,X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_887]) ).

cnf(c_0_888_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_888]) ).

cnf(c_0_888_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_888]) ).

cnf(c_0_888_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_888]) ).

cnf(c_0_889_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_889]) ).

cnf(c_0_889_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_889]) ).

cnf(c_0_889_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_889]) ).

cnf(c_0_890_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_890]) ).

cnf(c_0_890_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_890]) ).

cnf(c_0_891_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_891]) ).

cnf(c_0_891_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_891]) ).

cnf(c_0_892_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_892]) ).

cnf(c_0_892_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_892]) ).

cnf(c_0_893_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_893]) ).

cnf(c_0_893_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_893]) ).

cnf(c_0_894_0,axiom,
    ( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(X1,c_Lambda_OdB_OVar(X2),X3)))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_894]) ).

cnf(c_0_894_1,axiom,
    ( ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
    | hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(X1,c_Lambda_OdB_OVar(X2),X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_894]) ).

cnf(c_0_895_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_895]) ).

cnf(c_0_895_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_895]) ).

cnf(c_0_895_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_895]) ).

cnf(c_0_895_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_895]) ).

cnf(c_0_895_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_895]) ).

cnf(c_0_896_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_896]) ).

cnf(c_0_896_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_896]) ).

cnf(c_0_896_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_896]) ).

cnf(c_0_896_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_896]) ).

cnf(c_0_896_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_896]) ).

cnf(c_0_897_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_897]) ).

cnf(c_0_897_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_897]) ).

cnf(c_0_897_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_897]) ).

cnf(c_0_897_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_897]) ).

cnf(c_0_898_0,axiom,
    ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),c_Lambda_Osko__Lambda__Xbeta__cases__2__1(X1,X2)))
    | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OAbs(X1)),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_898]) ).

cnf(c_0_898_1,axiom,
    ( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OAbs(X1)),X2))
    | hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),c_Lambda_Osko__Lambda__Xbeta__cases__2__1(X1,X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_898]) ).

cnf(c_0_899_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_899]) ).

cnf(c_0_899_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_899]) ).

cnf(c_0_899_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_899]) ).

cnf(c_0_900_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_900]) ).

cnf(c_0_900_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_900]) ).

cnf(c_0_900_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_900]) ).

cnf(c_0_901_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_901]) ).

cnf(c_0_901_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_901]) ).

cnf(c_0_901_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_901]) ).

cnf(c_0_902_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_902]) ).

cnf(c_0_902_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_902]) ).

cnf(c_0_902_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_902]) ).

cnf(c_0_903_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_903]) ).

cnf(c_0_903_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_903]) ).

cnf(c_0_903_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_903]) ).

cnf(c_0_904_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_904]) ).

cnf(c_0_904_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_904]) ).

cnf(c_0_904_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_904]) ).

cnf(c_0_905_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_905]) ).

cnf(c_0_905_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_905]) ).

cnf(c_0_906_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_906]) ).

cnf(c_0_906_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_906]) ).

cnf(c_0_906_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_906]) ).

cnf(c_0_907_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_907]) ).

cnf(c_0_907_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_907]) ).

cnf(c_0_908_0,axiom,
    ( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,X1),c_Lambda_OdB_OVar(X2))))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_908]) ).

cnf(c_0_908_1,axiom,
    ( ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
    | hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,X1),c_Lambda_OdB_OVar(X2)))) ),
    inference(literals_permutation,[status(thm)],[c_0_908]) ).

cnf(c_0_909_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_909]) ).

cnf(c_0_909_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_909]) ).

cnf(c_0_909_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_909]) ).

cnf(c_0_909_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_909]) ).

cnf(c_0_910_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_910]) ).

cnf(c_0_910_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_910]) ).

cnf(c_0_910_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_910]) ).

cnf(c_0_910_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_910]) ).

cnf(c_0_911_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_911]) ).

cnf(c_0_911_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_911]) ).

cnf(c_0_912_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_912]) ).

cnf(c_0_912_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_912]) ).

cnf(c_0_913_0,axiom,
    ( c_Lambda_OdB_OAbs(c_Lambda_Osko__Lambda__Xbeta__cases__2__1(X1,X2)) = X2
    | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OAbs(X1)),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_913]) ).

cnf(c_0_913_1,axiom,
    ( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OAbs(X1)),X2))
    | c_Lambda_OdB_OAbs(c_Lambda_Osko__Lambda__Xbeta__cases__2__1(X1,X2)) = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_913]) ).

cnf(c_0_914_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_914]) ).

cnf(c_0_914_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_914]) ).

cnf(c_0_914_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_914]) ).

cnf(c_0_914_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_914]) ).

cnf(c_0_915_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_915]) ).

cnf(c_0_915_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_915]) ).

cnf(c_0_915_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_915]) ).

cnf(c_0_915_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_915]) ).

cnf(c_0_916_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_916]) ).

cnf(c_0_916_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_916]) ).

cnf(c_0_916_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_916]) ).

cnf(c_0_916_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_916]) ).

cnf(c_0_917_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_917]) ).

cnf(c_0_917_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_917]) ).

cnf(c_0_917_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_917]) ).

cnf(c_0_917_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_917]) ).

cnf(c_0_918_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_918]) ).

cnf(c_0_918_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_918]) ).

cnf(c_0_918_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_918]) ).

cnf(c_0_919_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_919]) ).

cnf(c_0_919_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_919]) ).

cnf(c_0_919_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_919]) ).

cnf(c_0_920_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_920]) ).

cnf(c_0_920_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_920]) ).

cnf(c_0_920_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_920]) ).

cnf(c_0_921_0,axiom,
    ( X2 = X3
    | ~ hBOOL(hAPP(hAPP(c_fequal(X1),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_921]) ).

cnf(c_0_921_1,axiom,
    ( ~ hBOOL(hAPP(hAPP(c_fequal(X1),X2),X3))
    | X2 = X3 ),
    inference(literals_permutation,[status(thm)],[c_0_921]) ).

cnf(c_0_922_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_922]) ).

cnf(c_0_922_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_922]) ).

cnf(c_0_923_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_923]) ).

cnf(c_0_923_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_923]) ).

cnf(c_0_924_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_924]) ).

cnf(c_0_924_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_924]) ).

cnf(c_0_925_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_925]) ).

cnf(c_0_925_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_925]) ).

cnf(c_0_925_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_925]) ).

cnf(c_0_925_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_925]) ).

cnf(c_0_925_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_925]) ).

cnf(c_0_925_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_925]) ).

cnf(c_0_926_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_926]) ).

cnf(c_0_926_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_926]) ).

cnf(c_0_926_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_926]) ).

cnf(c_0_926_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_926]) ).

cnf(c_0_926_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_926]) ).

cnf(c_0_927_0,axiom,
    ( hBOOL(hAPP(X1,X2))
    | hBOOL(hAPP(X1,X3))
    | c_Type_Osko__Type__Xtype__induct__1__1(X1) != hAPP(hAPP(c_Type_Otype_OFun,X4),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_927]) ).

cnf(c_0_927_1,axiom,
    ( hBOOL(hAPP(X1,X3))
    | hBOOL(hAPP(X1,X2))
    | c_Type_Osko__Type__Xtype__induct__1__1(X1) != hAPP(hAPP(c_Type_Otype_OFun,X4),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_927]) ).

cnf(c_0_927_2,axiom,
    ( c_Type_Osko__Type__Xtype__induct__1__1(X1) != hAPP(hAPP(c_Type_Otype_OFun,X4),X2)
    | hBOOL(hAPP(X1,X3))
    | hBOOL(hAPP(X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_927]) ).

cnf(c_0_928_0,axiom,
    ( hBOOL(hAPP(X1,X2))
    | hBOOL(hAPP(X1,X3))
    | c_Type_Osko__Type__Xtype__induct__1__1(X1) != hAPP(hAPP(c_Type_Otype_OFun,X2),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_928]) ).

cnf(c_0_928_1,axiom,
    ( hBOOL(hAPP(X1,X3))
    | hBOOL(hAPP(X1,X2))
    | c_Type_Osko__Type__Xtype__induct__1__1(X1) != hAPP(hAPP(c_Type_Otype_OFun,X2),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_928]) ).

cnf(c_0_928_2,axiom,
    ( c_Type_Osko__Type__Xtype__induct__1__1(X1) != hAPP(hAPP(c_Type_Otype_OFun,X2),X4)
    | hBOOL(hAPP(X1,X3))
    | hBOOL(hAPP(X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_928]) ).

cnf(c_0_929_0,axiom,
    ( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Olift(X1,X2)))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_929]) ).

cnf(c_0_929_1,axiom,
    ( ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
    | hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Olift(X1,X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_929]) ).

cnf(c_0_930_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_930]) ).

cnf(c_0_930_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_930]) ).

cnf(c_0_931_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_931]) ).

cnf(c_0_931_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_931]) ).

cnf(c_0_932_0,axiom,
    ( X1 = X2
    | hAPP(hAPP(c_Type_Otype_OFun,X1),X3) != hAPP(hAPP(c_Type_Otype_OFun,X2),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_932]) ).

cnf(c_0_932_1,axiom,
    ( hAPP(hAPP(c_Type_Otype_OFun,X1),X3) != hAPP(hAPP(c_Type_Otype_OFun,X2),X4)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_932]) ).

cnf(c_0_933_0,axiom,
    ( X1 = X2
    | hAPP(hAPP(c_Type_Otype_OFun,X3),X1) != hAPP(hAPP(c_Type_Otype_OFun,X4),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_933]) ).

cnf(c_0_933_1,axiom,
    ( hAPP(hAPP(c_Type_Otype_OFun,X3),X1) != hAPP(hAPP(c_Type_Otype_OFun,X4),X2)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_933]) ).

cnf(c_0_934_0,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_HOL_Oone__class_Oone(X2)),c_Nat_Osemiring__1__class_Oof__nat(X1,X2)) = c_Nat_Osemiring__1__class_Oof__nat(c_Suc(X1),X2)
    | ~ class_Ring__and__Field_Osemiring__1(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_934]) ).

cnf(c_0_934_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring__1(X2)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_HOL_Oone__class_Oone(X2)),c_Nat_Osemiring__1__class_Oof__nat(X1,X2)) = c_Nat_Osemiring__1__class_Oof__nat(c_Suc(X1),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_934]) ).

cnf(c_0_935_0,axiom,
    ( c_lessequals(X1,X2,X3)
    | c_lessequals(X2,X1,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_935]) ).

cnf(c_0_935_1,axiom,
    ( c_lessequals(X2,X1,X3)
    | c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_935]) ).

cnf(c_0_935_2,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | c_lessequals(X2,X1,X3)
    | c_lessequals(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_935]) ).

cnf(c_0_936_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_936]) ).

cnf(c_0_936_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_936]) ).

cnf(c_0_937_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_937]) ).

cnf(c_0_937_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_937]) ).

cnf(c_0_938_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_938]) ).

cnf(c_0_938_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_938]) ).

cnf(c_0_939_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_939]) ).

cnf(c_0_939_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_939]) ).

cnf(c_0_940_0,axiom,
    ( hAPP(X1,X2) = X3
    | ~ c_Type_Otyping(X1,c_Lambda_OdB_OVar(X2),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_940]) ).

cnf(c_0_940_1,axiom,
    ( ~ c_Type_Otyping(X1,c_Lambda_OdB_OVar(X2),X3)
    | hAPP(X1,X2) = X3 ),
    inference(literals_permutation,[status(thm)],[c_0_940]) ).

cnf(c_0_941_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_941]) ).

cnf(c_0_941_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_941]) ).

cnf(c_0_941_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_941]) ).

cnf(c_0_942_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_942]) ).

cnf(c_0_942_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_942]) ).

cnf(c_0_942_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_942]) ).

cnf(c_0_942_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_942]) ).

cnf(c_0_943_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_943]) ).

cnf(c_0_943_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_943]) ).

cnf(c_0_943_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_943]) ).

cnf(c_0_944_0,axiom,
    ( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    inference(literals_permutation,[status(thm)],[c_0_944]) ).

cnf(c_0_944_1,axiom,
    ( X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    inference(literals_permutation,[status(thm)],[c_0_944]) ).

cnf(c_0_944_2,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    inference(literals_permutation,[status(thm)],[c_0_944]) ).

cnf(c_0_945_0,axiom,
    ( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    inference(literals_permutation,[status(thm)],[c_0_945]) ).

cnf(c_0_945_1,axiom,
    ( X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    inference(literals_permutation,[status(thm)],[c_0_945]) ).

cnf(c_0_945_2,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    inference(literals_permutation,[status(thm)],[c_0_945]) ).

cnf(c_0_946_0,axiom,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,c_Type_Osko__Type__Xtype__induct__1__1(X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_946]) ).

cnf(c_0_946_1,axiom,
    ( ~ hBOOL(hAPP(X1,c_Type_Osko__Type__Xtype__induct__1__1(X1)))
    | hBOOL(hAPP(X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_946]) ).

cnf(c_0_947_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_947]) ).

cnf(c_0_947_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_947]) ).

cnf(c_0_947_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_947]) ).

cnf(c_0_947_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_947]) ).

cnf(c_0_947_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_947]) ).

cnf(c_0_947_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_947]) ).

cnf(c_0_948_0,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    inference(literals_permutation,[status(thm)],[c_0_948]) ).

cnf(c_0_948_1,axiom,
    ( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    inference(literals_permutation,[status(thm)],[c_0_948]) ).

cnf(c_0_948_2,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_948]) ).

cnf(c_0_949_0,axiom,
    ( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    inference(literals_permutation,[status(thm)],[c_0_949]) ).

cnf(c_0_949_1,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    inference(literals_permutation,[status(thm)],[c_0_949]) ).

cnf(c_0_949_2,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    inference(literals_permutation,[status(thm)],[c_0_949]) ).

cnf(c_0_950_0,axiom,
    ( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    inference(literals_permutation,[status(thm)],[c_0_950]) ).

cnf(c_0_950_1,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    inference(literals_permutation,[status(thm)],[c_0_950]) ).

cnf(c_0_950_2,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    inference(literals_permutation,[status(thm)],[c_0_950]) ).

cnf(c_0_951_0,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    inference(literals_permutation,[status(thm)],[c_0_951]) ).

cnf(c_0_951_1,axiom,
    ( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    inference(literals_permutation,[status(thm)],[c_0_951]) ).

cnf(c_0_951_2,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_951]) ).

cnf(c_0_952_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_952]) ).

cnf(c_0_952_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_952]) ).

cnf(c_0_953_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_953]) ).

cnf(c_0_953_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_953]) ).

cnf(c_0_954_0,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X2 = c_HOL_Ozero__class_Ozero(tc_nat)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    inference(literals_permutation,[status(thm)],[c_0_954]) ).

cnf(c_0_954_1,axiom,
    ( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    inference(literals_permutation,[status(thm)],[c_0_954]) ).

cnf(c_0_954_2,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | X2 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_954]) ).

cnf(c_0_955_0,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X2 = c_HOL_Ozero__class_Ozero(tc_nat)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    inference(literals_permutation,[status(thm)],[c_0_955]) ).

cnf(c_0_955_1,axiom,
    ( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    inference(literals_permutation,[status(thm)],[c_0_955]) ).

cnf(c_0_955_2,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | X2 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_955]) ).

cnf(c_0_956_0,axiom,
    ( c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),c_Suc(X2),X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Power_Opower(X1)
    | ~ class_Ring__and__Field_Osemiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_956]) ).

cnf(c_0_956_1,axiom,
    ( ~ class_Power_Opower(X1)
    | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X1),c_Suc(X2),X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Osemiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_956]) ).

cnf(c_0_956_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_Suc(X2),X1) = c_HOL_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_956]) ).

cnf(c_0_957_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_957]) ).

cnf(c_0_957_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_957]) ).

cnf(c_0_957_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_957]) ).

cnf(c_0_957_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_957]) ).

cnf(c_0_958_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_958]) ).

cnf(c_0_958_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_958]) ).

cnf(c_0_959_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_959]) ).

cnf(c_0_959_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_959]) ).

cnf(c_0_959_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_959]) ).

cnf(c_0_960_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_960]) ).

cnf(c_0_960_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_960]) ).

cnf(c_0_961_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_961]) ).

cnf(c_0_961_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_961]) ).

cnf(c_0_962_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_962]) ).

cnf(c_0_962_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_962]) ).

cnf(c_0_963_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_963]) ).

cnf(c_0_963_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_963]) ).

cnf(c_0_964_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_964]) ).

cnf(c_0_964_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_964]) ).

cnf(c_0_965_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_965]) ).

cnf(c_0_965_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_965]) ).

cnf(c_0_966_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_966]) ).

cnf(c_0_966_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_966]) ).

cnf(c_0_966_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_966]) ).

cnf(c_0_967_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_967]) ).

cnf(c_0_967_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_967]) ).

cnf(c_0_968_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_968]) ).

cnf(c_0_968_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_968]) ).

cnf(c_0_969_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_969]) ).

cnf(c_0_969_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_969]) ).

cnf(c_0_970_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_970]) ).

cnf(c_0_970_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_970]) ).

cnf(c_0_971_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_971]) ).

cnf(c_0_971_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_971]) ).

cnf(c_0_972_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_972]) ).

cnf(c_0_972_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_972]) ).

cnf(c_0_973_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_973]) ).

cnf(c_0_973_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_973]) ).

cnf(c_0_974_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_974]) ).

cnf(c_0_974_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_974]) ).

cnf(c_0_975_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_975]) ).

cnf(c_0_975_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_975]) ).

cnf(c_0_976_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_976]) ).

cnf(c_0_976_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_976]) ).

cnf(c_0_977_0,axiom,
    ( c_lessequals(X1,X1,X2)
    | ~ class_Orderings_Oorder(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_977]) ).

cnf(c_0_977_1,axiom,
    ( ~ class_Orderings_Oorder(X2)
    | c_lessequals(X1,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_977]) ).

cnf(c_0_978_0,axiom,
    ( c_lessequals(X1,X1,X2)
    | ~ class_Orderings_Opreorder(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_978]) ).

cnf(c_0_978_1,axiom,
    ( ~ class_Orderings_Opreorder(X2)
    | c_lessequals(X1,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_978]) ).

cnf(c_0_979_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_979]) ).

cnf(c_0_979_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_979]) ).

cnf(c_0_979_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_979]) ).

cnf(c_0_980_0,axiom,
    ( class_Orderings_Opreorder(tc_fun(X2,X1))
    | ~ class_Orderings_Opreorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_980]) ).

cnf(c_0_980_1,axiom,
    ( ~ class_Orderings_Opreorder(X1)
    | class_Orderings_Opreorder(tc_fun(X2,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_980]) ).

cnf(c_0_981_0,axiom,
    ( class_Orderings_Oorder(tc_fun(X2,X1))
    | ~ class_Orderings_Oorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_981]) ).

cnf(c_0_981_1,axiom,
    ( ~ class_Orderings_Oorder(X1)
    | class_Orderings_Oorder(tc_fun(X2,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_981]) ).

cnf(c_0_982_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_982]) ).

cnf(c_0_982_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_982]) ).

cnf(c_0_983_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_983]) ).

cnf(c_0_983_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_983]) ).

cnf(c_0_984_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_984]) ).

cnf(c_0_984_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_984]) ).

cnf(c_0_985_0,axiom,
    ( X1 = X2
    | c_Suc(X1) != c_Suc(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_985]) ).

cnf(c_0_985_1,axiom,
    ( c_Suc(X1) != c_Suc(X2)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_985]) ).

cnf(c_0_986_0,axiom,
    ( X1 = X2
    | c_Suc(X1) != c_Suc(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_986]) ).

cnf(c_0_986_1,axiom,
    ( c_Suc(X1) != c_Suc(X2)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_986]) ).

cnf(c_0_987_0,axiom,
    ( X1 = X2
    | c_Type_Otype_OAtom(X1) != c_Type_Otype_OAtom(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_987]) ).

cnf(c_0_987_1,axiom,
    ( c_Type_Otype_OAtom(X1) != c_Type_Otype_OAtom(X2)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_987]) ).

cnf(c_0_988_0,axiom,
    ( X1 = X2
    | c_Lambda_OdB_OAbs(X1) != c_Lambda_OdB_OAbs(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_988]) ).

cnf(c_0_988_1,axiom,
    ( c_Lambda_OdB_OAbs(X1) != c_Lambda_OdB_OAbs(X2)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_988]) ).

cnf(c_0_989_0,axiom,
    ( X1 = X2
    | c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OVar(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_989]) ).

cnf(c_0_989_1,axiom,
    ( c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OVar(X2)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_989]) ).

% CNF of non-axioms
% Start CNF derivation
fof(c_0_0_486,negated_conjecture,
    ~ c_Type_Otyping(v_ea____,v_s____,hAPP(hAPP(c_Type_Otype_OFun,v_Ta____),v_U____)),
    file('<stdin>',cls_conjecture_0) ).

fof(c_0_1_487,negated_conjecture,
    ~ c_Type_Otyping(v_ea____,v_s____,hAPP(hAPP(c_Type_Otype_OFun,v_Ta____),v_U____)),
    inference(fof_simplification,[status(thm)],[c_0_0]) ).

fof(c_0_2_488,negated_conjecture,
    ~ c_Type_Otyping(v_ea____,v_s____,hAPP(hAPP(c_Type_Otype_OFun,v_Ta____),v_U____)),
    c_0_1 ).

cnf(c_0_3_489,negated_conjecture,
    ~ c_Type_Otyping(v_ea____,v_s____,hAPP(hAPP(c_Type_Otype_OFun,v_Ta____),v_U____)),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

cnf(c_0_4_490,negated_conjecture,
    ~ c_Type_Otyping(v_ea____,v_s____,hAPP(hAPP(c_Type_Otype_OFun,v_Ta____),v_U____)),
    c_0_3,
    [final] ).

% End CNF derivation

%-------------------------------------------------------------
% Proof by iprover

cnf(c_516,plain,
    c_Type_Otyping(v_ea____,v_s____,hAPP(hAPP(c_Type_Otype_OFun,v_Ta____),v_U____)),
    file('/export/starexec/sandbox/tmp/iprover_modulo_b60e92.p',c_0_476_0) ).

cnf(c_605,negated_conjecture,
    ~ c_Type_Otyping(v_ea____,v_s____,hAPP(hAPP(c_Type_Otype_OFun,v_Ta____),v_U____)),
    file('/export/starexec/sandbox/tmp/iprover_modulo_b60e92.p',c_0_4) ).

cnf(contradiction,plain,
    $false,
    inference(minisat,[status(thm)],[c_516,c_605]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem  : LCL854-1 : TPTP v8.1.0. Released v4.1.0.
% 0.10/0.12  % Command  : iprover_modulo %s %d
% 0.13/0.33  % Computer : n025.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 600
% 0.13/0.33  % DateTime : Sat Jul  2 18:25:40 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.34  % Running in mono-core mode
% 0.19/0.44  % Orienting using strategy Equiv(ClausalAll)
% 0.19/0.44  % Orientation found
% 0.19/0.44  % 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/sandbox/tmp/iprover_proof_d7a7b7.s --tptp_safe_out true --time_out_real 150 /export/starexec/sandbox/tmp/iprover_modulo_b60e92.p | tee /export/starexec/sandbox/tmp/iprover_modulo_out_59c967 | grep -v "SZS"
% 0.19/0.45  
% 0.19/0.45  %---------------- iProver v2.5 (CASC-J8 2016) ----------------%
% 0.19/0.45  
% 0.19/0.45  % 
% 0.19/0.45  % ------  iProver source info 
% 0.19/0.45  
% 0.19/0.45  % git: sha1: 57accf6c58032223c7708532cf852a99fa48c1b3
% 0.19/0.45  % git: non_committed_changes: true
% 0.19/0.45  % git: last_make_outside_of_git: true
% 0.19/0.45  
% 0.19/0.45  % 
% 0.19/0.45  % ------ Input Options
% 0.19/0.45  
% 0.19/0.45  % --out_options                         all
% 0.19/0.45  % --tptp_safe_out                       true
% 0.19/0.45  % --problem_path                        ""
% 0.19/0.45  % --include_path                        ""
% 0.19/0.45  % --clausifier                          .//eprover
% 0.19/0.45  % --clausifier_options                  --tstp-format  
% 0.19/0.45  % --stdin                               false
% 0.19/0.45  % --dbg_backtrace                       false
% 0.19/0.45  % --dbg_dump_prop_clauses               false
% 0.19/0.45  % --dbg_dump_prop_clauses_file          -
% 0.19/0.45  % --dbg_out_stat                        false
% 0.19/0.45  
% 0.19/0.45  % ------ General Options
% 0.19/0.45  
% 0.19/0.45  % --fof                                 false
% 0.19/0.45  % --time_out_real                       150.
% 0.19/0.45  % --time_out_prep_mult                  0.2
% 0.19/0.45  % --time_out_virtual                    -1.
% 0.19/0.45  % --schedule                            none
% 0.19/0.45  % --ground_splitting                    input
% 0.19/0.45  % --splitting_nvd                       16
% 0.19/0.45  % --non_eq_to_eq                        false
% 0.19/0.45  % --prep_gs_sim                         true
% 0.19/0.45  % --prep_unflatten                      false
% 0.19/0.45  % --prep_res_sim                        true
% 0.19/0.45  % --prep_upred                          true
% 0.19/0.45  % --res_sim_input                       true
% 0.19/0.45  % --clause_weak_htbl                    true
% 0.19/0.45  % --gc_record_bc_elim                   false
% 0.19/0.45  % --symbol_type_check                   false
% 0.19/0.45  % --clausify_out                        false
% 0.19/0.45  % --large_theory_mode                   false
% 0.19/0.45  % --prep_sem_filter                     none
% 0.19/0.45  % --prep_sem_filter_out                 false
% 0.19/0.45  % --preprocessed_out                    false
% 0.19/0.45  % --sub_typing                          false
% 0.19/0.45  % --brand_transform                     false
% 0.19/0.45  % --pure_diseq_elim                     true
% 0.19/0.45  % --min_unsat_core                      false
% 0.19/0.45  % --pred_elim                           true
% 0.19/0.45  % --add_important_lit                   false
% 0.19/0.45  % --soft_assumptions                    false
% 0.19/0.45  % --reset_solvers                       false
% 0.19/0.45  % --bc_imp_inh                          []
% 0.19/0.45  % --conj_cone_tolerance                 1.5
% 0.19/0.45  % --prolific_symb_bound                 500
% 0.19/0.45  % --lt_threshold                        2000
% 0.19/0.45  
% 0.19/0.45  % ------ SAT Options
% 0.19/0.45  
% 0.19/0.45  % --sat_mode                            false
% 0.19/0.45  % --sat_fm_restart_options              ""
% 0.19/0.45  % --sat_gr_def                          false
% 0.19/0.45  % --sat_epr_types                       true
% 0.19/0.45  % --sat_non_cyclic_types                false
% 0.19/0.45  % --sat_finite_models                   false
% 0.19/0.45  % --sat_fm_lemmas                       false
% 0.19/0.45  % --sat_fm_prep                         false
% 0.19/0.45  % --sat_fm_uc_incr                      true
% 0.19/0.45  % --sat_out_model                       small
% 0.19/0.45  % --sat_out_clauses                     false
% 0.19/0.45  
% 0.19/0.45  % ------ QBF Options
% 0.19/0.45  
% 0.19/0.45  % --qbf_mode                            false
% 0.19/0.45  % --qbf_elim_univ                       true
% 0.19/0.45  % --qbf_sk_in                           true
% 0.19/0.45  % --qbf_pred_elim                       true
% 0.19/0.45  % --qbf_split                           32
% 0.19/0.45  
% 0.19/0.45  % ------ BMC1 Options
% 0.19/0.45  
% 0.19/0.45  % --bmc1_incremental                    false
% 0.19/0.45  % --bmc1_axioms                         reachable_all
% 0.19/0.45  % --bmc1_min_bound                      0
% 0.19/0.45  % --bmc1_max_bound                      -1
% 0.19/0.45  % --bmc1_max_bound_default              -1
% 0.19/0.45  % --bmc1_symbol_reachability            true
% 0.19/0.45  % --bmc1_property_lemmas                false
% 0.19/0.45  % --bmc1_k_induction                    false
% 0.19/0.45  % --bmc1_non_equiv_states               false
% 0.19/0.45  % --bmc1_deadlock                       false
% 0.19/0.45  % --bmc1_ucm                            false
% 0.19/0.45  % --bmc1_add_unsat_core                 none
% 0.19/0.45  % --bmc1_unsat_core_children            false
% 0.19/0.45  % --bmc1_unsat_core_extrapolate_axioms  false
% 0.19/0.45  % --bmc1_out_stat                       full
% 0.19/0.45  % --bmc1_ground_init                    false
% 0.19/0.45  % --bmc1_pre_inst_next_state            false
% 0.19/0.45  % --bmc1_pre_inst_state                 false
% 0.19/0.45  % --bmc1_pre_inst_reach_state           false
% 0.19/0.45  % --bmc1_out_unsat_core                 false
% 0.19/0.45  % --bmc1_aig_witness_out                false
% 0.19/0.45  % --bmc1_verbose                        false
% 0.19/0.45  % --bmc1_dump_clauses_tptp              false
% 0.19/0.48  % --bmc1_dump_unsat_core_tptp           false
% 0.19/0.48  % --bmc1_dump_file                      -
% 0.19/0.48  % --bmc1_ucm_expand_uc_limit            128
% 0.19/0.48  % --bmc1_ucm_n_expand_iterations        6
% 0.19/0.48  % --bmc1_ucm_extend_mode                1
% 0.19/0.48  % --bmc1_ucm_init_mode                  2
% 0.19/0.48  % --bmc1_ucm_cone_mode                  none
% 0.19/0.48  % --bmc1_ucm_reduced_relation_type      0
% 0.19/0.48  % --bmc1_ucm_relax_model                4
% 0.19/0.48  % --bmc1_ucm_full_tr_after_sat          true
% 0.19/0.48  % --bmc1_ucm_expand_neg_assumptions     false
% 0.19/0.48  % --bmc1_ucm_layered_model              none
% 0.19/0.48  % --bmc1_ucm_max_lemma_size             10
% 0.19/0.48  
% 0.19/0.48  % ------ AIG Options
% 0.19/0.48  
% 0.19/0.48  % --aig_mode                            false
% 0.19/0.48  
% 0.19/0.48  % ------ Instantiation Options
% 0.19/0.48  
% 0.19/0.48  % --instantiation_flag                  true
% 0.19/0.48  % --inst_lit_sel                        [+prop;+sign;+ground;-num_var;-num_symb]
% 0.19/0.48  % --inst_solver_per_active              750
% 0.19/0.48  % --inst_solver_calls_frac              0.5
% 0.19/0.48  % --inst_passive_queue_type             priority_queues
% 0.19/0.48  % --inst_passive_queues                 [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 0.19/0.48  % --inst_passive_queues_freq            [25;2]
% 0.19/0.48  % --inst_dismatching                    true
% 0.19/0.48  % --inst_eager_unprocessed_to_passive   true
% 0.19/0.48  % --inst_prop_sim_given                 true
% 0.19/0.48  % --inst_prop_sim_new                   false
% 0.19/0.48  % --inst_orphan_elimination             true
% 0.19/0.48  % --inst_learning_loop_flag             true
% 0.19/0.48  % --inst_learning_start                 3000
% 0.19/0.48  % --inst_learning_factor                2
% 0.19/0.48  % --inst_start_prop_sim_after_learn     3
% 0.19/0.48  % --inst_sel_renew                      solver
% 0.19/0.48  % --inst_lit_activity_flag              true
% 0.19/0.48  % --inst_out_proof                      true
% 0.19/0.48  
% 0.19/0.48  % ------ Resolution Options
% 0.19/0.48  
% 0.19/0.48  % --resolution_flag                     true
% 0.19/0.48  % --res_lit_sel                         kbo_max
% 0.19/0.48  % --res_to_prop_solver                  none
% 0.19/0.48  % --res_prop_simpl_new                  false
% 0.19/0.48  % --res_prop_simpl_given                false
% 0.19/0.48  % --res_passive_queue_type              priority_queues
% 0.19/0.48  % --res_passive_queues                  [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 0.19/0.48  % --res_passive_queues_freq             [15;5]
% 0.19/0.48  % --res_forward_subs                    full
% 0.19/0.48  % --res_backward_subs                   full
% 0.19/0.48  % --res_forward_subs_resolution         true
% 0.19/0.48  % --res_backward_subs_resolution        true
% 0.19/0.48  % --res_orphan_elimination              false
% 0.19/0.48  % --res_time_limit                      1000.
% 0.19/0.48  % --res_out_proof                       true
% 0.19/0.48  % --proof_out_file                      /export/starexec/sandbox/tmp/iprover_proof_d7a7b7.s
% 0.19/0.48  % --modulo                              true
% 0.19/0.48  
% 0.19/0.48  % ------ Combination Options
% 0.19/0.48  
% 0.19/0.48  % --comb_res_mult                       1000
% 0.19/0.48  % --comb_inst_mult                      300
% 0.19/0.48  % ------ 
% 0.19/0.48  
% 0.19/0.48  % ------ Parsing...% successful
% 0.19/0.48  
% 0.19/0.48  % 
% 0.19/0.48  
% 0.19/0.48  
% 0.19/0.48  % ------                             Statistics
% 0.19/0.48  
% 0.19/0.48  % ------ General
% 0.19/0.48  
% 0.19/0.48  % num_of_input_clauses:                 606
% 0.19/0.48  % num_of_input_neg_conjectures:         1
% 0.19/0.48  % num_of_splits:                        0
% 0.19/0.48  % num_of_split_atoms:                   0
% 0.19/0.48  % num_of_sem_filtered_clauses:          0
% 0.19/0.48  % num_of_subtypes:                      0
% 0.19/0.48  % monotx_restored_types:                0
% 0.19/0.48  % sat_num_of_epr_types:                 0
% 0.19/0.48  % sat_num_of_non_cyclic_types:          0
% 0.19/0.48  % sat_guarded_non_collapsed_types:      0
% 0.19/0.48  % is_epr:                               0
% 0.19/0.48  % is_horn:                              0
% 0.19/0.48  % has_eq:                               0
% 0.19/0.48  % num_pure_diseq_elim:                  0
% 0.19/0.48  % simp_replaced_by:                     0
% 0.19/0.48  % res_preprocessed:                     0
% 0.19/0.48  % prep_upred:                           0
% 0.19/0.48  % prep_unflattend:                      0
% 0.19/0.48  % pred_elim_cands:                      0
% 0.19/0.48  % pred_elim:                            0
% 0.19/0.48  % pred_elim_cl:                         0
% 0.19/0.48  % pred_elim_cycles:                     0
% 0.19/0.48  % forced_gc_time:                       0
% 0.19/0.48  % gc_basic_clause_elim:                 0
% 0.19/0.48  % parsing_time:                         0.022
% 0.19/0.48  % sem_filter_time:                      0.
% 0.19/0.48  % pred_elim_time:                       0.
% 0.19/0.48  % out_proof_time:                       0.
% 0.19/0.48  % monotx_time:                          0.
% 0.19/0.48  % subtype_inf_time:                     0.
% 0.19/0.48  % unif_index_cands_time:                0.
% 0.19/0.48  % unif_index_add_time:                  0.
% 0.19/0.48  % total_time:                           0.036
% 0.19/0.48  % num_of_symbols:                       111
% 0.19/0.48  % num_of_terms:                         2230
% 0.19/0.48  
% 0.19/0.48  % ------ Propositional Solver
% 0.19/0.48  
% 0.19/0.48  % prop_solver_calls:                    0
% 0.19/0.48  % prop_fast_solver_calls:               0
% 0.19/0.48  % prop_num_of_clauses:                  147
% 0.19/0.48  % prop_preprocess_simplified:           7
% 0.19/0.48  % prop_fo_subsumed:                     0
% 0.19/0.48  % prop_solver_time:                     0.
% 0.19/0.48  % prop_fast_solver_time:                0.
% 0.19/0.48  % prop_unsat_core_time:                 0.
% 0.19/0.48  
% 0.19/0.48  % ------ QBF 
% 0.19/0.48  
% 0.19/0.48  % qbf_q_res:                            0
% 0.19/0.48  % qbf_num_tautologies:                  0
% 0.19/0.48  % qbf_prep_cycles:                      0
% 0.19/0.48  
% 0.19/0.48  % ------ BMC1
% 0.19/0.48  
% 0.19/0.48  % bmc1_current_bound:                   -1
% 0.19/0.48  % bmc1_last_solved_bound:               -1
% 0.19/0.48  % bmc1_unsat_core_size:                 -1
% 0.19/0.48  % bmc1_unsat_core_parents_size:         -1
% 0.19/0.48  % bmc1_merge_next_fun:                  0
% 0.19/0.48  % bmc1_unsat_core_clauses_time:         0.
% 0.19/0.48  
% 0.19/0.48  % ------ Instantiation
% 0.19/0.48  
% 0.19/0.48  % inst_num_of_clauses:                  undef
% 0.19/0.48  % inst_num_in_passive:                  undef
% 0.19/0.48  % inst_num_in_active:                   0
% 0.19/0.48  % inst_num_in_unprocessed:              0
% 0.19/0.48  % inst_num_of_loops:                    0
% 0.19/0.48  % inst_num_of_learning_restarts:        0
% 0.19/0.48  % inst_num_moves_active_passive:        0
% 0.19/0.48  % inst_lit_activity:                    0
% 0.19/0.48  % inst_lit_activity_moves:              0
% 0.19/0.48  % inst_num_tautologies:                 0
% 0.19/0.48  % inst_num_prop_implied:                0
% 0.19/0.48  % inst_num_existing_simplified:         0
% 0.19/0.48  % inst_num_eq_res_simplified:           0
% 0.19/0.48  % inst_num_child_elim:                  0
% 0.19/0.48  % inst_num_of_dismatching_blockings:    0
% 0.19/0.48  % inst_num_of_non_proper_insts:         0
% 0.19/0.48  % inst_num_of_duplicates:               0
% 0.19/0.48  % inst_inst_num_from_inst_to_res:       0
% 0.19/0.48  % inst_dismatching_checking_time:       0.
% 0.19/0.48  
% 0.19/0.48  % ------ Resolution
% 0.19/0.48  
% 0.19/0.48  % res_num_of_clauses:                   undef
% 0.19/0.48  % res_num_in_passive:                   undef
% 0.19/0.48  % res_num_in_active:                    0
% 0.19/0.48  % res_num_of_loops:                     0
% 0.19/0.48  % res_forward_subset_subsumed:          0
% 0.19/0.48  % res_backward_subset_subsumed:         0
% 0.19/0.48  % res_forward_subsumed:                 0
% 0.19/0.48  % res_backward_subsumed:                0
% 0.19/0.48  % res_forward_subsumption_resolution:   0
% 0.19/0.48  % res_backward_subsumption_resolution:  0
% 0.19/0.48  % res_clause_to_clause_subsumption:     0
% 0.19/0.48  % res_orphan_elimination:               0
% 0.19/0.48  % res_tautology_del:                    0
% 0.19/0.48  % res_num_eq_res_simplified:            0
% 0.19/0.48  % res_num_sel_changes:                  0
% 0.19/0.48  % res_moves_from_active_to_pass:        0
% 0.19/0.48  
% 0.19/0.48  % Status Unsatisfiable
% 0.19/0.48  % SZS status Unsatisfiable
% 0.19/0.48  % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------