%------------------------------------------------------------------------------
% File     : iProverMo---2.5-0.1
% Problem  : LCL760-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : iprover_modulo %s %d

% Computer : n015.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 600s
% DateTime : Sun Jul 17 11:39:10 EDT 2022

% Result   : Unsatisfiable 3.15s 3.36s
% Output   : CNFRefutation 3.15s
% 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,
    c_fequal(V_x,V_x,T_a),
    input ).

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

cnf(cls_ATP__Linkup_OCOMBB__def_0,axiom,
    c_COMBB(V_P,V_Q,V_R,T_b,T_a,T_c) = hAPP(V_P,hAPP(V_Q,V_R)),
    input ).

fof(cls_ATP__Linkup_OCOMBB__def_0_0,plain,
    ! [T_a,T_b,T_c,V_P,V_Q,V_R] :
      ( c_COMBB(V_P,V_Q,V_R,T_b,T_a,T_c) = hAPP(V_P,hAPP(V_Q,V_R))
      | $false ),
    inference(orientation,[status(thm)],[cls_ATP__Linkup_OCOMBB__def_0]) ).

cnf(cls_ATP__Linkup_OCOMBC__def_0,axiom,
    hAPP(c_COMBC(V_P,V_Q,T_b,T_c,T_a),V_R) = hAPP(hAPP(V_P,V_R),V_Q),
    input ).

fof(cls_ATP__Linkup_OCOMBC__def_0_0,plain,
    ! [T_a,T_b,T_c,V_P,V_Q,V_R] :
      ( hAPP(c_COMBC(V_P,V_Q,T_b,T_c,T_a),V_R) = hAPP(hAPP(V_P,V_R),V_Q)
      | $false ),
    inference(orientation,[status(thm)],[cls_ATP__Linkup_OCOMBC__def_0]) ).

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__Ring__and__Field_Odvd,axiom,
    class_Ring__and__Field_Odvd(tc_nat),
    input ).

fof(clsarity_nat__Ring__and__Field_Odvd_0,plain,
    ( class_Ring__and__Field_Odvd(tc_nat)
    | $false ),
    inference(orientation,[status(thm)],[clsarity_nat__Ring__and__Field_Odvd]) ).

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__Divides_Osemiring__div,axiom,
    class_Divides_Osemiring__div(tc_nat),
    input ).

fof(clsarity_nat__Divides_Osemiring__div_0,plain,
    ( class_Divides_Osemiring__div(tc_nat)
    | $false ),
    inference(orientation,[status(thm)],[clsarity_nat__Divides_Osemiring__div]) ).

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__Ring__and__Field_Osemiring,axiom,
    class_Ring__and__Field_Osemiring(tc_nat),
    input ).

fof(clsarity_nat__Ring__and__Field_Osemiring_0,plain,
    ( class_Ring__and__Field_Osemiring(tc_nat)
    | $false ),
    inference(orientation,[status(thm)],[clsarity_nat__Ring__and__Field_Osemiring]) ).

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__Ring__and__Field_Ocomm__semiring,axiom,
    class_Ring__and__Field_Ocomm__semiring(tc_nat),
    input ).

fof(clsarity_nat__Ring__and__Field_Ocomm__semiring_0,plain,
    ( class_Ring__and__Field_Ocomm__semiring(tc_nat)
    | $false ),
    inference(orientation,[status(thm)],[clsarity_nat__Ring__and__Field_Ocomm__semiring]) ).

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__OrderedGroup_Ocomm__monoid__mult,axiom,
    class_OrderedGroup_Ocomm__monoid__mult(tc_nat),
    input ).

fof(clsarity_nat__OrderedGroup_Ocomm__monoid__mult_0,plain,
    ( class_OrderedGroup_Ocomm__monoid__mult(tc_nat)
    | $false ),
    inference(orientation,[status(thm)],[clsarity_nat__OrderedGroup_Ocomm__monoid__mult]) ).

cnf(clsarity_nat__OrderedGroup_Oab__semigroup__mult,axiom,
    class_OrderedGroup_Oab__semigroup__mult(tc_nat),
    input ).

fof(clsarity_nat__OrderedGroup_Oab__semigroup__mult_0,plain,
    ( class_OrderedGroup_Oab__semigroup__mult(tc_nat)
    | $false ),
    inference(orientation,[status(thm)],[clsarity_nat__OrderedGroup_Oab__semigroup__mult]) ).

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__Ring__and__Field_Oordered__semiring__strict,axiom,
    class_Ring__and__Field_Oordered__semiring__strict(tc_nat),
    input ).

fof(clsarity_nat__Ring__and__Field_Oordered__semiring__strict_0,plain,
    ( class_Ring__and__Field_Oordered__semiring__strict(tc_nat)
    | $false ),
    inference(orientation,[status(thm)],[clsarity_nat__Ring__and__Field_Oordered__semiring__strict]) ).

cnf(clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict,axiom,
    class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat),
    input ).

fof(clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict_0,plain,
    ( class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat)
    | $false ),
    inference(orientation,[status(thm)],[clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict]) ).

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

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

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

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

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

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

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

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

cnf(cls_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_subst__map_0,axiom,
    hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB)),V_u),V_i) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_u),V_i),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,V_u,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),V_i,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
    input ).

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

cnf(cls_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_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_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,
    hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(V_k)),V_u),V_k) = V_u,
    input ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

cnf(cls_div__1_0,axiom,
    c_Divides_Odiv__class_Odiv(V_m,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = V_m,
    input ).

fof(cls_div__1_0_0,plain,
    ! [V_m] :
      ( c_Divides_Odiv__class_Odiv(V_m,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = V_m
      | $false ),
    inference(orientation,[status(thm)],[cls_div__1_0]) ).

cnf(cls_power__Suc__0_0,axiom,
    c_Power_Opower__class_Opower(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_n,tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
    input ).

fof(cls_power__Suc__0_0_0,plain,
    ! [V_n] :
      ( c_Power_Opower__class_Opower(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_n,tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | $false ),
    inference(orientation,[status(thm)],[cls_power__Suc__0_0]) ).

cnf(cls_nat__power__eq__Suc__0__iff_2,axiom,
    c_Power_Opower__class_Opower(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_m,tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
    input ).

fof(cls_nat__power__eq__Suc__0__iff_2_0,plain,
    ! [V_m] :
      ( c_Power_Opower__class_Opower(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_m,tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | $false ),
    inference(orientation,[status(thm)],[cls_nat__power__eq__Suc__0__iff_2]) ).

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

fof(cls_gr0__conv__Suc_1_0,plain,
    ! [V_x] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(V_x),tc_nat)
      | $false ),
    inference(orientation,[status(thm)],[cls_gr0__conv__Suc_1]) ).

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

fof(cls_zero__less__Suc_0_0,plain,
    ! [V_n] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(V_n),tc_nat)
      | $false ),
    inference(orientation,[status(thm)],[cls_zero__less__Suc_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_dvd__1__left_0,axiom,
    c_Ring__and__Field_Odvd__class_Odvd(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_k,tc_nat),
    input ).

fof(cls_dvd__1__left_0_0,plain,
    ! [V_k] :
      ( c_Ring__and__Field_Odvd__class_Odvd(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_k,tc_nat)
      | $false ),
    inference(orientation,[status(thm)],[cls_dvd__1__left_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_nat__power__eq__Suc__0__iff_1,axiom,
    c_Power_Opower__class_Opower(V_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
    input ).

fof(cls_nat__power__eq__Suc__0__iff_1_0,plain,
    ! [V_x] :
      ( c_Power_Opower__class_Opower(V_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | $false ),
    inference(orientation,[status(thm)],[cls_nat__power__eq__Suc__0__iff_1]) ).

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_One__nat__def_0,axiom,
    c_HOL_Oone__class_Oone(tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
    input ).

fof(cls_One__nat__def_0_0,plain,
    ( c_HOL_Oone__class_Oone(tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | $false ),
    inference(orientation,[status(thm)],[cls_One__nat__def_0]) ).

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

fof(cls_less__Suc0_1_0,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)
    | $false ),
    inference(orientation,[status(thm)],[cls_less__Suc0_1]) ).

cnf(cls_dvd__1__iff__1_1,axiom,
    c_Ring__and__Field_Odvd__class_Odvd(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),
    input ).

fof(cls_dvd__1__iff__1_1_0,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)
    | $false ),
    inference(orientation,[status(thm)],[cls_dvd__1__iff__1_1]) ).

cnf(cls_mult__eq__1__iff_2,axiom,
    c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
    input ).

fof(cls_mult__eq__1__iff_2_0,plain,
    ( c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | $false ),
    inference(orientation,[status(thm)],[cls_mult__eq__1__iff_2]) ).

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

fof(cls_mod__1_0_0,plain,
    ! [V_m] :
      ( c_Divides_Odiv__class_Omod(V_m,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
      | $false ),
    inference(orientation,[status(thm)],[cls_mod__1_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_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_beta_0,axiom,
    c_Lambda_Obeta(hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_s)),V_t),hAPP(hAPP(hAPP(c_Lambda_Osubst,V_s),V_t),c_HOL_Ozero__class_Ozero(tc_nat))),
    input ).

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

cnf(cls_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_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_typing_OVar_0,axiom,
    c_Type_Otyping(V_env,c_Lambda_OdB_OVar(V_x),hAPP(V_env,V_x)),
    input ).

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

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

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

cnf(cls_add__mult__distrib2_0,axiom,
    c_HOL_Otimes__class_Otimes(V_k,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n),tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat)),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat)),
    input ).

fof(cls_add__mult__distrib2_0_0,plain,
    ! [V_k,V_m,V_n] :
      ( c_HOL_Otimes__class_Otimes(V_k,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n),tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat)),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat))
      | $false ),
    inference(orientation,[status(thm)],[cls_add__mult__distrib2_0]) ).

cnf(cls_add__mult__distrib_0,axiom,
    c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n),V_k,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_m,V_k,tc_nat)),c_HOL_Otimes__class_Otimes(V_n,V_k,tc_nat)),
    input ).

fof(cls_add__mult__distrib_0_0,plain,
    ! [V_k,V_m,V_n] :
      ( c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n),V_k,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_m,V_k,tc_nat)),c_HOL_Otimes__class_Otimes(V_n,V_k,tc_nat))
      | $false ),
    inference(orientation,[status(thm)],[cls_add__mult__distrib_0]) ).

cnf(cls_nat__mult__assoc_0,axiom,
    c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),V_k,tc_nat) = c_HOL_Otimes__class_Otimes(V_m,c_HOL_Otimes__class_Otimes(V_n,V_k,tc_nat),tc_nat),
    input ).

fof(cls_nat__mult__assoc_0_0,plain,
    ! [V_k,V_m,V_n] :
      ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),V_k,tc_nat) = c_HOL_Otimes__class_Otimes(V_m,c_HOL_Otimes__class_Otimes(V_n,V_k,tc_nat),tc_nat)
      | $false ),
    inference(orientation,[status(thm)],[cls_nat__mult__assoc_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_lift_Osimps_I3_J_0,axiom,
    hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OAbs(V_s)),V_k) = c_Lambda_OdB_OAbs(hAPP(hAPP(c_Lambda_Olift,V_s),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),c_HOL_Oone__class_Oone(tc_nat)))),
    input ).

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

cnf(cls_mod__eq__0__iff_1,axiom,
    c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_d,V_x,tc_nat),V_d,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
    input ).

fof(cls_mod__eq__0__iff_1_0,plain,
    ! [V_d,V_x] :
      ( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_d,V_x,tc_nat),V_d,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
      | $false ),
    inference(orientation,[status(thm)],[cls_mod__eq__0__iff_1]) ).

cnf(cls_div__mult2__eq_0,axiom,
    c_Divides_Odiv__class_Odiv(V_a,c_HOL_Otimes__class_Otimes(V_b,V_c,tc_nat),tc_nat) = c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Odiv(V_a,V_b,tc_nat),V_c,tc_nat),
    input ).

fof(cls_div__mult2__eq_0_0,plain,
    ! [V_a,V_b,V_c] :
      ( c_Divides_Odiv__class_Odiv(V_a,c_HOL_Otimes__class_Otimes(V_b,V_c,tc_nat),tc_nat) = c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Odiv(V_a,V_b,tc_nat),V_c,tc_nat)
      | $false ),
    inference(orientation,[status(thm)],[cls_div__mult2__eq_0]) ).

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

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

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

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

cnf(cls_mod__mult2__eq_0,axiom,
    c_Divides_Odiv__class_Omod(V_a,c_HOL_Otimes__class_Otimes(V_b,V_c,tc_nat),tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_b,c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Odiv(V_a,V_b,tc_nat),V_c,tc_nat),tc_nat)),c_Divides_Odiv__class_Omod(V_a,V_b,tc_nat)),
    input ).

fof(cls_mod__mult2__eq_0_0,plain,
    ! [V_a,V_b,V_c] :
      ( c_Divides_Odiv__class_Omod(V_a,c_HOL_Otimes__class_Otimes(V_b,V_c,tc_nat),tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_b,c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Odiv(V_a,V_b,tc_nat),V_c,tc_nat),tc_nat)),c_Divides_Odiv__class_Omod(V_a,V_b,tc_nat))
      | $false ),
    inference(orientation,[status(thm)],[cls_mod__mult2__eq_0]) ).

cnf(cls_nat__mult__div__cancel__disj_0,axiom,
    c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
    input ).

fof(cls_nat__mult__div__cancel__disj_0_0,plain,
    ! [V_m,V_n] :
      ( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
      | $false ),
    inference(orientation,[status(thm)],[cls_nat__mult__div__cancel__disj_0]) ).

cnf(cls_power__eq__if_0,axiom,
    c_Power_Opower__class_Opower(V_p,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Oone__class_Oone(tc_nat),
    input ).

fof(cls_power__eq__if_0_0,plain,
    ! [V_p] :
      ( c_Power_Opower__class_Opower(V_p,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Oone__class_Oone(tc_nat)
      | $false ),
    inference(orientation,[status(thm)],[cls_power__eq__if_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_beta__cases_I1_J_0,axiom,
    ~ 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] :
      ( ~ c_Lambda_Obeta(c_Lambda_OdB_OVar(V_i),V_t)
      | $false ),
    inference(orientation,[status(thm)],[cls_beta__cases_I1_J_0]) ).

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

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

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

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

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

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

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

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

cnf(cls_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_Nil__is__map__conv_1,axiom,
    c_List_Olist_ONil(T_a) = c_List_Omap(V_f,c_List_Olist_ONil(T_b),T_b,T_a),
    input ).

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

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

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

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

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

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

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

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

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

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

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

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

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

cnf(cls_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_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_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_lessI_0,axiom,
    c_HOL_Oord__class_Oless(V_n,c_Suc(V_n),tc_nat),
    input ).

fof(cls_lessI_0_0,plain,
    ! [V_n] :
      ( c_HOL_Oord__class_Oless(V_n,c_Suc(V_n),tc_nat)
      | $false ),
    inference(orientation,[status(thm)],[cls_lessI_0]) ).

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

fof(cls_less__Suc__eq_2_0,plain,
    ! [V_x] :
      ( c_HOL_Oord__class_Oless(V_x,c_Suc(V_x),tc_nat)
      | $false ),
    inference(orientation,[status(thm)],[cls_less__Suc__eq_2]) ).

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

fof(cls_mod__Suc__eq__Suc__mod_0_0,plain,
    ! [V_m,V_n] :
      ( c_Divides_Odiv__class_Omod(c_Suc(V_m),V_n,tc_nat) = c_Divides_Odiv__class_Omod(c_Suc(c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat)),V_n,tc_nat)
      | $false ),
    inference(orientation,[status(thm)],[cls_mod__Suc__eq__Suc__mod_0]) ).

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

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

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

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

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

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

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

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

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

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

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

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

cnf(cls_mult__is__0_1,axiom,
    c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
    input ).

fof(cls_mult__is__0_1_0,plain,
    ! [V_n] :
      ( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
      | $false ),
    inference(orientation,[status(thm)],[cls_mult__is__0_1]) ).

cnf(cls_mult__is__0_2,axiom,
    c_HOL_Otimes__class_Otimes(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
    input ).

fof(cls_mult__is__0_2_0,plain,
    ! [V_m] :
      ( c_HOL_Otimes__class_Otimes(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
      | $false ),
    inference(orientation,[status(thm)],[cls_mult__is__0_2]) ).

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

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

cnf(cls_mult__cancel1_1,axiom,
    c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat),
    input ).

fof(cls_mult__cancel1_1_0,plain,
    ! [V_m,V_n] :
      ( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)
      | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ),
    inference(orientation,[status(thm)],[cls_mult__cancel1_1]) ).

cnf(cls_mult__cancel2_1,axiom,
    c_HOL_Otimes__class_Otimes(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    input ).

fof(cls_mult__cancel2_1_0,plain,
    ! [V_m,V_n] :
      ( c_HOL_Otimes__class_Otimes(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
      | c_HOL_Otimes__class_Otimes(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
    inference(orientation,[status(thm)],[cls_mult__cancel2_1]) ).

cnf(cls_div__mult1__eq_0,axiom,
    c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(V_a,V_b,tc_nat),V_c,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_a,c_Divides_Odiv__class_Odiv(V_b,V_c,tc_nat),tc_nat)),c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(V_a,c_Divides_Odiv__class_Omod(V_b,V_c,tc_nat),tc_nat),V_c,tc_nat)),
    input ).

fof(cls_div__mult1__eq_0_0,plain,
    ! [V_a,V_b,V_c] :
      ( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(V_a,V_b,tc_nat),V_c,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_a,c_Divides_Odiv__class_Odiv(V_b,V_c,tc_nat),tc_nat)),c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(V_a,c_Divides_Odiv__class_Omod(V_b,V_c,tc_nat),tc_nat),V_c,tc_nat))
      | $false ),
    inference(orientation,[status(thm)],[cls_div__mult1__eq_0]) ).

cnf(cls_nat__mult__dvd__cancel__disj_1,axiom,
    c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat),tc_nat),
    input ).

fof(cls_nat__mult__dvd__cancel__disj_1_0,plain,
    ! [V_m,V_n] :
      ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat),tc_nat)
      | $false ),
    inference(orientation,[status(thm)],[cls_nat__mult__dvd__cancel__disj_1]) ).

cnf(cls_dvd_Oeq__iff_0,axiom,
    c_Ring__and__Field_Odvd__class_Odvd(V_x,V_x,tc_nat),
    input ).

fof(cls_dvd_Oeq__iff_0_0,plain,
    ! [V_x] :
      ( c_Ring__and__Field_Odvd__class_Odvd(V_x,V_x,tc_nat)
      | $false ),
    inference(orientation,[status(thm)],[cls_dvd_Oeq__iff_0]) ).

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

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

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

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

cnf(cls_mod__mult__self4_0,axiom,
    c_Divides_Odiv__class_Omod(c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat)),V_m)),V_n,tc_nat) = c_Divides_Odiv__class_Omod(c_Suc(V_m),V_n,tc_nat),
    input ).

fof(cls_mod__mult__self4_0_0,plain,
    ! [V_k,V_m,V_n] :
      ( c_Divides_Odiv__class_Omod(c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat)),V_m)),V_n,tc_nat) = c_Divides_Odiv__class_Omod(c_Suc(V_m),V_n,tc_nat)
      | $false ),
    inference(orientation,[status(thm)],[cls_mod__mult__self4_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_mult__Suc_0,axiom,
    c_HOL_Otimes__class_Otimes(c_Suc(V_m),V_n,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat)),
    input ).

fof(cls_mult__Suc_0_0,plain,
    ! [V_m,V_n] :
      ( c_HOL_Otimes__class_Otimes(c_Suc(V_m),V_n,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat))
      | $false ),
    inference(orientation,[status(thm)],[cls_mult__Suc_0]) ).

cnf(cls_mult__Suc__right_0,axiom,
    c_HOL_Otimes__class_Otimes(V_m,c_Suc(V_n),tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat)),
    input ).

fof(cls_mult__Suc__right_0_0,plain,
    ! [V_m,V_n] :
      ( c_HOL_Otimes__class_Otimes(V_m,c_Suc(V_n),tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat))
      | $false ),
    inference(orientation,[status(thm)],[cls_mult__Suc__right_0]) ).

cnf(cls_nat__zero__less__power__iff_2,axiom,
    c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Power_Opower__class_Opower(V_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),tc_nat),
    input ).

fof(cls_nat__zero__less__power__iff_2_0,plain,
    ! [V_x] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Power_Opower__class_Opower(V_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),tc_nat)
      | $false ),
    inference(orientation,[status(thm)],[cls_nat__zero__less__power__iff_2]) ).

cnf(cls_mod__mult__self3_0,axiom,
    c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat)),V_m),V_n,tc_nat) = c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat),
    input ).

fof(cls_mod__mult__self3_0_0,plain,
    ! [V_k,V_m,V_n] :
      ( c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat)),V_m),V_n,tc_nat) = c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat)
      | $false ),
    inference(orientation,[status(thm)],[cls_mod__mult__self3_0]) ).

cnf(cls_div__add1__eq_0,axiom,
    c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_a),V_b),V_c,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Odiv(V_a,V_c,tc_nat)),c_Divides_Odiv__class_Odiv(V_b,V_c,tc_nat))),c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Omod(V_a,V_c,tc_nat)),c_Divides_Odiv__class_Omod(V_b,V_c,tc_nat)),V_c,tc_nat)),
    input ).

fof(cls_div__add1__eq_0_0,plain,
    ! [V_a,V_b,V_c] :
      ( c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_a),V_b),V_c,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Odiv(V_a,V_c,tc_nat)),c_Divides_Odiv__class_Odiv(V_b,V_c,tc_nat))),c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Omod(V_a,V_c,tc_nat)),c_Divides_Odiv__class_Omod(V_b,V_c,tc_nat)),V_c,tc_nat))
      | $false ),
    inference(orientation,[status(thm)],[cls_div__add1__eq_0]) ).

cnf(cls_mod__mult__distrib_0,axiom,
    c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat),V_k,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_m,V_k,tc_nat),c_HOL_Otimes__class_Otimes(V_n,V_k,tc_nat),tc_nat),
    input ).

fof(cls_mod__mult__distrib_0_0,plain,
    ! [V_k,V_m,V_n] :
      ( c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat),V_k,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_m,V_k,tc_nat),c_HOL_Otimes__class_Otimes(V_n,V_k,tc_nat),tc_nat)
      | $false ),
    inference(orientation,[status(thm)],[cls_mod__mult__distrib_0]) ).

cnf(cls_mod__mult__distrib2_0,axiom,
    c_HOL_Otimes__class_Otimes(V_k,c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat),tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat),
    input ).

fof(cls_mod__mult__distrib2_0_0,plain,
    ! [V_k,V_m,V_n] :
      ( c_HOL_Otimes__class_Otimes(V_k,c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat),tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat)
      | $false ),
    inference(orientation,[status(thm)],[cls_mod__mult__distrib2_0]) ).

cnf(cls_nat__mult__eq__1__iff_2,axiom,
    c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_HOL_Oone__class_Oone(tc_nat),
    input ).

fof(cls_nat__mult__eq__1__iff_2_0,plain,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_HOL_Oone__class_Oone(tc_nat)
    | $false ),
    inference(orientation,[status(thm)],[cls_nat__mult__eq__1__iff_2]) ).

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_subst__Abs_0,axiom,
    hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OAbs(V_t)),V_s),V_k) = c_Lambda_OdB_OAbs(hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),hAPP(hAPP(c_Lambda_Olift,V_s),c_HOL_Ozero__class_Ozero(tc_nat))),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),c_HOL_Oone__class_Oone(tc_nat)))),
    input ).

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

cnf(cls_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_substn_Osimps_I3_J_0,axiom,
    c_Lambda_Osubstn(c_Lambda_OdB_OAbs(V_t),V_s,V_k) = c_Lambda_OdB_OAbs(c_Lambda_Osubstn(V_t,V_s,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),c_HOL_Oone__class_Oone(tc_nat)))),
    input ).

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

cnf(cls_nat__1__eq__mult__iff_2,axiom,
    c_HOL_Oone__class_Oone(tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),
    input ).

fof(cls_nat__1__eq__mult__iff_2_0,plain,
    ( c_HOL_Oone__class_Oone(tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
    | $false ),
    inference(orientation,[status(thm)],[cls_nat__1__eq__mult__iff_2]) ).

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

fof(cls_less__iff__Suc__add_1_0,plain,
    ! [V_m,V_x] :
      ( c_HOL_Oord__class_Oless(V_m,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_x)),tc_nat)
      | $false ),
    inference(orientation,[status(thm)],[cls_less__iff__Suc__add_1]) ).

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

fof(cls_less__add__Suc2_0_0,plain,
    ! [V_i,V_m] :
      ( c_HOL_Oord__class_Oless(V_i,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_i)),tc_nat)
      | $false ),
    inference(orientation,[status(thm)],[cls_less__add__Suc2_0]) ).

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

fof(cls_less__add__Suc1_0_0,plain,
    ! [V_i,V_m] :
      ( c_HOL_Oord__class_Oless(V_i,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_m)),tc_nat)
      | $false ),
    inference(orientation,[status(thm)],[cls_less__add__Suc1_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_nat__mult__1__right_0,axiom,
    c_HOL_Otimes__class_Otimes(V_n,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = V_n,
    input ).

fof(cls_nat__mult__1__right_0_0,plain,
    ! [V_n] :
      ( c_HOL_Otimes__class_Otimes(V_n,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = V_n
      | $false ),
    inference(orientation,[status(thm)],[cls_nat__mult__1__right_0]) ).

cnf(cls_nat__mult__1_0,axiom,
    c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),V_n,tc_nat) = V_n,
    input ).

fof(cls_nat__mult__1_0_0,plain,
    ! [V_n] :
      ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),V_n,tc_nat) = V_n
      | $false ),
    inference(orientation,[status(thm)],[cls_nat__mult__1_0]) ).

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

fof(cls_Suc__eq__plus1__left_0_0,plain,
    ! [V_n] :
      ( c_Suc(V_n) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),V_n)
      | $false ),
    inference(orientation,[status(thm)],[cls_Suc__eq__plus1__left_0]) ).

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

fof(cls_Suc__eq__plus1_0_0,plain,
    ! [V_n] :
      ( c_Suc(V_n) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),c_HOL_Oone__class_Oone(tc_nat))
      | $false ),
    inference(orientation,[status(thm)],[cls_Suc__eq__plus1_0]) ).

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

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

cnf(cls_natgb_Oadd__mul__solve_1,axiom,
    hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_x,V_y,tc_nat)),c_HOL_Otimes__class_Otimes(V_x,V_z,tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_x,V_z,tc_nat)),c_HOL_Otimes__class_Otimes(V_x,V_y,tc_nat)),
    input ).

fof(cls_natgb_Oadd__mul__solve_1_0,plain,
    ! [V_x,V_y,V_z] :
      ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_x,V_y,tc_nat)),c_HOL_Otimes__class_Otimes(V_x,V_z,tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_x,V_z,tc_nat)),c_HOL_Otimes__class_Otimes(V_x,V_y,tc_nat))
      | $false ),
    inference(orientation,[status(thm)],[cls_natgb_Oadd__mul__solve_1]) ).

cnf(cls_natgb_Onoteq__reduce_1,axiom,
    hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_x,V_c,tc_nat)),c_HOL_Otimes__class_Otimes(V_x,V_d,tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_x,V_d,tc_nat)),c_HOL_Otimes__class_Otimes(V_x,V_c,tc_nat)),
    input ).

fof(cls_natgb_Onoteq__reduce_1_0,plain,
    ! [V_c,V_d,V_x] :
      ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_x,V_c,tc_nat)),c_HOL_Otimes__class_Otimes(V_x,V_d,tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_x,V_d,tc_nat)),c_HOL_Otimes__class_Otimes(V_x,V_c,tc_nat))
      | $false ),
    inference(orientation,[status(thm)],[cls_natgb_Onoteq__reduce_1]) ).

cnf(cls_nat__mult__commute_0,axiom,
    c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat) = c_HOL_Otimes__class_Otimes(V_n,V_m,tc_nat),
    input ).

fof(cls_nat__mult__commute_0_0,plain,
    ! [V_m,V_n] :
      ( c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat) = c_HOL_Otimes__class_Otimes(V_n,V_m,tc_nat)
      | $false ),
    inference(orientation,[status(thm)],[cls_nat__mult__commute_0]) ).

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

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

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

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

cnf(cls_left__add__mult__distrib_0,axiom,
    hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_i,V_u,tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_j,V_u,tc_nat)),V_k)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_j),V_u,tc_nat)),V_k),
    input ).

fof(cls_left__add__mult__distrib_0_0,plain,
    ! [V_i,V_j,V_k,V_u] :
      ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_i,V_u,tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_j,V_u,tc_nat)),V_k)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_j),V_u,tc_nat)),V_k)
      | $false ),
    inference(orientation,[status(thm)],[cls_left__add__mult__distrib_0]) ).

cnf(cls_nat__dvd__1__iff__1_1,axiom,
    c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),
    input ).

fof(cls_nat__dvd__1__iff__1_1_0,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
    | $false ),
    inference(orientation,[status(thm)],[cls_nat__dvd__1__iff__1_1]) ).

fof(def_lhs_atom1,axiom,
    ( lhs_atom1
  <=> c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_0,plain,
    ( lhs_atom1
    | $false ),
    inference(fold_definition,[status(thm)],[cls_nat__dvd__1__iff__1_1_0,def_lhs_atom1]) ).

fof(def_lhs_atom2,axiom,
    ! [V_u,V_k,V_j,V_i] :
      ( lhs_atom2(V_u,V_k,V_j,V_i)
    <=> hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_i,V_u,tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_j,V_u,tc_nat)),V_k)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_j),V_u,tc_nat)),V_k) ),
    inference(definition,[],]) ).

fof(to_be_clausified_1,plain,
    ! [V_i,V_j,V_k,V_u] :
      ( lhs_atom2(V_u,V_k,V_j,V_i)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_left__add__mult__distrib_0_0,def_lhs_atom2]) ).

fof(def_lhs_atom3,axiom,
    ! [V_n,V_m,V_k] :
      ( lhs_atom3(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_2,plain,
    ! [V_k,V_m,V_n] :
      ( lhs_atom3(V_n,V_m,V_k)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_nat__add__assoc_0_0,def_lhs_atom3]) ).

fof(def_lhs_atom4,axiom,
    ! [V_z,V_y,V_x] :
      ( lhs_atom4(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_3,plain,
    ! [V_x,V_y,V_z] :
      ( lhs_atom4(V_z,V_y,V_x)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_nat__add__left__commute_0_0,def_lhs_atom4]) ).

fof(def_lhs_atom5,axiom,
    ! [V_n,V_m] :
      ( lhs_atom5(V_n,V_m)
    <=> c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat) = c_HOL_Otimes__class_Otimes(V_n,V_m,tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_4,plain,
    ! [V_m,V_n] :
      ( lhs_atom5(V_n,V_m)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_nat__mult__commute_0_0,def_lhs_atom5]) ).

fof(def_lhs_atom6,axiom,
    ! [V_x,V_d,V_c] :
      ( lhs_atom6(V_x,V_d,V_c)
    <=> hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_x,V_c,tc_nat)),c_HOL_Otimes__class_Otimes(V_x,V_d,tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_x,V_d,tc_nat)),c_HOL_Otimes__class_Otimes(V_x,V_c,tc_nat)) ),
    inference(definition,[],]) ).

fof(to_be_clausified_5,plain,
    ! [V_c,V_d,V_x] :
      ( lhs_atom6(V_x,V_d,V_c)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_natgb_Onoteq__reduce_1_0,def_lhs_atom6]) ).

fof(def_lhs_atom7,axiom,
    ! [V_z,V_y,V_x] :
      ( lhs_atom7(V_z,V_y,V_x)
    <=> hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_x,V_y,tc_nat)),c_HOL_Otimes__class_Otimes(V_x,V_z,tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_x,V_z,tc_nat)),c_HOL_Otimes__class_Otimes(V_x,V_y,tc_nat)) ),
    inference(definition,[],]) ).

fof(to_be_clausified_6,plain,
    ! [V_x,V_y,V_z] :
      ( lhs_atom7(V_z,V_y,V_x)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_natgb_Oadd__mul__solve_1_0,def_lhs_atom7]) ).

fof(def_lhs_atom8,axiom,
    ! [V_f3,V_f2,V_f1,V_dB,T_a] :
      ( lhs_atom8(V_f3,V_f2,V_f1,V_dB,T_a)
    <=> c_Lambda_OdB_OdB__case(V_f1,V_f2,V_f3,c_Lambda_OdB_OAbs(V_dB),T_a) = hAPP(V_f3,V_dB) ),
    inference(definition,[],]) ).

fof(to_be_clausified_7,plain,
    ! [T_a,V_dB,V_f1,V_f2,V_f3] :
      ( lhs_atom8(V_f3,V_f2,V_f1,V_dB,T_a)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_dB_Osimps_I12_J_0_0,def_lhs_atom8]) ).

fof(def_lhs_atom9,axiom,
    ! [V_n] :
      ( lhs_atom9(V_n)
    <=> c_Suc(V_n) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),c_HOL_Oone__class_Oone(tc_nat)) ),
    inference(definition,[],]) ).

fof(to_be_clausified_8,plain,
    ! [V_n] :
      ( lhs_atom9(V_n)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_Suc__eq__plus1_0_0,def_lhs_atom9]) ).

fof(def_lhs_atom10,axiom,
    ! [V_n] :
      ( lhs_atom10(V_n)
    <=> c_Suc(V_n) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),V_n) ),
    inference(definition,[],]) ).

fof(to_be_clausified_9,plain,
    ! [V_n] :
      ( lhs_atom10(V_n)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_Suc__eq__plus1__left_0_0,def_lhs_atom10]) ).

fof(def_lhs_atom11,axiom,
    ! [V_n] :
      ( lhs_atom11(V_n)
    <=> c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),V_n,tc_nat) = V_n ),
    inference(definition,[],]) ).

fof(to_be_clausified_10,plain,
    ! [V_n] :
      ( lhs_atom11(V_n)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_nat__mult__1_0_0,def_lhs_atom11]) ).

fof(def_lhs_atom12,axiom,
    ! [V_n] :
      ( lhs_atom12(V_n)
    <=> c_HOL_Otimes__class_Otimes(V_n,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = V_n ),
    inference(definition,[],]) ).

fof(to_be_clausified_11,plain,
    ! [V_n] :
      ( lhs_atom12(V_n)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_nat__mult__1__right_0_0,def_lhs_atom12]) ).

fof(def_lhs_atom13,axiom,
    ! [V_A,T_a] :
      ( lhs_atom13(V_A,T_a)
    <=> c_List_Olistsp(V_A,c_List_Olist_ONil(T_a),T_a) ),
    inference(definition,[],]) ).

fof(to_be_clausified_12,plain,
    ! [T_a,V_A] :
      ( lhs_atom13(V_A,T_a)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_listsp_ONil_0_0,def_lhs_atom13]) ).

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

fof(to_be_clausified_13,plain,
    ! [V_i,V_m] :
      ( lhs_atom14(V_m,V_i)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_less__add__Suc1_0_0,def_lhs_atom14]) ).

fof(def_lhs_atom15,axiom,
    ! [V_m,V_i] :
      ( lhs_atom15(V_m,V_i)
    <=> c_HOL_Oord__class_Oless(V_i,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_i)),tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_14,plain,
    ! [V_i,V_m] :
      ( lhs_atom15(V_m,V_i)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_less__add__Suc2_0_0,def_lhs_atom15]) ).

fof(def_lhs_atom16,axiom,
    ! [V_x,V_m] :
      ( lhs_atom16(V_x,V_m)
    <=> c_HOL_Oord__class_Oless(V_m,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_x)),tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_15,plain,
    ! [V_m,V_x] :
      ( lhs_atom16(V_x,V_m)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_less__iff__Suc__add_1_0,def_lhs_atom16]) ).

fof(def_lhs_atom17,axiom,
    ( lhs_atom17
  <=> c_HOL_Oone__class_Oone(tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_16,plain,
    ( lhs_atom17
    | $false ),
    inference(fold_definition,[status(thm)],[cls_nat__1__eq__mult__iff_2_0,def_lhs_atom17]) ).

fof(def_lhs_atom18,axiom,
    ! [V_t,V_s,V_k] :
      ( lhs_atom18(V_t,V_s,V_k)
    <=> c_Lambda_Osubstn(c_Lambda_OdB_OAbs(V_t),V_s,V_k) = c_Lambda_OdB_OAbs(c_Lambda_Osubstn(V_t,V_s,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),c_HOL_Oone__class_Oone(tc_nat)))) ),
    inference(definition,[],]) ).

fof(to_be_clausified_17,plain,
    ! [V_k,V_s,V_t] :
      ( lhs_atom18(V_t,V_s,V_k)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_substn_Osimps_I3_J_0_0,def_lhs_atom18]) ).

fof(def_lhs_atom19,axiom,
    ! [V_n,V_m] :
      ( lhs_atom19(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_18,plain,
    ! [V_m,V_n] :
      ( lhs_atom19(V_n,V_m)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_nat__add__commute_0_0,def_lhs_atom19]) ).

fof(def_lhs_atom20,axiom,
    ! [V_t,V_s,V_k] :
      ( lhs_atom20(V_t,V_s,V_k)
    <=> hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OAbs(V_t)),V_s),V_k) = c_Lambda_OdB_OAbs(hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),hAPP(hAPP(c_Lambda_Olift,V_s),c_HOL_Ozero__class_Ozero(tc_nat))),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),c_HOL_Oone__class_Oone(tc_nat)))) ),
    inference(definition,[],]) ).

fof(to_be_clausified_19,plain,
    ! [V_k,V_s,V_t] :
      ( lhs_atom20(V_t,V_s,V_k)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_subst__Abs_0_0,def_lhs_atom20]) ).

fof(def_lhs_atom21,axiom,
    ! [V_dB] :
      ( lhs_atom21(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_20,plain,
    ! [V_dB] :
      ( lhs_atom21(V_dB)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_dB_Osize_I6_J_0_0,def_lhs_atom21]) ).

fof(def_lhs_atom22,axiom,
    ( lhs_atom22
  <=> c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_HOL_Oone__class_Oone(tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_21,plain,
    ( lhs_atom22
    | $false ),
    inference(fold_definition,[status(thm)],[cls_nat__mult__eq__1__iff_2_0,def_lhs_atom22]) ).

fof(def_lhs_atom23,axiom,
    ! [V_n,V_m,V_k] :
      ( lhs_atom23(V_n,V_m,V_k)
    <=> c_HOL_Otimes__class_Otimes(V_k,c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat),tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_22,plain,
    ! [V_k,V_m,V_n] :
      ( lhs_atom23(V_n,V_m,V_k)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_mod__mult__distrib2_0_0,def_lhs_atom23]) ).

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

fof(to_be_clausified_23,plain,
    ! [V_k,V_m,V_n] :
      ( lhs_atom24(V_n,V_m,V_k)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_mod__mult__distrib_0_0,def_lhs_atom24]) ).

fof(def_lhs_atom25,axiom,
    ! [V_c,V_b,V_a] :
      ( lhs_atom25(V_c,V_b,V_a)
    <=> c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_a),V_b),V_c,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Odiv(V_a,V_c,tc_nat)),c_Divides_Odiv__class_Odiv(V_b,V_c,tc_nat))),c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Omod(V_a,V_c,tc_nat)),c_Divides_Odiv__class_Omod(V_b,V_c,tc_nat)),V_c,tc_nat)) ),
    inference(definition,[],]) ).

fof(to_be_clausified_24,plain,
    ! [V_a,V_b,V_c] :
      ( lhs_atom25(V_c,V_b,V_a)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_div__add1__eq_0_0,def_lhs_atom25]) ).

fof(def_lhs_atom26,axiom,
    ! [V_n,V_m,V_k] :
      ( lhs_atom26(V_n,V_m,V_k)
    <=> c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat)),V_m),V_n,tc_nat) = c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_25,plain,
    ! [V_k,V_m,V_n] :
      ( lhs_atom26(V_n,V_m,V_k)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_mod__mult__self3_0_0,def_lhs_atom26]) ).

fof(def_lhs_atom27,axiom,
    ! [V_x] :
      ( lhs_atom27(V_x)
    <=> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Power_Opower__class_Opower(V_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_26,plain,
    ! [V_x] :
      ( lhs_atom27(V_x)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_nat__zero__less__power__iff_2_0,def_lhs_atom27]) ).

fof(def_lhs_atom28,axiom,
    ! [V_n,V_m] :
      ( lhs_atom28(V_n,V_m)
    <=> c_HOL_Otimes__class_Otimes(V_m,c_Suc(V_n),tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat)) ),
    inference(definition,[],]) ).

fof(to_be_clausified_27,plain,
    ! [V_m,V_n] :
      ( lhs_atom28(V_n,V_m)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_mult__Suc__right_0_0,def_lhs_atom28]) ).

fof(def_lhs_atom29,axiom,
    ! [V_n,V_m] :
      ( lhs_atom29(V_n,V_m)
    <=> c_HOL_Otimes__class_Otimes(c_Suc(V_m),V_n,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat)) ),
    inference(definition,[],]) ).

fof(to_be_clausified_28,plain,
    ! [V_m,V_n] :
      ( lhs_atom29(V_n,V_m)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_mult__Suc_0_0,def_lhs_atom29]) ).

fof(def_lhs_atom30,axiom,
    ! [V_x,V_e,V_T,T_a] :
      ( lhs_atom30(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_29,plain,
    ! [T_a,V_T,V_e,V_x] :
      ( lhs_atom30(V_x,V_e,V_T,T_a)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_shift__eq_0_0,def_lhs_atom30]) ).

fof(def_lhs_atom31,axiom,
    ! [V_n,V_m,V_k] :
      ( lhs_atom31(V_n,V_m,V_k)
    <=> c_Divides_Odiv__class_Omod(c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat)),V_m)),V_n,tc_nat) = c_Divides_Odiv__class_Omod(c_Suc(V_m),V_n,tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_30,plain,
    ! [V_k,V_m,V_n] :
      ( lhs_atom31(V_n,V_m,V_k)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_mod__mult__self4_0_0,def_lhs_atom31]) ).

fof(def_lhs_atom32,axiom,
    ! [V_x] :
      ( lhs_atom32(V_x)
    <=> ~ c_HOL_Oord__class_Oless(V_x,V_x,tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_31,plain,
    ! [V_x] :
      ( lhs_atom32(V_x)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_nat__less__le_1_0,def_lhs_atom32]) ).

fof(def_lhs_atom33,axiom,
    ! [V_n] :
      ( lhs_atom33(V_n)
    <=> ~ c_HOL_Oord__class_Oless(V_n,V_n,tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_32,plain,
    ! [V_n] :
      ( lhs_atom33(V_n)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_less__not__refl_0_0,def_lhs_atom33]) ).

fof(def_lhs_atom34,axiom,
    ! [V_x] :
      ( lhs_atom34(V_x)
    <=> c_Ring__and__Field_Odvd__class_Odvd(V_x,V_x,tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_33,plain,
    ! [V_x] :
      ( lhs_atom34(V_x)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_dvd_Oeq__iff_0_0,def_lhs_atom34]) ).

fof(def_lhs_atom35,axiom,
    ! [V_n,V_m] :
      ( lhs_atom35(V_n,V_m)
    <=> c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat),tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_34,plain,
    ! [V_m,V_n] :
      ( lhs_atom35(V_n,V_m)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_nat__mult__dvd__cancel__disj_1_0,def_lhs_atom35]) ).

fof(def_lhs_atom36,axiom,
    ! [V_c,V_b,V_a] :
      ( lhs_atom36(V_c,V_b,V_a)
    <=> c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(V_a,V_b,tc_nat),V_c,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_a,c_Divides_Odiv__class_Odiv(V_b,V_c,tc_nat),tc_nat)),c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(V_a,c_Divides_Odiv__class_Omod(V_b,V_c,tc_nat),tc_nat),V_c,tc_nat)) ),
    inference(definition,[],]) ).

fof(to_be_clausified_35,plain,
    ! [V_a,V_b,V_c] :
      ( lhs_atom36(V_c,V_b,V_a)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_div__mult1__eq_0_0,def_lhs_atom36]) ).

fof(def_lhs_atom37,axiom,
    ! [V_n,V_m] :
      ( lhs_atom37(V_n,V_m)
    <=> c_HOL_Otimes__class_Otimes(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_36,plain,
    ! [V_m,V_n] :
      ( lhs_atom37(V_n,V_m)
      | c_HOL_Otimes__class_Otimes(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
    inference(fold_definition,[status(thm)],[cls_mult__cancel2_1_0,def_lhs_atom37]) ).

fof(def_lhs_atom38,axiom,
    ! [V_n,V_m] :
      ( lhs_atom38(V_n,V_m)
    <=> c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_37,plain,
    ! [V_m,V_n] :
      ( lhs_atom38(V_n,V_m)
      | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ),
    inference(fold_definition,[status(thm)],[cls_mult__cancel1_1_0,def_lhs_atom38]) ).

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

fof(to_be_clausified_38,plain,
    ( lhs_atom39
    | $false ),
    inference(fold_definition,[status(thm)],[cls_neq0__conv_1_0,def_lhs_atom39]) ).

fof(def_lhs_atom40,axiom,
    ! [V_m] :
      ( lhs_atom40(V_m)
    <=> c_HOL_Otimes__class_Otimes(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_39,plain,
    ! [V_m] :
      ( lhs_atom40(V_m)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_mult__is__0_2_0,def_lhs_atom40]) ).

fof(def_lhs_atom41,axiom,
    ! [V_n] :
      ( lhs_atom41(V_n)
    <=> c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_40,plain,
    ! [V_n] :
      ( lhs_atom41(V_n)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_mult__is__0_1_0,def_lhs_atom41]) ).

fof(def_lhs_atom42,axiom,
    ( lhs_atom42
  <=> 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_41,plain,
    ( lhs_atom42
    | $false ),
    inference(fold_definition,[status(thm)],[cls_add__is__0_2_0,def_lhs_atom42]) ).

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

fof(to_be_clausified_42,plain,
    ! [V_m] :
      ( lhs_atom43(V_m)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_gr__implies__not0_0_0,def_lhs_atom43]) ).

fof(def_lhs_atom44,axiom,
    ! [V_n] :
      ( lhs_atom44(V_n)
    <=> ~ c_HOL_Oord__class_Oless(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_43,plain,
    ! [V_n] :
      ( lhs_atom44(V_n)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_not__less0_0_0,def_lhs_atom44]) ).

fof(def_lhs_atom45,axiom,
    ! [V_x] :
      ( lhs_atom45(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_44,plain,
    ! [V_x] :
      ( lhs_atom45(V_x)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_natgb_Oadd__r0__iff_1_0,def_lhs_atom45]) ).

fof(def_lhs_atom46,axiom,
    ! [V_n] :
      ( lhs_atom46(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_45,plain,
    ! [V_n] :
      ( lhs_atom46(V_n)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_plus__nat_Oadd__0_0_0,def_lhs_atom46]) ).

fof(def_lhs_atom47,axiom,
    ! [V_m] :
      ( lhs_atom47(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_46,plain,
    ! [V_m] :
      ( lhs_atom47(V_m)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_Nat_Oadd__0__right_0_0,def_lhs_atom47]) ).

fof(def_lhs_atom48,axiom,
    ! [V_n,V_m] :
      ( lhs_atom48(V_n,V_m)
    <=> c_Divides_Odiv__class_Omod(c_Suc(V_m),V_n,tc_nat) = c_Divides_Odiv__class_Omod(c_Suc(c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat)),V_n,tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_47,plain,
    ! [V_m,V_n] :
      ( lhs_atom48(V_n,V_m)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_mod__Suc__eq__Suc__mod_0_0,def_lhs_atom48]) ).

fof(def_lhs_atom49,axiom,
    ! [V_x] :
      ( lhs_atom49(V_x)
    <=> c_HOL_Oord__class_Oless(V_x,c_Suc(V_x),tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_48,plain,
    ! [V_x] :
      ( lhs_atom49(V_x)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_less__Suc__eq_2_0,def_lhs_atom49]) ).

fof(def_lhs_atom50,axiom,
    ! [V_n] :
      ( lhs_atom50(V_n)
    <=> c_HOL_Oord__class_Oless(V_n,c_Suc(V_n),tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_49,plain,
    ! [V_n] :
      ( lhs_atom50(V_n)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_lessI_0_0,def_lhs_atom50]) ).

fof(def_lhs_atom51,axiom,
    ! [V_n,V_m] :
      ( lhs_atom51(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_50,plain,
    ! [V_m,V_n] :
      ( lhs_atom51(V_n,V_m)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_add__Suc_0_0,def_lhs_atom51]) ).

fof(def_lhs_atom52,axiom,
    ! [V_n,V_m] :
      ( lhs_atom52(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_51,plain,
    ! [V_m,V_n] :
      ( lhs_atom52(V_n,V_m)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_add__Suc__right_0_0,def_lhs_atom52]) ).

fof(def_lhs_atom53,axiom,
    ! [V_n,V_m] :
      ( lhs_atom53(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_52,plain,
    ! [V_m,V_n] :
      ( lhs_atom53(V_n,V_m)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_add__Suc__shift_0_0,def_lhs_atom53]) ).

fof(def_lhs_atom54,axiom,
    ! [V_dB_H,V_dB2,V_dB1] :
      ( lhs_atom54(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_53,plain,
    ! [V_dB1,V_dB2,V_dB_H] :
      ( lhs_atom54(V_dB_H,V_dB2,V_dB1)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_dB_Osimps_I8_J_0_0,def_lhs_atom54]) ).

fof(def_lhs_atom55,axiom,
    ! [V_dB_H,V_dB2,V_dB1] :
      ( lhs_atom55(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_54,plain,
    ! [V_dB1,V_dB2,V_dB_H] :
      ( lhs_atom55(V_dB_H,V_dB2,V_dB1)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_dB_Osimps_I9_J_0_0,def_lhs_atom55]) ).

fof(def_lhs_atom56,axiom,
    ! [V_t,V_s,V_k] :
      ( lhs_atom56(V_t,V_s,V_k)
    <=> hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_t)),V_k) = hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_Olift,V_s),V_k)),hAPP(hAPP(c_Lambda_Olift,V_t),V_k)) ),
    inference(definition,[],]) ).

fof(to_be_clausified_55,plain,
    ! [V_k,V_s,V_t] :
      ( lhs_atom56(V_t,V_s,V_k)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_lift_Osimps_I2_J_0_0,def_lhs_atom56]) ).

fof(def_lhs_atom57,axiom,
    ! [V_f3,V_f2,V_f1,V_dB2,V_dB1,T_a] :
      ( lhs_atom57(V_f3,V_f2,V_f1,V_dB2,V_dB1,T_a)
    <=> c_Lambda_OdB_OdB__case(V_f1,V_f2,V_f3,hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2),T_a) = hAPP(hAPP(V_f2,V_dB1),V_dB2) ),
    inference(definition,[],]) ).

fof(to_be_clausified_56,plain,
    ! [T_a,V_dB1,V_dB2,V_f1,V_f2,V_f3] :
      ( lhs_atom57(V_f3,V_f2,V_f1,V_dB2,V_dB1,T_a)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_dB_Osimps_I11_J_0_0,def_lhs_atom57]) ).

fof(def_lhs_atom58,axiom,
    ! [V_u,V_t,V_s,V_k] :
      ( lhs_atom58(V_u,V_t,V_s,V_k)
    <=> c_Lambda_Osubstn(hAPP(hAPP(c_Lambda_OdB_OApp,V_t),V_u),V_s,V_k) = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Osubstn(V_t,V_s,V_k)),c_Lambda_Osubstn(V_u,V_s,V_k)) ),
    inference(definition,[],]) ).

fof(to_be_clausified_57,plain,
    ! [V_k,V_s,V_t,V_u] :
      ( lhs_atom58(V_u,V_t,V_s,V_k)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_substn_Osimps_I2_J_0_0,def_lhs_atom58]) ).

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

fof(to_be_clausified_58,plain,
    ! [T_a,T_b,V_f] :
      ( lhs_atom59(V_f,T_b,T_a)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_map__is__Nil__conv_1_0,def_lhs_atom59]) ).

fof(to_be_clausified_59,plain,
    ! [T_a,T_b,V_f] :
      ( lhs_atom59(V_f,T_b,T_a)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_Nil__is__map__conv_1_0,def_lhs_atom59]) ).

fof(def_lhs_atom60,axiom,
    ! [V_r] :
      ( lhs_atom60(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_60,plain,
    ! [V_r] :
      ( lhs_atom60(V_r)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_Abs__eq__apps__conv_2_0,def_lhs_atom60]) ).

fof(def_lhs_atom61,axiom,
    ! [V_r] :
      ( lhs_atom61(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_61,plain,
    ! [V_r] :
      ( lhs_atom61(V_r)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_apps__eq__Abs__conv_2_0,def_lhs_atom61]) ).

fof(def_lhs_atom62,axiom,
    ! [V_f,V_a,T_b,T_a] :
      ( lhs_atom62(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_62,plain,
    ! [T_a,T_b,V_a,V_f] :
      ( lhs_atom62(V_f,V_a,T_b,T_a)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_foldl__Nil_0_0,def_lhs_atom62]) ).

fof(def_lhs_atom63,axiom,
    ! [V_t,V_s,V_k] :
      ( lhs_atom63(V_t,V_s,V_k)
    <=> hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,V_t),V_k)),V_s),V_k) = V_t ),
    inference(definition,[],]) ).

fof(to_be_clausified_63,plain,
    ! [V_k,V_s,V_t] :
      ( lhs_atom63(V_t,V_s,V_k)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_subst__lift_0_0,def_lhs_atom63]) ).

fof(def_lhs_atom64,axiom,
    ! [V_nat,V_dB_H] :
      ( lhs_atom64(V_nat,V_dB_H)
    <=> c_Lambda_OdB_OAbs(V_dB_H) != c_Lambda_OdB_OVar(V_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_64,plain,
    ! [V_dB_H,V_nat] :
      ( lhs_atom64(V_nat,V_dB_H)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_dB_Osimps_I7_J_0_0,def_lhs_atom64]) ).

fof(def_lhs_atom65,axiom,
    ! [V_t,V_i] :
      ( lhs_atom65(V_t,V_i)
    <=> ~ c_Lambda_Obeta(c_Lambda_OdB_OVar(V_i),V_t) ),
    inference(definition,[],]) ).

fof(to_be_clausified_65,plain,
    ! [V_i,V_t] :
      ( lhs_atom65(V_t,V_i)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_beta__cases_I1_J_0_0,def_lhs_atom65]) ).

fof(def_lhs_atom66,axiom,
    ! [V_nat,V_dB_H] :
      ( lhs_atom66(V_nat,V_dB_H)
    <=> c_Lambda_OdB_OVar(V_nat) != c_Lambda_OdB_OAbs(V_dB_H) ),
    inference(definition,[],]) ).

fof(to_be_clausified_66,plain,
    ! [V_dB_H,V_nat] :
      ( lhs_atom66(V_nat,V_dB_H)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_dB_Osimps_I6_J_0_0,def_lhs_atom66]) ).

fof(def_lhs_atom67,axiom,
    ! [V_p] :
      ( lhs_atom67(V_p)
    <=> c_Power_Opower__class_Opower(V_p,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Oone__class_Oone(tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_67,plain,
    ! [V_p] :
      ( lhs_atom67(V_p)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_power__eq__if_0_0,def_lhs_atom67]) ).

fof(def_lhs_atom68,axiom,
    ! [V_n,V_m] :
      ( lhs_atom68(V_n,V_m)
    <=> c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_68,plain,
    ! [V_m,V_n] :
      ( lhs_atom68(V_n,V_m)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_nat__mult__div__cancel__disj_0_0,def_lhs_atom68]) ).

fof(def_lhs_atom69,axiom,
    ! [V_c,V_b,V_a] :
      ( lhs_atom69(V_c,V_b,V_a)
    <=> c_Divides_Odiv__class_Omod(V_a,c_HOL_Otimes__class_Otimes(V_b,V_c,tc_nat),tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_b,c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Odiv(V_a,V_b,tc_nat),V_c,tc_nat),tc_nat)),c_Divides_Odiv__class_Omod(V_a,V_b,tc_nat)) ),
    inference(definition,[],]) ).

fof(to_be_clausified_69,plain,
    ! [V_a,V_b,V_c] :
      ( lhs_atom69(V_c,V_b,V_a)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_mod__mult2__eq_0_0,def_lhs_atom69]) ).

fof(def_lhs_atom70,axiom,
    ! [V_j,V_i] :
      ( lhs_atom70(V_j,V_i)
    <=> ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_j),V_i,tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_70,plain,
    ! [V_i,V_j] :
      ( lhs_atom70(V_j,V_i)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_not__add__less1_0_0,def_lhs_atom70]) ).

fof(def_lhs_atom71,axiom,
    ! [V_j,V_i] :
      ( lhs_atom71(V_j,V_i)
    <=> ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_j),V_i),V_i,tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_71,plain,
    ! [V_i,V_j] :
      ( lhs_atom71(V_j,V_i)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_not__add__less2_0_0,def_lhs_atom71]) ).

fof(def_lhs_atom72,axiom,
    ! [V_c,V_b,V_a] :
      ( lhs_atom72(V_c,V_b,V_a)
    <=> c_Divides_Odiv__class_Odiv(V_a,c_HOL_Otimes__class_Otimes(V_b,V_c,tc_nat),tc_nat) = c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Odiv(V_a,V_b,tc_nat),V_c,tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_72,plain,
    ! [V_a,V_b,V_c] :
      ( lhs_atom72(V_c,V_b,V_a)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_div__mult2__eq_0_0,def_lhs_atom72]) ).

fof(def_lhs_atom73,axiom,
    ! [V_x,V_d] :
      ( lhs_atom73(V_x,V_d)
    <=> c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_d,V_x,tc_nat),V_d,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_73,plain,
    ! [V_d,V_x] :
      ( lhs_atom73(V_x,V_d)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_mod__eq__0__iff_1_0,def_lhs_atom73]) ).

fof(def_lhs_atom74,axiom,
    ! [V_s,V_k] :
      ( lhs_atom74(V_s,V_k)
    <=> hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OAbs(V_s)),V_k) = c_Lambda_OdB_OAbs(hAPP(hAPP(c_Lambda_Olift,V_s),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),c_HOL_Oone__class_Oone(tc_nat)))) ),
    inference(definition,[],]) ).

fof(to_be_clausified_74,plain,
    ! [V_k,V_s] :
      ( lhs_atom74(V_s,V_k)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_lift_Osimps_I3_J_0_0,def_lhs_atom74]) ).

fof(def_lhs_atom75,axiom,
    ! [V_dB] :
      ( lhs_atom75(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_75,plain,
    ! [V_dB] :
      ( lhs_atom75(V_dB)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_dB_Osize_I3_J_0_0,def_lhs_atom75]) ).

fof(def_lhs_atom76,axiom,
    ! [V_n,V_m,V_k] :
      ( lhs_atom76(V_n,V_m,V_k)
    <=> c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),V_k,tc_nat) = c_HOL_Otimes__class_Otimes(V_m,c_HOL_Otimes__class_Otimes(V_n,V_k,tc_nat),tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_76,plain,
    ! [V_k,V_m,V_n] :
      ( lhs_atom76(V_n,V_m,V_k)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_nat__mult__assoc_0_0,def_lhs_atom76]) ).

fof(def_lhs_atom77,axiom,
    ! [V_n,V_m,V_k] :
      ( lhs_atom77(V_n,V_m,V_k)
    <=> c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n),V_k,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_m,V_k,tc_nat)),c_HOL_Otimes__class_Otimes(V_n,V_k,tc_nat)) ),
    inference(definition,[],]) ).

fof(to_be_clausified_77,plain,
    ! [V_k,V_m,V_n] :
      ( lhs_atom77(V_n,V_m,V_k)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_add__mult__distrib_0_0,def_lhs_atom77]) ).

fof(def_lhs_atom78,axiom,
    ! [V_n,V_m,V_k] :
      ( lhs_atom78(V_n,V_m,V_k)
    <=> c_HOL_Otimes__class_Otimes(V_k,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n),tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat)),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat)) ),
    inference(definition,[],]) ).

fof(to_be_clausified_78,plain,
    ! [V_k,V_m,V_n] :
      ( lhs_atom78(V_n,V_m,V_k)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_add__mult__distrib2_0_0,def_lhs_atom78]) ).

fof(def_lhs_atom79,axiom,
    ! [V_nat,V_f3,V_f2,V_f1,T_a] :
      ( lhs_atom79(V_nat,V_f3,V_f2,V_f1,T_a)
    <=> c_Lambda_OdB_OdB__case(V_f1,V_f2,V_f3,c_Lambda_OdB_OVar(V_nat),T_a) = hAPP(V_f1,V_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_79,plain,
    ! [T_a,V_f1,V_f2,V_f3,V_nat] :
      ( lhs_atom79(V_nat,V_f3,V_f2,V_f1,T_a)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_dB_Osimps_I10_J_0_0,def_lhs_atom79]) ).

fof(def_lhs_atom80,axiom,
    ! [V_x,V_env] :
      ( lhs_atom80(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_80,plain,
    ! [V_env,V_x] :
      ( lhs_atom80(V_x,V_env)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_typing_OVar_0_0,def_lhs_atom80]) ).

fof(def_lhs_atom81,axiom,
    ! [V_dB2,V_dB1] :
      ( lhs_atom81(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_81,plain,
    ! [V_dB1,V_dB2] :
      ( lhs_atom81(V_dB2,V_dB1)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_dB_Osize_I2_J_0_0,def_lhs_atom81]) ).

fof(def_lhs_atom82,axiom,
    ! [V_dB2,V_dB1] :
      ( lhs_atom82(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_82,plain,
    ! [V_dB1,V_dB2] :
      ( lhs_atom82(V_dB2,V_dB1)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_dB_Osize_I5_J_0_0,def_lhs_atom82]) ).

fof(def_lhs_atom83,axiom,
    ! [V_t,V_s] :
      ( lhs_atom83(V_t,V_s)
    <=> c_Lambda_Obeta(hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_s)),V_t),hAPP(hAPP(hAPP(c_Lambda_Osubst,V_s),V_t),c_HOL_Ozero__class_Ozero(tc_nat))) ),
    inference(definition,[],]) ).

fof(to_be_clausified_83,plain,
    ! [V_s,V_t] :
      ( lhs_atom83(V_t,V_s)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_beta_0_0,def_lhs_atom83]) ).

fof(def_lhs_atom84,axiom,
    ( lhs_atom84
  <=> 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_84,plain,
    ( lhs_atom84
    | $false ),
    inference(fold_definition,[status(thm)],[cls_add__is__1_5_0,def_lhs_atom84]) ).

fof(def_lhs_atom85,axiom,
    ( lhs_atom85
  <=> 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_85,plain,
    ( lhs_atom85
    | $false ),
    inference(fold_definition,[status(thm)],[cls_one__is__add_4_0,def_lhs_atom85]) ).

fof(def_lhs_atom86,axiom,
    ! [V_m] :
      ( lhs_atom86(V_m)
    <=> c_Divides_Odiv__class_Omod(V_m,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_86,plain,
    ! [V_m] :
      ( lhs_atom86(V_m)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_mod__1_0_0,def_lhs_atom86]) ).

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

fof(to_be_clausified_87,plain,
    ( lhs_atom87
    | $false ),
    inference(fold_definition,[status(thm)],[cls_mult__eq__1__iff_2_0,def_lhs_atom87]) ).

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

fof(to_be_clausified_88,plain,
    ( lhs_atom88
    | $false ),
    inference(fold_definition,[status(thm)],[cls_dvd__1__iff__1_1_0,def_lhs_atom88]) ).

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

fof(to_be_clausified_89,plain,
    ( lhs_atom89
    | $false ),
    inference(fold_definition,[status(thm)],[cls_less__Suc0_1_0,def_lhs_atom89]) ).

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

fof(to_be_clausified_90,plain,
    ( lhs_atom90
    | $false ),
    inference(fold_definition,[status(thm)],[cls_One__nat__def_0_0,def_lhs_atom90]) ).

fof(def_lhs_atom91,axiom,
    ! [V_i,V_e,V_U,V_T,T_a] :
      ( lhs_atom91(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_91,plain,
    ! [T_a,V_T,V_U,V_e,V_i] :
      ( lhs_atom91(V_i,V_e,V_U,V_T,T_a)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_shift__commute_0_0,def_lhs_atom91]) ).

fof(def_lhs_atom92,axiom,
    ! [V_x] :
      ( lhs_atom92(V_x)
    <=> c_Power_Opower__class_Opower(V_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    inference(definition,[],]) ).

fof(to_be_clausified_92,plain,
    ! [V_x] :
      ( lhs_atom92(V_x)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_nat__power__eq__Suc__0__iff_1_0,def_lhs_atom92]) ).

fof(def_lhs_atom93,axiom,
    ( lhs_atom93
  <=> 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_93,plain,
    ( lhs_atom93
    | $false ),
    inference(fold_definition,[status(thm)],[cls_add__is__1_4_0,def_lhs_atom93]) ).

fof(def_lhs_atom94,axiom,
    ! [V_k] :
      ( lhs_atom94(V_k)
    <=> c_Ring__and__Field_Odvd__class_Odvd(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_k,tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_94,plain,
    ! [V_k] :
      ( lhs_atom94(V_k)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_dvd__1__left_0_0,def_lhs_atom94]) ).

fof(def_lhs_atom95,axiom,
    ( lhs_atom95
  <=> 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_95,plain,
    ( lhs_atom95
    | $false ),
    inference(fold_definition,[status(thm)],[cls_one__is__add_5_0,def_lhs_atom95]) ).

fof(def_lhs_atom96,axiom,
    ! [V_n] :
      ( lhs_atom96(V_n)
    <=> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(V_n),tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_96,plain,
    ! [V_n] :
      ( lhs_atom96(V_n)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_zero__less__Suc_0_0,def_lhs_atom96]) ).

fof(def_lhs_atom97,axiom,
    ! [V_x] :
      ( lhs_atom97(V_x)
    <=> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(V_x),tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_97,plain,
    ! [V_x] :
      ( lhs_atom97(V_x)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_gr0__conv__Suc_1_0,def_lhs_atom97]) ).

fof(def_lhs_atom98,axiom,
    ! [V_m] :
      ( lhs_atom98(V_m)
    <=> c_Power_Opower__class_Opower(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_m,tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    inference(definition,[],]) ).

fof(to_be_clausified_98,plain,
    ! [V_m] :
      ( lhs_atom98(V_m)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_nat__power__eq__Suc__0__iff_2_0,def_lhs_atom98]) ).

fof(def_lhs_atom99,axiom,
    ! [V_n] :
      ( lhs_atom99(V_n)
    <=> c_Power_Opower__class_Opower(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_n,tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    inference(definition,[],]) ).

fof(to_be_clausified_99,plain,
    ! [V_n] :
      ( lhs_atom99(V_n)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_power__Suc__0_0_0,def_lhs_atom99]) ).

fof(def_lhs_atom100,axiom,
    ! [V_m] :
      ( lhs_atom100(V_m)
    <=> c_Divides_Odiv__class_Odiv(V_m,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = V_m ),
    inference(definition,[],]) ).

fof(to_be_clausified_100,plain,
    ! [V_m] :
      ( lhs_atom100(V_m)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_div__1_0_0,def_lhs_atom100]) ).

fof(def_lhs_atom101,axiom,
    ! [V_t,V_s] :
      ( lhs_atom101(V_t,V_s)
    <=> c_Lambda_Osubstn(V_t,V_s,c_HOL_Ozero__class_Ozero(tc_nat)) = hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_s),c_HOL_Ozero__class_Ozero(tc_nat)) ),
    inference(definition,[],]) ).

fof(to_be_clausified_101,plain,
    ! [V_s,V_t] :
      ( lhs_atom101(V_t,V_s)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_substn__subst__0_0_0,def_lhs_atom101]) ).

fof(def_lhs_atom102,axiom,
    ! [V_nat] :
      ( lhs_atom102(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_102,plain,
    ! [V_nat] :
      ( lhs_atom102(V_nat)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_dB_Osize_I4_J_0_0,def_lhs_atom102]) ).

fof(def_lhs_atom103,axiom,
    ! [V_nat] :
      ( lhs_atom103(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_103,plain,
    ! [V_nat] :
      ( lhs_atom103(V_nat)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_dB_Osize_I1_J_0_0,def_lhs_atom103]) ).

fof(def_lhs_atom104,axiom,
    ! [V_s,V_r] :
      ( lhs_atom104(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_104,plain,
    ! [V_r,V_s] :
      ( lhs_atom104(V_s,V_r)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_App__eq__foldl__conv_4_0,def_lhs_atom104]) ).

fof(def_lhs_atom105,axiom,
    ! [V_ts,V_ss,V_r,V_n] :
      ( lhs_atom105(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_105,plain,
    ! [V_n,V_r,V_ss,V_ts] :
      ( lhs_atom105(V_ts,V_ss,V_r,V_n)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_Var__apps__neq__Abs__apps_0_0,def_lhs_atom105]) ).

fof(def_lhs_atom106,axiom,
    ! [V_m] :
      ( lhs_atom106(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_106,plain,
    ! [V_m] :
      ( lhs_atom106(V_m)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_Var__eq__apps__conv_2_0,def_lhs_atom106]) ).

fof(def_lhs_atom107,axiom,
    ! [V_t,V_ss,V_s,V_n] :
      ( lhs_atom107(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_107,plain,
    ! [V_n,V_s,V_ss,V_t] :
      ( lhs_atom107(V_t,V_ss,V_s,V_n)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_Abs__App__neq__Var__apps_0_0,def_lhs_atom107]) ).

fof(def_lhs_atom108,axiom,
    ! [V_ts,V_t,V_i] :
      ( lhs_atom108(V_ts,V_t,V_i)
    <=> hAPP(hAPP(c_Lambda_Olift,c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB)),V_i) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_Olift,V_t),V_i),c_List_Omap(c_COMBC(c_Lambda_Olift,V_i,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) ),
    inference(definition,[],]) ).

fof(to_be_clausified_108,plain,
    ! [V_i,V_t,V_ts] :
      ( lhs_atom108(V_ts,V_t,V_i)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_lift__map_0_0,def_lhs_atom108]) ).

fof(def_lhs_atom109,axiom,
    ! [V_u,V_t,V_s,V_k] :
      ( lhs_atom109(V_u,V_t,V_s,V_k)
    <=> hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_OdB_OApp,V_t),V_u)),V_s),V_k) = hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_s),V_k)),hAPP(hAPP(hAPP(c_Lambda_Osubst,V_u),V_s),V_k)) ),
    inference(definition,[],]) ).

fof(to_be_clausified_109,plain,
    ! [V_k,V_s,V_t,V_u] :
      ( lhs_atom109(V_u,V_t,V_s,V_k)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_subst__App_0_0,def_lhs_atom109]) ).

fof(def_lhs_atom110,axiom,
    ! [V_u,V_k] :
      ( lhs_atom110(V_u,V_k)
    <=> hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(V_k)),V_u),V_k) = V_u ),
    inference(definition,[],]) ).

fof(to_be_clausified_110,plain,
    ! [V_k,V_u] :
      ( lhs_atom110(V_u,V_k)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_subst__eq_0_0,def_lhs_atom110]) ).

fof(def_lhs_atom111,axiom,
    ! [V_n] :
      ( lhs_atom111(V_n)
    <=> V_n != c_Suc(V_n) ),
    inference(definition,[],]) ).

fof(to_be_clausified_111,plain,
    ! [V_n] :
      ( lhs_atom111(V_n)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_n__not__Suc__n_0_0,def_lhs_atom111]) ).

fof(def_lhs_atom112,axiom,
    ! [V_n] :
      ( lhs_atom112(V_n)
    <=> c_Suc(V_n) != V_n ),
    inference(definition,[],]) ).

fof(to_be_clausified_112,plain,
    ! [V_n] :
      ( lhs_atom112(V_n)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_Suc__n__not__n_0_0,def_lhs_atom112]) ).

fof(def_lhs_atom113,axiom,
    ! [V_m] :
      ( lhs_atom113(V_m)
    <=> c_Suc(V_m) != c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_113,plain,
    ! [V_m] :
      ( lhs_atom113(V_m)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_Suc__neq__Zero_0_0,def_lhs_atom113]) ).

fof(def_lhs_atom114,axiom,
    ! [V_nat_H] :
      ( lhs_atom114(V_nat_H)
    <=> c_Suc(V_nat_H) != c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_114,plain,
    ! [V_nat_H] :
      ( lhs_atom114(V_nat_H)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_nat_Osimps_I3_J_0_0,def_lhs_atom114]) ).

fof(def_lhs_atom115,axiom,
    ! [V_nat,V_dB2_H,V_dB1_H] :
      ( lhs_atom115(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_115,plain,
    ! [V_dB1_H,V_dB2_H,V_nat] :
      ( lhs_atom115(V_nat,V_dB2_H,V_dB1_H)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_dB_Osimps_I4_J_0_0,def_lhs_atom115]) ).

fof(def_lhs_atom116,axiom,
    ! [V_u,V_ts,V_t,V_i] :
      ( lhs_atom116(V_u,V_ts,V_t,V_i)
    <=> hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB)),V_u),V_i) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_u),V_i),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,V_u,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),V_i,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) ),
    inference(definition,[],]) ).

fof(to_be_clausified_116,plain,
    ! [V_i,V_t,V_ts,V_u] :
      ( lhs_atom116(V_u,V_ts,V_t,V_i)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_subst__map_0_0,def_lhs_atom116]) ).

fof(def_lhs_atom117,axiom,
    ! [V_m] :
      ( lhs_atom117(V_m)
    <=> c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(V_m) ),
    inference(definition,[],]) ).

fof(to_be_clausified_117,plain,
    ! [V_m] :
      ( lhs_atom117(V_m)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_Zero__neq__Suc_0_0,def_lhs_atom117]) ).

fof(def_lhs_atom118,axiom,
    ! [V_nat_H] :
      ( lhs_atom118(V_nat_H)
    <=> c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(V_nat_H) ),
    inference(definition,[],]) ).

fof(to_be_clausified_118,plain,
    ! [V_nat_H] :
      ( lhs_atom118(V_nat_H)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_nat_Osimps_I2_J_0_0,def_lhs_atom118]) ).

fof(def_lhs_atom119,axiom,
    ! [V_R,V_Q,V_P,T_c,T_b,T_a] :
      ( lhs_atom119(V_R,V_Q,V_P,T_c,T_b,T_a)
    <=> hAPP(c_COMBC(V_P,V_Q,T_b,T_c,T_a),V_R) = hAPP(hAPP(V_P,V_R),V_Q) ),
    inference(definition,[],]) ).

fof(to_be_clausified_119,plain,
    ! [T_a,T_b,T_c,V_P,V_Q,V_R] :
      ( lhs_atom119(V_R,V_Q,V_P,T_c,T_b,T_a)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_COMBC__def_0_0,def_lhs_atom119]) ).

fof(def_lhs_atom120,axiom,
    ! [V_nat,V_dB2_H,V_dB1_H] :
      ( lhs_atom120(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_120,plain,
    ! [V_dB1_H,V_dB2_H,V_nat] :
      ( lhs_atom120(V_nat,V_dB2_H,V_dB1_H)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_dB_Osimps_I5_J_0_0,def_lhs_atom120]) ).

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

fof(to_be_clausified_121,plain,
    ( lhs_atom121
    | $false ),
    inference(fold_definition,[status(thm)],[clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add_0,def_lhs_atom121]) ).

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

fof(to_be_clausified_122,plain,
    ( lhs_atom122
    | $false ),
    inference(fold_definition,[status(thm)],[clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le_0,def_lhs_atom122]) ).

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

fof(to_be_clausified_123,plain,
    ( lhs_atom123
    | $false ),
    inference(fold_definition,[status(thm)],[clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict_0,def_lhs_atom123]) ).

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

fof(to_be_clausified_124,plain,
    ( lhs_atom124
    | $false ),
    inference(fold_definition,[status(thm)],[clsarity_nat__Ring__and__Field_Oordered__semiring__strict_0,def_lhs_atom124]) ).

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

fof(to_be_clausified_125,plain,
    ( lhs_atom125
    | $false ),
    inference(fold_definition,[status(thm)],[clsarity_nat__OrderedGroup_Opordered__comm__monoid__add_0,def_lhs_atom125]) ).

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

fof(to_be_clausified_126,plain,
    ( lhs_atom126
    | $false ),
    inference(fold_definition,[status(thm)],[clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add_0,def_lhs_atom126]) ).

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

fof(to_be_clausified_127,plain,
    ( lhs_atom127
    | $false ),
    inference(fold_definition,[status(thm)],[clsarity_nat__OrderedGroup_Ocancel__semigroup__add_0,def_lhs_atom127]) ).

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

fof(to_be_clausified_128,plain,
    ( lhs_atom128
    | $false ),
    inference(fold_definition,[status(thm)],[clsarity_nat__Ring__and__Field_Ono__zero__divisors_0,def_lhs_atom128]) ).

fof(def_lhs_atom129,axiom,
    ( lhs_atom129
  <=> class_Ring__and__Field_Oordered__semidom(tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_129,plain,
    ( lhs_atom129
    | $false ),
    inference(fold_definition,[status(thm)],[clsarity_nat__Ring__and__Field_Oordered__semidom_0,def_lhs_atom129]) ).

fof(def_lhs_atom130,axiom,
    ( lhs_atom130
  <=> class_Ring__and__Field_Ocomm__semiring__1(tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_130,plain,
    ( lhs_atom130
    | $false ),
    inference(fold_definition,[status(thm)],[clsarity_nat__Ring__and__Field_Ocomm__semiring__1_0,def_lhs_atom130]) ).

fof(def_lhs_atom131,axiom,
    ( lhs_atom131
  <=> class_OrderedGroup_Oab__semigroup__mult(tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_131,plain,
    ( lhs_atom131
    | $false ),
    inference(fold_definition,[status(thm)],[clsarity_nat__OrderedGroup_Oab__semigroup__mult_0,def_lhs_atom131]) ).

fof(def_lhs_atom132,axiom,
    ( lhs_atom132
  <=> class_OrderedGroup_Ocomm__monoid__mult(tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_132,plain,
    ( lhs_atom132
    | $false ),
    inference(fold_definition,[status(thm)],[clsarity_nat__OrderedGroup_Ocomm__monoid__mult_0,def_lhs_atom132]) ).

fof(def_lhs_atom133,axiom,
    ( lhs_atom133
  <=> class_OrderedGroup_Oab__semigroup__add(tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_133,plain,
    ( lhs_atom133
    | $false ),
    inference(fold_definition,[status(thm)],[clsarity_nat__OrderedGroup_Oab__semigroup__add_0,def_lhs_atom133]) ).

fof(def_lhs_atom134,axiom,
    ( lhs_atom134
  <=> class_Ring__and__Field_Ocomm__semiring(tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_134,plain,
    ( lhs_atom134
    | $false ),
    inference(fold_definition,[status(thm)],[clsarity_nat__Ring__and__Field_Ocomm__semiring_0,def_lhs_atom134]) ).

fof(def_lhs_atom135,axiom,
    ( lhs_atom135
  <=> class_OrderedGroup_Ocomm__monoid__add(tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_135,plain,
    ( lhs_atom135
    | $false ),
    inference(fold_definition,[status(thm)],[clsarity_nat__OrderedGroup_Ocomm__monoid__add_0,def_lhs_atom135]) ).

fof(def_lhs_atom136,axiom,
    ( lhs_atom136
  <=> class_Ring__and__Field_Ozero__neq__one(tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_136,plain,
    ( lhs_atom136
    | $false ),
    inference(fold_definition,[status(thm)],[clsarity_nat__Ring__and__Field_Ozero__neq__one_0,def_lhs_atom136]) ).

fof(def_lhs_atom137,axiom,
    ( lhs_atom137
  <=> class_OrderedGroup_Osemigroup__add(tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_137,plain,
    ( lhs_atom137
    | $false ),
    inference(fold_definition,[status(thm)],[clsarity_nat__OrderedGroup_Osemigroup__add_0,def_lhs_atom137]) ).

fof(def_lhs_atom138,axiom,
    ( lhs_atom138
  <=> class_Ring__and__Field_Osemiring__1(tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_138,plain,
    ( lhs_atom138
    | $false ),
    inference(fold_definition,[status(thm)],[clsarity_nat__Ring__and__Field_Osemiring__1_0,def_lhs_atom138]) ).

fof(def_lhs_atom139,axiom,
    ( lhs_atom139
  <=> class_Ring__and__Field_Osemiring__0(tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_139,plain,
    ( lhs_atom139
    | $false ),
    inference(fold_definition,[status(thm)],[clsarity_nat__Ring__and__Field_Osemiring__0_0,def_lhs_atom139]) ).

fof(def_lhs_atom140,axiom,
    ( lhs_atom140
  <=> class_Ring__and__Field_Omult__zero(tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_140,plain,
    ( lhs_atom140
    | $false ),
    inference(fold_definition,[status(thm)],[clsarity_nat__Ring__and__Field_Omult__zero_0,def_lhs_atom140]) ).

fof(def_lhs_atom141,axiom,
    ( lhs_atom141
  <=> class_OrderedGroup_Omonoid__mult(tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_141,plain,
    ( lhs_atom141
    | $false ),
    inference(fold_definition,[status(thm)],[clsarity_nat__OrderedGroup_Omonoid__mult_0,def_lhs_atom141]) ).

fof(def_lhs_atom142,axiom,
    ( lhs_atom142
  <=> class_Ring__and__Field_Osemiring(tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_142,plain,
    ( lhs_atom142
    | $false ),
    inference(fold_definition,[status(thm)],[clsarity_nat__Ring__and__Field_Osemiring_0,def_lhs_atom142]) ).

fof(def_lhs_atom143,axiom,
    ( lhs_atom143
  <=> class_OrderedGroup_Omonoid__add(tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_143,plain,
    ( lhs_atom143
    | $false ),
    inference(fold_definition,[status(thm)],[clsarity_nat__OrderedGroup_Omonoid__add_0,def_lhs_atom143]) ).

fof(def_lhs_atom144,axiom,
    ( lhs_atom144
  <=> class_Divides_Osemiring__div(tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_144,plain,
    ( lhs_atom144
    | $false ),
    inference(fold_definition,[status(thm)],[clsarity_nat__Divides_Osemiring__div_0,def_lhs_atom144]) ).

fof(def_lhs_atom145,axiom,
    ( lhs_atom145
  <=> class_Nat_Osemiring__char__0(tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_145,plain,
    ( lhs_atom145
    | $false ),
    inference(fold_definition,[status(thm)],[clsarity_nat__Nat_Osemiring__char__0_0,def_lhs_atom145]) ).

fof(def_lhs_atom146,axiom,
    ( lhs_atom146
  <=> class_Ring__and__Field_Odvd(tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_146,plain,
    ( lhs_atom146
    | $false ),
    inference(fold_definition,[status(thm)],[clsarity_nat__Ring__and__Field_Odvd_0,def_lhs_atom146]) ).

fof(def_lhs_atom147,axiom,
    ( lhs_atom147
  <=> class_Orderings_Opreorder(tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_147,plain,
    ( lhs_atom147
    | $false ),
    inference(fold_definition,[status(thm)],[clsarity_nat__Orderings_Opreorder_0,def_lhs_atom147]) ).

fof(def_lhs_atom148,axiom,
    ( lhs_atom148
  <=> class_Orderings_Olinorder(tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_148,plain,
    ( lhs_atom148
    | $false ),
    inference(fold_definition,[status(thm)],[clsarity_nat__Orderings_Olinorder_0,def_lhs_atom148]) ).

fof(def_lhs_atom149,axiom,
    ( lhs_atom149
  <=> class_Orderings_Oorder(tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_149,plain,
    ( lhs_atom149
    | $false ),
    inference(fold_definition,[status(thm)],[clsarity_nat__Orderings_Oorder_0,def_lhs_atom149]) ).

fof(def_lhs_atom150,axiom,
    ( lhs_atom150
  <=> class_Power_Opower(tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_150,plain,
    ( lhs_atom150
    | $false ),
    inference(fold_definition,[status(thm)],[clsarity_nat__Power_Opower_0,def_lhs_atom150]) ).

fof(to_be_clausified_151,plain,
    ! [T_a,T_b,T_c,V_P,V_Q,V_R] :
      ( lhs_atom119(V_R,V_Q,V_P,T_c,T_b,T_a)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_ATP__Linkup_OCOMBC__def_0_0,def_lhs_atom119]) ).

fof(def_lhs_atom151,axiom,
    ! [V_R,V_Q,V_P,T_c,T_b,T_a] :
      ( lhs_atom151(V_R,V_Q,V_P,T_c,T_b,T_a)
    <=> c_COMBB(V_P,V_Q,V_R,T_b,T_a,T_c) = hAPP(V_P,hAPP(V_Q,V_R)) ),
    inference(definition,[],]) ).

fof(to_be_clausified_152,plain,
    ! [T_a,T_b,T_c,V_P,V_Q,V_R] :
      ( lhs_atom151(V_R,V_Q,V_P,T_c,T_b,T_a)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_ATP__Linkup_OCOMBB__def_0_0,def_lhs_atom151]) ).

fof(def_lhs_atom152,axiom,
    ! [V_x,T_a] :
      ( lhs_atom152(V_x,T_a)
    <=> c_fequal(V_x,V_x,T_a) ),
    inference(definition,[],]) ).

fof(to_be_clausified_153,plain,
    ! [T_a,V_x] :
      ( lhs_atom152(V_x,T_a)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_ATP__Linkup_Oequal__imp__fequal_0_0,def_lhs_atom152]) ).

% Start CNF derivation
fof(c_0_0,axiom,
    ! [X39,X40,X41,X42,X28,X16] :
      ( lhs_atom151(X39,X40,X41,X42,X28,X16)
      | ~ $true ),
    file('<stdin>',to_be_clausified_152) ).

fof(c_0_1,axiom,
    ! [X39,X40,X41,X42,X28,X16] :
      ( lhs_atom119(X39,X40,X41,X42,X28,X16)
      | ~ $true ),
    file('<stdin>',to_be_clausified_151) ).

fof(c_0_2,axiom,
    ! [X39,X40,X41,X42,X28,X16] :
      ( lhs_atom119(X39,X40,X41,X42,X28,X16)
      | ~ $true ),
    file('<stdin>',to_be_clausified_119) ).

fof(c_0_3,axiom,
    ! [X12,X13,X14,X25,X26,X16] :
      ( lhs_atom57(X12,X13,X14,X25,X26,X16)
      | ~ $true ),
    file('<stdin>',to_be_clausified_56) ).

fof(c_0_4,axiom,
    ! [X4,X22,X33,X23,X16] :
      ( lhs_atom91(X4,X22,X33,X23,X16)
      | ~ $true ),
    file('<stdin>',to_be_clausified_91) ).

fof(c_0_5,axiom,
    ! [X30,X12,X13,X14,X16] :
      ( lhs_atom79(X30,X12,X13,X14,X16)
      | ~ $true ),
    file('<stdin>',to_be_clausified_79) ).

fof(c_0_6,axiom,
    ! [X12,X13,X14,X15,X16] :
      ( lhs_atom8(X12,X13,X14,X15,X16)
      | ~ $true ),
    file('<stdin>',to_be_clausified_7) ).

fof(c_0_7,axiom,
    ! [X1,X34,X18,X4] :
      ( lhs_atom116(X1,X34,X18,X4)
      | ~ $true ),
    file('<stdin>',to_be_clausified_116) ).

fof(c_0_8,axiom,
    ! [X1,X18,X19,X2] :
      ( lhs_atom109(X1,X18,X19,X2)
      | ~ $true ),
    file('<stdin>',to_be_clausified_109) ).

fof(c_0_9,axiom,
    ! [X18,X35,X19,X5] :
      ( lhs_atom107(X18,X35,X19,X5)
      | ~ $true ),
    file('<stdin>',to_be_clausified_107) ).

fof(c_0_10,axiom,
    ! [X34,X35,X29,X5] :
      ( lhs_atom105(X34,X35,X29,X5)
      | ~ $true ),
    file('<stdin>',to_be_clausified_105) ).

fof(c_0_11,axiom,
    ! [X27,X21,X28,X16] :
      ( lhs_atom62(X27,X21,X28,X16)
      | ~ $true ),
    file('<stdin>',to_be_clausified_62) ).

fof(c_0_12,axiom,
    ! [X1,X18,X19,X2] :
      ( lhs_atom58(X1,X18,X19,X2)
      | ~ $true ),
    file('<stdin>',to_be_clausified_57) ).

fof(c_0_13,axiom,
    ! [X9,X22,X23,X16] :
      ( lhs_atom30(X9,X22,X23,X16)
      | ~ $true ),
    file('<stdin>',to_be_clausified_29) ).

fof(c_0_14,axiom,
    ! [X1,X2,X3,X4] :
      ( lhs_atom2(X1,X2,X3,X4)
      | ~ $true ),
    file('<stdin>',to_be_clausified_1) ).

fof(c_0_15,axiom,
    ! [X5,X6] :
      ( lhs_atom38(X5,X6)
      | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X6,tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat) ),
    file('<stdin>',to_be_clausified_37) ).

fof(c_0_16,axiom,
    ! [X5,X6] :
      ( lhs_atom37(X5,X6)
      | c_HOL_Otimes__class_Otimes(X6,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(X5,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
    file('<stdin>',to_be_clausified_36) ).

fof(c_0_17,axiom,
    ! [X30,X37,X38] :
      ( lhs_atom120(X30,X37,X38)
      | ~ $true ),
    file('<stdin>',to_be_clausified_120) ).

fof(c_0_18,axiom,
    ! [X30,X37,X38] :
      ( lhs_atom115(X30,X37,X38)
      | ~ $true ),
    file('<stdin>',to_be_clausified_115) ).

fof(c_0_19,axiom,
    ! [X34,X18,X4] :
      ( lhs_atom108(X34,X18,X4)
      | ~ $true ),
    file('<stdin>',to_be_clausified_108) ).

fof(c_0_20,axiom,
    ! [X5,X6,X2] :
      ( lhs_atom78(X5,X6,X2)
      | ~ $true ),
    file('<stdin>',to_be_clausified_78) ).

fof(c_0_21,axiom,
    ! [X5,X6,X2] :
      ( lhs_atom77(X5,X6,X2)
      | ~ $true ),
    file('<stdin>',to_be_clausified_77) ).

fof(c_0_22,axiom,
    ! [X5,X6,X2] :
      ( lhs_atom76(X5,X6,X2)
      | ~ $true ),
    file('<stdin>',to_be_clausified_76) ).

fof(c_0_23,axiom,
    ! [X11,X20,X21] :
      ( lhs_atom72(X11,X20,X21)
      | ~ $true ),
    file('<stdin>',to_be_clausified_72) ).

fof(c_0_24,axiom,
    ! [X11,X20,X21] :
      ( lhs_atom69(X11,X20,X21)
      | ~ $true ),
    file('<stdin>',to_be_clausified_69) ).

fof(c_0_25,axiom,
    ! [X18,X19,X2] :
      ( lhs_atom63(X18,X19,X2)
      | ~ $true ),
    file('<stdin>',to_be_clausified_63) ).

fof(c_0_26,axiom,
    ! [X27,X28,X16] :
      ( lhs_atom59(X27,X28,X16)
      | ~ $true ),
    file('<stdin>',to_be_clausified_59) ).

fof(c_0_27,axiom,
    ! [X27,X28,X16] :
      ( lhs_atom59(X27,X28,X16)
      | ~ $true ),
    file('<stdin>',to_be_clausified_58) ).

fof(c_0_28,axiom,
    ! [X18,X19,X2] :
      ( lhs_atom56(X18,X19,X2)
      | ~ $true ),
    file('<stdin>',to_be_clausified_55) ).

fof(c_0_29,axiom,
    ! [X24,X25,X26] :
      ( lhs_atom55(X24,X25,X26)
      | ~ $true ),
    file('<stdin>',to_be_clausified_54) ).

fof(c_0_30,axiom,
    ! [X24,X25,X26] :
      ( lhs_atom54(X24,X25,X26)
      | ~ $true ),
    file('<stdin>',to_be_clausified_53) ).

fof(c_0_31,axiom,
    ! [X11,X20,X21] :
      ( lhs_atom36(X11,X20,X21)
      | ~ $true ),
    file('<stdin>',to_be_clausified_35) ).

fof(c_0_32,axiom,
    ! [X5,X6,X2] :
      ( lhs_atom31(X5,X6,X2)
      | ~ $true ),
    file('<stdin>',to_be_clausified_30) ).

fof(c_0_33,axiom,
    ! [X5,X6,X2] :
      ( lhs_atom26(X5,X6,X2)
      | ~ $true ),
    file('<stdin>',to_be_clausified_25) ).

fof(c_0_34,axiom,
    ! [X11,X20,X21] :
      ( lhs_atom25(X11,X20,X21)
      | ~ $true ),
    file('<stdin>',to_be_clausified_24) ).

fof(c_0_35,axiom,
    ! [X5,X6,X2] :
      ( lhs_atom24(X5,X6,X2)
      | ~ $true ),
    file('<stdin>',to_be_clausified_23) ).

fof(c_0_36,axiom,
    ! [X5,X6,X2] :
      ( lhs_atom23(X5,X6,X2)
      | ~ $true ),
    file('<stdin>',to_be_clausified_22) ).

fof(c_0_37,axiom,
    ! [X18,X19,X2] :
      ( lhs_atom20(X18,X19,X2)
      | ~ $true ),
    file('<stdin>',to_be_clausified_19) ).

fof(c_0_38,axiom,
    ! [X18,X19,X2] :
      ( lhs_atom18(X18,X19,X2)
      | ~ $true ),
    file('<stdin>',to_be_clausified_17) ).

fof(c_0_39,axiom,
    ! [X7,X8,X9] :
      ( lhs_atom7(X7,X8,X9)
      | ~ $true ),
    file('<stdin>',to_be_clausified_6) ).

fof(c_0_40,axiom,
    ! [X9,X10,X11] :
      ( lhs_atom6(X9,X10,X11)
      | ~ $true ),
    file('<stdin>',to_be_clausified_5) ).

fof(c_0_41,axiom,
    ! [X7,X8,X9] :
      ( lhs_atom4(X7,X8,X9)
      | ~ $true ),
    file('<stdin>',to_be_clausified_3) ).

fof(c_0_42,axiom,
    ! [X5,X6,X2] :
      ( lhs_atom3(X5,X6,X2)
      | ~ $true ),
    file('<stdin>',to_be_clausified_2) ).

fof(c_0_43,axiom,
    ! [X9,X16] :
      ( lhs_atom152(X9,X16)
      | ~ $true ),
    file('<stdin>',to_be_clausified_153) ).

fof(c_0_44,axiom,
    ! [X1,X2] :
      ( lhs_atom110(X1,X2)
      | ~ $true ),
    file('<stdin>',to_be_clausified_110) ).

fof(c_0_45,axiom,
    ! [X19,X29] :
      ( lhs_atom104(X19,X29)
      | ~ $true ),
    file('<stdin>',to_be_clausified_104) ).

fof(c_0_46,axiom,
    ! [X18,X19] :
      ( lhs_atom101(X18,X19)
      | ~ $true ),
    file('<stdin>',to_be_clausified_101) ).

fof(c_0_47,axiom,
    ! [X18,X19] :
      ( lhs_atom83(X18,X19)
      | ~ $true ),
    file('<stdin>',to_be_clausified_83) ).

fof(c_0_48,axiom,
    ! [X25,X26] :
      ( lhs_atom82(X25,X26)
      | ~ $true ),
    file('<stdin>',to_be_clausified_82) ).

fof(c_0_49,axiom,
    ! [X25,X26] :
      ( lhs_atom81(X25,X26)
      | ~ $true ),
    file('<stdin>',to_be_clausified_81) ).

fof(c_0_50,axiom,
    ! [X9,X32] :
      ( lhs_atom80(X9,X32)
      | ~ $true ),
    file('<stdin>',to_be_clausified_80) ).

fof(c_0_51,axiom,
    ! [X19,X2] :
      ( lhs_atom74(X19,X2)
      | ~ $true ),
    file('<stdin>',to_be_clausified_74) ).

fof(c_0_52,axiom,
    ! [X9,X10] :
      ( lhs_atom73(X9,X10)
      | ~ $true ),
    file('<stdin>',to_be_clausified_73) ).

fof(c_0_53,axiom,
    ! [X3,X4] :
      ( lhs_atom71(X3,X4)
      | ~ $true ),
    file('<stdin>',to_be_clausified_71) ).

fof(c_0_54,axiom,
    ! [X3,X4] :
      ( lhs_atom70(X3,X4)
      | ~ $true ),
    file('<stdin>',to_be_clausified_70) ).

fof(c_0_55,axiom,
    ! [X5,X6] :
      ( lhs_atom68(X5,X6)
      | ~ $true ),
    file('<stdin>',to_be_clausified_68) ).

fof(c_0_56,axiom,
    ! [X30,X24] :
      ( lhs_atom66(X30,X24)
      | ~ $true ),
    file('<stdin>',to_be_clausified_66) ).

fof(c_0_57,axiom,
    ! [X18,X4] :
      ( lhs_atom65(X18,X4)
      | ~ $true ),
    file('<stdin>',to_be_clausified_65) ).

fof(c_0_58,axiom,
    ! [X30,X24] :
      ( lhs_atom64(X30,X24)
      | ~ $true ),
    file('<stdin>',to_be_clausified_64) ).

fof(c_0_59,axiom,
    ! [X5,X6] :
      ( lhs_atom53(X5,X6)
      | ~ $true ),
    file('<stdin>',to_be_clausified_52) ).

fof(c_0_60,axiom,
    ! [X5,X6] :
      ( lhs_atom52(X5,X6)
      | ~ $true ),
    file('<stdin>',to_be_clausified_51) ).

fof(c_0_61,axiom,
    ! [X5,X6] :
      ( lhs_atom51(X5,X6)
      | ~ $true ),
    file('<stdin>',to_be_clausified_50) ).

fof(c_0_62,axiom,
    ! [X5,X6] :
      ( lhs_atom48(X5,X6)
      | ~ $true ),
    file('<stdin>',to_be_clausified_47) ).

fof(c_0_63,axiom,
    ! [X5,X6] :
      ( lhs_atom35(X5,X6)
      | ~ $true ),
    file('<stdin>',to_be_clausified_34) ).

fof(c_0_64,axiom,
    ! [X5,X6] :
      ( lhs_atom29(X5,X6)
      | ~ $true ),
    file('<stdin>',to_be_clausified_28) ).

fof(c_0_65,axiom,
    ! [X5,X6] :
      ( lhs_atom28(X5,X6)
      | ~ $true ),
    file('<stdin>',to_be_clausified_27) ).

fof(c_0_66,axiom,
    ! [X5,X6] :
      ( lhs_atom19(X5,X6)
      | ~ $true ),
    file('<stdin>',to_be_clausified_18) ).

fof(c_0_67,axiom,
    ! [X9,X6] :
      ( lhs_atom16(X9,X6)
      | ~ $true ),
    file('<stdin>',to_be_clausified_15) ).

fof(c_0_68,axiom,
    ! [X6,X4] :
      ( lhs_atom15(X6,X4)
      | ~ $true ),
    file('<stdin>',to_be_clausified_14) ).

fof(c_0_69,axiom,
    ! [X6,X4] :
      ( lhs_atom14(X6,X4)
      | ~ $true ),
    file('<stdin>',to_be_clausified_13) ).

fof(c_0_70,axiom,
    ! [X17,X16] :
      ( lhs_atom13(X17,X16)
      | ~ $true ),
    file('<stdin>',to_be_clausified_12) ).

fof(c_0_71,axiom,
    ! [X5,X6] :
      ( lhs_atom5(X5,X6)
      | ~ $true ),
    file('<stdin>',to_be_clausified_4) ).

fof(c_0_72,axiom,
    ! [X36] :
      ( lhs_atom118(X36)
      | ~ $true ),
    file('<stdin>',to_be_clausified_118) ).

fof(c_0_73,axiom,
    ! [X6] :
      ( lhs_atom117(X6)
      | ~ $true ),
    file('<stdin>',to_be_clausified_117) ).

fof(c_0_74,axiom,
    ! [X36] :
      ( lhs_atom114(X36)
      | ~ $true ),
    file('<stdin>',to_be_clausified_114) ).

fof(c_0_75,axiom,
    ! [X6] :
      ( lhs_atom113(X6)
      | ~ $true ),
    file('<stdin>',to_be_clausified_113) ).

fof(c_0_76,axiom,
    ! [X5] :
      ( lhs_atom112(X5)
      | ~ $true ),
    file('<stdin>',to_be_clausified_112) ).

fof(c_0_77,axiom,
    ! [X5] :
      ( lhs_atom111(X5)
      | ~ $true ),
    file('<stdin>',to_be_clausified_111) ).

fof(c_0_78,axiom,
    ! [X6] :
      ( lhs_atom106(X6)
      | ~ $true ),
    file('<stdin>',to_be_clausified_106) ).

fof(c_0_79,axiom,
    ! [X30] :
      ( lhs_atom103(X30)
      | ~ $true ),
    file('<stdin>',to_be_clausified_103) ).

fof(c_0_80,axiom,
    ! [X30] :
      ( lhs_atom102(X30)
      | ~ $true ),
    file('<stdin>',to_be_clausified_102) ).

fof(c_0_81,axiom,
    ! [X6] :
      ( lhs_atom100(X6)
      | ~ $true ),
    file('<stdin>',to_be_clausified_100) ).

fof(c_0_82,axiom,
    ! [X5] :
      ( lhs_atom99(X5)
      | ~ $true ),
    file('<stdin>',to_be_clausified_99) ).

fof(c_0_83,axiom,
    ! [X6] :
      ( lhs_atom98(X6)
      | ~ $true ),
    file('<stdin>',to_be_clausified_98) ).

fof(c_0_84,axiom,
    ! [X9] :
      ( lhs_atom97(X9)
      | ~ $true ),
    file('<stdin>',to_be_clausified_97) ).

fof(c_0_85,axiom,
    ! [X5] :
      ( lhs_atom96(X5)
      | ~ $true ),
    file('<stdin>',to_be_clausified_96) ).

fof(c_0_86,axiom,
    ! [X2] :
      ( lhs_atom94(X2)
      | ~ $true ),
    file('<stdin>',to_be_clausified_94) ).

fof(c_0_87,axiom,
    ! [X9] :
      ( lhs_atom92(X9)
      | ~ $true ),
    file('<stdin>',to_be_clausified_92) ).

fof(c_0_88,axiom,
    ! [X6] :
      ( lhs_atom86(X6)
      | ~ $true ),
    file('<stdin>',to_be_clausified_86) ).

fof(c_0_89,axiom,
    ! [X15] :
      ( lhs_atom75(X15)
      | ~ $true ),
    file('<stdin>',to_be_clausified_75) ).

fof(c_0_90,axiom,
    ! [X31] :
      ( lhs_atom67(X31)
      | ~ $true ),
    file('<stdin>',to_be_clausified_67) ).

fof(c_0_91,axiom,
    ! [X29] :
      ( lhs_atom61(X29)
      | ~ $true ),
    file('<stdin>',to_be_clausified_61) ).

fof(c_0_92,axiom,
    ! [X29] :
      ( lhs_atom60(X29)
      | ~ $true ),
    file('<stdin>',to_be_clausified_60) ).

fof(c_0_93,axiom,
    ! [X5] :
      ( lhs_atom50(X5)
      | ~ $true ),
    file('<stdin>',to_be_clausified_49) ).

fof(c_0_94,axiom,
    ! [X9] :
      ( lhs_atom49(X9)
      | ~ $true ),
    file('<stdin>',to_be_clausified_48) ).

fof(c_0_95,axiom,
    ! [X6] :
      ( lhs_atom47(X6)
      | ~ $true ),
    file('<stdin>',to_be_clausified_46) ).

fof(c_0_96,axiom,
    ! [X5] :
      ( lhs_atom46(X5)
      | ~ $true ),
    file('<stdin>',to_be_clausified_45) ).

fof(c_0_97,axiom,
    ! [X9] :
      ( lhs_atom45(X9)
      | ~ $true ),
    file('<stdin>',to_be_clausified_44) ).

fof(c_0_98,axiom,
    ! [X5] :
      ( lhs_atom44(X5)
      | ~ $true ),
    file('<stdin>',to_be_clausified_43) ).

fof(c_0_99,axiom,
    ! [X6] :
      ( lhs_atom43(X6)
      | ~ $true ),
    file('<stdin>',to_be_clausified_42) ).

fof(c_0_100,axiom,
    ! [X5] :
      ( lhs_atom41(X5)
      | ~ $true ),
    file('<stdin>',to_be_clausified_40) ).

fof(c_0_101,axiom,
    ! [X6] :
      ( lhs_atom40(X6)
      | ~ $true ),
    file('<stdin>',to_be_clausified_39) ).

fof(c_0_102,axiom,
    ! [X9] :
      ( lhs_atom34(X9)
      | ~ $true ),
    file('<stdin>',to_be_clausified_33) ).

fof(c_0_103,axiom,
    ! [X5] :
      ( lhs_atom33(X5)
      | ~ $true ),
    file('<stdin>',to_be_clausified_32) ).

fof(c_0_104,axiom,
    ! [X9] :
      ( lhs_atom32(X9)
      | ~ $true ),
    file('<stdin>',to_be_clausified_31) ).

fof(c_0_105,axiom,
    ! [X9] :
      ( lhs_atom27(X9)
      | ~ $true ),
    file('<stdin>',to_be_clausified_26) ).

fof(c_0_106,axiom,
    ! [X15] :
      ( lhs_atom21(X15)
      | ~ $true ),
    file('<stdin>',to_be_clausified_20) ).

fof(c_0_107,axiom,
    ! [X5] :
      ( lhs_atom12(X5)
      | ~ $true ),
    file('<stdin>',to_be_clausified_11) ).

fof(c_0_108,axiom,
    ! [X5] :
      ( lhs_atom11(X5)
      | ~ $true ),
    file('<stdin>',to_be_clausified_10) ).

fof(c_0_109,axiom,
    ! [X5] :
      ( lhs_atom10(X5)
      | ~ $true ),
    file('<stdin>',to_be_clausified_9) ).

fof(c_0_110,axiom,
    ! [X5] :
      ( lhs_atom9(X5)
      | ~ $true ),
    file('<stdin>',to_be_clausified_8) ).

fof(c_0_111,axiom,
    ( lhs_atom150
    | ~ $true ),
    file('<stdin>',to_be_clausified_150) ).

fof(c_0_112,axiom,
    ( lhs_atom149
    | ~ $true ),
    file('<stdin>',to_be_clausified_149) ).

fof(c_0_113,axiom,
    ( lhs_atom148
    | ~ $true ),
    file('<stdin>',to_be_clausified_148) ).

fof(c_0_114,axiom,
    ( lhs_atom147
    | ~ $true ),
    file('<stdin>',to_be_clausified_147) ).

fof(c_0_115,axiom,
    ( lhs_atom146
    | ~ $true ),
    file('<stdin>',to_be_clausified_146) ).

fof(c_0_116,axiom,
    ( lhs_atom145
    | ~ $true ),
    file('<stdin>',to_be_clausified_145) ).

fof(c_0_117,axiom,
    ( lhs_atom144
    | ~ $true ),
    file('<stdin>',to_be_clausified_144) ).

fof(c_0_118,axiom,
    ( lhs_atom143
    | ~ $true ),
    file('<stdin>',to_be_clausified_143) ).

fof(c_0_119,axiom,
    ( lhs_atom142
    | ~ $true ),
    file('<stdin>',to_be_clausified_142) ).

fof(c_0_120,axiom,
    ( lhs_atom141
    | ~ $true ),
    file('<stdin>',to_be_clausified_141) ).

fof(c_0_121,axiom,
    ( lhs_atom140
    | ~ $true ),
    file('<stdin>',to_be_clausified_140) ).

fof(c_0_122,axiom,
    ( lhs_atom139
    | ~ $true ),
    file('<stdin>',to_be_clausified_139) ).

fof(c_0_123,axiom,
    ( lhs_atom138
    | ~ $true ),
    file('<stdin>',to_be_clausified_138) ).

fof(c_0_124,axiom,
    ( lhs_atom137
    | ~ $true ),
    file('<stdin>',to_be_clausified_137) ).

fof(c_0_125,axiom,
    ( lhs_atom136
    | ~ $true ),
    file('<stdin>',to_be_clausified_136) ).

fof(c_0_126,axiom,
    ( lhs_atom135
    | ~ $true ),
    file('<stdin>',to_be_clausified_135) ).

fof(c_0_127,axiom,
    ( lhs_atom134
    | ~ $true ),
    file('<stdin>',to_be_clausified_134) ).

fof(c_0_128,axiom,
    ( lhs_atom133
    | ~ $true ),
    file('<stdin>',to_be_clausified_133) ).

fof(c_0_129,axiom,
    ( lhs_atom132
    | ~ $true ),
    file('<stdin>',to_be_clausified_132) ).

fof(c_0_130,axiom,
    ( lhs_atom131
    | ~ $true ),
    file('<stdin>',to_be_clausified_131) ).

fof(c_0_131,axiom,
    ( lhs_atom130
    | ~ $true ),
    file('<stdin>',to_be_clausified_130) ).

fof(c_0_132,axiom,
    ( lhs_atom129
    | ~ $true ),
    file('<stdin>',to_be_clausified_129) ).

fof(c_0_133,axiom,
    ( lhs_atom128
    | ~ $true ),
    file('<stdin>',to_be_clausified_128) ).

fof(c_0_134,axiom,
    ( lhs_atom127
    | ~ $true ),
    file('<stdin>',to_be_clausified_127) ).

fof(c_0_135,axiom,
    ( lhs_atom126
    | ~ $true ),
    file('<stdin>',to_be_clausified_126) ).

fof(c_0_136,axiom,
    ( lhs_atom125
    | ~ $true ),
    file('<stdin>',to_be_clausified_125) ).

fof(c_0_137,axiom,
    ( lhs_atom124
    | ~ $true ),
    file('<stdin>',to_be_clausified_124) ).

fof(c_0_138,axiom,
    ( lhs_atom123
    | ~ $true ),
    file('<stdin>',to_be_clausified_123) ).

fof(c_0_139,axiom,
    ( lhs_atom122
    | ~ $true ),
    file('<stdin>',to_be_clausified_122) ).

fof(c_0_140,axiom,
    ( lhs_atom121
    | ~ $true ),
    file('<stdin>',to_be_clausified_121) ).

fof(c_0_141,axiom,
    ( lhs_atom95
    | ~ $true ),
    file('<stdin>',to_be_clausified_95) ).

fof(c_0_142,axiom,
    ( lhs_atom93
    | ~ $true ),
    file('<stdin>',to_be_clausified_93) ).

fof(c_0_143,axiom,
    ( lhs_atom90
    | ~ $true ),
    file('<stdin>',to_be_clausified_90) ).

fof(c_0_144,axiom,
    ( lhs_atom89
    | ~ $true ),
    file('<stdin>',to_be_clausified_89) ).

fof(c_0_145,axiom,
    ( lhs_atom88
    | ~ $true ),
    file('<stdin>',to_be_clausified_88) ).

fof(c_0_146,axiom,
    ( lhs_atom87
    | ~ $true ),
    file('<stdin>',to_be_clausified_87) ).

fof(c_0_147,axiom,
    ( lhs_atom85
    | ~ $true ),
    file('<stdin>',to_be_clausified_85) ).

fof(c_0_148,axiom,
    ( lhs_atom84
    | ~ $true ),
    file('<stdin>',to_be_clausified_84) ).

fof(c_0_149,axiom,
    ( lhs_atom42
    | ~ $true ),
    file('<stdin>',to_be_clausified_41) ).

fof(c_0_150,axiom,
    ( lhs_atom39
    | ~ $true ),
    file('<stdin>',to_be_clausified_38) ).

fof(c_0_151,axiom,
    ( lhs_atom22
    | ~ $true ),
    file('<stdin>',to_be_clausified_21) ).

fof(c_0_152,axiom,
    ( lhs_atom17
    | ~ $true ),
    file('<stdin>',to_be_clausified_16) ).

fof(c_0_153,axiom,
    ( lhs_atom1
    | ~ $true ),
    file('<stdin>',to_be_clausified_0) ).

fof(c_0_154,plain,
    ! [X39,X40,X41,X42,X28,X16] : lhs_atom151(X39,X40,X41,X42,X28,X16),
    inference(fof_simplification,[status(thm)],[c_0_0]) ).

fof(c_0_155,plain,
    ! [X39,X40,X41,X42,X28,X16] : lhs_atom119(X39,X40,X41,X42,X28,X16),
    inference(fof_simplification,[status(thm)],[c_0_1]) ).

fof(c_0_156,plain,
    ! [X39,X40,X41,X42,X28,X16] : lhs_atom119(X39,X40,X41,X42,X28,X16),
    inference(fof_simplification,[status(thm)],[c_0_2]) ).

fof(c_0_157,plain,
    ! [X12,X13,X14,X25,X26,X16] : lhs_atom57(X12,X13,X14,X25,X26,X16),
    inference(fof_simplification,[status(thm)],[c_0_3]) ).

fof(c_0_158,plain,
    ! [X4,X22,X33,X23,X16] : lhs_atom91(X4,X22,X33,X23,X16),
    inference(fof_simplification,[status(thm)],[c_0_4]) ).

fof(c_0_159,plain,
    ! [X30,X12,X13,X14,X16] : lhs_atom79(X30,X12,X13,X14,X16),
    inference(fof_simplification,[status(thm)],[c_0_5]) ).

fof(c_0_160,plain,
    ! [X12,X13,X14,X15,X16] : lhs_atom8(X12,X13,X14,X15,X16),
    inference(fof_simplification,[status(thm)],[c_0_6]) ).

fof(c_0_161,plain,
    ! [X1,X34,X18,X4] : lhs_atom116(X1,X34,X18,X4),
    inference(fof_simplification,[status(thm)],[c_0_7]) ).

fof(c_0_162,plain,
    ! [X1,X18,X19,X2] : lhs_atom109(X1,X18,X19,X2),
    inference(fof_simplification,[status(thm)],[c_0_8]) ).

fof(c_0_163,plain,
    ! [X18,X35,X19,X5] : lhs_atom107(X18,X35,X19,X5),
    inference(fof_simplification,[status(thm)],[c_0_9]) ).

fof(c_0_164,plain,
    ! [X34,X35,X29,X5] : lhs_atom105(X34,X35,X29,X5),
    inference(fof_simplification,[status(thm)],[c_0_10]) ).

fof(c_0_165,plain,
    ! [X27,X21,X28,X16] : lhs_atom62(X27,X21,X28,X16),
    inference(fof_simplification,[status(thm)],[c_0_11]) ).

fof(c_0_166,plain,
    ! [X1,X18,X19,X2] : lhs_atom58(X1,X18,X19,X2),
    inference(fof_simplification,[status(thm)],[c_0_12]) ).

fof(c_0_167,plain,
    ! [X9,X22,X23,X16] : lhs_atom30(X9,X22,X23,X16),
    inference(fof_simplification,[status(thm)],[c_0_13]) ).

fof(c_0_168,plain,
    ! [X1,X2,X3,X4] : lhs_atom2(X1,X2,X3,X4),
    inference(fof_simplification,[status(thm)],[c_0_14]) ).

fof(c_0_169,axiom,
    ! [X5,X6] :
      ( lhs_atom38(X5,X6)
      | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X6,tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat) ),
    c_0_15 ).

fof(c_0_170,axiom,
    ! [X5,X6] :
      ( lhs_atom37(X5,X6)
      | c_HOL_Otimes__class_Otimes(X6,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(X5,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
    c_0_16 ).

fof(c_0_171,plain,
    ! [X30,X37,X38] : lhs_atom120(X30,X37,X38),
    inference(fof_simplification,[status(thm)],[c_0_17]) ).

fof(c_0_172,plain,
    ! [X30,X37,X38] : lhs_atom115(X30,X37,X38),
    inference(fof_simplification,[status(thm)],[c_0_18]) ).

fof(c_0_173,plain,
    ! [X34,X18,X4] : lhs_atom108(X34,X18,X4),
    inference(fof_simplification,[status(thm)],[c_0_19]) ).

fof(c_0_174,plain,
    ! [X5,X6,X2] : lhs_atom78(X5,X6,X2),
    inference(fof_simplification,[status(thm)],[c_0_20]) ).

fof(c_0_175,plain,
    ! [X5,X6,X2] : lhs_atom77(X5,X6,X2),
    inference(fof_simplification,[status(thm)],[c_0_21]) ).

fof(c_0_176,plain,
    ! [X5,X6,X2] : lhs_atom76(X5,X6,X2),
    inference(fof_simplification,[status(thm)],[c_0_22]) ).

fof(c_0_177,plain,
    ! [X11,X20,X21] : lhs_atom72(X11,X20,X21),
    inference(fof_simplification,[status(thm)],[c_0_23]) ).

fof(c_0_178,plain,
    ! [X11,X20,X21] : lhs_atom69(X11,X20,X21),
    inference(fof_simplification,[status(thm)],[c_0_24]) ).

fof(c_0_179,plain,
    ! [X18,X19,X2] : lhs_atom63(X18,X19,X2),
    inference(fof_simplification,[status(thm)],[c_0_25]) ).

fof(c_0_180,plain,
    ! [X27,X28,X16] : lhs_atom59(X27,X28,X16),
    inference(fof_simplification,[status(thm)],[c_0_26]) ).

fof(c_0_181,plain,
    ! [X27,X28,X16] : lhs_atom59(X27,X28,X16),
    inference(fof_simplification,[status(thm)],[c_0_27]) ).

fof(c_0_182,plain,
    ! [X18,X19,X2] : lhs_atom56(X18,X19,X2),
    inference(fof_simplification,[status(thm)],[c_0_28]) ).

fof(c_0_183,plain,
    ! [X24,X25,X26] : lhs_atom55(X24,X25,X26),
    inference(fof_simplification,[status(thm)],[c_0_29]) ).

fof(c_0_184,plain,
    ! [X24,X25,X26] : lhs_atom54(X24,X25,X26),
    inference(fof_simplification,[status(thm)],[c_0_30]) ).

fof(c_0_185,plain,
    ! [X11,X20,X21] : lhs_atom36(X11,X20,X21),
    inference(fof_simplification,[status(thm)],[c_0_31]) ).

fof(c_0_186,plain,
    ! [X5,X6,X2] : lhs_atom31(X5,X6,X2),
    inference(fof_simplification,[status(thm)],[c_0_32]) ).

fof(c_0_187,plain,
    ! [X5,X6,X2] : lhs_atom26(X5,X6,X2),
    inference(fof_simplification,[status(thm)],[c_0_33]) ).

fof(c_0_188,plain,
    ! [X11,X20,X21] : lhs_atom25(X11,X20,X21),
    inference(fof_simplification,[status(thm)],[c_0_34]) ).

fof(c_0_189,plain,
    ! [X5,X6,X2] : lhs_atom24(X5,X6,X2),
    inference(fof_simplification,[status(thm)],[c_0_35]) ).

fof(c_0_190,plain,
    ! [X5,X6,X2] : lhs_atom23(X5,X6,X2),
    inference(fof_simplification,[status(thm)],[c_0_36]) ).

fof(c_0_191,plain,
    ! [X18,X19,X2] : lhs_atom20(X18,X19,X2),
    inference(fof_simplification,[status(thm)],[c_0_37]) ).

fof(c_0_192,plain,
    ! [X18,X19,X2] : lhs_atom18(X18,X19,X2),
    inference(fof_simplification,[status(thm)],[c_0_38]) ).

fof(c_0_193,plain,
    ! [X7,X8,X9] : lhs_atom7(X7,X8,X9),
    inference(fof_simplification,[status(thm)],[c_0_39]) ).

fof(c_0_194,plain,
    ! [X9,X10,X11] : lhs_atom6(X9,X10,X11),
    inference(fof_simplification,[status(thm)],[c_0_40]) ).

fof(c_0_195,plain,
    ! [X7,X8,X9] : lhs_atom4(X7,X8,X9),
    inference(fof_simplification,[status(thm)],[c_0_41]) ).

fof(c_0_196,plain,
    ! [X5,X6,X2] : lhs_atom3(X5,X6,X2),
    inference(fof_simplification,[status(thm)],[c_0_42]) ).

fof(c_0_197,plain,
    ! [X9,X16] : lhs_atom152(X9,X16),
    inference(fof_simplification,[status(thm)],[c_0_43]) ).

fof(c_0_198,plain,
    ! [X1,X2] : lhs_atom110(X1,X2),
    inference(fof_simplification,[status(thm)],[c_0_44]) ).

fof(c_0_199,plain,
    ! [X19,X29] : lhs_atom104(X19,X29),
    inference(fof_simplification,[status(thm)],[c_0_45]) ).

fof(c_0_200,plain,
    ! [X18,X19] : lhs_atom101(X18,X19),
    inference(fof_simplification,[status(thm)],[c_0_46]) ).

fof(c_0_201,plain,
    ! [X18,X19] : lhs_atom83(X18,X19),
    inference(fof_simplification,[status(thm)],[c_0_47]) ).

fof(c_0_202,plain,
    ! [X25,X26] : lhs_atom82(X25,X26),
    inference(fof_simplification,[status(thm)],[c_0_48]) ).

fof(c_0_203,plain,
    ! [X25,X26] : lhs_atom81(X25,X26),
    inference(fof_simplification,[status(thm)],[c_0_49]) ).

fof(c_0_204,plain,
    ! [X9,X32] : lhs_atom80(X9,X32),
    inference(fof_simplification,[status(thm)],[c_0_50]) ).

fof(c_0_205,plain,
    ! [X19,X2] : lhs_atom74(X19,X2),
    inference(fof_simplification,[status(thm)],[c_0_51]) ).

fof(c_0_206,plain,
    ! [X9,X10] : lhs_atom73(X9,X10),
    inference(fof_simplification,[status(thm)],[c_0_52]) ).

fof(c_0_207,plain,
    ! [X3,X4] : lhs_atom71(X3,X4),
    inference(fof_simplification,[status(thm)],[c_0_53]) ).

fof(c_0_208,plain,
    ! [X3,X4] : lhs_atom70(X3,X4),
    inference(fof_simplification,[status(thm)],[c_0_54]) ).

fof(c_0_209,plain,
    ! [X5,X6] : lhs_atom68(X5,X6),
    inference(fof_simplification,[status(thm)],[c_0_55]) ).

fof(c_0_210,plain,
    ! [X30,X24] : lhs_atom66(X30,X24),
    inference(fof_simplification,[status(thm)],[c_0_56]) ).

fof(c_0_211,plain,
    ! [X18,X4] : lhs_atom65(X18,X4),
    inference(fof_simplification,[status(thm)],[c_0_57]) ).

fof(c_0_212,plain,
    ! [X30,X24] : lhs_atom64(X30,X24),
    inference(fof_simplification,[status(thm)],[c_0_58]) ).

fof(c_0_213,plain,
    ! [X5,X6] : lhs_atom53(X5,X6),
    inference(fof_simplification,[status(thm)],[c_0_59]) ).

fof(c_0_214,plain,
    ! [X5,X6] : lhs_atom52(X5,X6),
    inference(fof_simplification,[status(thm)],[c_0_60]) ).

fof(c_0_215,plain,
    ! [X5,X6] : lhs_atom51(X5,X6),
    inference(fof_simplification,[status(thm)],[c_0_61]) ).

fof(c_0_216,plain,
    ! [X5,X6] : lhs_atom48(X5,X6),
    inference(fof_simplification,[status(thm)],[c_0_62]) ).

fof(c_0_217,plain,
    ! [X5,X6] : lhs_atom35(X5,X6),
    inference(fof_simplification,[status(thm)],[c_0_63]) ).

fof(c_0_218,plain,
    ! [X5,X6] : lhs_atom29(X5,X6),
    inference(fof_simplification,[status(thm)],[c_0_64]) ).

fof(c_0_219,plain,
    ! [X5,X6] : lhs_atom28(X5,X6),
    inference(fof_simplification,[status(thm)],[c_0_65]) ).

fof(c_0_220,plain,
    ! [X5,X6] : lhs_atom19(X5,X6),
    inference(fof_simplification,[status(thm)],[c_0_66]) ).

fof(c_0_221,plain,
    ! [X9,X6] : lhs_atom16(X9,X6),
    inference(fof_simplification,[status(thm)],[c_0_67]) ).

fof(c_0_222,plain,
    ! [X6,X4] : lhs_atom15(X6,X4),
    inference(fof_simplification,[status(thm)],[c_0_68]) ).

fof(c_0_223,plain,
    ! [X6,X4] : lhs_atom14(X6,X4),
    inference(fof_simplification,[status(thm)],[c_0_69]) ).

fof(c_0_224,plain,
    ! [X17,X16] : lhs_atom13(X17,X16),
    inference(fof_simplification,[status(thm)],[c_0_70]) ).

fof(c_0_225,plain,
    ! [X5,X6] : lhs_atom5(X5,X6),
    inference(fof_simplification,[status(thm)],[c_0_71]) ).

fof(c_0_226,plain,
    ! [X36] : lhs_atom118(X36),
    inference(fof_simplification,[status(thm)],[c_0_72]) ).

fof(c_0_227,plain,
    ! [X6] : lhs_atom117(X6),
    inference(fof_simplification,[status(thm)],[c_0_73]) ).

fof(c_0_228,plain,
    ! [X36] : lhs_atom114(X36),
    inference(fof_simplification,[status(thm)],[c_0_74]) ).

fof(c_0_229,plain,
    ! [X6] : lhs_atom113(X6),
    inference(fof_simplification,[status(thm)],[c_0_75]) ).

fof(c_0_230,plain,
    ! [X5] : lhs_atom112(X5),
    inference(fof_simplification,[status(thm)],[c_0_76]) ).

fof(c_0_231,plain,
    ! [X5] : lhs_atom111(X5),
    inference(fof_simplification,[status(thm)],[c_0_77]) ).

fof(c_0_232,plain,
    ! [X6] : lhs_atom106(X6),
    inference(fof_simplification,[status(thm)],[c_0_78]) ).

fof(c_0_233,plain,
    ! [X30] : lhs_atom103(X30),
    inference(fof_simplification,[status(thm)],[c_0_79]) ).

fof(c_0_234,plain,
    ! [X30] : lhs_atom102(X30),
    inference(fof_simplification,[status(thm)],[c_0_80]) ).

fof(c_0_235,plain,
    ! [X6] : lhs_atom100(X6),
    inference(fof_simplification,[status(thm)],[c_0_81]) ).

fof(c_0_236,plain,
    ! [X5] : lhs_atom99(X5),
    inference(fof_simplification,[status(thm)],[c_0_82]) ).

fof(c_0_237,plain,
    ! [X6] : lhs_atom98(X6),
    inference(fof_simplification,[status(thm)],[c_0_83]) ).

fof(c_0_238,plain,
    ! [X9] : lhs_atom97(X9),
    inference(fof_simplification,[status(thm)],[c_0_84]) ).

fof(c_0_239,plain,
    ! [X5] : lhs_atom96(X5),
    inference(fof_simplification,[status(thm)],[c_0_85]) ).

fof(c_0_240,plain,
    ! [X2] : lhs_atom94(X2),
    inference(fof_simplification,[status(thm)],[c_0_86]) ).

fof(c_0_241,plain,
    ! [X9] : lhs_atom92(X9),
    inference(fof_simplification,[status(thm)],[c_0_87]) ).

fof(c_0_242,plain,
    ! [X6] : lhs_atom86(X6),
    inference(fof_simplification,[status(thm)],[c_0_88]) ).

fof(c_0_243,plain,
    ! [X15] : lhs_atom75(X15),
    inference(fof_simplification,[status(thm)],[c_0_89]) ).

fof(c_0_244,plain,
    ! [X31] : lhs_atom67(X31),
    inference(fof_simplification,[status(thm)],[c_0_90]) ).

fof(c_0_245,plain,
    ! [X29] : lhs_atom61(X29),
    inference(fof_simplification,[status(thm)],[c_0_91]) ).

fof(c_0_246,plain,
    ! [X29] : lhs_atom60(X29),
    inference(fof_simplification,[status(thm)],[c_0_92]) ).

fof(c_0_247,plain,
    ! [X5] : lhs_atom50(X5),
    inference(fof_simplification,[status(thm)],[c_0_93]) ).

fof(c_0_248,plain,
    ! [X9] : lhs_atom49(X9),
    inference(fof_simplification,[status(thm)],[c_0_94]) ).

fof(c_0_249,plain,
    ! [X6] : lhs_atom47(X6),
    inference(fof_simplification,[status(thm)],[c_0_95]) ).

fof(c_0_250,plain,
    ! [X5] : lhs_atom46(X5),
    inference(fof_simplification,[status(thm)],[c_0_96]) ).

fof(c_0_251,plain,
    ! [X9] : lhs_atom45(X9),
    inference(fof_simplification,[status(thm)],[c_0_97]) ).

fof(c_0_252,plain,
    ! [X5] : lhs_atom44(X5),
    inference(fof_simplification,[status(thm)],[c_0_98]) ).

fof(c_0_253,plain,
    ! [X6] : lhs_atom43(X6),
    inference(fof_simplification,[status(thm)],[c_0_99]) ).

fof(c_0_254,plain,
    ! [X5] : lhs_atom41(X5),
    inference(fof_simplification,[status(thm)],[c_0_100]) ).

fof(c_0_255,plain,
    ! [X6] : lhs_atom40(X6),
    inference(fof_simplification,[status(thm)],[c_0_101]) ).

fof(c_0_256,plain,
    ! [X9] : lhs_atom34(X9),
    inference(fof_simplification,[status(thm)],[c_0_102]) ).

fof(c_0_257,plain,
    ! [X5] : lhs_atom33(X5),
    inference(fof_simplification,[status(thm)],[c_0_103]) ).

fof(c_0_258,plain,
    ! [X9] : lhs_atom32(X9),
    inference(fof_simplification,[status(thm)],[c_0_104]) ).

fof(c_0_259,plain,
    ! [X9] : lhs_atom27(X9),
    inference(fof_simplification,[status(thm)],[c_0_105]) ).

fof(c_0_260,plain,
    ! [X15] : lhs_atom21(X15),
    inference(fof_simplification,[status(thm)],[c_0_106]) ).

fof(c_0_261,plain,
    ! [X5] : lhs_atom12(X5),
    inference(fof_simplification,[status(thm)],[c_0_107]) ).

fof(c_0_262,plain,
    ! [X5] : lhs_atom11(X5),
    inference(fof_simplification,[status(thm)],[c_0_108]) ).

fof(c_0_263,plain,
    ! [X5] : lhs_atom10(X5),
    inference(fof_simplification,[status(thm)],[c_0_109]) ).

fof(c_0_264,plain,
    ! [X5] : lhs_atom9(X5),
    inference(fof_simplification,[status(thm)],[c_0_110]) ).

fof(c_0_265,plain,
    lhs_atom150,
    inference(fof_simplification,[status(thm)],[c_0_111]) ).

fof(c_0_266,plain,
    lhs_atom149,
    inference(fof_simplification,[status(thm)],[c_0_112]) ).

fof(c_0_267,plain,
    lhs_atom148,
    inference(fof_simplification,[status(thm)],[c_0_113]) ).

fof(c_0_268,plain,
    lhs_atom147,
    inference(fof_simplification,[status(thm)],[c_0_114]) ).

fof(c_0_269,plain,
    lhs_atom146,
    inference(fof_simplification,[status(thm)],[c_0_115]) ).

fof(c_0_270,plain,
    lhs_atom145,
    inference(fof_simplification,[status(thm)],[c_0_116]) ).

fof(c_0_271,plain,
    lhs_atom144,
    inference(fof_simplification,[status(thm)],[c_0_117]) ).

fof(c_0_272,plain,
    lhs_atom143,
    inference(fof_simplification,[status(thm)],[c_0_118]) ).

fof(c_0_273,plain,
    lhs_atom142,
    inference(fof_simplification,[status(thm)],[c_0_119]) ).

fof(c_0_274,plain,
    lhs_atom141,
    inference(fof_simplification,[status(thm)],[c_0_120]) ).

fof(c_0_275,plain,
    lhs_atom140,
    inference(fof_simplification,[status(thm)],[c_0_121]) ).

fof(c_0_276,plain,
    lhs_atom139,
    inference(fof_simplification,[status(thm)],[c_0_122]) ).

fof(c_0_277,plain,
    lhs_atom138,
    inference(fof_simplification,[status(thm)],[c_0_123]) ).

fof(c_0_278,plain,
    lhs_atom137,
    inference(fof_simplification,[status(thm)],[c_0_124]) ).

fof(c_0_279,plain,
    lhs_atom136,
    inference(fof_simplification,[status(thm)],[c_0_125]) ).

fof(c_0_280,plain,
    lhs_atom135,
    inference(fof_simplification,[status(thm)],[c_0_126]) ).

fof(c_0_281,plain,
    lhs_atom134,
    inference(fof_simplification,[status(thm)],[c_0_127]) ).

fof(c_0_282,plain,
    lhs_atom133,
    inference(fof_simplification,[status(thm)],[c_0_128]) ).

fof(c_0_283,plain,
    lhs_atom132,
    inference(fof_simplification,[status(thm)],[c_0_129]) ).

fof(c_0_284,plain,
    lhs_atom131,
    inference(fof_simplification,[status(thm)],[c_0_130]) ).

fof(c_0_285,plain,
    lhs_atom130,
    inference(fof_simplification,[status(thm)],[c_0_131]) ).

fof(c_0_286,plain,
    lhs_atom129,
    inference(fof_simplification,[status(thm)],[c_0_132]) ).

fof(c_0_287,plain,
    lhs_atom128,
    inference(fof_simplification,[status(thm)],[c_0_133]) ).

fof(c_0_288,plain,
    lhs_atom127,
    inference(fof_simplification,[status(thm)],[c_0_134]) ).

fof(c_0_289,plain,
    lhs_atom126,
    inference(fof_simplification,[status(thm)],[c_0_135]) ).

fof(c_0_290,plain,
    lhs_atom125,
    inference(fof_simplification,[status(thm)],[c_0_136]) ).

fof(c_0_291,plain,
    lhs_atom124,
    inference(fof_simplification,[status(thm)],[c_0_137]) ).

fof(c_0_292,plain,
    lhs_atom123,
    inference(fof_simplification,[status(thm)],[c_0_138]) ).

fof(c_0_293,plain,
    lhs_atom122,
    inference(fof_simplification,[status(thm)],[c_0_139]) ).

fof(c_0_294,plain,
    lhs_atom121,
    inference(fof_simplification,[status(thm)],[c_0_140]) ).

fof(c_0_295,plain,
    lhs_atom95,
    inference(fof_simplification,[status(thm)],[c_0_141]) ).

fof(c_0_296,plain,
    lhs_atom93,
    inference(fof_simplification,[status(thm)],[c_0_142]) ).

fof(c_0_297,plain,
    lhs_atom90,
    inference(fof_simplification,[status(thm)],[c_0_143]) ).

fof(c_0_298,plain,
    lhs_atom89,
    inference(fof_simplification,[status(thm)],[c_0_144]) ).

fof(c_0_299,plain,
    lhs_atom88,
    inference(fof_simplification,[status(thm)],[c_0_145]) ).

fof(c_0_300,plain,
    lhs_atom87,
    inference(fof_simplification,[status(thm)],[c_0_146]) ).

fof(c_0_301,plain,
    lhs_atom85,
    inference(fof_simplification,[status(thm)],[c_0_147]) ).

fof(c_0_302,plain,
    lhs_atom84,
    inference(fof_simplification,[status(thm)],[c_0_148]) ).

fof(c_0_303,plain,
    lhs_atom42,
    inference(fof_simplification,[status(thm)],[c_0_149]) ).

fof(c_0_304,plain,
    lhs_atom39,
    inference(fof_simplification,[status(thm)],[c_0_150]) ).

fof(c_0_305,plain,
    lhs_atom22,
    inference(fof_simplification,[status(thm)],[c_0_151]) ).

fof(c_0_306,plain,
    lhs_atom17,
    inference(fof_simplification,[status(thm)],[c_0_152]) ).

fof(c_0_307,plain,
    lhs_atom1,
    inference(fof_simplification,[status(thm)],[c_0_153]) ).

fof(c_0_308,plain,
    ! [X43,X44,X45,X46,X47,X48] : lhs_atom151(X43,X44,X45,X46,X47,X48),
    inference(variable_rename,[status(thm)],[c_0_154]) ).

fof(c_0_309,plain,
    ! [X43,X44,X45,X46,X47,X48] : lhs_atom119(X43,X44,X45,X46,X47,X48),
    inference(variable_rename,[status(thm)],[c_0_155]) ).

fof(c_0_310,plain,
    ! [X43,X44,X45,X46,X47,X48] : lhs_atom119(X43,X44,X45,X46,X47,X48),
    inference(variable_rename,[status(thm)],[c_0_156]) ).

fof(c_0_311,plain,
    ! [X27,X28,X29,X30,X31,X32] : lhs_atom57(X27,X28,X29,X30,X31,X32),
    inference(variable_rename,[status(thm)],[c_0_157]) ).

fof(c_0_312,plain,
    ! [X34,X35,X36,X37,X38] : lhs_atom91(X34,X35,X36,X37,X38),
    inference(variable_rename,[status(thm)],[c_0_158]) ).

fof(c_0_313,plain,
    ! [X31,X32,X33,X34,X35] : lhs_atom79(X31,X32,X33,X34,X35),
    inference(variable_rename,[status(thm)],[c_0_159]) ).

fof(c_0_314,plain,
    ! [X17,X18,X19,X20,X21] : lhs_atom8(X17,X18,X19,X20,X21),
    inference(variable_rename,[status(thm)],[c_0_160]) ).

fof(c_0_315,plain,
    ! [X35,X36,X37,X38] : lhs_atom116(X35,X36,X37,X38),
    inference(variable_rename,[status(thm)],[c_0_161]) ).

fof(c_0_316,plain,
    ! [X20,X21,X22,X23] : lhs_atom109(X20,X21,X22,X23),
    inference(variable_rename,[status(thm)],[c_0_162]) ).

fof(c_0_317,plain,
    ! [X36,X37,X38,X39] : lhs_atom107(X36,X37,X38,X39),
    inference(variable_rename,[status(thm)],[c_0_163]) ).

fof(c_0_318,plain,
    ! [X36,X37,X38,X39] : lhs_atom105(X36,X37,X38,X39),
    inference(variable_rename,[status(thm)],[c_0_164]) ).

fof(c_0_319,plain,
    ! [X29,X30,X31,X32] : lhs_atom62(X29,X30,X31,X32),
    inference(variable_rename,[status(thm)],[c_0_165]) ).

fof(c_0_320,plain,
    ! [X20,X21,X22,X23] : lhs_atom58(X20,X21,X22,X23),
    inference(variable_rename,[status(thm)],[c_0_166]) ).

fof(c_0_321,plain,
    ! [X24,X25,X26,X27] : lhs_atom30(X24,X25,X26,X27),
    inference(variable_rename,[status(thm)],[c_0_167]) ).

fof(c_0_322,plain,
    ! [X5,X6,X7,X8] : lhs_atom2(X5,X6,X7,X8),
    inference(variable_rename,[status(thm)],[c_0_168]) ).

fof(c_0_323,plain,
    ! [X7,X8] :
      ( lhs_atom38(X7,X8)
      | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X8,tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_169]) ).

fof(c_0_324,plain,
    ! [X7,X8] :
      ( lhs_atom37(X7,X8)
      | c_HOL_Otimes__class_Otimes(X8,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(X7,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_170]) ).

fof(c_0_325,plain,
    ! [X39,X40,X41] : lhs_atom120(X39,X40,X41),
    inference(variable_rename,[status(thm)],[c_0_171]) ).

fof(c_0_326,plain,
    ! [X39,X40,X41] : lhs_atom115(X39,X40,X41),
    inference(variable_rename,[status(thm)],[c_0_172]) ).

fof(c_0_327,plain,
    ! [X35,X36,X37] : lhs_atom108(X35,X36,X37),
    inference(variable_rename,[status(thm)],[c_0_173]) ).

fof(c_0_328,plain,
    ! [X7,X8,X9] : lhs_atom78(X7,X8,X9),
    inference(variable_rename,[status(thm)],[c_0_174]) ).

fof(c_0_329,plain,
    ! [X7,X8,X9] : lhs_atom77(X7,X8,X9),
    inference(variable_rename,[status(thm)],[c_0_175]) ).

fof(c_0_330,plain,
    ! [X7,X8,X9] : lhs_atom76(X7,X8,X9),
    inference(variable_rename,[status(thm)],[c_0_176]) ).

fof(c_0_331,plain,
    ! [X22,X23,X24] : lhs_atom72(X22,X23,X24),
    inference(variable_rename,[status(thm)],[c_0_177]) ).

fof(c_0_332,plain,
    ! [X22,X23,X24] : lhs_atom69(X22,X23,X24),
    inference(variable_rename,[status(thm)],[c_0_178]) ).

fof(c_0_333,plain,
    ! [X20,X21,X22] : lhs_atom63(X20,X21,X22),
    inference(variable_rename,[status(thm)],[c_0_179]) ).

fof(c_0_334,plain,
    ! [X29,X30,X31] : lhs_atom59(X29,X30,X31),
    inference(variable_rename,[status(thm)],[c_0_180]) ).

fof(c_0_335,plain,
    ! [X29,X30,X31] : lhs_atom59(X29,X30,X31),
    inference(variable_rename,[status(thm)],[c_0_181]) ).

fof(c_0_336,plain,
    ! [X20,X21,X22] : lhs_atom56(X20,X21,X22),
    inference(variable_rename,[status(thm)],[c_0_182]) ).

fof(c_0_337,plain,
    ! [X27,X28,X29] : lhs_atom55(X27,X28,X29),
    inference(variable_rename,[status(thm)],[c_0_183]) ).

fof(c_0_338,plain,
    ! [X27,X28,X29] : lhs_atom54(X27,X28,X29),
    inference(variable_rename,[status(thm)],[c_0_184]) ).

fof(c_0_339,plain,
    ! [X22,X23,X24] : lhs_atom36(X22,X23,X24),
    inference(variable_rename,[status(thm)],[c_0_185]) ).

fof(c_0_340,plain,
    ! [X7,X8,X9] : lhs_atom31(X7,X8,X9),
    inference(variable_rename,[status(thm)],[c_0_186]) ).

fof(c_0_341,plain,
    ! [X7,X8,X9] : lhs_atom26(X7,X8,X9),
    inference(variable_rename,[status(thm)],[c_0_187]) ).

fof(c_0_342,plain,
    ! [X22,X23,X24] : lhs_atom25(X22,X23,X24),
    inference(variable_rename,[status(thm)],[c_0_188]) ).

fof(c_0_343,plain,
    ! [X7,X8,X9] : lhs_atom24(X7,X8,X9),
    inference(variable_rename,[status(thm)],[c_0_189]) ).

fof(c_0_344,plain,
    ! [X7,X8,X9] : lhs_atom23(X7,X8,X9),
    inference(variable_rename,[status(thm)],[c_0_190]) ).

fof(c_0_345,plain,
    ! [X20,X21,X22] : lhs_atom20(X20,X21,X22),
    inference(variable_rename,[status(thm)],[c_0_191]) ).

fof(c_0_346,plain,
    ! [X20,X21,X22] : lhs_atom18(X20,X21,X22),
    inference(variable_rename,[status(thm)],[c_0_192]) ).

fof(c_0_347,plain,
    ! [X10,X11,X12] : lhs_atom7(X10,X11,X12),
    inference(variable_rename,[status(thm)],[c_0_193]) ).

fof(c_0_348,plain,
    ! [X12,X13,X14] : lhs_atom6(X12,X13,X14),
    inference(variable_rename,[status(thm)],[c_0_194]) ).

fof(c_0_349,plain,
    ! [X10,X11,X12] : lhs_atom4(X10,X11,X12),
    inference(variable_rename,[status(thm)],[c_0_195]) ).

fof(c_0_350,plain,
    ! [X7,X8,X9] : lhs_atom3(X7,X8,X9),
    inference(variable_rename,[status(thm)],[c_0_196]) ).

fof(c_0_351,plain,
    ! [X17,X18] : lhs_atom152(X17,X18),
    inference(variable_rename,[status(thm)],[c_0_197]) ).

fof(c_0_352,plain,
    ! [X3,X4] : lhs_atom110(X3,X4),
    inference(variable_rename,[status(thm)],[c_0_198]) ).

fof(c_0_353,plain,
    ! [X30,X31] : lhs_atom104(X30,X31),
    inference(variable_rename,[status(thm)],[c_0_199]) ).

fof(c_0_354,plain,
    ! [X20,X21] : lhs_atom101(X20,X21),
    inference(variable_rename,[status(thm)],[c_0_200]) ).

fof(c_0_355,plain,
    ! [X20,X21] : lhs_atom83(X20,X21),
    inference(variable_rename,[status(thm)],[c_0_201]) ).

fof(c_0_356,plain,
    ! [X27,X28] : lhs_atom82(X27,X28),
    inference(variable_rename,[status(thm)],[c_0_202]) ).

fof(c_0_357,plain,
    ! [X27,X28] : lhs_atom81(X27,X28),
    inference(variable_rename,[status(thm)],[c_0_203]) ).

fof(c_0_358,plain,
    ! [X33,X34] : lhs_atom80(X33,X34),
    inference(variable_rename,[status(thm)],[c_0_204]) ).

fof(c_0_359,plain,
    ! [X20,X21] : lhs_atom74(X20,X21),
    inference(variable_rename,[status(thm)],[c_0_205]) ).

fof(c_0_360,plain,
    ! [X11,X12] : lhs_atom73(X11,X12),
    inference(variable_rename,[status(thm)],[c_0_206]) ).

fof(c_0_361,plain,
    ! [X5,X6] : lhs_atom71(X5,X6),
    inference(variable_rename,[status(thm)],[c_0_207]) ).

fof(c_0_362,plain,
    ! [X5,X6] : lhs_atom70(X5,X6),
    inference(variable_rename,[status(thm)],[c_0_208]) ).

fof(c_0_363,plain,
    ! [X7,X8] : lhs_atom68(X7,X8),
    inference(variable_rename,[status(thm)],[c_0_209]) ).

fof(c_0_364,plain,
    ! [X31,X32] : lhs_atom66(X31,X32),
    inference(variable_rename,[status(thm)],[c_0_210]) ).

fof(c_0_365,plain,
    ! [X19,X20] : lhs_atom65(X19,X20),
    inference(variable_rename,[status(thm)],[c_0_211]) ).

fof(c_0_366,plain,
    ! [X31,X32] : lhs_atom64(X31,X32),
    inference(variable_rename,[status(thm)],[c_0_212]) ).

fof(c_0_367,plain,
    ! [X7,X8] : lhs_atom53(X7,X8),
    inference(variable_rename,[status(thm)],[c_0_213]) ).

fof(c_0_368,plain,
    ! [X7,X8] : lhs_atom52(X7,X8),
    inference(variable_rename,[status(thm)],[c_0_214]) ).

fof(c_0_369,plain,
    ! [X7,X8] : lhs_atom51(X7,X8),
    inference(variable_rename,[status(thm)],[c_0_215]) ).

fof(c_0_370,plain,
    ! [X7,X8] : lhs_atom48(X7,X8),
    inference(variable_rename,[status(thm)],[c_0_216]) ).

fof(c_0_371,plain,
    ! [X7,X8] : lhs_atom35(X7,X8),
    inference(variable_rename,[status(thm)],[c_0_217]) ).

fof(c_0_372,plain,
    ! [X7,X8] : lhs_atom29(X7,X8),
    inference(variable_rename,[status(thm)],[c_0_218]) ).

fof(c_0_373,plain,
    ! [X7,X8] : lhs_atom28(X7,X8),
    inference(variable_rename,[status(thm)],[c_0_219]) ).

fof(c_0_374,plain,
    ! [X7,X8] : lhs_atom19(X7,X8),
    inference(variable_rename,[status(thm)],[c_0_220]) ).

fof(c_0_375,plain,
    ! [X10,X11] : lhs_atom16(X10,X11),
    inference(variable_rename,[status(thm)],[c_0_221]) ).

fof(c_0_376,plain,
    ! [X7,X8] : lhs_atom15(X7,X8),
    inference(variable_rename,[status(thm)],[c_0_222]) ).

fof(c_0_377,plain,
    ! [X7,X8] : lhs_atom14(X7,X8),
    inference(variable_rename,[status(thm)],[c_0_223]) ).

fof(c_0_378,plain,
    ! [X18,X19] : lhs_atom13(X18,X19),
    inference(variable_rename,[status(thm)],[c_0_224]) ).

fof(c_0_379,plain,
    ! [X7,X8] : lhs_atom5(X7,X8),
    inference(variable_rename,[status(thm)],[c_0_225]) ).

fof(c_0_380,plain,
    ! [X37] : lhs_atom118(X37),
    inference(variable_rename,[status(thm)],[c_0_226]) ).

fof(c_0_381,plain,
    ! [X7] : lhs_atom117(X7),
    inference(variable_rename,[status(thm)],[c_0_227]) ).

fof(c_0_382,plain,
    ! [X37] : lhs_atom114(X37),
    inference(variable_rename,[status(thm)],[c_0_228]) ).

fof(c_0_383,plain,
    ! [X7] : lhs_atom113(X7),
    inference(variable_rename,[status(thm)],[c_0_229]) ).

fof(c_0_384,plain,
    ! [X6] : lhs_atom112(X6),
    inference(variable_rename,[status(thm)],[c_0_230]) ).

fof(c_0_385,plain,
    ! [X6] : lhs_atom111(X6),
    inference(variable_rename,[status(thm)],[c_0_231]) ).

fof(c_0_386,plain,
    ! [X7] : lhs_atom106(X7),
    inference(variable_rename,[status(thm)],[c_0_232]) ).

fof(c_0_387,plain,
    ! [X31] : lhs_atom103(X31),
    inference(variable_rename,[status(thm)],[c_0_233]) ).

fof(c_0_388,plain,
    ! [X31] : lhs_atom102(X31),
    inference(variable_rename,[status(thm)],[c_0_234]) ).

fof(c_0_389,plain,
    ! [X7] : lhs_atom100(X7),
    inference(variable_rename,[status(thm)],[c_0_235]) ).

fof(c_0_390,plain,
    ! [X6] : lhs_atom99(X6),
    inference(variable_rename,[status(thm)],[c_0_236]) ).

fof(c_0_391,plain,
    ! [X7] : lhs_atom98(X7),
    inference(variable_rename,[status(thm)],[c_0_237]) ).

fof(c_0_392,plain,
    ! [X10] : lhs_atom97(X10),
    inference(variable_rename,[status(thm)],[c_0_238]) ).

fof(c_0_393,plain,
    ! [X6] : lhs_atom96(X6),
    inference(variable_rename,[status(thm)],[c_0_239]) ).

fof(c_0_394,plain,
    ! [X3] : lhs_atom94(X3),
    inference(variable_rename,[status(thm)],[c_0_240]) ).

fof(c_0_395,plain,
    ! [X10] : lhs_atom92(X10),
    inference(variable_rename,[status(thm)],[c_0_241]) ).

fof(c_0_396,plain,
    ! [X7] : lhs_atom86(X7),
    inference(variable_rename,[status(thm)],[c_0_242]) ).

fof(c_0_397,plain,
    ! [X16] : lhs_atom75(X16),
    inference(variable_rename,[status(thm)],[c_0_243]) ).

fof(c_0_398,plain,
    ! [X32] : lhs_atom67(X32),
    inference(variable_rename,[status(thm)],[c_0_244]) ).

fof(c_0_399,plain,
    ! [X30] : lhs_atom61(X30),
    inference(variable_rename,[status(thm)],[c_0_245]) ).

fof(c_0_400,plain,
    ! [X30] : lhs_atom60(X30),
    inference(variable_rename,[status(thm)],[c_0_246]) ).

fof(c_0_401,plain,
    ! [X6] : lhs_atom50(X6),
    inference(variable_rename,[status(thm)],[c_0_247]) ).

fof(c_0_402,plain,
    ! [X10] : lhs_atom49(X10),
    inference(variable_rename,[status(thm)],[c_0_248]) ).

fof(c_0_403,plain,
    ! [X7] : lhs_atom47(X7),
    inference(variable_rename,[status(thm)],[c_0_249]) ).

fof(c_0_404,plain,
    ! [X6] : lhs_atom46(X6),
    inference(variable_rename,[status(thm)],[c_0_250]) ).

fof(c_0_405,plain,
    ! [X10] : lhs_atom45(X10),
    inference(variable_rename,[status(thm)],[c_0_251]) ).

fof(c_0_406,plain,
    ! [X6] : lhs_atom44(X6),
    inference(variable_rename,[status(thm)],[c_0_252]) ).

fof(c_0_407,plain,
    ! [X7] : lhs_atom43(X7),
    inference(variable_rename,[status(thm)],[c_0_253]) ).

fof(c_0_408,plain,
    ! [X6] : lhs_atom41(X6),
    inference(variable_rename,[status(thm)],[c_0_254]) ).

fof(c_0_409,plain,
    ! [X7] : lhs_atom40(X7),
    inference(variable_rename,[status(thm)],[c_0_255]) ).

fof(c_0_410,plain,
    ! [X10] : lhs_atom34(X10),
    inference(variable_rename,[status(thm)],[c_0_256]) ).

fof(c_0_411,plain,
    ! [X6] : lhs_atom33(X6),
    inference(variable_rename,[status(thm)],[c_0_257]) ).

fof(c_0_412,plain,
    ! [X10] : lhs_atom32(X10),
    inference(variable_rename,[status(thm)],[c_0_258]) ).

fof(c_0_413,plain,
    ! [X10] : lhs_atom27(X10),
    inference(variable_rename,[status(thm)],[c_0_259]) ).

fof(c_0_414,plain,
    ! [X16] : lhs_atom21(X16),
    inference(variable_rename,[status(thm)],[c_0_260]) ).

fof(c_0_415,plain,
    ! [X6] : lhs_atom12(X6),
    inference(variable_rename,[status(thm)],[c_0_261]) ).

fof(c_0_416,plain,
    ! [X6] : lhs_atom11(X6),
    inference(variable_rename,[status(thm)],[c_0_262]) ).

fof(c_0_417,plain,
    ! [X6] : lhs_atom10(X6),
    inference(variable_rename,[status(thm)],[c_0_263]) ).

fof(c_0_418,plain,
    ! [X6] : lhs_atom9(X6),
    inference(variable_rename,[status(thm)],[c_0_264]) ).

fof(c_0_419,plain,
    lhs_atom150,
    c_0_265 ).

fof(c_0_420,plain,
    lhs_atom149,
    c_0_266 ).

fof(c_0_421,plain,
    lhs_atom148,
    c_0_267 ).

fof(c_0_422,plain,
    lhs_atom147,
    c_0_268 ).

fof(c_0_423,plain,
    lhs_atom146,
    c_0_269 ).

fof(c_0_424,plain,
    lhs_atom145,
    c_0_270 ).

fof(c_0_425,plain,
    lhs_atom144,
    c_0_271 ).

fof(c_0_426,plain,
    lhs_atom143,
    c_0_272 ).

fof(c_0_427,plain,
    lhs_atom142,
    c_0_273 ).

fof(c_0_428,plain,
    lhs_atom141,
    c_0_274 ).

fof(c_0_429,plain,
    lhs_atom140,
    c_0_275 ).

fof(c_0_430,plain,
    lhs_atom139,
    c_0_276 ).

fof(c_0_431,plain,
    lhs_atom138,
    c_0_277 ).

fof(c_0_432,plain,
    lhs_atom137,
    c_0_278 ).

fof(c_0_433,plain,
    lhs_atom136,
    c_0_279 ).

fof(c_0_434,plain,
    lhs_atom135,
    c_0_280 ).

fof(c_0_435,plain,
    lhs_atom134,
    c_0_281 ).

fof(c_0_436,plain,
    lhs_atom133,
    c_0_282 ).

fof(c_0_437,plain,
    lhs_atom132,
    c_0_283 ).

fof(c_0_438,plain,
    lhs_atom131,
    c_0_284 ).

fof(c_0_439,plain,
    lhs_atom130,
    c_0_285 ).

fof(c_0_440,plain,
    lhs_atom129,
    c_0_286 ).

fof(c_0_441,plain,
    lhs_atom128,
    c_0_287 ).

fof(c_0_442,plain,
    lhs_atom127,
    c_0_288 ).

fof(c_0_443,plain,
    lhs_atom126,
    c_0_289 ).

fof(c_0_444,plain,
    lhs_atom125,
    c_0_290 ).

fof(c_0_445,plain,
    lhs_atom124,
    c_0_291 ).

fof(c_0_446,plain,
    lhs_atom123,
    c_0_292 ).

fof(c_0_447,plain,
    lhs_atom122,
    c_0_293 ).

fof(c_0_448,plain,
    lhs_atom121,
    c_0_294 ).

fof(c_0_449,plain,
    lhs_atom95,
    c_0_295 ).

fof(c_0_450,plain,
    lhs_atom93,
    c_0_296 ).

fof(c_0_451,plain,
    lhs_atom90,
    c_0_297 ).

fof(c_0_452,plain,
    lhs_atom89,
    c_0_298 ).

fof(c_0_453,plain,
    lhs_atom88,
    c_0_299 ).

fof(c_0_454,plain,
    lhs_atom87,
    c_0_300 ).

fof(c_0_455,plain,
    lhs_atom85,
    c_0_301 ).

fof(c_0_456,plain,
    lhs_atom84,
    c_0_302 ).

fof(c_0_457,plain,
    lhs_atom42,
    c_0_303 ).

fof(c_0_458,plain,
    lhs_atom39,
    c_0_304 ).

fof(c_0_459,plain,
    lhs_atom22,
    c_0_305 ).

fof(c_0_460,plain,
    lhs_atom17,
    c_0_306 ).

fof(c_0_461,plain,
    lhs_atom1,
    c_0_307 ).

cnf(c_0_462,plain,
    lhs_atom151(X1,X2,X3,X4,X5,X6),
    inference(split_conjunct,[status(thm)],[c_0_308]) ).

cnf(c_0_463,plain,
    lhs_atom119(X1,X2,X3,X4,X5,X6),
    inference(split_conjunct,[status(thm)],[c_0_309]) ).

cnf(c_0_464,plain,
    lhs_atom119(X1,X2,X3,X4,X5,X6),
    inference(split_conjunct,[status(thm)],[c_0_310]) ).

cnf(c_0_465,plain,
    lhs_atom57(X1,X2,X3,X4,X5,X6),
    inference(split_conjunct,[status(thm)],[c_0_311]) ).

cnf(c_0_466,plain,
    lhs_atom91(X1,X2,X3,X4,X5),
    inference(split_conjunct,[status(thm)],[c_0_312]) ).

cnf(c_0_467,plain,
    lhs_atom79(X1,X2,X3,X4,X5),
    inference(split_conjunct,[status(thm)],[c_0_313]) ).

cnf(c_0_468,plain,
    lhs_atom8(X1,X2,X3,X4,X5),
    inference(split_conjunct,[status(thm)],[c_0_314]) ).

cnf(c_0_469,plain,
    lhs_atom116(X1,X2,X3,X4),
    inference(split_conjunct,[status(thm)],[c_0_315]) ).

cnf(c_0_470,plain,
    lhs_atom109(X1,X2,X3,X4),
    inference(split_conjunct,[status(thm)],[c_0_316]) ).

cnf(c_0_471,plain,
    lhs_atom107(X1,X2,X3,X4),
    inference(split_conjunct,[status(thm)],[c_0_317]) ).

cnf(c_0_472,plain,
    lhs_atom105(X1,X2,X3,X4),
    inference(split_conjunct,[status(thm)],[c_0_318]) ).

cnf(c_0_473,plain,
    lhs_atom62(X1,X2,X3,X4),
    inference(split_conjunct,[status(thm)],[c_0_319]) ).

cnf(c_0_474,plain,
    lhs_atom58(X1,X2,X3,X4),
    inference(split_conjunct,[status(thm)],[c_0_320]) ).

cnf(c_0_475,plain,
    lhs_atom30(X1,X2,X3,X4),
    inference(split_conjunct,[status(thm)],[c_0_321]) ).

cnf(c_0_476,plain,
    lhs_atom2(X1,X2,X3,X4),
    inference(split_conjunct,[status(thm)],[c_0_322]) ).

cnf(c_0_477,plain,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
    | lhs_atom38(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_323]) ).

cnf(c_0_478,plain,
    ( c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
    | lhs_atom37(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_324]) ).

cnf(c_0_479,plain,
    lhs_atom120(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_325]) ).

cnf(c_0_480,plain,
    lhs_atom115(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_326]) ).

cnf(c_0_481,plain,
    lhs_atom108(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_327]) ).

cnf(c_0_482,plain,
    lhs_atom78(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_328]) ).

cnf(c_0_483,plain,
    lhs_atom77(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_329]) ).

cnf(c_0_484,plain,
    lhs_atom76(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_330]) ).

cnf(c_0_485,plain,
    lhs_atom72(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_331]) ).

cnf(c_0_486,plain,
    lhs_atom69(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_332]) ).

cnf(c_0_487,plain,
    lhs_atom63(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_333]) ).

cnf(c_0_488,plain,
    lhs_atom59(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_334]) ).

cnf(c_0_489,plain,
    lhs_atom59(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_335]) ).

cnf(c_0_490,plain,
    lhs_atom56(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_336]) ).

cnf(c_0_491,plain,
    lhs_atom55(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_337]) ).

cnf(c_0_492,plain,
    lhs_atom54(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_338]) ).

cnf(c_0_493,plain,
    lhs_atom36(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_339]) ).

cnf(c_0_494,plain,
    lhs_atom31(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_340]) ).

cnf(c_0_495,plain,
    lhs_atom26(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_341]) ).

cnf(c_0_496,plain,
    lhs_atom25(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_342]) ).

cnf(c_0_497,plain,
    lhs_atom24(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_343]) ).

cnf(c_0_498,plain,
    lhs_atom23(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_344]) ).

cnf(c_0_499,plain,
    lhs_atom20(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_345]) ).

cnf(c_0_500,plain,
    lhs_atom18(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_346]) ).

cnf(c_0_501,plain,
    lhs_atom7(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_347]) ).

cnf(c_0_502,plain,
    lhs_atom6(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_348]) ).

cnf(c_0_503,plain,
    lhs_atom4(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_349]) ).

cnf(c_0_504,plain,
    lhs_atom3(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_350]) ).

cnf(c_0_505,plain,
    lhs_atom152(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_351]) ).

cnf(c_0_506,plain,
    lhs_atom110(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_352]) ).

cnf(c_0_507,plain,
    lhs_atom104(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_353]) ).

cnf(c_0_508,plain,
    lhs_atom101(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_354]) ).

cnf(c_0_509,plain,
    lhs_atom83(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_355]) ).

cnf(c_0_510,plain,
    lhs_atom82(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_356]) ).

cnf(c_0_511,plain,
    lhs_atom81(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_357]) ).

cnf(c_0_512,plain,
    lhs_atom80(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_358]) ).

cnf(c_0_513,plain,
    lhs_atom74(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_359]) ).

cnf(c_0_514,plain,
    lhs_atom73(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_360]) ).

cnf(c_0_515,plain,
    lhs_atom71(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_361]) ).

cnf(c_0_516,plain,
    lhs_atom70(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_362]) ).

cnf(c_0_517,plain,
    lhs_atom68(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_363]) ).

cnf(c_0_518,plain,
    lhs_atom66(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_364]) ).

cnf(c_0_519,plain,
    lhs_atom65(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_365]) ).

cnf(c_0_520,plain,
    lhs_atom64(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_366]) ).

cnf(c_0_521,plain,
    lhs_atom53(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_367]) ).

cnf(c_0_522,plain,
    lhs_atom52(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_368]) ).

cnf(c_0_523,plain,
    lhs_atom51(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_369]) ).

cnf(c_0_524,plain,
    lhs_atom48(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_370]) ).

cnf(c_0_525,plain,
    lhs_atom35(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_371]) ).

cnf(c_0_526,plain,
    lhs_atom29(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_372]) ).

cnf(c_0_527,plain,
    lhs_atom28(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_373]) ).

cnf(c_0_528,plain,
    lhs_atom19(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_374]) ).

cnf(c_0_529,plain,
    lhs_atom16(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_375]) ).

cnf(c_0_530,plain,
    lhs_atom15(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_376]) ).

cnf(c_0_531,plain,
    lhs_atom14(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_377]) ).

cnf(c_0_532,plain,
    lhs_atom13(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_378]) ).

cnf(c_0_533,plain,
    lhs_atom5(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_379]) ).

cnf(c_0_534,plain,
    lhs_atom118(X1),
    inference(split_conjunct,[status(thm)],[c_0_380]) ).

cnf(c_0_535,plain,
    lhs_atom117(X1),
    inference(split_conjunct,[status(thm)],[c_0_381]) ).

cnf(c_0_536,plain,
    lhs_atom114(X1),
    inference(split_conjunct,[status(thm)],[c_0_382]) ).

cnf(c_0_537,plain,
    lhs_atom113(X1),
    inference(split_conjunct,[status(thm)],[c_0_383]) ).

cnf(c_0_538,plain,
    lhs_atom112(X1),
    inference(split_conjunct,[status(thm)],[c_0_384]) ).

cnf(c_0_539,plain,
    lhs_atom111(X1),
    inference(split_conjunct,[status(thm)],[c_0_385]) ).

cnf(c_0_540,plain,
    lhs_atom106(X1),
    inference(split_conjunct,[status(thm)],[c_0_386]) ).

cnf(c_0_541,plain,
    lhs_atom103(X1),
    inference(split_conjunct,[status(thm)],[c_0_387]) ).

cnf(c_0_542,plain,
    lhs_atom102(X1),
    inference(split_conjunct,[status(thm)],[c_0_388]) ).

cnf(c_0_543,plain,
    lhs_atom100(X1),
    inference(split_conjunct,[status(thm)],[c_0_389]) ).

cnf(c_0_544,plain,
    lhs_atom99(X1),
    inference(split_conjunct,[status(thm)],[c_0_390]) ).

cnf(c_0_545,plain,
    lhs_atom98(X1),
    inference(split_conjunct,[status(thm)],[c_0_391]) ).

cnf(c_0_546,plain,
    lhs_atom97(X1),
    inference(split_conjunct,[status(thm)],[c_0_392]) ).

cnf(c_0_547,plain,
    lhs_atom96(X1),
    inference(split_conjunct,[status(thm)],[c_0_393]) ).

cnf(c_0_548,plain,
    lhs_atom94(X1),
    inference(split_conjunct,[status(thm)],[c_0_394]) ).

cnf(c_0_549,plain,
    lhs_atom92(X1),
    inference(split_conjunct,[status(thm)],[c_0_395]) ).

cnf(c_0_550,plain,
    lhs_atom86(X1),
    inference(split_conjunct,[status(thm)],[c_0_396]) ).

cnf(c_0_551,plain,
    lhs_atom75(X1),
    inference(split_conjunct,[status(thm)],[c_0_397]) ).

cnf(c_0_552,plain,
    lhs_atom67(X1),
    inference(split_conjunct,[status(thm)],[c_0_398]) ).

cnf(c_0_553,plain,
    lhs_atom61(X1),
    inference(split_conjunct,[status(thm)],[c_0_399]) ).

cnf(c_0_554,plain,
    lhs_atom60(X1),
    inference(split_conjunct,[status(thm)],[c_0_400]) ).

cnf(c_0_555,plain,
    lhs_atom50(X1),
    inference(split_conjunct,[status(thm)],[c_0_401]) ).

cnf(c_0_556,plain,
    lhs_atom49(X1),
    inference(split_conjunct,[status(thm)],[c_0_402]) ).

cnf(c_0_557,plain,
    lhs_atom47(X1),
    inference(split_conjunct,[status(thm)],[c_0_403]) ).

cnf(c_0_558,plain,
    lhs_atom46(X1),
    inference(split_conjunct,[status(thm)],[c_0_404]) ).

cnf(c_0_559,plain,
    lhs_atom45(X1),
    inference(split_conjunct,[status(thm)],[c_0_405]) ).

cnf(c_0_560,plain,
    lhs_atom44(X1),
    inference(split_conjunct,[status(thm)],[c_0_406]) ).

cnf(c_0_561,plain,
    lhs_atom43(X1),
    inference(split_conjunct,[status(thm)],[c_0_407]) ).

cnf(c_0_562,plain,
    lhs_atom41(X1),
    inference(split_conjunct,[status(thm)],[c_0_408]) ).

cnf(c_0_563,plain,
    lhs_atom40(X1),
    inference(split_conjunct,[status(thm)],[c_0_409]) ).

cnf(c_0_564,plain,
    lhs_atom34(X1),
    inference(split_conjunct,[status(thm)],[c_0_410]) ).

cnf(c_0_565,plain,
    lhs_atom33(X1),
    inference(split_conjunct,[status(thm)],[c_0_411]) ).

cnf(c_0_566,plain,
    lhs_atom32(X1),
    inference(split_conjunct,[status(thm)],[c_0_412]) ).

cnf(c_0_567,plain,
    lhs_atom27(X1),
    inference(split_conjunct,[status(thm)],[c_0_413]) ).

cnf(c_0_568,plain,
    lhs_atom21(X1),
    inference(split_conjunct,[status(thm)],[c_0_414]) ).

cnf(c_0_569,plain,
    lhs_atom12(X1),
    inference(split_conjunct,[status(thm)],[c_0_415]) ).

cnf(c_0_570,plain,
    lhs_atom11(X1),
    inference(split_conjunct,[status(thm)],[c_0_416]) ).

cnf(c_0_571,plain,
    lhs_atom10(X1),
    inference(split_conjunct,[status(thm)],[c_0_417]) ).

cnf(c_0_572,plain,
    lhs_atom9(X1),
    inference(split_conjunct,[status(thm)],[c_0_418]) ).

cnf(c_0_573,plain,
    lhs_atom150,
    inference(split_conjunct,[status(thm)],[c_0_419]) ).

cnf(c_0_574,plain,
    lhs_atom149,
    inference(split_conjunct,[status(thm)],[c_0_420]) ).

cnf(c_0_575,plain,
    lhs_atom148,
    inference(split_conjunct,[status(thm)],[c_0_421]) ).

cnf(c_0_576,plain,
    lhs_atom147,
    inference(split_conjunct,[status(thm)],[c_0_422]) ).

cnf(c_0_577,plain,
    lhs_atom146,
    inference(split_conjunct,[status(thm)],[c_0_423]) ).

cnf(c_0_578,plain,
    lhs_atom145,
    inference(split_conjunct,[status(thm)],[c_0_424]) ).

cnf(c_0_579,plain,
    lhs_atom144,
    inference(split_conjunct,[status(thm)],[c_0_425]) ).

cnf(c_0_580,plain,
    lhs_atom143,
    inference(split_conjunct,[status(thm)],[c_0_426]) ).

cnf(c_0_581,plain,
    lhs_atom142,
    inference(split_conjunct,[status(thm)],[c_0_427]) ).

cnf(c_0_582,plain,
    lhs_atom141,
    inference(split_conjunct,[status(thm)],[c_0_428]) ).

cnf(c_0_583,plain,
    lhs_atom140,
    inference(split_conjunct,[status(thm)],[c_0_429]) ).

cnf(c_0_584,plain,
    lhs_atom139,
    inference(split_conjunct,[status(thm)],[c_0_430]) ).

cnf(c_0_585,plain,
    lhs_atom138,
    inference(split_conjunct,[status(thm)],[c_0_431]) ).

cnf(c_0_586,plain,
    lhs_atom137,
    inference(split_conjunct,[status(thm)],[c_0_432]) ).

cnf(c_0_587,plain,
    lhs_atom136,
    inference(split_conjunct,[status(thm)],[c_0_433]) ).

cnf(c_0_588,plain,
    lhs_atom135,
    inference(split_conjunct,[status(thm)],[c_0_434]) ).

cnf(c_0_589,plain,
    lhs_atom134,
    inference(split_conjunct,[status(thm)],[c_0_435]) ).

cnf(c_0_590,plain,
    lhs_atom133,
    inference(split_conjunct,[status(thm)],[c_0_436]) ).

cnf(c_0_591,plain,
    lhs_atom132,
    inference(split_conjunct,[status(thm)],[c_0_437]) ).

cnf(c_0_592,plain,
    lhs_atom131,
    inference(split_conjunct,[status(thm)],[c_0_438]) ).

cnf(c_0_593,plain,
    lhs_atom130,
    inference(split_conjunct,[status(thm)],[c_0_439]) ).

cnf(c_0_594,plain,
    lhs_atom129,
    inference(split_conjunct,[status(thm)],[c_0_440]) ).

cnf(c_0_595,plain,
    lhs_atom128,
    inference(split_conjunct,[status(thm)],[c_0_441]) ).

cnf(c_0_596,plain,
    lhs_atom127,
    inference(split_conjunct,[status(thm)],[c_0_442]) ).

cnf(c_0_597,plain,
    lhs_atom126,
    inference(split_conjunct,[status(thm)],[c_0_443]) ).

cnf(c_0_598,plain,
    lhs_atom125,
    inference(split_conjunct,[status(thm)],[c_0_444]) ).

cnf(c_0_599,plain,
    lhs_atom124,
    inference(split_conjunct,[status(thm)],[c_0_445]) ).

cnf(c_0_600,plain,
    lhs_atom123,
    inference(split_conjunct,[status(thm)],[c_0_446]) ).

cnf(c_0_601,plain,
    lhs_atom122,
    inference(split_conjunct,[status(thm)],[c_0_447]) ).

cnf(c_0_602,plain,
    lhs_atom121,
    inference(split_conjunct,[status(thm)],[c_0_448]) ).

cnf(c_0_603,plain,
    lhs_atom95,
    inference(split_conjunct,[status(thm)],[c_0_449]) ).

cnf(c_0_604,plain,
    lhs_atom93,
    inference(split_conjunct,[status(thm)],[c_0_450]) ).

cnf(c_0_605,plain,
    lhs_atom90,
    inference(split_conjunct,[status(thm)],[c_0_451]) ).

cnf(c_0_606,plain,
    lhs_atom89,
    inference(split_conjunct,[status(thm)],[c_0_452]) ).

cnf(c_0_607,plain,
    lhs_atom88,
    inference(split_conjunct,[status(thm)],[c_0_453]) ).

cnf(c_0_608,plain,
    lhs_atom87,
    inference(split_conjunct,[status(thm)],[c_0_454]) ).

cnf(c_0_609,plain,
    lhs_atom85,
    inference(split_conjunct,[status(thm)],[c_0_455]) ).

cnf(c_0_610,plain,
    lhs_atom84,
    inference(split_conjunct,[status(thm)],[c_0_456]) ).

cnf(c_0_611,plain,
    lhs_atom42,
    inference(split_conjunct,[status(thm)],[c_0_457]) ).

cnf(c_0_612,plain,
    lhs_atom39,
    inference(split_conjunct,[status(thm)],[c_0_458]) ).

cnf(c_0_613,plain,
    lhs_atom22,
    inference(split_conjunct,[status(thm)],[c_0_459]) ).

cnf(c_0_614,plain,
    lhs_atom17,
    inference(split_conjunct,[status(thm)],[c_0_460]) ).

cnf(c_0_615,plain,
    lhs_atom1,
    inference(split_conjunct,[status(thm)],[c_0_461]) ).

cnf(c_0_616,plain,
    lhs_atom151(X1,X2,X3,X4,X5,X6),
    c_0_462,
    [final] ).

cnf(c_0_617,plain,
    lhs_atom119(X1,X2,X3,X4,X5,X6),
    c_0_463,
    [final] ).

cnf(c_0_618,plain,
    lhs_atom119(X1,X2,X3,X4,X5,X6),
    c_0_464,
    [final] ).

cnf(c_0_619,plain,
    lhs_atom57(X1,X2,X3,X4,X5,X6),
    c_0_465,
    [final] ).

cnf(c_0_620,plain,
    lhs_atom91(X1,X2,X3,X4,X5),
    c_0_466,
    [final] ).

cnf(c_0_621,plain,
    lhs_atom79(X1,X2,X3,X4,X5),
    c_0_467,
    [final] ).

cnf(c_0_622,plain,
    lhs_atom8(X1,X2,X3,X4,X5),
    c_0_468,
    [final] ).

cnf(c_0_623,plain,
    lhs_atom116(X1,X2,X3,X4),
    c_0_469,
    [final] ).

cnf(c_0_624,plain,
    lhs_atom109(X1,X2,X3,X4),
    c_0_470,
    [final] ).

cnf(c_0_625,plain,
    lhs_atom107(X1,X2,X3,X4),
    c_0_471,
    [final] ).

cnf(c_0_626,plain,
    lhs_atom105(X1,X2,X3,X4),
    c_0_472,
    [final] ).

cnf(c_0_627,plain,
    lhs_atom62(X1,X2,X3,X4),
    c_0_473,
    [final] ).

cnf(c_0_628,plain,
    lhs_atom58(X1,X2,X3,X4),
    c_0_474,
    [final] ).

cnf(c_0_629,plain,
    lhs_atom30(X1,X2,X3,X4),
    c_0_475,
    [final] ).

cnf(c_0_630,plain,
    lhs_atom2(X1,X2,X3,X4),
    c_0_476,
    [final] ).

cnf(c_0_631,plain,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
    | lhs_atom38(X2,X1) ),
    c_0_477,
    [final] ).

cnf(c_0_632,plain,
    ( c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
    | lhs_atom37(X2,X1) ),
    c_0_478,
    [final] ).

cnf(c_0_633,plain,
    lhs_atom120(X1,X2,X3),
    c_0_479,
    [final] ).

cnf(c_0_634,plain,
    lhs_atom115(X1,X2,X3),
    c_0_480,
    [final] ).

cnf(c_0_635,plain,
    lhs_atom108(X1,X2,X3),
    c_0_481,
    [final] ).

cnf(c_0_636,plain,
    lhs_atom78(X1,X2,X3),
    c_0_482,
    [final] ).

cnf(c_0_637,plain,
    lhs_atom77(X1,X2,X3),
    c_0_483,
    [final] ).

cnf(c_0_638,plain,
    lhs_atom76(X1,X2,X3),
    c_0_484,
    [final] ).

cnf(c_0_639,plain,
    lhs_atom72(X1,X2,X3),
    c_0_485,
    [final] ).

cnf(c_0_640,plain,
    lhs_atom69(X1,X2,X3),
    c_0_486,
    [final] ).

cnf(c_0_641,plain,
    lhs_atom63(X1,X2,X3),
    c_0_487,
    [final] ).

cnf(c_0_642,plain,
    lhs_atom59(X1,X2,X3),
    c_0_488,
    [final] ).

cnf(c_0_643,plain,
    lhs_atom59(X1,X2,X3),
    c_0_489,
    [final] ).

cnf(c_0_644,plain,
    lhs_atom56(X1,X2,X3),
    c_0_490,
    [final] ).

cnf(c_0_645,plain,
    lhs_atom55(X1,X2,X3),
    c_0_491,
    [final] ).

cnf(c_0_646,plain,
    lhs_atom54(X1,X2,X3),
    c_0_492,
    [final] ).

cnf(c_0_647,plain,
    lhs_atom36(X1,X2,X3),
    c_0_493,
    [final] ).

cnf(c_0_648,plain,
    lhs_atom31(X1,X2,X3),
    c_0_494,
    [final] ).

cnf(c_0_649,plain,
    lhs_atom26(X1,X2,X3),
    c_0_495,
    [final] ).

cnf(c_0_650,plain,
    lhs_atom25(X1,X2,X3),
    c_0_496,
    [final] ).

cnf(c_0_651,plain,
    lhs_atom24(X1,X2,X3),
    c_0_497,
    [final] ).

cnf(c_0_652,plain,
    lhs_atom23(X1,X2,X3),
    c_0_498,
    [final] ).

cnf(c_0_653,plain,
    lhs_atom20(X1,X2,X3),
    c_0_499,
    [final] ).

cnf(c_0_654,plain,
    lhs_atom18(X1,X2,X3),
    c_0_500,
    [final] ).

cnf(c_0_655,plain,
    lhs_atom7(X1,X2,X3),
    c_0_501,
    [final] ).

cnf(c_0_656,plain,
    lhs_atom6(X1,X2,X3),
    c_0_502,
    [final] ).

cnf(c_0_657,plain,
    lhs_atom4(X1,X2,X3),
    c_0_503,
    [final] ).

cnf(c_0_658,plain,
    lhs_atom3(X1,X2,X3),
    c_0_504,
    [final] ).

cnf(c_0_659,plain,
    lhs_atom152(X1,X2),
    c_0_505,
    [final] ).

cnf(c_0_660,plain,
    lhs_atom110(X1,X2),
    c_0_506,
    [final] ).

cnf(c_0_661,plain,
    lhs_atom104(X1,X2),
    c_0_507,
    [final] ).

cnf(c_0_662,plain,
    lhs_atom101(X1,X2),
    c_0_508,
    [final] ).

cnf(c_0_663,plain,
    lhs_atom83(X1,X2),
    c_0_509,
    [final] ).

cnf(c_0_664,plain,
    lhs_atom82(X1,X2),
    c_0_510,
    [final] ).

cnf(c_0_665,plain,
    lhs_atom81(X1,X2),
    c_0_511,
    [final] ).

cnf(c_0_666,plain,
    lhs_atom80(X1,X2),
    c_0_512,
    [final] ).

cnf(c_0_667,plain,
    lhs_atom74(X1,X2),
    c_0_513,
    [final] ).

cnf(c_0_668,plain,
    lhs_atom73(X1,X2),
    c_0_514,
    [final] ).

cnf(c_0_669,plain,
    lhs_atom71(X1,X2),
    c_0_515,
    [final] ).

cnf(c_0_670,plain,
    lhs_atom70(X1,X2),
    c_0_516,
    [final] ).

cnf(c_0_671,plain,
    lhs_atom68(X1,X2),
    c_0_517,
    [final] ).

cnf(c_0_672,plain,
    lhs_atom66(X1,X2),
    c_0_518,
    [final] ).

cnf(c_0_673,plain,
    lhs_atom65(X1,X2),
    c_0_519,
    [final] ).

cnf(c_0_674,plain,
    lhs_atom64(X1,X2),
    c_0_520,
    [final] ).

cnf(c_0_675,plain,
    lhs_atom53(X1,X2),
    c_0_521,
    [final] ).

cnf(c_0_676,plain,
    lhs_atom52(X1,X2),
    c_0_522,
    [final] ).

cnf(c_0_677,plain,
    lhs_atom51(X1,X2),
    c_0_523,
    [final] ).

cnf(c_0_678,plain,
    lhs_atom48(X1,X2),
    c_0_524,
    [final] ).

cnf(c_0_679,plain,
    lhs_atom35(X1,X2),
    c_0_525,
    [final] ).

cnf(c_0_680,plain,
    lhs_atom29(X1,X2),
    c_0_526,
    [final] ).

cnf(c_0_681,plain,
    lhs_atom28(X1,X2),
    c_0_527,
    [final] ).

cnf(c_0_682,plain,
    lhs_atom19(X1,X2),
    c_0_528,
    [final] ).

cnf(c_0_683,plain,
    lhs_atom16(X1,X2),
    c_0_529,
    [final] ).

cnf(c_0_684,plain,
    lhs_atom15(X1,X2),
    c_0_530,
    [final] ).

cnf(c_0_685,plain,
    lhs_atom14(X1,X2),
    c_0_531,
    [final] ).

cnf(c_0_686,plain,
    lhs_atom13(X1,X2),
    c_0_532,
    [final] ).

cnf(c_0_687,plain,
    lhs_atom5(X1,X2),
    c_0_533,
    [final] ).

cnf(c_0_688,plain,
    lhs_atom118(X1),
    c_0_534,
    [final] ).

cnf(c_0_689,plain,
    lhs_atom117(X1),
    c_0_535,
    [final] ).

cnf(c_0_690,plain,
    lhs_atom114(X1),
    c_0_536,
    [final] ).

cnf(c_0_691,plain,
    lhs_atom113(X1),
    c_0_537,
    [final] ).

cnf(c_0_692,plain,
    lhs_atom112(X1),
    c_0_538,
    [final] ).

cnf(c_0_693,plain,
    lhs_atom111(X1),
    c_0_539,
    [final] ).

cnf(c_0_694,plain,
    lhs_atom106(X1),
    c_0_540,
    [final] ).

cnf(c_0_695,plain,
    lhs_atom103(X1),
    c_0_541,
    [final] ).

cnf(c_0_696,plain,
    lhs_atom102(X1),
    c_0_542,
    [final] ).

cnf(c_0_697,plain,
    lhs_atom100(X1),
    c_0_543,
    [final] ).

cnf(c_0_698,plain,
    lhs_atom99(X1),
    c_0_544,
    [final] ).

cnf(c_0_699,plain,
    lhs_atom98(X1),
    c_0_545,
    [final] ).

cnf(c_0_700,plain,
    lhs_atom97(X1),
    c_0_546,
    [final] ).

cnf(c_0_701,plain,
    lhs_atom96(X1),
    c_0_547,
    [final] ).

cnf(c_0_702,plain,
    lhs_atom94(X1),
    c_0_548,
    [final] ).

cnf(c_0_703,plain,
    lhs_atom92(X1),
    c_0_549,
    [final] ).

cnf(c_0_704,plain,
    lhs_atom86(X1),
    c_0_550,
    [final] ).

cnf(c_0_705,plain,
    lhs_atom75(X1),
    c_0_551,
    [final] ).

cnf(c_0_706,plain,
    lhs_atom67(X1),
    c_0_552,
    [final] ).

cnf(c_0_707,plain,
    lhs_atom61(X1),
    c_0_553,
    [final] ).

cnf(c_0_708,plain,
    lhs_atom60(X1),
    c_0_554,
    [final] ).

cnf(c_0_709,plain,
    lhs_atom50(X1),
    c_0_555,
    [final] ).

cnf(c_0_710,plain,
    lhs_atom49(X1),
    c_0_556,
    [final] ).

cnf(c_0_711,plain,
    lhs_atom47(X1),
    c_0_557,
    [final] ).

cnf(c_0_712,plain,
    lhs_atom46(X1),
    c_0_558,
    [final] ).

cnf(c_0_713,plain,
    lhs_atom45(X1),
    c_0_559,
    [final] ).

cnf(c_0_714,plain,
    lhs_atom44(X1),
    c_0_560,
    [final] ).

cnf(c_0_715,plain,
    lhs_atom43(X1),
    c_0_561,
    [final] ).

cnf(c_0_716,plain,
    lhs_atom41(X1),
    c_0_562,
    [final] ).

cnf(c_0_717,plain,
    lhs_atom40(X1),
    c_0_563,
    [final] ).

cnf(c_0_718,plain,
    lhs_atom34(X1),
    c_0_564,
    [final] ).

cnf(c_0_719,plain,
    lhs_atom33(X1),
    c_0_565,
    [final] ).

cnf(c_0_720,plain,
    lhs_atom32(X1),
    c_0_566,
    [final] ).

cnf(c_0_721,plain,
    lhs_atom27(X1),
    c_0_567,
    [final] ).

cnf(c_0_722,plain,
    lhs_atom21(X1),
    c_0_568,
    [final] ).

cnf(c_0_723,plain,
    lhs_atom12(X1),
    c_0_569,
    [final] ).

cnf(c_0_724,plain,
    lhs_atom11(X1),
    c_0_570,
    [final] ).

cnf(c_0_725,plain,
    lhs_atom10(X1),
    c_0_571,
    [final] ).

cnf(c_0_726,plain,
    lhs_atom9(X1),
    c_0_572,
    [final] ).

cnf(c_0_727,plain,
    lhs_atom150,
    c_0_573,
    [final] ).

cnf(c_0_728,plain,
    lhs_atom149,
    c_0_574,
    [final] ).

cnf(c_0_729,plain,
    lhs_atom148,
    c_0_575,
    [final] ).

cnf(c_0_730,plain,
    lhs_atom147,
    c_0_576,
    [final] ).

cnf(c_0_731,plain,
    lhs_atom146,
    c_0_577,
    [final] ).

cnf(c_0_732,plain,
    lhs_atom145,
    c_0_578,
    [final] ).

cnf(c_0_733,plain,
    lhs_atom144,
    c_0_579,
    [final] ).

cnf(c_0_734,plain,
    lhs_atom143,
    c_0_580,
    [final] ).

cnf(c_0_735,plain,
    lhs_atom142,
    c_0_581,
    [final] ).

cnf(c_0_736,plain,
    lhs_atom141,
    c_0_582,
    [final] ).

cnf(c_0_737,plain,
    lhs_atom140,
    c_0_583,
    [final] ).

cnf(c_0_738,plain,
    lhs_atom139,
    c_0_584,
    [final] ).

cnf(c_0_739,plain,
    lhs_atom138,
    c_0_585,
    [final] ).

cnf(c_0_740,plain,
    lhs_atom137,
    c_0_586,
    [final] ).

cnf(c_0_741,plain,
    lhs_atom136,
    c_0_587,
    [final] ).

cnf(c_0_742,plain,
    lhs_atom135,
    c_0_588,
    [final] ).

cnf(c_0_743,plain,
    lhs_atom134,
    c_0_589,
    [final] ).

cnf(c_0_744,plain,
    lhs_atom133,
    c_0_590,
    [final] ).

cnf(c_0_745,plain,
    lhs_atom132,
    c_0_591,
    [final] ).

cnf(c_0_746,plain,
    lhs_atom131,
    c_0_592,
    [final] ).

cnf(c_0_747,plain,
    lhs_atom130,
    c_0_593,
    [final] ).

cnf(c_0_748,plain,
    lhs_atom129,
    c_0_594,
    [final] ).

cnf(c_0_749,plain,
    lhs_atom128,
    c_0_595,
    [final] ).

cnf(c_0_750,plain,
    lhs_atom127,
    c_0_596,
    [final] ).

cnf(c_0_751,plain,
    lhs_atom126,
    c_0_597,
    [final] ).

cnf(c_0_752,plain,
    lhs_atom125,
    c_0_598,
    [final] ).

cnf(c_0_753,plain,
    lhs_atom124,
    c_0_599,
    [final] ).

cnf(c_0_754,plain,
    lhs_atom123,
    c_0_600,
    [final] ).

cnf(c_0_755,plain,
    lhs_atom122,
    c_0_601,
    [final] ).

cnf(c_0_756,plain,
    lhs_atom121,
    c_0_602,
    [final] ).

cnf(c_0_757,plain,
    lhs_atom95,
    c_0_603,
    [final] ).

cnf(c_0_758,plain,
    lhs_atom93,
    c_0_604,
    [final] ).

cnf(c_0_759,plain,
    lhs_atom90,
    c_0_605,
    [final] ).

cnf(c_0_760,plain,
    lhs_atom89,
    c_0_606,
    [final] ).

cnf(c_0_761,plain,
    lhs_atom88,
    c_0_607,
    [final] ).

cnf(c_0_762,plain,
    lhs_atom87,
    c_0_608,
    [final] ).

cnf(c_0_763,plain,
    lhs_atom85,
    c_0_609,
    [final] ).

cnf(c_0_764,plain,
    lhs_atom84,
    c_0_610,
    [final] ).

cnf(c_0_765,plain,
    lhs_atom42,
    c_0_611,
    [final] ).

cnf(c_0_766,plain,
    lhs_atom39,
    c_0_612,
    [final] ).

cnf(c_0_767,plain,
    lhs_atom22,
    c_0_613,
    [final] ).

cnf(c_0_768,plain,
    lhs_atom17,
    c_0_614,
    [final] ).

cnf(c_0_769,plain,
    lhs_atom1,
    c_0_615,
    [final] ).

% End CNF derivation
cnf(c_0_631_0,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
    | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
    inference(unfold_definition,[status(thm)],[c_0_631,def_lhs_atom38]) ).

cnf(c_0_632_0,axiom,
    ( c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
    | c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
    inference(unfold_definition,[status(thm)],[c_0_632,def_lhs_atom37]) ).

cnf(c_0_616_0,axiom,
    c_COMBB(X3,X2,X1,X5,X6,X4) = hAPP(X3,hAPP(X2,X1)),
    inference(unfold_definition,[status(thm)],[c_0_616,def_lhs_atom151]) ).

cnf(c_0_617_0,axiom,
    hAPP(c_COMBC(X3,X2,X5,X4,X6),X1) = hAPP(hAPP(X3,X1),X2),
    inference(unfold_definition,[status(thm)],[c_0_617,def_lhs_atom119]) ).

cnf(c_0_618_0,axiom,
    hAPP(c_COMBC(X3,X2,X5,X4,X6),X1) = hAPP(hAPP(X3,X1),X2),
    inference(unfold_definition,[status(thm)],[c_0_618,def_lhs_atom119]) ).

cnf(c_0_619_0,axiom,
    c_Lambda_OdB_OdB__case(X3,X2,X1,hAPP(hAPP(c_Lambda_OdB_OApp,X5),X4),X6) = hAPP(hAPP(X2,X5),X4),
    inference(unfold_definition,[status(thm)],[c_0_619,def_lhs_atom57]) ).

cnf(c_0_620_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_620,def_lhs_atom91]) ).

cnf(c_0_621_0,axiom,
    c_Lambda_OdB_OdB__case(X4,X3,X2,c_Lambda_OdB_OVar(X1),X5) = hAPP(X4,X1),
    inference(unfold_definition,[status(thm)],[c_0_621,def_lhs_atom79]) ).

cnf(c_0_622_0,axiom,
    c_Lambda_OdB_OdB__case(X3,X2,X1,c_Lambda_OdB_OAbs(X4),X5) = hAPP(X1,X4),
    inference(unfold_definition,[status(thm)],[c_0_622,def_lhs_atom8]) ).

cnf(c_0_623_0,axiom,
    hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X2,tc_Lambda_OdB,tc_Lambda_OdB)),X1),X4) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X3),X1),X4),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,X1,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),X4,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X2,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
    inference(unfold_definition,[status(thm)],[c_0_623,def_lhs_atom116]) ).

cnf(c_0_624_0,axiom,
    hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_OdB_OApp,X2),X1)),X3),X4) = hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X2),X3),X4)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X3),X4)),
    inference(unfold_definition,[status(thm)],[c_0_624,def_lhs_atom109]) ).

cnf(c_0_625_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_625,def_lhs_atom107]) ).

cnf(c_0_626_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_626,def_lhs_atom105]) ).

cnf(c_0_627_0,axiom,
    c_List_Ofoldl(X1,X2,c_List_Olist_ONil(X3),X4,X3) = X2,
    inference(unfold_definition,[status(thm)],[c_0_627,def_lhs_atom62]) ).

cnf(c_0_628_0,axiom,
    c_Lambda_Osubstn(hAPP(hAPP(c_Lambda_OdB_OApp,X2),X1),X3,X4) = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Osubstn(X2,X3,X4)),c_Lambda_Osubstn(X1,X3,X4)),
    inference(unfold_definition,[status(thm)],[c_0_628,def_lhs_atom58]) ).

cnf(c_0_629_0,axiom,
    hAPP(c_Type_Oshift(X2,X1,X3,X4),X1) = X3,
    inference(unfold_definition,[status(thm)],[c_0_629,def_lhs_atom30]) ).

cnf(c_0_630_0,axiom,
    hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X4,X1,tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X3,X1,tc_nat)),X2)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),X3),X1,tc_nat)),X2),
    inference(unfold_definition,[status(thm)],[c_0_630,def_lhs_atom2]) ).

cnf(c_0_633_0,axiom,
    hAPP(hAPP(c_Lambda_OdB_OApp,X3),X2) != c_Lambda_OdB_OVar(X1),
    inference(unfold_definition,[status(thm)],[c_0_633,def_lhs_atom120]) ).

cnf(c_0_634_0,axiom,
    c_Lambda_OdB_OVar(X1) != hAPP(hAPP(c_Lambda_OdB_OApp,X3),X2),
    inference(unfold_definition,[status(thm)],[c_0_634,def_lhs_atom115]) ).

cnf(c_0_635_0,axiom,
    hAPP(hAPP(c_Lambda_Olift,c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X1,tc_Lambda_OdB,tc_Lambda_OdB)),X3) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_Olift,X2),X3),c_List_Omap(c_COMBC(c_Lambda_Olift,X3,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X1,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
    inference(unfold_definition,[status(thm)],[c_0_635,def_lhs_atom108]) ).

cnf(c_0_636_0,axiom,
    c_HOL_Otimes__class_Otimes(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1),tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat)),c_HOL_Otimes__class_Otimes(X3,X1,tc_nat)),
    inference(unfold_definition,[status(thm)],[c_0_636,def_lhs_atom78]) ).

cnf(c_0_637_0,axiom,
    c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1),X3,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat)),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat)),
    inference(unfold_definition,[status(thm)],[c_0_637,def_lhs_atom77]) ).

cnf(c_0_638_0,axiom,
    c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),X3,tc_nat) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_638,def_lhs_atom76]) ).

cnf(c_0_639_0,axiom,
    c_Divides_Odiv__class_Odiv(X3,c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),tc_nat) = c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Odiv(X3,X2,tc_nat),X1,tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_639,def_lhs_atom72]) ).

cnf(c_0_640_0,axiom,
    c_Divides_Odiv__class_Omod(X3,c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X2,c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Odiv(X3,X2,tc_nat),X1,tc_nat),tc_nat)),c_Divides_Odiv__class_Omod(X3,X2,tc_nat)),
    inference(unfold_definition,[status(thm)],[c_0_640,def_lhs_atom69]) ).

cnf(c_0_641_0,axiom,
    hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,X1),X3)),X2),X3) = X1,
    inference(unfold_definition,[status(thm)],[c_0_641,def_lhs_atom63]) ).

cnf(c_0_642_0,axiom,
    c_List_Omap(X1,c_List_Olist_ONil(X2),X2,X3) = c_List_Olist_ONil(X3),
    inference(unfold_definition,[status(thm)],[c_0_642,def_lhs_atom59]) ).

cnf(c_0_643_0,axiom,
    c_List_Omap(X1,c_List_Olist_ONil(X2),X2,X3) = c_List_Olist_ONil(X3),
    inference(unfold_definition,[status(thm)],[c_0_643,def_lhs_atom59]) ).

cnf(c_0_644_0,axiom,
    hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_OdB_OApp,X2),X1)),X3) = hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_Olift,X2),X3)),hAPP(hAPP(c_Lambda_Olift,X1),X3)),
    inference(unfold_definition,[status(thm)],[c_0_644,def_lhs_atom56]) ).

cnf(c_0_645_0,axiom,
    c_Lambda_OdB_OAbs(X1) != hAPP(hAPP(c_Lambda_OdB_OApp,X3),X2),
    inference(unfold_definition,[status(thm)],[c_0_645,def_lhs_atom55]) ).

cnf(c_0_646_0,axiom,
    hAPP(hAPP(c_Lambda_OdB_OApp,X3),X2) != c_Lambda_OdB_OAbs(X1),
    inference(unfold_definition,[status(thm)],[c_0_646,def_lhs_atom54]) ).

cnf(c_0_647_0,axiom,
    c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),X1,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X3,c_Divides_Odiv__class_Odiv(X2,X1,tc_nat),tc_nat)),c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X3,c_Divides_Odiv__class_Omod(X2,X1,tc_nat),tc_nat),X1,tc_nat)),
    inference(unfold_definition,[status(thm)],[c_0_647,def_lhs_atom36]) ).

cnf(c_0_648_0,axiom,
    c_Divides_Odiv__class_Omod(c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X3,X1,tc_nat)),X2)),X1,tc_nat) = c_Divides_Odiv__class_Omod(c_Suc(X2),X1,tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_648,def_lhs_atom31]) ).

cnf(c_0_649_0,axiom,
    c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X3,X1,tc_nat)),X2),X1,tc_nat) = c_Divides_Odiv__class_Omod(X2,X1,tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_649,def_lhs_atom26]) ).

cnf(c_0_650_0,axiom,
    c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),X1,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Odiv(X3,X1,tc_nat)),c_Divides_Odiv__class_Odiv(X2,X1,tc_nat))),c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Omod(X3,X1,tc_nat)),c_Divides_Odiv__class_Omod(X2,X1,tc_nat)),X1,tc_nat)),
    inference(unfold_definition,[status(thm)],[c_0_650,def_lhs_atom25]) ).

cnf(c_0_651_0,axiom,
    c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X2,X1,tc_nat),X3,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_651,def_lhs_atom24]) ).

cnf(c_0_652_0,axiom,
    c_HOL_Otimes__class_Otimes(X3,c_Divides_Odiv__class_Omod(X2,X1,tc_nat),tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_652,def_lhs_atom23]) ).

cnf(c_0_653_0,axiom,
    hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OAbs(X1)),X2),X3) = c_Lambda_OdB_OAbs(hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),hAPP(hAPP(c_Lambda_Olift,X2),c_HOL_Ozero__class_Ozero(tc_nat))),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat)))),
    inference(unfold_definition,[status(thm)],[c_0_653,def_lhs_atom20]) ).

cnf(c_0_654_0,axiom,
    c_Lambda_Osubstn(c_Lambda_OdB_OAbs(X1),X2,X3) = c_Lambda_OdB_OAbs(c_Lambda_Osubstn(X1,X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat)))),
    inference(unfold_definition,[status(thm)],[c_0_654,def_lhs_atom18]) ).

cnf(c_0_655_0,axiom,
    hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat)),c_HOL_Otimes__class_Otimes(X3,X1,tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X3,X1,tc_nat)),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat)),
    inference(unfold_definition,[status(thm)],[c_0_655,def_lhs_atom7]) ).

cnf(c_0_656_0,axiom,
    hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat)),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat)),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat)),
    inference(unfold_definition,[status(thm)],[c_0_656,def_lhs_atom6]) ).

cnf(c_0_657_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_657,def_lhs_atom4]) ).

cnf(c_0_658_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_658,def_lhs_atom3]) ).

cnf(c_0_659_0,axiom,
    c_fequal(X1,X1,X2),
    inference(unfold_definition,[status(thm)],[c_0_659,def_lhs_atom152]) ).

cnf(c_0_660_0,axiom,
    hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X2)),X1),X2) = X1,
    inference(unfold_definition,[status(thm)],[c_0_660,def_lhs_atom110]) ).

cnf(c_0_661_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_661,def_lhs_atom104]) ).

cnf(c_0_662_0,axiom,
    c_Lambda_Osubstn(X1,X2,c_HOL_Ozero__class_Ozero(tc_nat)) = hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X2),c_HOL_Ozero__class_Ozero(tc_nat)),
    inference(unfold_definition,[status(thm)],[c_0_662,def_lhs_atom101]) ).

cnf(c_0_663_0,axiom,
    c_Lambda_Obeta(hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X2)),X1),hAPP(hAPP(hAPP(c_Lambda_Osubst,X2),X1),c_HOL_Ozero__class_Ozero(tc_nat))),
    inference(unfold_definition,[status(thm)],[c_0_663,def_lhs_atom83]) ).

cnf(c_0_664_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_664,def_lhs_atom82]) ).

cnf(c_0_665_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_665,def_lhs_atom81]) ).

cnf(c_0_666_0,axiom,
    c_Type_Otyping(X2,c_Lambda_OdB_OVar(X1),hAPP(X2,X1)),
    inference(unfold_definition,[status(thm)],[c_0_666,def_lhs_atom80]) ).

cnf(c_0_667_0,axiom,
    hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OAbs(X1)),X2) = c_Lambda_OdB_OAbs(hAPP(hAPP(c_Lambda_Olift,X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)))),
    inference(unfold_definition,[status(thm)],[c_0_667,def_lhs_atom74]) ).

cnf(c_0_668_0,axiom,
    c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),X2,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_668,def_lhs_atom73]) ).

cnf(c_0_669_0,axiom,
    ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X2,tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_669,def_lhs_atom71]) ).

cnf(c_0_670_0,axiom,
    ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1),X2,tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_670,def_lhs_atom70]) ).

cnf(c_0_671_0,axiom,
    c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_671,def_lhs_atom68]) ).

cnf(c_0_672_0,axiom,
    c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OAbs(X2),
    inference(unfold_definition,[status(thm)],[c_0_672,def_lhs_atom66]) ).

cnf(c_0_673_0,axiom,
    ~ c_Lambda_Obeta(c_Lambda_OdB_OVar(X2),X1),
    inference(unfold_definition,[status(thm)],[c_0_673,def_lhs_atom65]) ).

cnf(c_0_674_0,axiom,
    c_Lambda_OdB_OAbs(X2) != c_Lambda_OdB_OVar(X1),
    inference(unfold_definition,[status(thm)],[c_0_674,def_lhs_atom64]) ).

cnf(c_0_675_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_675,def_lhs_atom53]) ).

cnf(c_0_676_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_676,def_lhs_atom52]) ).

cnf(c_0_677_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_677,def_lhs_atom51]) ).

cnf(c_0_678_0,axiom,
    c_Divides_Odiv__class_Omod(c_Suc(X2),X1,tc_nat) = c_Divides_Odiv__class_Omod(c_Suc(c_Divides_Odiv__class_Omod(X2,X1,tc_nat)),X1,tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_678,def_lhs_atom48]) ).

cnf(c_0_679_0,axiom,
    c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat),tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_679,def_lhs_atom35]) ).

cnf(c_0_680_0,axiom,
    c_HOL_Otimes__class_Otimes(c_Suc(X2),X1,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Otimes__class_Otimes(X2,X1,tc_nat)),
    inference(unfold_definition,[status(thm)],[c_0_680,def_lhs_atom29]) ).

cnf(c_0_681_0,axiom,
    c_HOL_Otimes__class_Otimes(X2,c_Suc(X1),tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Otimes__class_Otimes(X2,X1,tc_nat)),
    inference(unfold_definition,[status(thm)],[c_0_681,def_lhs_atom28]) ).

cnf(c_0_682_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_682,def_lhs_atom19]) ).

cnf(c_0_683_0,axiom,
    c_HOL_Oord__class_Oless(X2,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1)),tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_683,def_lhs_atom16]) ).

cnf(c_0_684_0,axiom,
    c_HOL_Oord__class_Oless(X2,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)),tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_684,def_lhs_atom15]) ).

cnf(c_0_685_0,axiom,
    c_HOL_Oord__class_Oless(X2,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1)),tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_685,def_lhs_atom14]) ).

cnf(c_0_686_0,axiom,
    c_List_Olistsp(X1,c_List_Olist_ONil(X2),X2),
    inference(unfold_definition,[status(thm)],[c_0_686,def_lhs_atom13]) ).

cnf(c_0_687_0,axiom,
    c_HOL_Otimes__class_Otimes(X2,X1,tc_nat) = c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_687,def_lhs_atom5]) ).

cnf(c_0_688_0,axiom,
    c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X1),
    inference(unfold_definition,[status(thm)],[c_0_688,def_lhs_atom118]) ).

cnf(c_0_689_0,axiom,
    c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X1),
    inference(unfold_definition,[status(thm)],[c_0_689,def_lhs_atom117]) ).

cnf(c_0_690_0,axiom,
    c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_690,def_lhs_atom114]) ).

cnf(c_0_691_0,axiom,
    c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_691,def_lhs_atom113]) ).

cnf(c_0_692_0,axiom,
    c_Suc(X1) != X1,
    inference(unfold_definition,[status(thm)],[c_0_692,def_lhs_atom112]) ).

cnf(c_0_693_0,axiom,
    X1 != c_Suc(X1),
    inference(unfold_definition,[status(thm)],[c_0_693,def_lhs_atom111]) ).

cnf(c_0_694_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_694,def_lhs_atom106]) ).

cnf(c_0_695_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_695,def_lhs_atom103]) ).

cnf(c_0_696_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_696,def_lhs_atom102]) ).

cnf(c_0_697_0,axiom,
    c_Divides_Odiv__class_Odiv(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = X1,
    inference(unfold_definition,[status(thm)],[c_0_697,def_lhs_atom100]) ).

cnf(c_0_698_0,axiom,
    c_Power_Opower__class_Opower(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
    inference(unfold_definition,[status(thm)],[c_0_698,def_lhs_atom99]) ).

cnf(c_0_699_0,axiom,
    c_Power_Opower__class_Opower(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
    inference(unfold_definition,[status(thm)],[c_0_699,def_lhs_atom98]) ).

cnf(c_0_700_0,axiom,
    c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X1),tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_700,def_lhs_atom97]) ).

cnf(c_0_701_0,axiom,
    c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X1),tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_701,def_lhs_atom96]) ).

cnf(c_0_702_0,axiom,
    c_Ring__and__Field_Odvd__class_Odvd(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_702,def_lhs_atom94]) ).

cnf(c_0_703_0,axiom,
    c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
    inference(unfold_definition,[status(thm)],[c_0_703,def_lhs_atom92]) ).

cnf(c_0_704_0,axiom,
    c_Divides_Odiv__class_Omod(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_704,def_lhs_atom86]) ).

cnf(c_0_705_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_705,def_lhs_atom75]) ).

cnf(c_0_706_0,axiom,
    c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Oone__class_Oone(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_706,def_lhs_atom67]) ).

cnf(c_0_707_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_707,def_lhs_atom61]) ).

cnf(c_0_708_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_708,def_lhs_atom60]) ).

cnf(c_0_709_0,axiom,
    c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_709,def_lhs_atom50]) ).

cnf(c_0_710_0,axiom,
    c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_710,def_lhs_atom49]) ).

cnf(c_0_711_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_711,def_lhs_atom47]) ).

cnf(c_0_712_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_712,def_lhs_atom46]) ).

cnf(c_0_713_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_713,def_lhs_atom45]) ).

cnf(c_0_714_0,axiom,
    ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_714,def_lhs_atom44]) ).

cnf(c_0_715_0,axiom,
    ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_715,def_lhs_atom43]) ).

cnf(c_0_716_0,axiom,
    c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_716,def_lhs_atom41]) ).

cnf(c_0_717_0,axiom,
    c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_717,def_lhs_atom40]) ).

cnf(c_0_718_0,axiom,
    c_Ring__and__Field_Odvd__class_Odvd(X1,X1,tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_718,def_lhs_atom34]) ).

cnf(c_0_719_0,axiom,
    ~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_719,def_lhs_atom33]) ).

cnf(c_0_720_0,axiom,
    ~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_720,def_lhs_atom32]) ).

cnf(c_0_721_0,axiom,
    c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_721,def_lhs_atom27]) ).

cnf(c_0_722_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_722,def_lhs_atom21]) ).

cnf(c_0_723_0,axiom,
    c_HOL_Otimes__class_Otimes(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X1,
    inference(unfold_definition,[status(thm)],[c_0_723,def_lhs_atom12]) ).

cnf(c_0_724_0,axiom,
    c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat) = X1,
    inference(unfold_definition,[status(thm)],[c_0_724,def_lhs_atom11]) ).

cnf(c_0_725_0,axiom,
    c_Suc(X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),X1),
    inference(unfold_definition,[status(thm)],[c_0_725,def_lhs_atom10]) ).

cnf(c_0_726_0,axiom,
    c_Suc(X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),
    inference(unfold_definition,[status(thm)],[c_0_726,def_lhs_atom9]) ).

cnf(c_0_727_0,axiom,
    class_Power_Opower(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_727,def_lhs_atom150]) ).

cnf(c_0_728_0,axiom,
    class_Orderings_Oorder(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_728,def_lhs_atom149]) ).

cnf(c_0_729_0,axiom,
    class_Orderings_Olinorder(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_729,def_lhs_atom148]) ).

cnf(c_0_730_0,axiom,
    class_Orderings_Opreorder(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_730,def_lhs_atom147]) ).

cnf(c_0_731_0,axiom,
    class_Ring__and__Field_Odvd(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_731,def_lhs_atom146]) ).

cnf(c_0_732_0,axiom,
    class_Nat_Osemiring__char__0(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_732,def_lhs_atom145]) ).

cnf(c_0_733_0,axiom,
    class_Divides_Osemiring__div(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_733,def_lhs_atom144]) ).

cnf(c_0_734_0,axiom,
    class_OrderedGroup_Omonoid__add(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_734,def_lhs_atom143]) ).

cnf(c_0_735_0,axiom,
    class_Ring__and__Field_Osemiring(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_735,def_lhs_atom142]) ).

cnf(c_0_736_0,axiom,
    class_OrderedGroup_Omonoid__mult(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_736,def_lhs_atom141]) ).

cnf(c_0_737_0,axiom,
    class_Ring__and__Field_Omult__zero(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_737,def_lhs_atom140]) ).

cnf(c_0_738_0,axiom,
    class_Ring__and__Field_Osemiring__0(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_738,def_lhs_atom139]) ).

cnf(c_0_739_0,axiom,
    class_Ring__and__Field_Osemiring__1(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_739,def_lhs_atom138]) ).

cnf(c_0_740_0,axiom,
    class_OrderedGroup_Osemigroup__add(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_740,def_lhs_atom137]) ).

cnf(c_0_741_0,axiom,
    class_Ring__and__Field_Ozero__neq__one(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_741,def_lhs_atom136]) ).

cnf(c_0_742_0,axiom,
    class_OrderedGroup_Ocomm__monoid__add(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_742,def_lhs_atom135]) ).

cnf(c_0_743_0,axiom,
    class_Ring__and__Field_Ocomm__semiring(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_743,def_lhs_atom134]) ).

cnf(c_0_744_0,axiom,
    class_OrderedGroup_Oab__semigroup__add(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_744,def_lhs_atom133]) ).

cnf(c_0_745_0,axiom,
    class_OrderedGroup_Ocomm__monoid__mult(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_745,def_lhs_atom132]) ).

cnf(c_0_746_0,axiom,
    class_OrderedGroup_Oab__semigroup__mult(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_746,def_lhs_atom131]) ).

cnf(c_0_747_0,axiom,
    class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_747,def_lhs_atom130]) ).

cnf(c_0_748_0,axiom,
    class_Ring__and__Field_Oordered__semidom(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_748,def_lhs_atom129]) ).

cnf(c_0_749_0,axiom,
    class_Ring__and__Field_Ono__zero__divisors(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_749,def_lhs_atom128]) ).

cnf(c_0_750_0,axiom,
    class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_750,def_lhs_atom127]) ).

cnf(c_0_751_0,axiom,
    class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_751,def_lhs_atom126]) ).

cnf(c_0_752_0,axiom,
    class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_752,def_lhs_atom125]) ).

cnf(c_0_753_0,axiom,
    class_Ring__and__Field_Oordered__semiring__strict(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_753,def_lhs_atom124]) ).

cnf(c_0_754_0,axiom,
    class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_754,def_lhs_atom123]) ).

cnf(c_0_755_0,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_755,def_lhs_atom122]) ).

cnf(c_0_756_0,axiom,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_756,def_lhs_atom121]) ).

cnf(c_0_757_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_757,def_lhs_atom95]) ).

cnf(c_0_758_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_758,def_lhs_atom93]) ).

cnf(c_0_759_0,axiom,
    c_HOL_Oone__class_Oone(tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
    inference(unfold_definition,[status(thm)],[c_0_759,def_lhs_atom90]) ).

cnf(c_0_760_0,axiom,
    c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_760,def_lhs_atom89]) ).

cnf(c_0_761_0,axiom,
    c_Ring__and__Field_Odvd__class_Odvd(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_761,def_lhs_atom88]) ).

cnf(c_0_762_0,axiom,
    c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
    inference(unfold_definition,[status(thm)],[c_0_762,def_lhs_atom87]) ).

cnf(c_0_763_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_763,def_lhs_atom85]) ).

cnf(c_0_764_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_764,def_lhs_atom84]) ).

cnf(c_0_765_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_765,def_lhs_atom42]) ).

cnf(c_0_766_0,axiom,
    ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_766,def_lhs_atom39]) ).

cnf(c_0_767_0,axiom,
    c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_HOL_Oone__class_Oone(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_767,def_lhs_atom22]) ).

cnf(c_0_768_0,axiom,
    c_HOL_Oone__class_Oone(tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_768,def_lhs_atom17]) ).

cnf(c_0_769_0,axiom,
    c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_769,def_lhs_atom1]) ).

% Orienting (remaining) axiom formulas using strategy ClausalAll
% CNF of (remaining) axioms:
% Start CNF derivation
fof(c_0_0_001,axiom,
    ! [X26,X6,X21,X22,X28,X24] :
      ( c_Type_Otypings(X22,c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,X26,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),X21,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X6,tc_Lambda_OdB,tc_Lambda_OdB),X28)
      | ~ c_Type_Otypings(c_Type_Oshift(X22,X21,X24,tc_Type_Otype),X6,X28)
      | ~ c_Type_Otyping(X22,X26,X24) ),
    file('<stdin>',cls_substs__lemma_0) ).

fof(c_0_1_002,axiom,
    ! [X13,X7,X8] :
      ( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X8)),X7),X13,tc_Lambda_OdB,tc_Lambda_OdB)))
      | ~ hBOOL(hAPP(c_InductTermi_OIT,X7))
      | ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X8),X7),c_HOL_Ozero__class_Ozero(tc_nat)),X13,tc_Lambda_OdB,tc_Lambda_OdB))) ),
    file('<stdin>',cls_Beta_0) ).

fof(c_0_2_003,axiom,
    ! [X54,X55,X47,X48,X49,X31] :
      ( ~ hBOOL(hAPP(X31,c_Lambda_OdB_OdB__case(X49,X48,X47,hAPP(hAPP(c_Lambda_OdB_OApp,X55),X54),t_a)))
      | hBOOL(hAPP(X31,hAPP(hAPP(X48,X55),X54))) ),
    file('<stdin>',cls_dB_Osplit__asm_1) ).

fof(c_0_3_004,axiom,
    ! [X47,X48,X49,X16,X18,X31] :
      ( ~ hBOOL(hAPP(X31,c_Lambda_OdB_OdB__case(X49,X48,X47,hAPP(hAPP(c_Lambda_OdB_OApp,X18),X16),t_a)))
      | hBOOL(hAPP(X31,hAPP(hAPP(X48,X18),X16))) ),
    file('<stdin>',cls_dB_Osplit_1) ).

fof(c_0_4_005,axiom,
    ! [X6,X21,X22,X23,X24] :
      ( X24 = X23
      | ~ c_Type_Otyping(X22,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X21),X6,tc_Lambda_OdB,tc_Lambda_OdB),X23)
      | ~ c_Type_Otyping(X22,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X21),X6,tc_Lambda_OdB,tc_Lambda_OdB),X24) ),
    file('<stdin>',cls_var__app__type__eq_0) ).

fof(c_0_5_006,axiom,
    ! [X51,X47,X48,X49,X31] :
      ( ~ hBOOL(hAPP(X31,c_Lambda_OdB_OdB__case(X49,X48,X47,c_Lambda_OdB_OVar(X51),t_a)))
      | hBOOL(hAPP(X31,hAPP(X49,X51))) ),
    file('<stdin>',cls_dB_Osplit__asm_0) ).

fof(c_0_6_007,axiom,
    ! [X12,X47,X48,X49,X31] :
      ( ~ hBOOL(hAPP(X31,c_Lambda_OdB_OdB__case(X49,X48,X47,c_Lambda_OdB_OVar(X12),t_a)))
      | hBOOL(hAPP(X31,hAPP(X49,X12))) ),
    file('<stdin>',cls_dB_Osplit_0) ).

fof(c_0_7_008,axiom,
    ! [X47,X48,X49,X50,X31] :
      ( ~ hBOOL(hAPP(X31,c_Lambda_OdB_OdB__case(X49,X48,X47,c_Lambda_OdB_OAbs(X50),t_a)))
      | hBOOL(hAPP(X31,hAPP(X47,X50))) ),
    file('<stdin>',cls_dB_Osplit_2) ).

fof(c_0_8_009,axiom,
    ! [X46,X47,X48,X49,X31] :
      ( ~ hBOOL(hAPP(X31,c_Lambda_OdB_OdB__case(X49,X48,X47,c_Lambda_OdB_OAbs(X46),t_a)))
      | hBOOL(hAPP(X31,hAPP(X47,X46))) ),
    file('<stdin>',cls_dB_Osplit__asm_2) ).

fof(c_0_9_010,axiom,
    ! [X6,X21,X22,X23,X28] :
      ( c_Type_Otypings(c_Type_Oshift(X22,X21,X23,tc_Type_Otype),c_List_Omap(c_COMBC(c_Lambda_Olift,X21,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X6,tc_Lambda_OdB,tc_Lambda_OdB),X28)
      | ~ c_Type_Otypings(X22,X6,X28) ),
    file('<stdin>',cls_lift__types_0) ).

fof(c_0_10_011,axiom,
    ! [X6] :
      ( c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X6,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)
      | ~ c_List_Olistsp(c_InductTermi_OIT,X6,tc_Lambda_OdB) ),
    file('<stdin>',cls_lifts__IT_0) ).

fof(c_0_11_012,axiom,
    ! [X32,X19,X20] :
      ( X32 = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X20),c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(X20,X19,X32),tc_Lambda_OdB,tc_Lambda_OdB)
      | ~ c_Lambda_Obeta(c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X20),X19,tc_Lambda_OdB,tc_Lambda_OdB),X32) ),
    file('<stdin>',cls_head__Var__reduction_1) ).

fof(c_0_12_013,axiom,
    ! [X19,X20] :
      ( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X20),X19,tc_Lambda_OdB,tc_Lambda_OdB)))
      | ~ c_List_Olistsp(c_InductTermi_OIT,X19,tc_Lambda_OdB) ),
    file('<stdin>',cls_IT_OVar_0) ).

fof(c_0_13_014,axiom,
    ! [X13,X7,X8] :
      ( c_Lambda_Obeta(c_List_Ofoldl(c_Lambda_OdB_OApp,X8,X13,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,X7,X13,tc_Lambda_OdB,tc_Lambda_OdB))
      | ~ c_Lambda_Obeta(X8,X7) ),
    file('<stdin>',cls_apps__preserves__beta_0) ).

fof(c_0_14_015,axiom,
    ! [X13,X7,X19,X8] :
      ( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X8),X19,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X7),X13,tc_Lambda_OdB,tc_Lambda_OdB)
      | X8 = X7 ),
    file('<stdin>',cls_Abs__apps__eq__Abs__apps__conv_0) ).

fof(c_0_15_016,axiom,
    ! [X13,X7,X19,X8] :
      ( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X8),X19,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X7),X13,tc_Lambda_OdB,tc_Lambda_OdB)
      | X19 = X13 ),
    file('<stdin>',cls_Abs__apps__eq__Abs__apps__conv_1) ).

fof(c_0_16_017,axiom,
    ! [X13,X19,X20,X14] :
      ( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X14),X19,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X20),X13,tc_Lambda_OdB,tc_Lambda_OdB)
      | X14 = X20 ),
    file('<stdin>',cls_Var__apps__eq__Var__apps__conv_0) ).

fof(c_0_17_018,axiom,
    ! [X13,X19,X20,X14] :
      ( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X14),X19,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X20),X13,tc_Lambda_OdB,tc_Lambda_OdB)
      | X19 = X13 ),
    file('<stdin>',cls_Var__apps__eq__Var__apps__conv_1) ).

fof(c_0_18_019,axiom,
    ! [X30,X9,X10,X3] :
      ( ~ class_OrderedGroup_Osemigroup__add(X3)
      | c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X10),X9),X30,X3,X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X10),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),X9,X30,X3,X3)) ),
    file('<stdin>',cls_foldl__assoc_0) ).

fof(c_0_19_020,axiom,
    ! [X6,X7,X8] :
      ( c_List_Ofoldl(c_Lambda_OdB_OApp,X8,X6,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,X7,X6,tc_Lambda_OdB,tc_Lambda_OdB)
      | X8 = X7 ),
    file('<stdin>',cls_apps__eq__tail__conv_0) ).

fof(c_0_20_021,axiom,
    ! [X30,X10,X3] :
      ( ~ class_OrderedGroup_Omonoid__add(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X10),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3),X30,X3,X3)) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),X10,X30,X3,X3) ),
    file('<stdin>',cls_foldl__absorb0_0) ).

fof(c_0_21_022,axiom,
    ! [X25,X27,X21,X31] :
      ( ~ c_HOL_Oord__class_Oless(X27,X25,tc_nat)
      | X25 = c_HOL_Ozero__class_Ozero(tc_nat)
      | ~ hBOOL(hAPP(X31,c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X25,X21,tc_nat)),X27),X25,tc_nat)))
      | hBOOL(hAPP(X31,X27)) ),
    file('<stdin>',cls_split__mod_1) ).

fof(c_0_22_023,axiom,
    ! [X25,X27,X21,X31] :
      ( ~ c_HOL_Oord__class_Oless(X27,X25,tc_nat)
      | X25 = c_HOL_Ozero__class_Ozero(tc_nat)
      | ~ hBOOL(hAPP(X31,c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X25,X21,tc_nat)),X27),X25,tc_nat)))
      | hBOOL(hAPP(X31,X21)) ),
    file('<stdin>',cls_split__div_1) ).

fof(c_0_23_024,axiom,
    ! [X37,X35,X33,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(X35,c_Divides_Odiv__class_Odiv(X33,X35,X3),X3)),c_Divides_Odiv__class_Omod(X33,X35,X3))),X37) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X37) ),
    file('<stdin>',cls_div__mod__equality2_0) ).

fof(c_0_24_025,axiom,
    ! [X37,X35,X33,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X33,X35,X3),X35,X3)),c_Divides_Odiv__class_Omod(X33,X35,X3))),X37) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X37) ),
    file('<stdin>',cls_div__mod__equality_0) ).

fof(c_0_25_026,axiom,
    ! [X32,X26,X29,X27,X21] :
      ( hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,X29),hAPP(hAPP(c_Lambda_Olift,X32),X21)),c_Suc(X27))),hAPP(hAPP(hAPP(c_Lambda_Osubst,X26),X32),X27)),X21) = hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,X29),X26),X21)),X32),X27)
      | ~ c_HOL_Oord__class_Oless(X21,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X27),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
    file('<stdin>',cls_subst__subst_0) ).

fof(c_0_26_027,axiom,
    ! [X29,X7,X8] :
      ( hAPP(hAPP(c_Lambda_OdB_OApp,X8),X7) != c_List_Ofoldl(c_Lambda_OdB_OApp,X29,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)
      | hAPP(hAPP(c_Lambda_OdB_OApp,X8),X7) = X29 ),
    file('<stdin>',cls_App__eq__foldl__conv_0) ).

fof(c_0_27_028,axiom,
    ! [X13,X7,X8] :
      ( c_List_Ofoldl(c_Lambda_OdB_OApp,X7,X13,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X8)
      | X7 = c_Lambda_OdB_OAbs(X8) ),
    file('<stdin>',cls_apps__eq__Abs__conv_0) ).

fof(c_0_28_029,axiom,
    ! [X13,X7,X8] :
      ( c_Lambda_OdB_OAbs(X8) != c_List_Ofoldl(c_Lambda_OdB_OApp,X7,X13,tc_Lambda_OdB,tc_Lambda_OdB)
      | c_Lambda_OdB_OAbs(X8) = X7 ),
    file('<stdin>',cls_Abs__eq__apps__conv_0) ).

fof(c_0_29_030,axiom,
    ! [X13,X7,X14] :
      ( c_Lambda_OdB_OVar(X14) != c_List_Ofoldl(c_Lambda_OdB_OApp,X7,X13,tc_Lambda_OdB,tc_Lambda_OdB)
      | c_Lambda_OdB_OVar(X14) = X7 ),
    file('<stdin>',cls_Var__eq__apps__conv_0) ).

fof(c_0_30_031,axiom,
    ! [X29,X7,X27,X21] :
      ( hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(hAPP(c_Lambda_Osubst,X29),X7),X27)),X21) = hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,X29),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X21),c_HOL_Oone__class_Oone(tc_nat)))),hAPP(hAPP(c_Lambda_Olift,X7),X21)),X27)
      | ~ c_HOL_Oord__class_Oless(X27,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X21),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
    file('<stdin>',cls_lift__subst_0) ).

fof(c_0_31_032,axiom,
    ! [X20,X14,X34,X3] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
      | c_Finite__Set_Osetsum(X34,c_SetInterval_Oord__class_OatLeastLessThan(X14,c_Suc(X20),tc_nat),tc_nat,X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_Finite__Set_Osetsum(X34,c_SetInterval_Oord__class_OatLeastLessThan(X14,X20,tc_nat),tc_nat,X3)),hAPP(X34,X20))
      | c_HOL_Oord__class_Oless(X20,X14,tc_nat) ),
    file('<stdin>',cls_setsum__op__ivl__Suc_1) ).

fof(c_0_32_033,axiom,
    ! [X13,X7,X8] :
      ( c_Lambda_OdB_OAbs(X8) != c_List_Ofoldl(c_Lambda_OdB_OApp,X7,X13,tc_Lambda_OdB,tc_Lambda_OdB)
      | X13 = c_List_Olist_ONil(tc_Lambda_OdB) ),
    file('<stdin>',cls_Abs__eq__apps__conv_1) ).

fof(c_0_33_034,axiom,
    ! [X13,X7,X8] :
      ( c_List_Ofoldl(c_Lambda_OdB_OApp,X7,X13,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X8)
      | X13 = c_List_Olist_ONil(tc_Lambda_OdB) ),
    file('<stdin>',cls_apps__eq__Abs__conv_1) ).

fof(c_0_34_035,axiom,
    ! [X13,X7,X14] :
      ( c_Lambda_OdB_OVar(X14) != c_List_Ofoldl(c_Lambda_OdB_OApp,X7,X13,tc_Lambda_OdB,tc_Lambda_OdB)
      | X13 = c_List_Olist_ONil(tc_Lambda_OdB) ),
    file('<stdin>',cls_Var__eq__apps__conv_1) ).

fof(c_0_35_036,axiom,
    ! [X8,X42,X37,X35] :
      ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X35,c_Divides_Odiv__class_Omod(X42,X37,tc_nat),tc_nat)),X8),c_HOL_Otimes__class_Otimes(X35,X37,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X8,X35,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X37,tc_nat) ),
    file('<stdin>',cls_mod__lemma_0) ).

fof(c_0_36_037,axiom,
    ! [X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(X3),X3)),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(X3),X3)),X3) ),
    file('<stdin>',cls_sum__squares__gt__zero__iff_0) ).

fof(c_0_37_038,axiom,
    ! [X22,X37,X35,X33,X3] :
      ( ~ class_Ring__and__Field_Osemiring(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(X33,X22,X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(X35,X22,X3)),X37)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X35),X22,X3)),X37) ),
    file('<stdin>',cls_combine__common__factor_0) ).

fof(c_0_38_039,axiom,
    ! [X9,X10,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(X10,X10,X3)),c_HOL_Otimes__class_Otimes(X9,X9,X3)),c_HOL_Ozero__class_Ozero(X3),X3) ),
    file('<stdin>',cls_not__sum__squares__lt__zero_0) ).

fof(c_0_39_040,axiom,
    ! [X20,X14,X34,X3] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
      | c_Finite__Set_Osetsum(X34,c_SetInterval_Oord__class_OatLeastLessThan(X14,X20,tc_nat),tc_nat,X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(X34,X14)),c_Finite__Set_Osetsum(X34,c_SetInterval_Oord__class_OatLeastLessThan(c_Suc(X14),X20,tc_nat),tc_nat,X3))
      | ~ c_HOL_Oord__class_Oless(X14,X20,tc_nat) ),
    file('<stdin>',cls_setsum__head__upt__Suc_0) ).

fof(c_0_40_041,axiom,
    ! [X29,X7,X27,X21] :
      ( hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(hAPP(c_Lambda_Osubst,X29),X7),X27)),X21) = hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,X29),X21)),hAPP(hAPP(c_Lambda_Olift,X7),X21)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X27),c_HOL_Oone__class_Oone(tc_nat)))
      | ~ c_HOL_Oord__class_Oless(X21,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X27),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
    file('<stdin>',cls_lift__subst__lt_0) ).

fof(c_0_41_042,axiom,
    ! [X36,X9,X10,X56,X3] :
      ( ~ class_Ring__and__Field_Oidom(X3)
      | ~ class_Int_Onumber__ring(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(X56,X9,X3)),c_HOL_Otimes__class_Otimes(X10,X36,X3)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(X56,X36,X3)),c_HOL_Otimes__class_Otimes(X10,X9,X3))
      | X9 = X36
      | X56 = X10 ),
    file('<stdin>',cls_class__ringb_Oadd__mul__solve_0) ).

fof(c_0_42_043,axiom,
    ! [X44,X37,X35,X33,X3] :
      ( ~ class_Ring__and__Field_Oidom(X3)
      | ~ class_Int_Onumber__ring(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(X33,X37,X3)),c_HOL_Otimes__class_Otimes(X35,X44,X3)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(X33,X44,X3)),c_HOL_Otimes__class_Otimes(X35,X37,X3))
      | X37 = X44
      | X33 = X35 ),
    file('<stdin>',cls_class__ringb_Onoteq__reduce_0) ).

fof(c_0_43_044,axiom,
    ! [X26,X29,X21,X62,X23,X24] :
      ( ~ c_Type_Otyping(X62,X26,X23)
      | ~ c_Type_Otyping(c_Type_Oshift(X62,X21,X23,tc_Type_Otype),X29,X24)
      | c_Type_Otyping(X62,hAPP(hAPP(hAPP(c_Lambda_Osubst,X29),X26),X21),X24) ),
    file('<stdin>',cls_subst__lemma_0) ).

fof(c_0_44_045,axiom,
    ! [X44,X37,X35,X33] :
      ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X33,X37,tc_nat)),c_HOL_Otimes__class_Otimes(X35,X44,tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X33,X44,tc_nat)),c_HOL_Otimes__class_Otimes(X35,X37,tc_nat))
      | X37 = X44
      | X33 = X35 ),
    file('<stdin>',cls_natgb_Onoteq__reduce_0) ).

fof(c_0_45_046,axiom,
    ! [X36,X9,X10,X56] :
      ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X56,X9,tc_nat)),c_HOL_Otimes__class_Otimes(X10,X36,tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X56,X36,tc_nat)),c_HOL_Otimes__class_Otimes(X10,X9,tc_nat))
      | X9 = X36
      | X56 = X10 ),
    file('<stdin>',cls_natgb_Oadd__mul__solve_0) ).

fof(c_0_46_047,axiom,
    ! [X37,X35,X33,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X35),X37,X3) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_Divides_Odiv__class_Omod(X33,X37,X3)),c_Divides_Odiv__class_Omod(X35,X37,X3)),X37,X3) ),
    file('<stdin>',cls_mod__add__eq_0) ).

fof(c_0_47_048,axiom,
    ! [X9,X10,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(X10,X10,X3)),c_HOL_Otimes__class_Otimes(X9,X9,X3)),X3)
      | X10 = c_HOL_Ozero__class_Ozero(X3) ),
    file('<stdin>',cls_sum__squares__gt__zero__iff_1) ).

fof(c_0_48_049,axiom,
    ! [X9,X10,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(X10,X10,X3)),c_HOL_Otimes__class_Otimes(X9,X9,X3)),X3)
      | X9 = c_HOL_Ozero__class_Ozero(X3) ),
    file('<stdin>',cls_sum__squares__gt__zero__iff_2) ).

fof(c_0_49_050,axiom,
    ! [X35,X33,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(X35,c_Divides_Odiv__class_Odiv(X33,X35,X3),X3)),c_Divides_Odiv__class_Omod(X33,X35,X3)) = X33 ),
    file('<stdin>',cls_mod__div__equality2_0) ).

fof(c_0_50_051,axiom,
    ! [X35,X33,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X33,X35,X3),X35,X3)),c_Divides_Odiv__class_Omod(X33,X35,X3)) = X33 ),
    file('<stdin>',cls_mod__div__equality_0) ).

fof(c_0_51_052,axiom,
    ! [X35,X33,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | X33 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X33,X35,X3),X35,X3)),c_Divides_Odiv__class_Omod(X33,X35,X3)) ),
    file('<stdin>',cls_mod__div__decomp_0) ).

fof(c_0_52_053,axiom,
    ! [X25,X34,X3] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
      | hAPP(X34,c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Ozero__class_Ozero(X3)
      | c_Finite__Set_Osetsum(X34,c_SetInterval_Oord__class_OatLeastLessThan(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X25,tc_nat),tc_nat,X3) = c_Finite__Set_Osetsum(X34,c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),X25,tc_nat),tc_nat,X3) ),
    file('<stdin>',cls_setsum__shift__lb__Suc0__0__upt_0) ).

fof(c_0_53_054,axiom,
    ! [X36,X9,X10,X3] :
      ( ~ class_Ring__and__Field_Oidom(X3)
      | ~ class_Int_Onumber__ring(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(X10,X9,X3)),c_HOL_Otimes__class_Otimes(X10,X36,X3)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(X10,X36,X3)),c_HOL_Otimes__class_Otimes(X10,X9,X3)) ),
    file('<stdin>',cls_class__ringb_Oadd__mul__solve_1) ).

fof(c_0_54_055,axiom,
    ! [X10,X44,X37,X3] :
      ( ~ class_Ring__and__Field_Oidom(X3)
      | ~ class_Int_Onumber__ring(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(X10,X37,X3)),c_HOL_Otimes__class_Otimes(X10,X44,X3)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(X10,X44,X3)),c_HOL_Otimes__class_Otimes(X10,X37,X3)) ),
    file('<stdin>',cls_class__ringb_Onoteq__reduce_1) ).

fof(c_0_55_056,axiom,
    ! [X37,X35,X33,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X33,X35,X3),X37,X3) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X33,X37,X3),c_Divides_Odiv__class_Omod(X35,X37,X3),X3),X37,X3) ),
    file('<stdin>',cls_mod__mult__eq_0) ).

fof(c_0_56_057,axiom,
    ! [X37,X35,X33,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X35),X37,X3) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_Divides_Odiv__class_Omod(X33,X37,X3)),X35),X37,X3) ),
    file('<stdin>',cls_mod__add__left__eq_0) ).

fof(c_0_57_058,axiom,
    ! [X37,X35,X33,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_Divides_Odiv__class_Omod(X33,X37,X3)),X35),X37,X3) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X35),X37,X3) ),
    file('<stdin>',cls_zmod__simps_I1_J_0) ).

fof(c_0_58_059,axiom,
    ! [X44,X37,X35,X33,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),X33),X35)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X37),X44)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X37)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X35),X44)) ),
    file('<stdin>',cls_class__semiring_Osemiring__rules_I20_J_0) ).

fof(c_0_59_060,axiom,
    ! [X36,X9,X10,X56,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X10,X9,X3),c_Divides_Odiv__class_Odiv(X56,X36,X3),X3) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X10,X56,X3),c_HOL_Otimes__class_Otimes(X9,X36,X3),X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X36,X56,X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X9,X10,X3) ),
    file('<stdin>',cls_div__mult__div__if__dvd_0) ).

fof(c_0_60_061,axiom,
    ! [X36,X9,X10,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X10),X9),X36,X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_Divides_Odiv__class_Odiv(X10,X36,X3)),c_Divides_Odiv__class_Odiv(X9,X36,X3))
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X36,X9,X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X36,X10,X3) ),
    file('<stdin>',cls_div__add_0) ).

fof(c_0_61_062,axiom,
    ! [X29,X21,X22,X23,X24] :
      ( c_Type_Otyping(c_Type_Oshift(X22,X21,X23,tc_Type_Otype),hAPP(hAPP(c_Lambda_Olift,X29),X21),X24)
      | ~ c_Type_Otyping(X22,X29,X24) ),
    file('<stdin>',cls_lift__type_0) ).

fof(c_0_62_063,axiom,
    ! [X20,X33,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X33,c_Power_Opower__class_Opower(X33,X20,X3),X3),c_Power_Opower__class_Opower(X33,X20,X3),X3)
      | ~ c_HOL_Oord__class_Oless(X33,c_HOL_Oone__class_Oone(X3),X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X33,X3) ),
    file('<stdin>',cls_power__Suc__less_0) ).

fof(c_0_63_064,axiom,
    ! [X20,X14] :
      ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X20,tc_nat)
      | c_HOL_Oord__class_Oless(X14,c_HOL_Otimes__class_Otimes(X20,c_Suc(c_Divides_Odiv__class_Odiv(X14,X20,tc_nat)),tc_nat),tc_nat) ),
    file('<stdin>',cls_split__div__lemma_2) ).

fof(c_0_64_065,axiom,
    ! [X37,X58,X35,X59,X33,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Omod(X35,X37,X3) != c_Divides_Odiv__class_Omod(X58,X37,X3)
      | c_Divides_Odiv__class_Omod(X33,X37,X3) != c_Divides_Odiv__class_Omod(X59,X37,X3)
      | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X33,X35,X3),X37,X3) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X59,X58,X3),X37,X3) ),
    file('<stdin>',cls_mod__mult__cong_0) ).

fof(c_0_65_066,axiom,
    ! [X37,X58,X35,X59,X33,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Omod(X35,X37,X3) != c_Divides_Odiv__class_Omod(X58,X37,X3)
      | c_Divides_Odiv__class_Omod(X33,X37,X3) != c_Divides_Odiv__class_Omod(X59,X37,X3)
      | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X35),X37,X3) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X59),X58),X37,X3) ),
    file('<stdin>',cls_mod__add__cong_0) ).

fof(c_0_66_067,axiom,
    ! [X37,X35,X33,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(X35,X37,X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(X35,X33,X3),c_Divides_Odiv__class_Odiv(X37,X33,X3),X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X33,X37,X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X33,X35,X3) ),
    file('<stdin>',cls_div__dvd__div_0) ).

fof(c_0_67_068,axiom,
    ! [X38,X39,X41,X40,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X40,X41,X3),c_HOL_Otimes__class_Otimes(X39,X38,X3),X3) = c_HOL_Otimes__class_Otimes(X40,c_HOL_Otimes__class_Otimes(X41,c_HOL_Otimes__class_Otimes(X39,X38,X3),X3),X3) ),
    file('<stdin>',cls_class__semiring_Osemiring__rules_I14_J_0) ).

fof(c_0_68_069,axiom,
    ! [X38,X39,X41,X40,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X40,X41,X3),c_HOL_Otimes__class_Otimes(X39,X38,X3),X3) = c_HOL_Otimes__class_Otimes(X39,c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X40,X41,X3),X38,X3),X3) ),
    file('<stdin>',cls_class__semiring_Osemiring__rules_I15_J_0) ).

fof(c_0_69_070,axiom,
    ! [X27,X21,X22,X24,X3] :
      ( hAPP(c_Type_Oshift(X22,X21,X24,X3),X27) = hAPP(X22,X27)
      | ~ c_HOL_Oord__class_Oless(X27,X21,tc_nat) ),
    file('<stdin>',cls_shift__gt_0) ).

fof(c_0_70_071,axiom,
    ! [X9,X10,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(X10,X10,X3)),c_HOL_Otimes__class_Otimes(X9,X9,X3)) != c_HOL_Ozero__class_Ozero(X3)
      | X9 = c_HOL_Ozero__class_Ozero(X3) ),
    file('<stdin>',cls_sum__squares__eq__zero__iff_1) ).

fof(c_0_71_072,axiom,
    ! [X9,X10,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(X10,X10,X3)),c_HOL_Otimes__class_Otimes(X9,X9,X3)) != c_HOL_Ozero__class_Ozero(X3)
      | X10 = c_HOL_Ozero__class_Ozero(X3) ),
    file('<stdin>',cls_sum__squares__eq__zero__iff_0) ).

fof(c_0_72_073,axiom,
    ! [X29,X25,X21] :
      ( hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_Olift,X29),X21)),c_Suc(X25)) = hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_Olift,X29),X25)),X21)
      | ~ c_HOL_Oord__class_Oless(X21,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X25),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
    file('<stdin>',cls_lift__lift_0) ).

fof(c_0_73_074,axiom,
    ! [X35,X33,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_Divides_Odiv__class_Omod(X33,X35,X3)),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X33,X35,X3),X35,X3)) = X33 ),
    file('<stdin>',cls_semiring__div__class_Omod__div__equality_H_0) ).

fof(c_0_74_075,axiom,
    ! [X20,X33,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X33,X20,X3),c_HOL_Otimes__class_Otimes(X33,c_Power_Opower__class_Opower(X33,X20,X3),X3),X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X33,X3) ),
    file('<stdin>',cls_power__less__power__Suc_0) ).

fof(c_0_75_076,axiom,
    ! [X37,X35,X33,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_HOL_Oord__class_Oless(X35,X33,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X37,X33,X3),c_HOL_Otimes__class_Otimes(X37,X35,X3),X3)
      | ~ c_HOL_Oord__class_Oless(X37,c_HOL_Ozero__class_Ozero(X3),X3) ),
    file('<stdin>',cls_mult__less__cancel__left__neg_0) ).

fof(c_0_76_077,axiom,
    ! [X37,X35,X33,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_HOL_Oord__class_Oless(X33,X35,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X37,X33,X3),c_HOL_Otimes__class_Otimes(X37,X35,X3),X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X37,X3) ),
    file('<stdin>',cls_mult__less__cancel__left__pos_0) ).

fof(c_0_77_078,axiom,
    ! [X9,X10,X35,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_HOL_Oord__class_Oless(X10,X9,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X35,X10,X3),c_Power_Opower__class_Opower(X35,X9,X3),X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X35,X3) ),
    file('<stdin>',cls_power__strict__increasing__iff_0) ).

fof(c_0_78_079,axiom,
    ! [X20,X14,X33,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_HOL_Oord__class_Oless(X14,X20,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X33,X14,X3),c_Power_Opower__class_Opower(X33,X20,X3),X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X33,X3) ),
    file('<stdin>',cls_power__less__imp__less__exp_0) ).

fof(c_0_79_080,axiom,
    ! [X9,X55,X46,X10,X20] :
      ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X10),c_HOL_Otimes__class_Otimes(X20,X46,tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X9),c_HOL_Otimes__class_Otimes(X20,X55,tc_nat))
      | c_Divides_Odiv__class_Omod(X10,X20,tc_nat) = c_Divides_Odiv__class_Omod(X9,X20,tc_nat) ),
    file('<stdin>',cls_nat__mod__eq__iff_1) ).

fof(c_0_80_081,axiom,
    ! [X20,X14,X25] :
      ( c_HOL_Oord__class_Oless(X14,X20,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X25,X14,tc_nat),c_HOL_Otimes__class_Otimes(X25,X20,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X25,tc_nat) ),
    file('<stdin>',cls_nat__mult__less__cancel1_0) ).

fof(c_0_81_082,axiom,
    ! [X20,X14,X21] :
      ( c_HOL_Oord__class_Oless(X14,X20,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X21,X14,tc_nat),c_Power_Opower__class_Opower(X21,X20,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X21,tc_nat) ),
    file('<stdin>',cls_nat__power__less__imp__less_0) ).

fof(c_0_82_083,axiom,
    ! [X20,X14,X25] :
      ( c_Ring__and__Field_Odvd__class_Odvd(X14,X20,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X25,X14,tc_nat),c_HOL_Otimes__class_Otimes(X25,X20,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X25,tc_nat) ),
    file('<stdin>',cls_nat__mult__dvd__cancel1_0) ).

fof(c_0_83_084,axiom,
    ! [X20,X14,X25] :
      ( c_Ring__and__Field_Odvd__class_Odvd(X14,X20,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X25,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X25,X14,tc_nat),c_HOL_Otimes__class_Otimes(X25,X20,tc_nat),tc_nat) ),
    file('<stdin>',cls_dvd__mult__cancel_0) ).

fof(c_0_84_085,axiom,
    ! [X20,X33,X45,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X33,X45,X3),c_Power_Opower__class_Opower(X33,X20,X3),X3)
      | ~ c_HOL_Oord__class_Oless(X33,c_HOL_Oone__class_Oone(X3),X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X33,X3)
      | ~ c_HOL_Oord__class_Oless(X20,X45,tc_nat) ),
    file('<stdin>',cls_power__strict__decreasing_0) ).

fof(c_0_85_086,axiom,
    ! [X37,X35,X33,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_HOL_Oord__class_Oless(X37,c_HOL_Ozero__class_Ozero(X3),X3)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X37,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X37,X33,X3),c_HOL_Otimes__class_Otimes(X37,X35,X3),X3) ),
    file('<stdin>',cls_mult__less__cancel__left__disj_0) ).

fof(c_0_86_087,axiom,
    ! [X37,X35,X33,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_HOL_Oord__class_Oless(X37,c_HOL_Ozero__class_Ozero(X3),X3)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X37,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X33,X37,X3),c_HOL_Otimes__class_Otimes(X35,X37,X3),X3) ),
    file('<stdin>',cls_mult__less__cancel__right__disj_0) ).

fof(c_0_87_088,axiom,
    ! [X37,X35,X33,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_HOL_Oord__class_Oless(X37,c_HOL_Ozero__class_Ozero(X3),X3)
      | c_HOL_Oord__class_Oless(X33,X35,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X33,X37,X3),c_HOL_Otimes__class_Otimes(X35,X37,X3),X3) ),
    file('<stdin>',cls_mult__less__cancel__right__disj_2) ).

fof(c_0_88_089,axiom,
    ! [X37,X35,X33,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_HOL_Oord__class_Oless(X35,X33,X3)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X37,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X33,X37,X3),c_HOL_Otimes__class_Otimes(X35,X37,X3),X3) ),
    file('<stdin>',cls_mult__less__cancel__right__disj_1) ).

fof(c_0_89_090,axiom,
    ! [X37,X35,X33,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_HOL_Oord__class_Oless(X37,c_HOL_Ozero__class_Ozero(X3),X3)
      | c_HOL_Oord__class_Oless(X33,X35,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X37,X33,X3),c_HOL_Otimes__class_Otimes(X37,X35,X3),X3) ),
    file('<stdin>',cls_mult__less__cancel__left__disj_2) ).

fof(c_0_90_091,axiom,
    ! [X37,X35,X33,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_HOL_Oord__class_Oless(X35,X33,X3)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X37,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X37,X33,X3),c_HOL_Otimes__class_Otimes(X37,X35,X3),X3) ),
    file('<stdin>',cls_mult__less__cancel__left__disj_1) ).

fof(c_0_91_092,axiom,
    ! [X37,X35,X33,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X33,X37,X3),X35,X3),X37,X3) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X33,X35,X3),X37,X3) ),
    file('<stdin>',cls_zmod__simps_I4_J_0) ).

fof(c_0_92_093,axiom,
    ! [X37,X35,X33,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X33,X35,X3),X37,X3) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X33,X37,X3),X35,X3),X37,X3) ),
    file('<stdin>',cls_mod__mult__left__eq_0) ).

fof(c_0_93_094,axiom,
    ! [X37,X35,X33,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X33,X35,X3),X37,X3) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X33,c_Divides_Odiv__class_Omod(X35,X37,X3),X3),X37,X3) ),
    file('<stdin>',cls_mod__mult__right__eq_0) ).

fof(c_0_94_095,axiom,
    ! [X38,X39,X41,X40,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X40,X41,X3),c_HOL_Otimes__class_Otimes(X39,X38,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X40,X39,X3),c_HOL_Otimes__class_Otimes(X41,X38,X3),X3) ),
    file('<stdin>',cls_class__semiring_Osemiring__rules_I13_J_0) ).

fof(c_0_95_096,axiom,
    ! [X37,X35,X33,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),c_HOL_Otimes__class_Otimes(X35,X37,X3)),X35,X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X37),c_Divides_Odiv__class_Odiv(X33,X35,X3))
      | X35 = c_HOL_Ozero__class_Ozero(X3) ),
    file('<stdin>',cls_div__mult__self2_0) ).

fof(c_0_96_097,axiom,
    ! [X37,X35,X33,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),c_HOL_Otimes__class_Otimes(X37,X35,X3)),X35,X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X37),c_Divides_Odiv__class_Odiv(X33,X35,X3))
      | X35 = c_HOL_Ozero__class_Ozero(X3) ),
    file('<stdin>',cls_div__mult__self1_0) ).

fof(c_0_97_098,axiom,
    ! [X37,X35,X33,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_HOL_Oord__class_Oless(X35,X33,X3)
      | c_HOL_Oord__class_Oless(X33,X35,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X37,X33,X3),c_HOL_Otimes__class_Otimes(X37,X35,X3),X3) ),
    file('<stdin>',cls_mult__less__cancel__left__disj_3) ).

fof(c_0_98_099,axiom,
    ! [X37,X35,X33,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_HOL_Oord__class_Oless(X35,X33,X3)
      | c_HOL_Oord__class_Oless(X33,X35,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X33,X37,X3),c_HOL_Otimes__class_Otimes(X35,X37,X3),X3) ),
    file('<stdin>',cls_mult__less__cancel__right__disj_3) ).

fof(c_0_99_100,axiom,
    ! [X14,X35,X33,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(X33,X14,X3)),c_HOL_Otimes__class_Otimes(X35,X14,X3)) = c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X35),X14,X3) ),
    file('<stdin>',cls_class__semiring_Osemiring__rules_I1_J_0) ).

fof(c_0_100_101,axiom,
    ! [X37,X35,X33,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X35),X37,X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(X33,X37,X3)),c_HOL_Otimes__class_Otimes(X35,X37,X3)) ),
    file('<stdin>',cls_class__semiring_Osemiring__rules_I8_J_0) ).

fof(c_0_101_102,axiom,
    ! [X37,X35,X33,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring(X3)
      | c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X35),X37,X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(X33,X37,X3)),c_HOL_Otimes__class_Otimes(X35,X37,X3)) ),
    file('<stdin>',cls_comm__semiring__class_Odistrib_0) ).

fof(c_0_102_103,axiom,
    ! [X36,X9,X10,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_HOL_Otimes__class_Otimes(X10,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X9),X36),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(X10,X9,X3)),c_HOL_Otimes__class_Otimes(X10,X36,X3)) ),
    file('<stdin>',cls_class__semiring_Omul__d_0) ).

fof(c_0_103_104,axiom,
    ! [X37,X35,X33,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(X35,X33,X3),c_Divides_Odiv__class_Odiv(X37,X33,X3),X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X35,X37,X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X33,X37,X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X33,X35,X3) ),
    file('<stdin>',cls_div__dvd__div_1) ).

fof(c_0_104_105,axiom,
    ! [X37,X35,X33,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X35),X37,X3) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),c_Divides_Odiv__class_Omod(X35,X37,X3)),X37,X3) ),
    file('<stdin>',cls_mod__add__right__eq_0) ).

fof(c_0_105_106,axiom,
    ! [X37,X35,X33,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),c_Divides_Odiv__class_Omod(X35,X37,X3)),X37,X3) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X35),X37,X3) ),
    file('<stdin>',cls_zmod__simps_I2_J_0) ).

fof(c_0_106_107,axiom,
    ! [X9,X10,X20,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Power_Opower__class_Opower(c_Divides_Odiv__class_Odiv(X10,X9,X3),X20,X3) = c_Divides_Odiv__class_Odiv(c_Power_Opower__class_Opower(X10,X20,X3),c_Power_Opower__class_Opower(X9,X20,X3),X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X9,X10,X3) ),
    file('<stdin>',cls_div__power_0) ).

fof(c_0_107_108,axiom,
    ! [X10,X8,X44,X37,X3] :
      ( ~ class_Ring__and__Field_Oidom(X3)
      | ~ class_Int_Onumber__ring(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X10),c_HOL_Otimes__class_Otimes(X8,X37,X3)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X10),c_HOL_Otimes__class_Otimes(X8,X44,X3))
      | X37 = X44
      | X8 = c_HOL_Ozero__class_Ozero(X3) ),
    file('<stdin>',cls_class__ringb_Oadd__scale__eq__noteq_0) ).

fof(c_0_108_109,axiom,
    ! [X37,X35,X33,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),X33),X35)),X37) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X37)),X35) ),
    file('<stdin>',cls_class__semiring_Osemiring__rules_I23_J_0) ).

fof(c_0_109_110,axiom,
    ! [X20,X14,X25] :
      ( c_HOL_Oord__class_Oless(X14,X20,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X25),X14,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X25),X20,tc_nat),tc_nat) ),
    file('<stdin>',cls_Suc__mult__less__cancel1_0) ).

fof(c_0_110_111,axiom,
    ! [X37,X35,X33,X3] :
      ( ~ class_Ring__and__Field_Oidom(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(X33,X35,X3)
      | X37 = c_HOL_Ozero__class_Ozero(X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X37,X33,X3),c_HOL_Otimes__class_Otimes(X37,X35,X3),X3) ),
    file('<stdin>',cls_dvd__mult__cancel__left_0) ).

fof(c_0_111_112,axiom,
    ! [X37,X35,X33,X3] :
      ( ~ class_Ring__and__Field_Oidom(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(X33,X35,X3)
      | X37 = c_HOL_Ozero__class_Ozero(X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X33,X37,X3),c_HOL_Otimes__class_Otimes(X35,X37,X3),X3) ),
    file('<stdin>',cls_dvd__mult__cancel__right_0) ).

fof(c_0_112_113,axiom,
    ! [X20,X33,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),c_HOL_Otimes__class_Otimes(X33,c_Power_Opower__class_Opower(X33,X20,X3),X3),X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X33,X3) ),
    file('<stdin>',cls_power__gt1__lemma_0) ).

fof(c_0_113_114,axiom,
    ! [X10,X8,X44,X37] :
      ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X10),c_HOL_Otimes__class_Otimes(X8,X37,tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X10),c_HOL_Otimes__class_Otimes(X8,X44,tc_nat))
      | X37 = X44
      | X8 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('<stdin>',cls_natgb_Oadd__scale__eq__noteq_0) ).

fof(c_0_114_115,axiom,
    ! [X37,X35,X33,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
      | c_HOL_Oord__class_Oless(X33,X35,X3)
      | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X37),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X35),X37),X3) ),
    file('<stdin>',cls_add__less__cancel__right_0) ).

fof(c_0_115_116,axiom,
    ! [X37,X35,X33,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
      | c_HOL_Oord__class_Oless(X33,X35,X3)
      | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X37),X33),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X37),X35),X3) ),
    file('<stdin>',cls_add__less__cancel__left_0) ).

fof(c_0_116_117,axiom,
    ! [X20,X14,X25] :
      ( c_Ring__and__Field_Odvd__class_Odvd(X14,X20,tc_nat)
      | X25 = c_HOL_Ozero__class_Ozero(tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X25,X14,tc_nat),c_HOL_Otimes__class_Otimes(X25,X20,tc_nat),tc_nat) ),
    file('<stdin>',cls_nat__mult__dvd__cancel__disj_0) ).

fof(c_0_117_118,axiom,
    ! [X20,X14,X25] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X25,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X25,X14,tc_nat),c_HOL_Otimes__class_Otimes(X25,X20,tc_nat),tc_nat) ),
    file('<stdin>',cls_mult__less__cancel1_0) ).

fof(c_0_118_119,axiom,
    ! [X20,X14,X25] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X25,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X14,X25,tc_nat),c_HOL_Otimes__class_Otimes(X20,X25,tc_nat),tc_nat) ),
    file('<stdin>',cls_mult__less__cancel2_0) ).

fof(c_0_119_120,axiom,
    ! [X20,X14,X25] :
      ( c_HOL_Oord__class_Oless(X14,X20,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X25,X14,tc_nat),c_HOL_Otimes__class_Otimes(X25,X20,tc_nat),tc_nat) ),
    file('<stdin>',cls_mult__less__cancel1_1) ).

fof(c_0_120_121,axiom,
    ! [X20,X14,X25] :
      ( c_HOL_Oord__class_Oless(X14,X20,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X14,X25,tc_nat),c_HOL_Otimes__class_Otimes(X20,X25,tc_nat),tc_nat) ),
    file('<stdin>',cls_mult__less__cancel2_1) ).

fof(c_0_121_122,axiom,
    ! [X37,X35,X33,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X37,X33,X3),c_HOL_Otimes__class_Otimes(X37,X35,X3),X3)
      | ~ c_HOL_Oord__class_Oless(X35,X33,X3)
      | ~ c_HOL_Oord__class_Oless(X37,c_HOL_Ozero__class_Ozero(X3),X3) ),
    file('<stdin>',cls_mult__less__cancel__left__neg_1) ).

fof(c_0_122_123,axiom,
    ! [X37,X35,X33,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X37,X33,X3),c_HOL_Otimes__class_Otimes(X37,X35,X3),X3)
      | ~ c_HOL_Oord__class_Oless(X33,X35,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X37,X3) ),
    file('<stdin>',cls_mult__less__cancel__left__pos_1) ).

fof(c_0_123_124,axiom,
    ! [X37,X35,X33,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X37,X33,X3),c_HOL_Otimes__class_Otimes(X37,X35,X3),X3)
      | ~ c_HOL_Oord__class_Oless(X37,c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_HOL_Oord__class_Oless(X35,X33,X3) ),
    file('<stdin>',cls_mult__strict__left__mono__neg_0) ).

fof(c_0_124_125,axiom,
    ! [X37,X35,X33,X3] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X37,X33,X3),c_HOL_Otimes__class_Otimes(X37,X35,X3),X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X37,X3)
      | ~ c_HOL_Oord__class_Oless(X33,X35,X3) ),
    file('<stdin>',cls_mult__strict__left__mono_0) ).

fof(c_0_125_126,axiom,
    ! [X37,X35,X33,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X37,X33,X3),c_HOL_Otimes__class_Otimes(X37,X35,X3),X3)
      | ~ c_HOL_Oord__class_Oless(X33,X35,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X37,X3) ),
    file('<stdin>',cls_mult__less__cancel__left__disj_4) ).

fof(c_0_126_127,axiom,
    ! [X37,X35,X33,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X37,X33,X3),c_HOL_Otimes__class_Otimes(X37,X35,X3),X3)
      | ~ c_HOL_Oord__class_Oless(X35,X33,X3)
      | ~ c_HOL_Oord__class_Oless(X37,c_HOL_Ozero__class_Ozero(X3),X3) ),
    file('<stdin>',cls_mult__less__cancel__left__disj_5) ).

fof(c_0_127_128,axiom,
    ! [X37,X35,X33,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X33,X37,X3),c_HOL_Otimes__class_Otimes(X35,X37,X3),X3)
      | ~ c_HOL_Oord__class_Oless(X37,c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_HOL_Oord__class_Oless(X35,X33,X3) ),
    file('<stdin>',cls_mult__strict__right__mono__neg_0) ).

fof(c_0_128_129,axiom,
    ! [X37,X35,X33,X3] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X33,X37,X3),c_HOL_Otimes__class_Otimes(X35,X37,X3),X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X37,X3)
      | ~ c_HOL_Oord__class_Oless(X33,X35,X3) ),
    file('<stdin>',cls_mult__strict__right__mono_0) ).

fof(c_0_129_130,axiom,
    ! [X37,X35,X33,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X33,X37,X3),c_HOL_Otimes__class_Otimes(X35,X37,X3),X3)
      | ~ c_HOL_Oord__class_Oless(X33,X35,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X37,X3) ),
    file('<stdin>',cls_mult__less__cancel__right__disj_4) ).

fof(c_0_130_131,axiom,
    ! [X37,X35,X33,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X33,X37,X3),c_HOL_Otimes__class_Otimes(X35,X37,X3),X3)
      | ~ c_HOL_Oord__class_Oless(X35,X33,X3)
      | ~ c_HOL_Oord__class_Oless(X37,c_HOL_Ozero__class_Ozero(X3),X3) ),
    file('<stdin>',cls_mult__less__cancel__right__disj_5) ).

fof(c_0_131_132,axiom,
    ! [X37,X35,X33,X3] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X37,X33,X3),c_HOL_Otimes__class_Otimes(X37,X35,X3),X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X37,X3)
      | ~ c_HOL_Oord__class_Oless(X33,X35,X3) ),
    file('<stdin>',cls_mult__strict__left__mono__comm_0) ).

fof(c_0_132_133,axiom,
    ! [X20,X14,X34,X3] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
      | c_Finite__Set_Osetsum(X34,c_SetInterval_Oord__class_OatLeastLessThan(X14,c_Suc(X20),tc_nat),tc_nat,X3) = c_HOL_Ozero__class_Ozero(X3)
      | ~ c_HOL_Oord__class_Oless(X20,X14,tc_nat) ),
    file('<stdin>',cls_setsum__op__ivl__Suc_0) ).

fof(c_0_133_134,axiom,
    ! [X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(X3),X3)),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(X3),X3)) = c_HOL_Ozero__class_Ozero(X3) ),
    file('<stdin>',cls_sum__squares__eq__zero__iff_2) ).

fof(c_0_134_135,axiom,
    ! [X9,X10,X35,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X35,X10,X3),c_Power_Opower__class_Opower(X35,X9,X3),X3)
      | ~ c_HOL_Oord__class_Oless(X10,X9,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X35,X3) ),
    file('<stdin>',cls_power__strict__increasing__iff_1) ).

fof(c_0_135_136,axiom,
    ! [X20,X33,X45,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X33,X20,X3),c_Power_Opower__class_Opower(X33,X45,X3),X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X33,X3)
      | ~ c_HOL_Oord__class_Oless(X20,X45,tc_nat) ),
    file('<stdin>',cls_power__strict__increasing_0) ).

fof(c_0_136_137,axiom,
    ! [X44,X37,X35,X33,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X33,X37,X3),c_HOL_Otimes__class_Otimes(X35,X44,X3),X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X37,X44,X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X33,X35,X3) ),
    file('<stdin>',cls_mult__dvd__mono_0) ).

fof(c_0_137_138,axiom,
    ! [X14,X33,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(X33,X14,X3)),X14) = c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),c_HOL_Oone__class_Oone(X3)),X14,X3) ),
    file('<stdin>',cls_class__semiring_Osemiring__rules_I2_J_0) ).

fof(c_0_138_139,axiom,
    ! [X35,X33,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X35),X33),X35,X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_Divides_Odiv__class_Odiv(X33,X35,X3)),c_HOL_Oone__class_Oone(X3))
      | X35 = c_HOL_Ozero__class_Ozero(X3) ),
    file('<stdin>',cls_div__add__self1_0) ).

fof(c_0_139_140,axiom,
    ! [X35,X33,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X35),X35,X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_Divides_Odiv__class_Odiv(X33,X35,X3)),c_HOL_Oone__class_Oone(X3))
      | X35 = c_HOL_Ozero__class_Ozero(X3) ),
    file('<stdin>',cls_div__add__self2_0) ).

fof(c_0_140_141,axiom,
    ! [X44,X37,X35,X33,X3] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X37),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X35),X44),X3)
      | ~ c_HOL_Oord__class_Oless(X37,X44,X3)
      | ~ c_HOL_Oord__class_Oless(X33,X35,X3) ),
    file('<stdin>',cls_add__strict__mono_0) ).

fof(c_0_141_142,axiom,
    ! [X20,X35,X33,X3] :
      ( ~ class_OrderedGroup_Ocomm__monoid__mult(X3)
      | c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X33,X35,X3),X20,X3) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X33,X20,X3),c_Power_Opower__class_Opower(X35,X20,X3),X3) ),
    file('<stdin>',cls_power__mult__distrib_0) ).

fof(c_0_142_143,axiom,
    ! [X9,X10,X42,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X10,X9,X3),X42,X3) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X10,X42,X3),c_Power_Opower__class_Opower(X9,X42,X3),X3) ),
    file('<stdin>',cls_class__semiring_Opwr__mul_0) ).

fof(c_0_143_144,axiom,
    ! [X37,X35,X33,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X33,X37,X3),c_HOL_Otimes__class_Otimes(X35,X37,X3),X3) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X33,X35,X3),X37,X3) ),
    file('<stdin>',cls_mod__mult__mult2_0) ).

fof(c_0_144_145,axiom,
    ! [X37,X35,X33,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X37,X33,X3),c_HOL_Otimes__class_Otimes(X37,X35,X3),X3) = c_HOL_Otimes__class_Otimes(X37,c_Divides_Odiv__class_Omod(X33,X35,X3),X3) ),
    file('<stdin>',cls_mod__mult__mult1_0) ).

fof(c_0_145_146,axiom,
    ! [X20,X14,X25] :
      ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X14,X25,tc_nat),c_HOL_Otimes__class_Otimes(X20,X25,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X14,X20,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X25,tc_nat) ),
    file('<stdin>',cls_mult__less__cancel2_2) ).

fof(c_0_146_147,axiom,
    ! [X20,X14,X25] :
      ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X25,X14,tc_nat),c_HOL_Otimes__class_Otimes(X25,X20,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X14,X20,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X25,tc_nat) ),
    file('<stdin>',cls_mult__less__cancel1_2) ).

fof(c_0_147_148,axiom,
    ! [X25,X27,X21] :
      ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X25,X21,tc_nat),c_HOL_Otimes__class_Otimes(X25,X27,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X25,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X21,X27,tc_nat) ),
    file('<stdin>',cls_mult__less__mono2_0) ).

fof(c_0_148_149,axiom,
    ! [X25,X27,X21] :
      ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X21,X25,tc_nat),c_HOL_Otimes__class_Otimes(X27,X25,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X25,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X21,X27,tc_nat) ),
    file('<stdin>',cls_mult__less__mono1_0) ).

fof(c_0_149_150,axiom,
    ! [X20,X14,X25] :
      ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X25,X14,tc_nat),c_HOL_Otimes__class_Otimes(X25,X20,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X14,X20,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X25,tc_nat) ),
    file('<stdin>',cls_nat__mult__less__cancel1_1) ).

fof(c_0_150_151,axiom,
    ! [X20,X14,X25] :
      ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X25,X14,tc_nat),c_HOL_Otimes__class_Otimes(X25,X20,tc_nat),tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X14,X20,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X25,tc_nat) ),
    file('<stdin>',cls_nat__mult__dvd__cancel1_1) ).

fof(c_0_151_152,axiom,
    ! [X37,X35,X33,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),c_HOL_Otimes__class_Otimes(X37,X35,X3)),X35,X3) = c_Divides_Odiv__class_Omod(X33,X35,X3) ),
    file('<stdin>',cls_mod__mult__self1_0) ).

fof(c_0_152_153,axiom,
    ! [X37,X35,X33,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),c_HOL_Otimes__class_Otimes(X35,X37,X3)),X35,X3) = c_Divides_Odiv__class_Omod(X33,X35,X3) ),
    file('<stdin>',cls_mod__mult__self2_0) ).

fof(c_0_153_154,axiom,
    ! [X20,X31] :
      ( ~ hBOOL(hAPP(X31,c_Divides_Odiv__class_Odiv(X20,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)))
      | hBOOL(hAPP(X31,c_HOL_Ozero__class_Ozero(tc_nat))) ),
    file('<stdin>',cls_split__div_0) ).

fof(c_0_154_155,axiom,
    ! [X35,X33,X3] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X35,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X33,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X35,X33,X3),X3) ),
    file('<stdin>',cls_zero__less__mult__pos2_0) ).

fof(c_0_155_156,axiom,
    ! [X35,X33,X3] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X35,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X33,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X33,X35,X3),X3) ),
    file('<stdin>',cls_zero__less__mult__pos_0) ).

fof(c_0_156_157,axiom,
    ! [X20,X31] :
      ( ~ hBOOL(hAPP(X31,c_Divides_Odiv__class_Omod(X20,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)))
      | hBOOL(hAPP(X31,X20)) ),
    file('<stdin>',cls_split__mod_0) ).

fof(c_0_157_158,axiom,
    ! [X20,X14,X25] :
      ( c_HOL_Oord__class_Oless(X14,X20,tc_nat)
      | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X25),X14),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X25),X20),tc_nat) ),
    file('<stdin>',cls_nat__add__left__cancel__less_0) ).

fof(c_0_158_159,axiom,
    ! [X20,X14,X33,X3] :
      ( ~ class_OrderedGroup_Omonoid__mult(X3)
      | c_Power_Opower__class_Opower(X33,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X20),X3) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X33,X14,X3),c_Power_Opower__class_Opower(X33,X20,X3),X3) ),
    file('<stdin>',cls_power__add_0) ).

fof(c_0_159_160,axiom,
    ! [X10,X42,X61,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X10,X61,X3),c_Power_Opower__class_Opower(X10,X42,X3),X3) = c_Power_Opower__class_Opower(X10,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X61),X42),X3) ),
    file('<stdin>',cls_class__semiring_Omul__pwr_0) ).

fof(c_0_160_161,axiom,
    ! [X37,X35,X33,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),X33),X35)),X37) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X35),X37)) ),
    file('<stdin>',cls_class__semiring_Osemiring__rules_I21_J_0) ).

fof(c_0_161_162,axiom,
    ! [X44,X37,X33,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X37),X44)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X37)),X44) ),
    file('<stdin>',cls_class__semiring_Osemiring__rules_I25_J_0) ).

fof(c_0_162_163,axiom,
    ! [X37,X35,X33,X3] :
      ( ~ class_OrderedGroup_Oab__semigroup__add(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X35)),X37) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X35),X37)) ),
    file('<stdin>',cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) ).

fof(c_0_163_164,axiom,
    ! [X37,X35,X33,X3] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X35)),X37) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X35),X37)) ),
    file('<stdin>',cls_comm__monoid__add_Omult__assoc_0) ).

fof(c_0_164_165,axiom,
    ! [X36,X9,X10,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X10),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X9),X36)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X10),X9)),X36) ),
    file('<stdin>',cls_class__semiring_Oadd__a_0) ).

fof(c_0_165_166,axiom,
    ! [X37,X35,X33,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X35,X33,X3),X37,X3) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X35,X37,X3),X33,X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X33,X35,X3) ),
    file('<stdin>',cls_dvd__div__mult_0) ).

fof(c_0_166_167,axiom,
    ! [X20,X14,X25,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(X25,X14,X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X25,X20,X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X25,c_Divides_Odiv__class_Omod(X14,X20,X3),X3) ),
    file('<stdin>',cls_dvd__mod__imp__dvd_0) ).

fof(c_0_167_168,axiom,
    ! [X20,X14,X25,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(X25,X14,X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X25,c_Divides_Odiv__class_Omod(X14,X20,X3),X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X25,X20,X3) ),
    file('<stdin>',cls_dvd__mod__iff_0) ).

fof(c_0_168_169,axiom,
    ! [X20,X14,X25] :
      ( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X25,X14,tc_nat),c_HOL_Otimes__class_Otimes(X25,X20,tc_nat),tc_nat) = c_Divides_Odiv__class_Odiv(X14,X20,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X25,tc_nat) ),
    file('<stdin>',cls_nat__mult__div__cancel1_0) ).

fof(c_0_169_170,axiom,
    ! [X57,X25,X27,X21] :
      ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X21),X25),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X27),X57),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X25,X57,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X21,X27,tc_nat) ),
    file('<stdin>',cls_add__less__mono_0) ).

fof(c_0_170_171,axiom,
    ! [X52,X34,X53,X3] :
      ( c_List_Omap(X34,X52,X53,X3) != c_List_Olist_ONil(X3)
      | X52 = c_List_Olist_ONil(X53) ),
    file('<stdin>',cls_map__is__Nil__conv_0) ).

fof(c_0_171_172,axiom,
    ! [X52,X34,X53,X3] :
      ( c_List_Olist_ONil(X3) != c_List_Omap(X34,X52,X53,X3)
      | X52 = c_List_Olist_ONil(X53) ),
    file('<stdin>',cls_Nil__is__map__conv_0) ).

fof(c_0_172_173,axiom,
    ! [X36,X9,X10,X26,X3] :
      ( ~ class_OrderedGroup_Oab__group__add(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X10),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X9),X36)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X9),X26)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X10),X36) = X26 ),
    file('<stdin>',cls_add__cancel__21_0) ).

fof(c_0_173_174,axiom,
    ! [X20,X33,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X33,c_Suc(X20),X3),c_HOL_Oone__class_Oone(X3),X3)
      | ~ c_HOL_Oord__class_Oless(X33,c_HOL_Oone__class_Oone(X3),X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X33,X3) ),
    file('<stdin>',cls_power__Suc__less__one_0) ).

fof(c_0_174_175,axiom,
    ! [X29,X7,X8,X21] :
      ( c_Lambda_Obeta(hAPP(hAPP(hAPP(c_Lambda_Osubst,X8),X29),X21),hAPP(hAPP(hAPP(c_Lambda_Osubst,X7),X29),X21))
      | ~ c_Lambda_Obeta(X8,X7) ),
    file('<stdin>',cls_subst__preserves__beta_0) ).

fof(c_0_175_176,axiom,
    ! [X20,X14] :
      ( c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X14,X20,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X14,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X20,tc_nat) ),
    file('<stdin>',cls_one__less__mult_0) ).

fof(c_0_176_177,axiom,
    ! [X20,X14,X25] :
      ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X25),X14,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X25),X20,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X14,X20,tc_nat) ),
    file('<stdin>',cls_Suc__mult__less__cancel1_1) ).

fof(c_0_177_178,axiom,
    ! [X20,X14,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),c_HOL_Otimes__class_Otimes(X14,X20,X3),X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X20,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X14,X3) ),
    file('<stdin>',cls_less__1__mult_0) ).

fof(c_0_178_179,axiom,
    ! [X35,X33,X3] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X33,X35,X3),X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X35,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X33,X3) ),
    file('<stdin>',cls_mult__pos__pos_0) ).

fof(c_0_179_180,axiom,
    ! [X35,X33,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X33,X35,X3),X3)
      | ~ c_HOL_Oord__class_Oless(X35,c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_HOL_Oord__class_Oless(X33,c_HOL_Ozero__class_Ozero(X3),X3) ),
    file('<stdin>',cls_mult__neg__neg_0) ).

fof(c_0_180_181,axiom,
    ! [X35,X33,X3] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X35,X33,X3),c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_HOL_Oord__class_Oless(X35,c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X33,X3) ),
    file('<stdin>',cls_mult__pos__neg2_0) ).

fof(c_0_181_182,axiom,
    ! [X35,X33,X3] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X33,X35,X3),c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_HOL_Oord__class_Oless(X35,c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X33,X3) ),
    file('<stdin>',cls_mult__pos__neg_0) ).

fof(c_0_182_183,axiom,
    ! [X35,X33,X3] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X33,X35,X3),c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X35,X3)
      | ~ c_HOL_Oord__class_Oless(X33,c_HOL_Ozero__class_Ozero(X3),X3) ),
    file('<stdin>',cls_mult__neg__pos_0) ).

fof(c_0_183_184,axiom,
    ! [X20,X14] :
      ( c_HOL_Oord__class_Oless(X20,c_HOL_Otimes__class_Otimes(X20,X14,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X14,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X20,tc_nat) ),
    file('<stdin>',cls_n__less__n__mult__m_0) ).

fof(c_0_184_185,axiom,
    ! [X20,X14] :
      ( c_HOL_Oord__class_Oless(X20,c_HOL_Otimes__class_Otimes(X14,X20,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X14,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X20,tc_nat) ),
    file('<stdin>',cls_n__less__m__mult__n_0) ).

fof(c_0_185_186,axiom,
    ! [X35,X33,X3] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X35),c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_HOL_Oord__class_Oless(X35,c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_HOL_Oord__class_Oless(X33,c_HOL_Ozero__class_Ozero(X3),X3) ),
    file('<stdin>',cls_add__neg__neg_0) ).

fof(c_0_186_187,axiom,
    ! [X35,X33,X3] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X35),X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X35,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X33,X3) ),
    file('<stdin>',cls_add__pos__pos_0) ).

fof(c_0_187_188,axiom,
    ! [X37,X35,X33,X3] :
      ( ~ class_Ring__and__Field_Oidom(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X33,X37,X3),c_HOL_Otimes__class_Otimes(X35,X37,X3),X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X33,X35,X3) ),
    file('<stdin>',cls_dvd__mult__cancel__right_2) ).

fof(c_0_188_189,axiom,
    ! [X37,X35,X33,X3] :
      ( ~ class_Ring__and__Field_Oidom(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X37,X33,X3),c_HOL_Otimes__class_Otimes(X37,X35,X3),X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X33,X35,X3) ),
    file('<stdin>',cls_dvd__mult__cancel__left_2) ).

fof(c_0_189_190,axiom,
    ! [X9,X10,X20,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(X10,X20,X3),c_Power_Opower__class_Opower(X9,X20,X3),X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X10,X9,X3) ),
    file('<stdin>',cls_dvd__power__same_0) ).

fof(c_0_190_191,axiom,
    ! [X20,X33,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),c_Power_Opower__class_Opower(X33,X20,X3),X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X20,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X33,X3) ),
    file('<stdin>',cls_one__less__power_0) ).

fof(c_0_191_192,axiom,
    ! [X36,X9,X10] :
      ( ~ c_Ring__and__Field_Odvd__class_Odvd(X36,X10,tc_nat)
      | c_Ring__and__Field_Odvd__class_Odvd(X36,X9,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X9,X36,tc_nat)
      | c_Ring__and__Field_Odvd__class_Odvd(X9,X10,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X10,X9,tc_nat) ),
    file('<stdin>',cls_dvd_Oless__trans_1) ).

fof(c_0_192_193,axiom,
    ! [X14,X25] :
      ( c_Divides_Odiv__class_Omod(c_Suc(c_HOL_Otimes__class_Otimes(X25,X14,tc_nat)),X25,tc_nat) = c_HOL_Oone__class_Oone(tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X25,tc_nat) ),
    file('<stdin>',cls_Suc__times__mod__eq_0) ).

fof(c_0_193_194,axiom,
    ! [X37,X35,X33,X3] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X37),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X35),X37),X3)
      | ~ c_HOL_Oord__class_Oless(X33,X35,X3) ),
    file('<stdin>',cls_add__strict__right__mono_0) ).

fof(c_0_194_195,axiom,
    ! [X37,X35,X33,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X37),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X35),X37),X3)
      | ~ c_HOL_Oord__class_Oless(X33,X35,X3) ),
    file('<stdin>',cls_add__less__cancel__right_1) ).

fof(c_0_195_196,axiom,
    ! [X37,X35,X33,X3] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X37),X33),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X37),X35),X3)
      | ~ c_HOL_Oord__class_Oless(X33,X35,X3) ),
    file('<stdin>',cls_add__strict__left__mono_0) ).

fof(c_0_196_197,axiom,
    ! [X37,X35,X33,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X37),X33),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X37),X35),X3)
      | ~ c_HOL_Oord__class_Oless(X33,X35,X3) ),
    file('<stdin>',cls_add__less__cancel__left_1) ).

fof(c_0_197_198,axiom,
    ! [X37,X35,X33,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_HOL_Oord__class_Oless(X35,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X37),X3)
      | ~ c_HOL_Oord__class_Oless(X35,X37,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X33,X3) ),
    file('<stdin>',cls_pos__add__strict_0) ).

fof(c_0_198_199,axiom,
    ! [X20,X14,X25] :
      ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X25,X14,tc_nat),c_HOL_Otimes__class_Otimes(X25,X20,tc_nat),tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X14,X20,tc_nat) ),
    file('<stdin>',cls_nat__mult__dvd__cancel__disj_2) ).

fof(c_0_199_200,axiom,
    ! [X20,X14] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X20,tc_nat)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X14,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X20),tc_nat) ),
    file('<stdin>',cls_add__gr__0_0) ).

fof(c_0_200_201,axiom,
    ! [X20,X14,X25,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(X25,c_Divides_Odiv__class_Omod(X14,X20,X3),X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X25,X14,X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X25,X20,X3) ),
    file('<stdin>',cls_dvd__mod__iff_1) ).

fof(c_0_201_202,axiom,
    ! [X20,X14,X25,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(X25,c_Divides_Odiv__class_Omod(X14,X20,X3),X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X25,X20,X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X25,X14,X3) ),
    file('<stdin>',cls_dvd__mod_0) ).

fof(c_0_202_203,axiom,
    ! [X20,X14] :
      ( X20 = c_HOL_Oone__class_Oone(tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X14,X20,tc_nat),X14,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X14,tc_nat) ),
    file('<stdin>',cls_dvd__mult__cancel1_0) ).

fof(c_0_203_204,axiom,
    ! [X20,X14] :
      ( X20 = c_HOL_Oone__class_Oone(tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X20,X14,tc_nat),X14,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X14,tc_nat) ),
    file('<stdin>',cls_dvd__mult__cancel2_0) ).

fof(c_0_204_205,axiom,
    ! [X20,X14] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X14,X20,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X20,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X14,tc_nat) ),
    file('<stdin>',cls_nat__0__less__mult__iff_2) ).

fof(c_0_205_206,axiom,
    ! [X37,X35,X33,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(X33,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X35),X37),X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X33,X37,X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X33,X35,X3) ),
    file('<stdin>',cls_dvd__add_0) ).

fof(c_0_206_207,axiom,
    ! [X37,X35,X33,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X37,X33,X3),c_HOL_Otimes__class_Otimes(X37,X35,X3),X3) = c_Divides_Odiv__class_Odiv(X33,X35,X3)
      | X37 = c_HOL_Ozero__class_Ozero(X3) ),
    file('<stdin>',cls_div__mult__mult1_0) ).

fof(c_0_207_208,axiom,
    ! [X37,X35,X33,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X33,X37,X3),c_HOL_Otimes__class_Otimes(X35,X37,X3),X3) = c_Divides_Odiv__class_Odiv(X33,X35,X3)
      | X37 = c_HOL_Ozero__class_Ozero(X3) ),
    file('<stdin>',cls_div__mult__mult2_0) ).

fof(c_0_208_209,axiom,
    ! [X14,X33,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X14),c_HOL_Otimes__class_Otimes(X33,X14,X3)) = c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),c_HOL_Oone__class_Oone(X3)),X14,X3) ),
    file('<stdin>',cls_class__semiring_Osemiring__rules_I3_J_0) ).

fof(c_0_209_210,axiom,
    ! [X20,X14] :
      ( c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Odiv(X14,X20,tc_nat),X14,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X14,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X20,tc_nat) ),
    file('<stdin>',cls_div__less__dividend_0) ).

fof(c_0_210_211,axiom,
    ! [X20,X33,X3] :
      ( ~ class_OrderedGroup_Omonoid__mult(X3)
      | c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X33,X20,X3),X33,X3) = c_HOL_Otimes__class_Otimes(X33,c_Power_Opower__class_Opower(X33,X20,X3),X3) ),
    file('<stdin>',cls_power__commutes_0) ).

fof(c_0_211_212,axiom,
    ! [X37,X35,X33,X3] :
      ( ~ class_OrderedGroup_Oab__semigroup__mult(X3)
      | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X33,X35,X3),X37,X3) = c_HOL_Otimes__class_Otimes(X33,c_HOL_Otimes__class_Otimes(X35,X37,X3),X3) ),
    file('<stdin>',cls_ab__semigroup__mult__class_Omult__ac_I1_J_0) ).

fof(c_0_212_213,axiom,
    ! [X39,X41,X40,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X40,X41,X3),X39,X3) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X40,X39,X3),X41,X3) ),
    file('<stdin>',cls_class__semiring_Osemiring__rules_I16_J_0) ).

fof(c_0_213_214,axiom,
    ! [X39,X41,X40,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X40,X41,X3),X39,X3) = c_HOL_Otimes__class_Otimes(X40,c_HOL_Otimes__class_Otimes(X41,X39,X3),X3) ),
    file('<stdin>',cls_class__semiring_Osemiring__rules_I17_J_0) ).

fof(c_0_214_215,axiom,
    ! [X38,X39,X40,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_HOL_Otimes__class_Otimes(X40,c_HOL_Otimes__class_Otimes(X39,X38,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X40,X39,X3),X38,X3) ),
    file('<stdin>',cls_class__semiring_Osemiring__rules_I18_J_0) ).

fof(c_0_215_216,axiom,
    ! [X38,X39,X40,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_HOL_Otimes__class_Otimes(X40,c_HOL_Otimes__class_Otimes(X39,X38,X3),X3) = c_HOL_Otimes__class_Otimes(X39,c_HOL_Otimes__class_Otimes(X40,X38,X3),X3) ),
    file('<stdin>',cls_class__semiring_Osemiring__rules_I19_J_0) ).

fof(c_0_216_217,axiom,
    ! [X36,X9,X10,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_HOL_Otimes__class_Otimes(X10,c_HOL_Otimes__class_Otimes(X9,X36,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X10,X9,X3),X36,X3) ),
    file('<stdin>',cls_class__semiring_Omul__a_0) ).

fof(c_0_217_218,axiom,
    ! [X36,X9,X10] :
      ( c_Ring__and__Field_Odvd__class_Odvd(X10,X36,tc_nat)
      | c_Ring__and__Field_Odvd__class_Odvd(X36,X9,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X9,X36,tc_nat)
      | c_Ring__and__Field_Odvd__class_Odvd(X9,X10,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X10,X9,tc_nat) ),
    file('<stdin>',cls_dvd_Oless__trans_0) ).

fof(c_0_218_219,axiom,
    ! [X10,X42,X61,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(X10,X61,X3),X42,X3) = c_Power_Opower__class_Opower(X10,c_HOL_Otimes__class_Otimes(X61,X42,tc_nat),X3) ),
    file('<stdin>',cls_class__semiring_Opwr__pwr_0) ).

fof(c_0_219_220,axiom,
    ! [X20,X14,X33,X3] :
      ( ~ class_OrderedGroup_Omonoid__mult(X3)
      | c_Power_Opower__class_Opower(X33,c_HOL_Otimes__class_Otimes(X14,X20,tc_nat),X3) = c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(X33,X14,X3),X20,X3) ),
    file('<stdin>',cls_power__mult_0) ).

fof(c_0_220_221,axiom,
    ! [X33,X3] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X33,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X33),X3) ),
    file('<stdin>',cls_zero__less__double__add__iff__zero__less__single__add_0) ).

fof(c_0_221_222,axiom,
    ! [X33,X3] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
      | c_HOL_Oord__class_Oless(X33,c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X33),c_HOL_Ozero__class_Ozero(X3),X3) ),
    file('<stdin>',cls_double__add__less__zero__iff__single__less__zero_0) ).

fof(c_0_222_223,axiom,
    ! [X33,X3] :
      ( ~ class_Ring__and__Field_Oordered__idom(X3)
      | c_HOL_Oord__class_Oless(X33,c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X33),c_HOL_Ozero__class_Ozero(X3),X3) ),
    file('<stdin>',cls_even__less__0__iff_0) ).

fof(c_0_223_224,axiom,
    ! [X20,X14,X25] :
      ( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X25,X14,tc_nat),c_HOL_Otimes__class_Otimes(X25,X20,tc_nat),tc_nat) = c_Divides_Odiv__class_Odiv(X14,X20,tc_nat)
      | X25 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('<stdin>',cls_nat__mult__div__cancel__disj_1) ).

fof(c_0_224_225,axiom,
    ! [X25,X27,X21] :
      ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X21),X25),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X27),X25),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X21,X27,tc_nat) ),
    file('<stdin>',cls_add__less__mono1_0) ).

fof(c_0_225_226,axiom,
    ! [X20,X14,X25] :
      ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X25),X14),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X25),X20),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X14,X20,tc_nat) ),
    file('<stdin>',cls_nat__add__left__cancel__less_1) ).

fof(c_0_226_227,axiom,
    ! [X37,X35,X33,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(X35,X37,X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X33,X35,X3),X37,X3) ),
    file('<stdin>',cls_dvd__mult__right_0) ).

fof(c_0_227_228,axiom,
    ! [X37,X35,X33,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(X33,X37,X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X33,X35,X3),X37,X3) ),
    file('<stdin>',cls_dvd__mult__left_0) ).

fof(c_0_228_229,axiom,
    ! [X44,X37,X33,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X37),X44)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X37),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X44)) ),
    file('<stdin>',cls_class__semiring_Osemiring__rules_I22_J_0) ).

fof(c_0_229_230,axiom,
    ! [X37,X35,X33,X3] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X35),X37)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X35),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X37)) ),
    file('<stdin>',cls_comm__monoid__add_Omult__left__commute_0) ).

fof(c_0_230_231,axiom,
    ! [X36,X9,X10,X3] :
      ( ~ class_OrderedGroup_Oab__group__add(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X10),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X9),X36)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X9),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X10),X36)) ),
    file('<stdin>',cls_add__cancel__21_1) ).

fof(c_0_231_232,axiom,
    ! [X10,X20] :
      ( X20 = c_HOL_Ozero__class_Ozero(tc_nat)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X10,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Power_Opower__class_Opower(X10,X20,tc_nat),tc_nat) ),
    file('<stdin>',cls_nat__zero__less__power__iff_0) ).

fof(c_0_232_233,axiom,
    ! [X37,X35,X33,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X33,X35,X3),X37,X3) = c_Divides_Odiv__class_Omod(X33,X37,X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X37,X35,X3) ),
    file('<stdin>',cls_mod__mod__cancel_0) ).

fof(c_0_233_234,axiom,
    ! [X20,X14] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X20,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X14,X20,tc_nat),tc_nat) ),
    file('<stdin>',cls_nat__0__less__mult__iff_1) ).

fof(c_0_234_235,axiom,
    ! [X20,X14] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X14,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X14,X20,tc_nat),tc_nat) ),
    file('<stdin>',cls_nat__0__less__mult__iff_0) ).

fof(c_0_235_236,axiom,
    ! [X14,X31] :
      ( hBOOL(hAPP(X31,c_Divides_Odiv__class_Odiv(X14,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)))
      | ~ hBOOL(hAPP(X31,c_HOL_Ozero__class_Ozero(tc_nat))) ),
    file('<stdin>',cls_split__div_H_6) ).

fof(c_0_236_237,axiom,
    ! [X20,X31] :
      ( ~ hBOOL(hAPP(X31,c_HOL_Ozero__class_Ozero(tc_nat)))
      | hBOOL(hAPP(X31,c_Divides_Odiv__class_Odiv(X20,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))) ),
    file('<stdin>',cls_split__div_5) ).

fof(c_0_237_238,axiom,
    ! [X36,X9,X10] :
      ( ~ c_Ring__and__Field_Odvd__class_Odvd(X36,X10,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X9,X36,tc_nat)
      | c_Ring__and__Field_Odvd__class_Odvd(X9,X10,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X10,X9,tc_nat) ),
    file('<stdin>',cls_dvd_Oless__le__trans_1) ).

fof(c_0_238_239,axiom,
    ! [X36,X9,X10] :
      ( ~ c_Ring__and__Field_Odvd__class_Odvd(X36,X10,tc_nat)
      | c_Ring__and__Field_Odvd__class_Odvd(X36,X9,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X9,X36,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X10,X9,tc_nat) ),
    file('<stdin>',cls_dvd_Ole__less__trans_1) ).

fof(c_0_239_240,axiom,
    ! [X35,X33,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),X33,X3),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),X35,X3),X3) = c_HOL_Ozero__class_Ozero(X3) ),
    file('<stdin>',cls_div__mult__mult1__if_0) ).

fof(c_0_240_241,axiom,
    ! [X35,X33,X3] :
      ( ~ class_Ring__and__Field_Oidom(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X33,c_HOL_Ozero__class_Ozero(X3),X3),c_HOL_Otimes__class_Otimes(X35,c_HOL_Ozero__class_Ozero(X3),X3),X3) ),
    file('<stdin>',cls_dvd__mult__cancel__right_1) ).

fof(c_0_241_242,axiom,
    ! [X35,X33,X3] :
      ( ~ class_Ring__and__Field_Oidom(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),X33,X3),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),X35,X3),X3) ),
    file('<stdin>',cls_dvd__mult__cancel__left_1) ).

fof(c_0_242_243,axiom,
    ! [X20,X31] :
      ( ~ hBOOL(hAPP(X31,X20))
      | hBOOL(hAPP(X31,c_Divides_Odiv__class_Omod(X20,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))) ),
    file('<stdin>',cls_split__mod_5) ).

fof(c_0_243_244,axiom,
    ! [X20,X33,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),c_Power_Opower__class_Opower(X33,c_Suc(X20),X3),X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X33,X3) ),
    file('<stdin>',cls_power__gt1_0) ).

fof(c_0_244_245,axiom,
    ! [X20,X14,X57,X25] :
      ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X57) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X25),X20)
      | ~ c_HOL_Oord__class_Oless(X25,X57,tc_nat)
      | c_HOL_Oord__class_Oless(X14,X20,tc_nat) ),
    file('<stdin>',cls_less__add__eq__less_0) ).

fof(c_0_245_246,axiom,
    ! [X25,X27,X21] :
      ( c_HOL_Oord__class_Oless(X21,X25,tc_nat)
      | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X21),X27),X25,tc_nat) ),
    file('<stdin>',cls_add__lessD1_0) ).

fof(c_0_246_247,axiom,
    ! [X20,X25] :
      ( c_Ring__and__Field_Odvd__class_Odvd(X25,X20,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X25,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X20),X25),tc_nat) ),
    file('<stdin>',cls_dvd__reduce_0) ).

fof(c_0_247_248,axiom,
    ! [X20,X14,X33,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_Power_Opower__class_Opower(X33,X14,X3) != c_Power_Opower__class_Opower(X33,X20,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X33,X3)
      | X14 = X20 ),
    file('<stdin>',cls_power__inject__exp_0) ).

fof(c_0_248_249,axiom,
    ! [X20,X14] :
      ( c_Divides_Odiv__class_Omod(c_Suc(X14),X20,tc_nat) = c_Suc(c_Divides_Odiv__class_Omod(X14,X20,tc_nat))
      | c_Suc(c_Divides_Odiv__class_Omod(X14,X20,tc_nat)) = X20 ),
    file('<stdin>',cls_mod__Suc_1) ).

fof(c_0_249_250,axiom,
    ! [X36,X9,X10] :
      ( c_Ring__and__Field_Odvd__class_Odvd(X10,X36,tc_nat)
      | c_Ring__and__Field_Odvd__class_Odvd(X36,X9,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X9,X36,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X10,X9,tc_nat) ),
    file('<stdin>',cls_dvd_Ole__less__trans_0) ).

fof(c_0_250_251,axiom,
    ! [X36,X9,X10] :
      ( c_Ring__and__Field_Odvd__class_Odvd(X10,X36,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X9,X36,tc_nat)
      | c_Ring__and__Field_Odvd__class_Odvd(X9,X10,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X10,X9,tc_nat) ),
    file('<stdin>',cls_dvd_Oless__le__trans_0) ).

fof(c_0_251_252,axiom,
    ! [X33,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X33,X33,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
    file('<stdin>',cls_not__square__less__zero_0) ).

fof(c_0_252_253,axiom,
    ! [X20,X33,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Power_Opower__class_Opower(X33,X20,X3),X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X33,X3) ),
    file('<stdin>',cls_zero__less__power_0) ).

fof(c_0_253_254,axiom,
    ! [X33,X3] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X33),X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X33,X3) ),
    file('<stdin>',cls_zero__less__double__add__iff__zero__less__single__add_1) ).

fof(c_0_254_255,axiom,
    ! [X33,X3] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X33),c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_HOL_Oord__class_Oless(X33,c_HOL_Ozero__class_Ozero(X3),X3) ),
    file('<stdin>',cls_double__add__less__zero__iff__single__less__zero_1) ).

fof(c_0_255_256,axiom,
    ! [X33,X3] :
      ( ~ class_Ring__and__Field_Oordered__idom(X3)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X33),c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_HOL_Oord__class_Oless(X33,c_HOL_Ozero__class_Ozero(X3),X3) ),
    file('<stdin>',cls_even__less__0__iff_1) ).

fof(c_0_256_257,axiom,
    ! [X20,X14,X25] :
      ( c_HOL_Otimes__class_Otimes(X25,X14,tc_nat) != c_HOL_Otimes__class_Otimes(X25,X20,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X25,tc_nat)
      | X14 = X20 ),
    file('<stdin>',cls_nat__mult__eq__cancel1_0) ).

fof(c_0_257_258,axiom,
    ! [X10,X20,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(X10,c_Power_Opower__class_Opower(X10,X20,X3),X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X20,tc_nat) ),
    file('<stdin>',cls_dvd__power_0) ).

fof(c_0_258_259,axiom,
    ! [X20,X14] :
      ( ~ c_Ring__and__Field_Odvd__class_Odvd(X20,X14,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X14,X20,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X14,tc_nat) ),
    file('<stdin>',cls_nat__dvd__not__less_0) ).

fof(c_0_259_260,axiom,
    ! [X35,X33,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X35,X33,X3),X33,X3) = X35
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X33,X35,X3) ),
    file('<stdin>',cls_dvd__div__mult__self_0) ).

fof(c_0_260_261,axiom,
    ! [X35,X33,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_HOL_Otimes__class_Otimes(X33,c_Divides_Odiv__class_Odiv(X35,X33,X3),X3) = X35
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X33,X35,X3) ),
    file('<stdin>',cls_dvd__mult__div__cancel_0) ).

fof(c_0_261_262,axiom,
    ! [X37,X35,X33,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(X33,c_HOL_Otimes__class_Otimes(X35,X37,X3),X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X33,X35,X3) ),
    file('<stdin>',cls_dvd__mult2_0) ).

fof(c_0_262_263,axiom,
    ! [X37,X35,X33,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(X33,c_HOL_Otimes__class_Otimes(X35,X37,X3),X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X33,X37,X3) ),
    file('<stdin>',cls_dvd__mult_0) ).

fof(c_0_263_264,axiom,
    ! [X14,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X14),X14) = c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Oone__class_Oone(X3)),c_HOL_Oone__class_Oone(X3)),X14,X3) ),
    file('<stdin>',cls_class__semiring_Osemiring__rules_I4_J_0) ).

fof(c_0_264_265,axiom,
    ! [X14] :
      ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X14,tc_nat)
      | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X14,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X14,tc_nat) ),
    file('<stdin>',cls_dvd__mult__cancel1_1) ).

fof(c_0_265_266,axiom,
    ! [X14] :
      ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X14,tc_nat)
      | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),X14,tc_nat),X14,tc_nat) ),
    file('<stdin>',cls_dvd__mult__cancel2_1) ).

fof(c_0_266_267,axiom,
    ! [X10,X20] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Power_Opower__class_Opower(X10,X20,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X10,tc_nat) ),
    file('<stdin>',cls_nat__zero__less__power__iff_1) ).

fof(c_0_267_268,axiom,
    ! [X20,X14] :
      ( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X14,X20,tc_nat),X20,tc_nat) = X14
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X20,tc_nat) ),
    file('<stdin>',cls_div__mult__self__is__m_0) ).

fof(c_0_268_269,axiom,
    ! [X20,X14] :
      ( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X20,X14,tc_nat),X20,tc_nat) = X14
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X20,tc_nat) ),
    file('<stdin>',cls_div__mult__self1__is__m_0) ).

fof(c_0_269_270,axiom,
    ! [X20,X14] :
      ( c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Omod(X14,X20,tc_nat),X20,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X20,tc_nat) ),
    file('<stdin>',cls_mod__less__divisor_0) ).

fof(c_0_270_271,axiom,
    ! [X20,X14,X3] :
      ( ~ class_Ring__and__Field_Osemiring__1(X3)
      | c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X20),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_Nat_Osemiring__1__class_Oof__nat(X14,X3)),c_Nat_Osemiring__1__class_Oof__nat(X20,X3)) ),
    file('<stdin>',cls_of__nat__add_0) ).

fof(c_0_271_272,axiom,
    ! [X20,X14] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X20),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X20,tc_nat) ),
    file('<stdin>',cls_add__gr__0_2) ).

fof(c_0_272_273,axiom,
    ! [X20,X14] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X20),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X14,tc_nat) ),
    file('<stdin>',cls_add__gr__0_1) ).

fof(c_0_273_274,axiom,
    ! [X36,X9,X10,X3] :
      ( ~ class_Orderings_Oorder(X3)
      | c_HOL_Oord__class_Oless(X36,X10,X3)
      | ~ c_HOL_Oord__class_Oless(X36,X9,X3)
      | ~ c_HOL_Oord__class_Oless(X9,X10,X3) ),
    file('<stdin>',cls_xt1_I10_J_0) ).

fof(c_0_274_275,axiom,
    ! [X36,X9,X10,X3] :
      ( ~ class_Orderings_Opreorder(X3)
      | c_HOL_Oord__class_Oless(X10,X36,X3)
      | ~ c_HOL_Oord__class_Oless(X9,X36,X3)
      | ~ c_HOL_Oord__class_Oless(X10,X9,X3) ),
    file('<stdin>',cls_order__less__trans_0) ).

fof(c_0_275_276,axiom,
    ! [X37,X35,X33,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(X33,X37,X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X35,X37,X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X33,X35,X3) ),
    file('<stdin>',cls_dvd__trans_0) ).

fof(c_0_276_277,axiom,
    ! [X20,X14] :
      ( c_Suc(c_Divides_Odiv__class_Omod(X14,X20,tc_nat)) != X20
      | c_Divides_Odiv__class_Omod(c_Suc(X14),X20,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('<stdin>',cls_mod__Suc_0) ).

fof(c_0_277_278,axiom,
    ! [X20,X14,X3] :
      ( ~ class_Ring__and__Field_Osemiring__1(X3)
      | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Otimes__class_Otimes(X14,X20,tc_nat),X3) = c_HOL_Otimes__class_Otimes(c_Nat_Osemiring__1__class_Oof__nat(X14,X3),c_Nat_Osemiring__1__class_Oof__nat(X20,X3),X3) ),
    file('<stdin>',cls_of__nat__mult_0) ).

fof(c_0_278_279,axiom,
    ! [X10,X42,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_Power_Opower__class_Opower(X10,c_Suc(X42),X3) = c_HOL_Otimes__class_Otimes(X10,c_Power_Opower__class_Opower(X10,X42,X3),X3) ),
    file('<stdin>',cls_class__semiring_Osemiring__rules_I35_J_0) ).

fof(c_0_279_280,axiom,
    ! [X10,X20,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_Power_Opower__class_Opower(X10,c_Suc(X20),X3) = c_HOL_Otimes__class_Otimes(X10,c_Power_Opower__class_Opower(X10,X20,X3),X3) ),
    file('<stdin>',cls_class__semiring_Opwr__Suc_0) ).

fof(c_0_280_281,axiom,
    ! [X20,X33,X3] :
      ( ~ class_Power_Opower(X3)
      | c_Power_Opower__class_Opower(X33,c_Suc(X20),X3) = c_HOL_Otimes__class_Otimes(X33,c_Power_Opower__class_Opower(X33,X20,X3),X3) ),
    file('<stdin>',cls_power__Suc_0) ).

fof(c_0_281_282,axiom,
    ! [X20,X33,X3] :
      ( ~ class_OrderedGroup_Omonoid__mult(X3)
      | c_Power_Opower__class_Opower(X33,c_Suc(X20),X3) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X33,X20,X3),X33,X3) ),
    file('<stdin>',cls_power__Suc2_0) ).

fof(c_0_282_283,axiom,
    ! [X10,X42,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_HOL_Otimes__class_Otimes(X10,c_Power_Opower__class_Opower(X10,X42,X3),X3) = c_Power_Opower__class_Opower(X10,c_Suc(X42),X3) ),
    file('<stdin>',cls_class__semiring_Osemiring__rules_I27_J_0) ).

fof(c_0_283_284,axiom,
    ! [X10,X42,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X10,X42,X3),X10,X3) = c_Power_Opower__class_Opower(X10,c_Suc(X42),X3) ),
    file('<stdin>',cls_class__semiring_Osemiring__rules_I28_J_0) ).

fof(c_0_284_285,axiom,
    ! [X20,X14,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_HOL_Oord__class_Oless(X14,X20,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X14,X3),c_Nat_Osemiring__1__class_Oof__nat(X20,X3),X3) ),
    file('<stdin>',cls_of__nat__less__iff_0) ).

fof(c_0_285_286,axiom,
    ! [X20,X14] :
      ( c_Divides_Odiv__class_Odiv(X14,X20,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
      | ~ c_HOL_Oord__class_Oless(X14,X20,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X20,tc_nat) ),
    file('<stdin>',cls_div__if_0) ).

fof(c_0_286_287,axiom,
    ! [X36,X9,X10] :
      ( c_HOL_Oord__class_Oless(X10,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X9),X36),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X10,X9,tc_nat) ),
    file('<stdin>',cls_termination__basic__simps_I1_J_0) ).

fof(c_0_287_288,axiom,
    ! [X36,X9,X10] :
      ( c_HOL_Oord__class_Oless(X10,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X9),X36),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X10,X36,tc_nat) ),
    file('<stdin>',cls_termination__basic__simps_I2_J_0) ).

fof(c_0_288_289,axiom,
    ! [X14,X27,X21] :
      ( c_HOL_Oord__class_Oless(X21,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X27),X14),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X21,X27,tc_nat) ),
    file('<stdin>',cls_trans__less__add1_0) ).

fof(c_0_289_290,axiom,
    ! [X14,X27,X21] :
      ( c_HOL_Oord__class_Oless(X21,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X27),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X21,X27,tc_nat) ),
    file('<stdin>',cls_trans__less__add2_0) ).

fof(c_0_290_291,axiom,
    ! [X20,X25] :
      ( c_Ring__and__Field_Odvd__class_Odvd(X25,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X20),X25),tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X25,X20,tc_nat) ),
    file('<stdin>',cls_dvd__reduce_1) ).

fof(c_0_291_292,axiom,
    ! [X25,X27,X21] :
      ( c_HOL_Oord__class_Oless(c_Suc(X21),X25,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X27,X25,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X21,X27,tc_nat) ),
    file('<stdin>',cls_less__trans__Suc_0) ).

fof(c_0_292_293,axiom,
    ! [X35,X33,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X33,X35,X3),X35,X3) = c_Divides_Odiv__class_Omod(X33,X35,X3) ),
    file('<stdin>',cls_mod__mod__trivial_0) ).

fof(c_0_293_294,axiom,
    ! [X9,X10,X3] :
      ( ~ class_OrderedGroup_Oab__semigroup__idem__mult(X3)
      | c_HOL_Otimes__class_Otimes(X10,c_HOL_Otimes__class_Otimes(X10,X9,X3),X3) = c_HOL_Otimes__class_Otimes(X10,X9,X3) ),
    file('<stdin>',cls_mult__left__idem_0) ).

fof(c_0_294_295,axiom,
    ! [X36,X9,X10] :
      ( c_Ring__and__Field_Odvd__class_Odvd(X10,X36,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X9,X36,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X10,X9,tc_nat) ),
    file('<stdin>',cls_dvd_Oorder__trans_0) ).

fof(c_0_295_296,axiom,
    ! [X35,X33,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X35),X35,X3) = c_Divides_Odiv__class_Omod(X33,X35,X3) ),
    file('<stdin>',cls_mod__add__self2_0) ).

fof(c_0_296_297,axiom,
    ! [X35,X33,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X35),X33),X35,X3) = c_Divides_Odiv__class_Omod(X33,X35,X3) ),
    file('<stdin>',cls_mod__add__self1_0) ).

fof(c_0_297_298,axiom,
    ! [X29,X21] :
      ( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_Olift,X29),X21)))
      | ~ hBOOL(hAPP(c_InductTermi_OIT,X29)) ),
    file('<stdin>',cls_lift__IT_0) ).

fof(c_0_298_299,axiom,
    ! [X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Oone__class_Oone(X3)),c_HOL_Oone__class_Oone(X3)),X3) ),
    file('<stdin>',cls_zero__less__two_0) ).

fof(c_0_299_300,axiom,
    ! [X20,X14,X3] :
      ( ~ class_Ring__and__Field_Osemiring__1(X3)
      | c_Nat_Osemiring__1__class_Oof__nat(c_Power_Opower__class_Opower(X14,X20,tc_nat),X3) = c_Power_Opower__class_Opower(c_Nat_Osemiring__1__class_Oof__nat(X14,X3),X20,X3) ),
    file('<stdin>',cls_of__nat__power_0) ).

fof(c_0_300_301,axiom,
    ! [X25,X21] :
      ( hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(X21)),X25) = c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X21),c_HOL_Oone__class_Oone(tc_nat)))
      | c_HOL_Oord__class_Oless(X21,X25,tc_nat) ),
    file('<stdin>',cls_lift_Osimps_I1_J_1) ).

fof(c_0_301_302,axiom,
    ! [X20,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X20,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Nat_Osemiring__1__class_Oof__nat(X20,X3),X3) ),
    file('<stdin>',cls_of__nat__0__less__iff_0) ).

fof(c_0_302_303,axiom,
    ! [X26,X27,X21] :
      ( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X27)),X26),X21) = c_Lambda_OdB_OVar(X27)
      | ~ c_HOL_Oord__class_Oless(X27,X21,tc_nat) ),
    file('<stdin>',cls_subst__lt_0) ).

fof(c_0_303_304,axiom,
    ! [X20,X14,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X14,X3),c_Nat_Osemiring__1__class_Oof__nat(X20,X3),X3)
      | ~ c_HOL_Oord__class_Oless(X14,X20,tc_nat) ),
    file('<stdin>',cls_of__nat__less__iff_1) ).

fof(c_0_304_305,axiom,
    ! [X12,X31] :
      ( hBOOL(hAPP(X31,X12))
      | ~ hBOOL(hAPP(X31,c_Suc(v_sko__List__Xlexn__Xinduct__1(X31))))
      | ~ hBOOL(hAPP(X31,c_HOL_Ozero__class_Ozero(tc_nat))) ),
    file('<stdin>',cls_lexn_Oinduct_1) ).

fof(c_0_305_306,axiom,
    ! [X20,X31] :
      ( hBOOL(hAPP(X31,X20))
      | ~ hBOOL(hAPP(X31,c_Suc(c_ATP__Linkup_Osko__Nat__Xnat__induct__1__1(X31))))
      | ~ hBOOL(hAPP(X31,c_HOL_Ozero__class_Ozero(tc_nat))) ),
    file('<stdin>',cls_nat__induct_1) ).

fof(c_0_306_307,axiom,
    ! [X12,X31] :
      ( hBOOL(hAPP(X31,X12))
      | ~ hBOOL(hAPP(X31,c_Suc(v_sko__List__Xreplicate__Xinduct__1(X31))))
      | ~ hBOOL(hAPP(X31,c_HOL_Ozero__class_Ozero(tc_nat))) ),
    file('<stdin>',cls_replicate_Oinduct_1) ).

fof(c_0_307_308,axiom,
    ! [X12,X31] :
      ( hBOOL(hAPP(X31,X12))
      | ~ hBOOL(hAPP(X31,c_Suc(v_sko__List__Xupt__Xinduct__1(X31))))
      | ~ hBOOL(hAPP(X31,c_HOL_Ozero__class_Ozero(tc_nat))) ),
    file('<stdin>',cls_upt_Oinduct_1) ).

fof(c_0_308_309,axiom,
    ! [X12,X31] :
      ( hBOOL(hAPP(X31,X12))
      | ~ hBOOL(hAPP(X31,c_Suc(v_sko__Nat__Xnat__Xinduct__1(X31))))
      | ~ hBOOL(hAPP(X31,c_HOL_Ozero__class_Ozero(tc_nat))) ),
    file('<stdin>',cls_nat_Oinduct_1) ).

fof(c_0_309_310,axiom,
    ! [X12,X31] :
      ( hBOOL(hAPP(X31,X12))
      | ~ hBOOL(hAPP(X31,c_Suc(v_sko__Nat__Xnat__Xinducts__1(X31))))
      | ~ hBOOL(hAPP(X31,c_HOL_Ozero__class_Ozero(tc_nat))) ),
    file('<stdin>',cls_nat_Oinducts_1) ).

fof(c_0_310_311,axiom,
    ! [X20,X14,X31] :
      ( hBOOL(hAPP(hAPP(X31,X20),X14))
      | c_HOL_Oord__class_Oless(X20,X14,tc_nat)
      | X14 = X20
      | c_HOL_Oord__class_Oless(X14,X20,tc_nat) ),
    file('<stdin>',cls_nat__less__cases_0) ).

fof(c_0_311_312,axiom,
    ! [X20,X14,X25] :
      ( c_HOL_Otimes__class_Otimes(c_Suc(X25),X14,tc_nat) != c_HOL_Otimes__class_Otimes(c_Suc(X25),X20,tc_nat)
      | X14 = X20 ),
    file('<stdin>',cls_Suc__mult__cancel1_0) ).

fof(c_0_312_313,axiom,
    ! [X20,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(X3),c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X3),X20,X3),X3) ),
    file('<stdin>',cls_dvd__power_1) ).

fof(c_0_313_314,axiom,
    ! [X20,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Nat_Osemiring__1__class_Oof__nat(X20,X3),X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X20,tc_nat) ),
    file('<stdin>',cls_of__nat__0__less__iff_1) ).

fof(c_0_314_315,axiom,
    ! [X36,X9,X10,X3] :
      ( ~ class_Ring__and__Field_Oidom(X3)
      | ~ class_Int_Onumber__ring(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X10),X9) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X10),X36)
      | X9 = X36 ),
    file('<stdin>',cls_class__ringb_Oadd__cancel_0) ).

fof(c_0_315_316,axiom,
    ! [X7,X8,X21] :
      ( c_Lambda_Obeta(hAPP(hAPP(c_Lambda_Olift,X8),X21),hAPP(hAPP(c_Lambda_Olift,X7),X21))
      | ~ c_Lambda_Obeta(X8,X7) ),
    file('<stdin>',cls_lift__preserves__beta_0) ).

fof(c_0_316_317,axiom,
    ! [X26,X29,X7] :
      ( c_Lambda_Obeta(hAPP(hAPP(c_Lambda_OdB_OApp,X26),X7),hAPP(hAPP(c_Lambda_OdB_OApp,X26),X29))
      | ~ c_Lambda_Obeta(X7,X29) ),
    file('<stdin>',cls_appR_0) ).

fof(c_0_317_318,axiom,
    ! [X26,X29,X7] :
      ( c_Lambda_Obeta(hAPP(hAPP(c_Lambda_OdB_OApp,X7),X26),hAPP(hAPP(c_Lambda_OdB_OApp,X29),X26))
      | ~ c_Lambda_Obeta(X7,X29) ),
    file('<stdin>',cls_appL_0) ).

fof(c_0_318_319,axiom,
    ! [X35,X33,X3] :
      ( ~ class_Orderings_Oorder(X3)
      | ~ c_HOL_Oord__class_Oless(X33,X35,X3)
      | ~ c_HOL_Oord__class_Oless(X35,X33,X3) ),
    file('<stdin>',cls_xt1_I9_J_0) ).

fof(c_0_319_320,axiom,
    ! [X9,X10,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | ~ c_HOL_Oord__class_Oless(X10,X9,X3)
      | ~ c_HOL_Oord__class_Oless(X9,X10,X3) ),
    file('<stdin>',cls_not__less__iff__gr__or__eq_1) ).

fof(c_0_320_321,axiom,
    ! [X9,X10,X3] :
      ( ~ class_Orderings_Opreorder(X3)
      | ~ c_HOL_Oord__class_Oless(X9,X10,X3)
      | ~ c_HOL_Oord__class_Oless(X10,X9,X3) ),
    file('<stdin>',cls_order__less__asym_0) ).

fof(c_0_321_322,axiom,
    ! [X35,X33,X3] :
      ( ~ class_Orderings_Opreorder(X3)
      | ~ c_HOL_Oord__class_Oless(X35,X33,X3)
      | ~ c_HOL_Oord__class_Oless(X33,X35,X3) ),
    file('<stdin>',cls_order__less__asym_H_0) ).

fof(c_0_322_323,axiom,
    ! [X20,X14] :
      ( ~ c_HOL_Oord__class_Oless(X14,X20,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X20,c_Suc(X14),tc_nat) ),
    file('<stdin>',cls_not__less__eq_1) ).

fof(c_0_323_324,axiom,
    ! [X33,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_HOL_Oord__class_Oless(X33,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),c_HOL_Oone__class_Oone(X3)),X3) ),
    file('<stdin>',cls_less__add__one_0) ).

fof(c_0_324_325,axiom,
    ! [X35,X33,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X33,X35,X3),X35,X3) = X33
      | X35 = c_HOL_Ozero__class_Ozero(X3) ),
    file('<stdin>',cls_div__mult__self2__is__id_0) ).

fof(c_0_325_326,axiom,
    ! [X35,X33,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X35,X33,X3),X35,X3) = X33
      | X35 = c_HOL_Ozero__class_Ozero(X3) ),
    file('<stdin>',cls_div__mult__self1__is__id_0) ).

fof(c_0_326_327,axiom,
    ! [X37,X35,X33,X3] :
      ( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X35) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X37)
      | X35 = X37 ),
    file('<stdin>',cls_add__imp__eq_0) ).

fof(c_0_327_328,axiom,
    ! [X37,X35,X33,X3] :
      ( ~ class_OrderedGroup_Ocancel__semigroup__add(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X35) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X37)
      | X35 = X37 ),
    file('<stdin>',cls_add__left__cancel_0) ).

fof(c_0_328_329,axiom,
    ! [X37,X35,X33,X3] :
      ( ~ class_OrderedGroup_Ocancel__semigroup__add(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X35),X33) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X37),X33)
      | X35 = X37 ),
    file('<stdin>',cls_add__right__cancel_0) ).

fof(c_0_329_330,axiom,
    ! [X35,X33,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Omod(X33,X35,X3),X35,X3) = c_HOL_Ozero__class_Ozero(X3) ),
    file('<stdin>',cls_mod__div__trivial_0) ).

fof(c_0_330_331,axiom,
    ! [X20,X14,X25] :
      ( c_HOL_Otimes__class_Otimes(X14,X25,tc_nat) != c_HOL_Otimes__class_Otimes(X20,X25,tc_nat)
      | X25 = c_HOL_Ozero__class_Ozero(tc_nat)
      | X14 = X20 ),
    file('<stdin>',cls_mult__cancel2_0) ).

fof(c_0_331_332,axiom,
    ! [X20,X14,X25] :
      ( c_HOL_Otimes__class_Otimes(X25,X14,tc_nat) != c_HOL_Otimes__class_Otimes(X25,X20,tc_nat)
      | X25 = c_HOL_Ozero__class_Ozero(tc_nat)
      | X14 = X20 ),
    file('<stdin>',cls_mult__cancel1_0) ).

fof(c_0_332_333,axiom,
    ! [X20,X14,X25] :
      ( c_HOL_Otimes__class_Otimes(X25,X14,tc_nat) != c_HOL_Otimes__class_Otimes(X25,X20,tc_nat)
      | X14 = X20
      | X25 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('<stdin>',cls_nat__mult__eq__cancel__disj_0) ).

fof(c_0_333_334,axiom,
    ! [X35,X33,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X33,X35,X3),X35,X3) = c_HOL_Ozero__class_Ozero(X3) ),
    file('<stdin>',cls_mod__mult__self2__is__0_0) ).

fof(c_0_334_335,axiom,
    ! [X35,X33,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X35,X33,X3),X35,X3) = c_HOL_Ozero__class_Ozero(X3) ),
    file('<stdin>',cls_mod__mult__self1__is__0_0) ).

fof(c_0_335_336,axiom,
    ! [X9,X10] :
      ( X10 = X9
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X9,X10,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X10,X9,tc_nat) ),
    file('<stdin>',cls_dvd_Oeq__iff_2) ).

fof(c_0_336_337,axiom,
    ! [X9,X10] :
      ( X10 = X9
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X9,X10,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X10,X9,tc_nat) ),
    file('<stdin>',cls_dvd_Oantisym_0) ).

fof(c_0_337_338,axiom,
    ! [X9,X10] :
      ( ~ c_Ring__and__Field_Odvd__class_Odvd(X9,X10,tc_nat)
      | X10 = X9
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X10,X9,tc_nat) ),
    file('<stdin>',cls_dvd_Oless__le_0) ).

fof(c_0_338_339,axiom,
    ! [X20,X14] :
      ( X14 = X20
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X20,X14,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X14,X20,tc_nat) ),
    file('<stdin>',cls_dvd__antisym_0) ).

fof(c_0_339_340,axiom,
    ! [X9,X10] :
      ( X10 = X9
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X10,X9,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X9,X10,tc_nat) ),
    file('<stdin>',cls_dvd_Oantisym__conv_0) ).

fof(c_0_340_341,axiom,
    ! [X35,X33] :
      ( ~ c_Ring__and__Field_Odvd__class_Odvd(X35,X33,tc_nat)
      | X33 = X35
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X33,X35,tc_nat) ),
    file('<stdin>',cls_dvd_Ole__neq__trans_0) ).

fof(c_0_341_342,axiom,
    ! [X35,X33] :
      ( ~ c_Ring__and__Field_Odvd__class_Odvd(X35,X33,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X33,X35,tc_nat)
      | X33 = X35 ),
    file('<stdin>',cls_dvd_Oneq__le__trans_0) ).

fof(c_0_342_343,axiom,
    ! [X7,X25,X21] :
      ( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X21)),X7),X25) = c_Lambda_OdB_OVar(X21)
      | X21 = X25
      | c_HOL_Oord__class_Oless(X25,X21,tc_nat) ),
    file('<stdin>',cls_subst__Var_2) ).

fof(c_0_343_344,axiom,
    ! [X35,X33,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(X33,c_HOL_Otimes__class_Otimes(X35,X33,X3),X3) ),
    file('<stdin>',cls_dvd__triv__right_0) ).

fof(c_0_344_345,axiom,
    ! [X35,X33,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(X33,c_HOL_Otimes__class_Otimes(X33,X35,X3),X3) ),
    file('<stdin>',cls_dvd__triv__left_0) ).

fof(c_0_345_346,axiom,
    ! [X25,X35,X3] :
      ( ~ class_Ring__and__Field_Odvd(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(X35,c_HOL_Otimes__class_Otimes(X35,X25,X3),X3) ),
    file('<stdin>',cls_dvdI_0) ).

fof(c_0_346_347,axiom,
    ! [X10,X7] :
      ( c_HOL_Oord__class_Oless(X10,X10,tc_nat)
      | hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X10)),X7),X10) = X7 ),
    file('<stdin>',cls_subst__Var_1) ).

fof(c_0_347_348,axiom,
    ! [X43,X29,X22,X24] :
      ( c_Type_Otyping(X22,X43,X24)
      | ~ c_Lambda_Obeta(X29,X43)
      | ~ c_Type_Otyping(X22,X29,X24) ),
    file('<stdin>',cls_subject__reduction_0) ).

fof(c_0_348_349,axiom,
    ! [X20,X14] :
      ( c_HOL_Oord__class_Oless(X14,X20,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_Suc(X14),c_Suc(X20),tc_nat) ),
    file('<stdin>',cls_Suc__less__eq_0) ).

fof(c_0_349_350,axiom,
    ! [X35,X33,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Omod(X35,X33,X3) != c_HOL_Ozero__class_Ozero(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(X33,X35,X3) ),
    file('<stdin>',cls_dvd__eq__mod__eq__0_1) ).

fof(c_0_350_351,axiom,
    ! [X35,X33,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Omod(X35,X33,X3) = c_HOL_Ozero__class_Ozero(X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X33,X35,X3) ),
    file('<stdin>',cls_dvd__imp__mod__0_0) ).

fof(c_0_351_352,axiom,
    ! [X25,X31] :
      ( hBOOL(hAPP(X31,c_HOL_Ozero__class_Ozero(tc_nat)))
      | ~ hBOOL(hAPP(X31,c_ATP__Linkup_Osko__Nat__Xzero__induct__1__1(X31)))
      | ~ hBOOL(hAPP(X31,X25)) ),
    file('<stdin>',cls_zero__induct_1) ).

fof(c_0_352_353,axiom,
    ! [X25,X31] :
      ( hBOOL(hAPP(X31,c_HOL_Ozero__class_Ozero(tc_nat)))
      | hBOOL(hAPP(X31,c_Suc(c_ATP__Linkup_Osko__Nat__Xzero__induct__1__1(X31))))
      | ~ hBOOL(hAPP(X31,X25)) ),
    file('<stdin>',cls_zero__induct_0) ).

fof(c_0_353_354,axiom,
    ! [X10,X20] :
      ( c_HOL_Oord__class_Oless(c_Suc(X10),c_Suc(X20),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X10,X20,tc_nat) ),
    file('<stdin>',cls_less__Suc__eq__0__disj_3) ).

fof(c_0_354_355,axiom,
    ! [X20,X14] :
      ( c_HOL_Oord__class_Oless(c_Suc(X14),c_Suc(X20),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X14,X20,tc_nat) ),
    file('<stdin>',cls_Suc__mono_0) ).

fof(c_0_355_356,axiom,
    ! [X20,X14] :
      ( X20 = X14
      | ~ c_HOL_Oord__class_Oless(X20,c_Suc(X14),tc_nat)
      | c_HOL_Oord__class_Oless(X20,X14,tc_nat) ),
    file('<stdin>',cls_not__less__less__Suc__eq_0) ).

fof(c_0_356_357,axiom,
    ! [X20,X14] :
      ( X14 = X20
      | ~ c_HOL_Oord__class_Oless(X20,c_Suc(X14),tc_nat)
      | c_HOL_Oord__class_Oless(X20,X14,tc_nat) ),
    file('<stdin>',cls_less__antisym_0) ).

fof(c_0_357_358,axiom,
    ! [X20,X14] :
      ( X14 = X20
      | c_HOL_Oord__class_Oless(X14,X20,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X14,c_Suc(X20),tc_nat) ),
    file('<stdin>',cls_less__SucE_0) ).

fof(c_0_358_359,axiom,
    ! [X20,X14] :
      ( c_HOL_Oord__class_Oless(c_Suc(X14),X20,tc_nat)
      | c_Suc(X14) = X20
      | ~ c_HOL_Oord__class_Oless(X14,X20,tc_nat) ),
    file('<stdin>',cls_Suc__lessI_0) ).

fof(c_0_359_360,axiom,
    ! [X36,X9,X10] :
      ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X10),X9) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X10),X36)
      | X9 = X36 ),
    file('<stdin>',cls_natgb_Oadd__cancel_0) ).

fof(c_0_360_361,axiom,
    ! [X20,X14,X25] :
      ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X25) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X20),X25)
      | X14 = X20 ),
    file('<stdin>',cls_nat__add__right__cancel_0) ).

fof(c_0_361_362,axiom,
    ! [X20,X14,X25] :
      ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X25),X14) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X25),X20)
      | X14 = X20 ),
    file('<stdin>',cls_nat__add__left__cancel_0) ).

fof(c_0_362_363,axiom,
    ! [X20,X14] :
      ( c_HOL_Oord__class_Oless(X14,X20,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_Suc(X14),X20,tc_nat) ),
    file('<stdin>',cls_Suc__lessD_0) ).

fof(c_0_363_364,axiom,
    ! [X14,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X14,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
    file('<stdin>',cls_of__nat__less__0__iff_0) ).

fof(c_0_364_365,axiom,
    ! [X20,X14] :
      ( c_HOL_Oord__class_Oless(X14,c_Suc(X20),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X14,X20,tc_nat) ),
    file('<stdin>',cls_less__SucI_0) ).

fof(c_0_365_366,axiom,
    ! [X20,X14] :
      ( c_Divides_Odiv__class_Odiv(X14,X20,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
      | ~ c_HOL_Oord__class_Oless(X14,X20,tc_nat) ),
    file('<stdin>',cls_div__less_0) ).

fof(c_0_366_367,axiom,
    ! [X20,X14] :
      ( c_Divides_Odiv__class_Omod(X14,X20,tc_nat) = X14
      | ~ c_HOL_Oord__class_Oless(X14,X20,tc_nat) ),
    file('<stdin>',cls_mod__if_0) ).

fof(c_0_367_368,axiom,
    ! [X25,X21] :
      ( hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(X21)),X25) = c_Lambda_OdB_OVar(X21)
      | ~ c_HOL_Oord__class_Oless(X21,X25,tc_nat) ),
    file('<stdin>',cls_lift_Osimps_I1_J_0) ).

fof(c_0_368_369,axiom,
    ! [X12,X31] :
      ( hBOOL(hAPP(X31,X12))
      | hBOOL(hAPP(X31,v_sko__List__Xlexn__Xinduct__1(X31)))
      | ~ hBOOL(hAPP(X31,c_HOL_Ozero__class_Ozero(tc_nat))) ),
    file('<stdin>',cls_lexn_Oinduct_0) ).

fof(c_0_369_370,axiom,
    ! [X20,X31] :
      ( hBOOL(hAPP(X31,X20))
      | hBOOL(hAPP(X31,c_ATP__Linkup_Osko__Nat__Xnat__induct__1__1(X31)))
      | ~ hBOOL(hAPP(X31,c_HOL_Ozero__class_Ozero(tc_nat))) ),
    file('<stdin>',cls_nat__induct_0) ).

fof(c_0_370_371,axiom,
    ! [X12,X31] :
      ( hBOOL(hAPP(X31,X12))
      | hBOOL(hAPP(X31,v_sko__List__Xreplicate__Xinduct__1(X31)))
      | ~ hBOOL(hAPP(X31,c_HOL_Ozero__class_Ozero(tc_nat))) ),
    file('<stdin>',cls_replicate_Oinduct_0) ).

fof(c_0_371_372,axiom,
    ! [X12,X31] :
      ( hBOOL(hAPP(X31,X12))
      | hBOOL(hAPP(X31,v_sko__Nat__Xnat__Xinducts__1(X31)))
      | ~ hBOOL(hAPP(X31,c_HOL_Ozero__class_Ozero(tc_nat))) ),
    file('<stdin>',cls_nat_Oinducts_0) ).

fof(c_0_372_373,axiom,
    ! [X12,X31] :
      ( hBOOL(hAPP(X31,X12))
      | hBOOL(hAPP(X31,v_sko__Nat__Xnat__Xinduct__1(X31)))
      | ~ hBOOL(hAPP(X31,c_HOL_Ozero__class_Ozero(tc_nat))) ),
    file('<stdin>',cls_nat_Oinduct_0) ).

fof(c_0_373_374,axiom,
    ! [X12,X31] :
      ( hBOOL(hAPP(X31,X12))
      | hBOOL(hAPP(X31,v_sko__List__Xupt__Xinduct__1(X31)))
      | ~ hBOOL(hAPP(X31,c_HOL_Ozero__class_Ozero(tc_nat))) ),
    file('<stdin>',cls_upt_Oinduct_0) ).

fof(c_0_374_375,axiom,
    ! [X20,X33,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(X33,X20,X3) != c_HOL_Ozero__class_Ozero(X3)
      | X33 = c_HOL_Ozero__class_Ozero(X3) ),
    file('<stdin>',cls_power__eq__0__iff_0) ).

fof(c_0_375_376,axiom,
    ! [X33,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(X33,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_376_377,axiom,
    ! [X7,X25,X21] :
      ( c_Lambda_Osubstn(c_Lambda_OdB_OVar(X21),X7,X25) = c_Lambda_OdB_OVar(X21)
      | X21 = X25
      | c_HOL_Oord__class_Oless(X25,X21,tc_nat) ),
    file('<stdin>',cls_substn_Osimps_I1_J_2) ).

fof(c_0_377_378,axiom,
    ! [X9,X10,X3] :
      ( ~ class_Ring__and__Field_Oordered__idom(X3)
      | c_HOL_Oord__class_Oless(X9,X10,X3)
      | c_HOL_Oord__class_Oless(X10,X9,X3)
      | X10 = X9 ),
    file('<stdin>',cls_linorder__neqE__ordered__idom_0) ).

fof(c_0_378_379,axiom,
    ! [X9,X10,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | X10 = X9
      | c_HOL_Oord__class_Oless(X9,X10,X3)
      | c_HOL_Oord__class_Oless(X10,X9,X3) ),
    file('<stdin>',cls_not__less__iff__gr__or__eq_0) ).

fof(c_0_379_380,axiom,
    ! [X9,X10,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_HOL_Oord__class_Oless(X9,X10,X3)
      | c_HOL_Oord__class_Oless(X10,X9,X3)
      | X10 = X9 ),
    file('<stdin>',cls_linorder__neqE_0) ).

fof(c_0_380_381,axiom,
    ! [X9,X10,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_HOL_Oord__class_Oless(X9,X10,X3)
      | X10 = X9
      | c_HOL_Oord__class_Oless(X10,X9,X3) ),
    file('<stdin>',cls_linorder__less__linear_0) ).

fof(c_0_381_382,axiom,
    ! [X9,X10,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | X10 = X9
      | c_HOL_Oord__class_Oless(X10,X9,X3)
      | c_HOL_Oord__class_Oless(X9,X10,X3) ),
    file('<stdin>',cls_linorder__antisym__conv3_0) ).

fof(c_0_382_383,axiom,
    ! [X15,X16,X17,X18] :
      ( hAPP(hAPP(c_Lambda_OdB_OApp,X18),X16) != hAPP(hAPP(c_Lambda_OdB_OApp,X17),X15)
      | X18 = X17 ),
    file('<stdin>',cls_dB_Osimps_I2_J_0) ).

fof(c_0_383_384,axiom,
    ! [X15,X16,X17,X18] :
      ( hAPP(hAPP(c_Lambda_OdB_OApp,X18),X16) != hAPP(hAPP(c_Lambda_OdB_OApp,X17),X15)
      | X16 = X15 ),
    file('<stdin>',cls_dB_Osimps_I2_J_1) ).

fof(c_0_384_385,axiom,
    ! [X14,X3] :
      ( ~ class_Ring__and__Field_Osemiring__1(X3)
      | c_Nat_Osemiring__1__class_Oof__nat(c_Suc(X14),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Oone__class_Oone(X3)),c_Nat_Osemiring__1__class_Oof__nat(X14,X3)) ),
    file('<stdin>',cls_of__nat__Suc_0) ).

fof(c_0_385_386,axiom,
    ! [X35,X33,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_HOL_Otimes__class_Otimes(X33,X35,X3) = c_HOL_Otimes__class_Otimes(X35,X33,X3) ),
    file('<stdin>',cls_class__semiring_Osemiring__rules_I7_J_0) ).

fof(c_0_386_387,axiom,
    ! [X9,X10,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_HOL_Otimes__class_Otimes(X10,X9,X3) = c_HOL_Otimes__class_Otimes(X9,X10,X3) ),
    file('<stdin>',cls_class__semiring_Omul__c_0) ).

fof(c_0_387_388,axiom,
    ! [X10] :
      ( c_HOL_Oord__class_Oless(X10,X10,tc_nat)
      | c_HOL_Oord__class_Oless(X10,c_Suc(X10),tc_nat) ),
    file('<stdin>',cls_not__less__less__Suc__eq_1) ).

fof(c_0_388_389,axiom,
    ! [X20,X14] :
      ( c_HOL_Oord__class_Oless(X20,c_Suc(X14),tc_nat)
      | c_HOL_Oord__class_Oless(X14,X20,tc_nat) ),
    file('<stdin>',cls_not__less__eq_0) ).

fof(c_0_389_390,axiom,
    ! [X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
    file('<stdin>',cls_not__one__less__zero_0) ).

fof(c_0_390_391,axiom,
    ! [X37,X33,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X37) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X37),X33) ),
    file('<stdin>',cls_class__semiring_Osemiring__rules_I24_J_0) ).

fof(c_0_391_392,axiom,
    ! [X35,X33,X3] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X35) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X35),X33) ),
    file('<stdin>',cls_comm__monoid__add_Omult__commute_0) ).

fof(c_0_392_393,axiom,
    ! [X9,X10,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X10),X9) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X9),X10) ),
    file('<stdin>',cls_class__semiring_Oadd__c_0) ).

fof(c_0_393_394,axiom,
    ! [X14] :
      ( X14 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X14,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
    file('<stdin>',cls_dvd__1__iff__1_0) ).

fof(c_0_394_395,axiom,
    ! [X21,X22,X24] :
      ( hAPP(X22,X21) = X24
      | ~ c_Type_Otyping(X22,c_Lambda_OdB_OVar(X21),X24) ),
    file('<stdin>',cls_typing__elims_I1_J_0) ).

fof(c_0_395_396,axiom,
    ! [X35,X33,X3] :
      ( ~ class_Ring__and__Field_Ono__zero__divisors(X3)
      | c_HOL_Otimes__class_Otimes(X33,X35,X3) != c_HOL_Ozero__class_Ozero(X3)
      | X33 = c_HOL_Ozero__class_Ozero(X3)
      | X35 = c_HOL_Ozero__class_Ozero(X3) ),
    file('<stdin>',cls_no__zero__divirors__neq0_0) ).

fof(c_0_396_397,axiom,
    ! [X35,X33,X3] :
      ( ~ class_Ring__and__Field_Ono__zero__divisors(X3)
      | c_HOL_Otimes__class_Otimes(X33,X35,X3) != c_HOL_Ozero__class_Ozero(X3)
      | X35 = c_HOL_Ozero__class_Ozero(X3)
      | X33 = c_HOL_Ozero__class_Ozero(X3) ),
    file('<stdin>',cls_no__zero__divisors_0) ).

fof(c_0_397_398,axiom,
    ! [X35,X33,X3] :
      ( ~ class_Ring__and__Field_Oring__no__zero__divisors(X3)
      | c_HOL_Otimes__class_Otimes(X33,X35,X3) != c_HOL_Ozero__class_Ozero(X3)
      | X35 = c_HOL_Ozero__class_Ozero(X3)
      | X33 = c_HOL_Ozero__class_Ozero(X3) ),
    file('<stdin>',cls_mult__eq__0__iff_0) ).

fof(c_0_398_399,axiom,
    ! [X20,X14] :
      ( c_HOL_Oord__class_Oless(X20,X14,tc_nat)
      | c_HOL_Oord__class_Oless(X14,X20,tc_nat)
      | X14 = X20 ),
    file('<stdin>',cls_nat__neq__iff_0) ).

fof(c_0_399_400,axiom,
    ! [X9,X10] :
      ( c_HOL_Oord__class_Oless(X9,X10,tc_nat)
      | c_HOL_Oord__class_Oless(X10,X9,tc_nat)
      | X10 = X9 ),
    file('<stdin>',cls_linorder__neqE__nat_0) ).

fof(c_0_400_401,axiom,
    ! [X33,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | X33 = c_HOL_Ozero__class_Ozero(X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(X3),X33,X3) ),
    file('<stdin>',cls_dvd__0__left_0) ).

fof(c_0_401_402,axiom,
    ! [X10,X14] :
      ( c_Power_Opower__class_Opower(X10,X14,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X10 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X14 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('<stdin>',cls_nat__power__eq__Suc__0__iff_0) ).

fof(c_0_402_403,axiom,
    ! [X20] :
      ( X20 = c_HOL_Ozero__class_Ozero(tc_nat)
      | ~ c_HOL_Oord__class_Oless(X20,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
    file('<stdin>',cls_less__Suc0_0) ).

fof(c_0_403_404,axiom,
    ! [X20,X33,X3] :
      ( ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X3)
      | c_Power_Opower__class_Opower(X33,X20,X3) != c_HOL_Ozero__class_Ozero(X3)
      | X33 = c_HOL_Ozero__class_Ozero(X3) ),
    file('<stdin>',cls_field__power__not__zero_0) ).

fof(c_0_404_405,axiom,
    ! [X10,X33,X3] :
      ( ~ class_Ring__and__Field_Oidom(X3)
      | ~ class_Int_Onumber__ring(X3)
      | X10 != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X10),X33)
      | X33 = c_HOL_Ozero__class_Ozero(X3) ),
    file('<stdin>',cls_class__ringb_Oadd__r0__iff_0) ).

fof(c_0_405_406,axiom,
    ! [X20,X14] :
      ( c_HOL_Otimes__class_Otimes(X14,X20,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X20 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    file('<stdin>',cls_mult__eq__1__iff_1) ).

fof(c_0_406_407,axiom,
    ! [X20,X14] :
      ( c_HOL_Otimes__class_Otimes(X14,X20,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X14 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    file('<stdin>',cls_mult__eq__1__iff_0) ).

fof(c_0_407_408,axiom,
    ! [X33,X3] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X33) != c_HOL_Ozero__class_Ozero(X3)
      | X33 = c_HOL_Ozero__class_Ozero(X3) ),
    file('<stdin>',cls_double__eq__0__iff_0) ).

fof(c_0_408_409,axiom,
    ! [X20,X14] :
      ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X20) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X20 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X14 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    file('<stdin>',cls_add__is__1_1) ).

fof(c_0_409_410,axiom,
    ! [X20,X14] :
      ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X20)
      | X20 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X14 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    file('<stdin>',cls_one__is__add_1) ).

fof(c_0_410_411,axiom,
    ! [X20,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),X20,X3) = c_HOL_Ozero__class_Ozero(X3)
      | X20 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('<stdin>',cls_power__eq__0__iff_2) ).

fof(c_0_411_412,axiom,
    ! [X20,X14] :
      ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X20)
      | X20 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X20 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('<stdin>',cls_one__is__add_3) ).

fof(c_0_412_413,axiom,
    ! [X20,X14] :
      ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X20)
      | X14 = c_HOL_Ozero__class_Ozero(tc_nat)
      | X14 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    file('<stdin>',cls_one__is__add_0) ).

fof(c_0_413_414,axiom,
    ! [X20,X14] :
      ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X20) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X20 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X20 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('<stdin>',cls_add__is__1_3) ).

fof(c_0_414_415,axiom,
    ! [X20,X14] :
      ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X20) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X14 = c_HOL_Ozero__class_Ozero(tc_nat)
      | X14 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    file('<stdin>',cls_add__is__1_0) ).

fof(c_0_415_416,axiom,
    ! [X20,X14] :
      ( c_HOL_Otimes__class_Otimes(X14,X20,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
      | X20 = c_HOL_Ozero__class_Ozero(tc_nat)
      | X14 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('<stdin>',cls_mult__is__0_0) ).

fof(c_0_416_417,axiom,
    ! [X10,X3] :
      ( ~ class_Orderings_Oorder(X3)
      | ~ c_HOL_Oord__class_Oless(X10,X10,X3) ),
    file('<stdin>',cls_order__less__le_1) ).

fof(c_0_417_418,axiom,
    ! [X10,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | ~ c_HOL_Oord__class_Oless(X10,X10,X3) ),
    file('<stdin>',cls_linorder__neq__iff_1) ).

fof(c_0_418_419,axiom,
    ! [X10,X3] :
      ( ~ class_Orderings_Opreorder(X3)
      | ~ c_HOL_Oord__class_Oless(X10,X10,X3) ),
    file('<stdin>',cls_order__less__irrefl_0) ).

fof(c_0_419_420,axiom,
    ! [X20,X14] :
      ( X14 != c_HOL_Otimes__class_Otimes(X14,X20,tc_nat)
      | X14 = c_HOL_Ozero__class_Ozero(tc_nat)
      | X20 = c_HOL_Oone__class_Oone(tc_nat) ),
    file('<stdin>',cls_mult__eq__self__implies__10_0) ).

fof(c_0_420_421,axiom,
    ! [X14] :
      ( X14 = c_HOL_Oone__class_Oone(tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X14,c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
    file('<stdin>',cls_nat__dvd__1__iff__1_0) ).

fof(c_0_421_422,axiom,
    ! [X20,X14] :
      ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X20) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X14 = c_HOL_Ozero__class_Ozero(tc_nat)
      | X20 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('<stdin>',cls_add__is__1_2) ).

fof(c_0_422_423,axiom,
    ! [X20,X14] :
      ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X20)
      | X14 = c_HOL_Ozero__class_Ozero(tc_nat)
      | X20 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('<stdin>',cls_one__is__add_2) ).

fof(c_0_423_424,axiom,
    ! [X20,X14] :
      ( c_HOL_Otimes__class_Otimes(X14,X20,tc_nat) != c_HOL_Oone__class_Oone(tc_nat)
      | X14 = c_HOL_Oone__class_Oone(tc_nat) ),
    file('<stdin>',cls_nat__mult__eq__1__iff_0) ).

fof(c_0_424_425,axiom,
    ! [X20,X14] :
      ( c_HOL_Otimes__class_Otimes(X14,X20,tc_nat) != c_HOL_Oone__class_Oone(tc_nat)
      | X20 = c_HOL_Oone__class_Oone(tc_nat) ),
    file('<stdin>',cls_nat__mult__eq__1__iff_1) ).

fof(c_0_425_426,axiom,
    ! [X20,X14] :
      ( c_HOL_Oone__class_Oone(tc_nat) != c_HOL_Otimes__class_Otimes(X14,X20,tc_nat)
      | X14 = c_HOL_Oone__class_Oone(tc_nat) ),
    file('<stdin>',cls_nat__1__eq__mult__iff_0) ).

fof(c_0_426_427,axiom,
    ! [X20,X14] :
      ( c_HOL_Oone__class_Oone(tc_nat) != c_HOL_Otimes__class_Otimes(X14,X20,tc_nat)
      | X20 = c_HOL_Oone__class_Oone(tc_nat) ),
    file('<stdin>',cls_nat__1__eq__mult__iff_1) ).

fof(c_0_427_428,axiom,
    ! [X1,X2,X3] :
      ( X2 = X1
      | ~ c_fequal(X2,X1,X3) ),
    file('<stdin>',cls_ATP__Linkup_Ofequal__imp__equal_0) ).

fof(c_0_428_429,axiom,
    ! [X20,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(X20),X3) = c_HOL_Ozero__class_Ozero(X3) ),
    file('<stdin>',cls_power__0__Suc_0) ).

fof(c_0_429_430,axiom,
    ! [X20,X3] :
      ( ~ class_Ring__and__Field_Osemiring__0(X3)
      | ~ class_Power_Opower(X3)
      | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X3),X20,X3) = c_HOL_Ozero__class_Ozero(X3)
      | X20 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('<stdin>',cls_power__0__left_1) ).

fof(c_0_430_431,axiom,
    ! [X8] :
      ( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(X8)))
      | ~ hBOOL(hAPP(c_InductTermi_OIT,X8)) ),
    file('<stdin>',cls_Lambda_0) ).

fof(c_0_431_432,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_432_433,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_433_434,axiom,
    ! [X20,X14] :
      ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X20) != c_HOL_Ozero__class_Ozero(tc_nat)
      | X20 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('<stdin>',cls_add__is__0_1) ).

fof(c_0_434_435,axiom,
    ! [X20,X14] :
      ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X20) != c_HOL_Ozero__class_Ozero(tc_nat)
      | X14 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('<stdin>',cls_add__is__0_0) ).

fof(c_0_435_436,axiom,
    ! [X10,X33] :
      ( X10 != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X10),X33)
      | X33 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('<stdin>',cls_natgb_Oadd__r0__iff_0) ).

fof(c_0_436_437,axiom,
    ! [X20,X14] :
      ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X20) != X14
      | X20 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('<stdin>',cls_add__eq__self__zero_0) ).

fof(c_0_437_438,axiom,
    ! [X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oone__class_Oone(X3),X3) ),
    file('<stdin>',cls_zero__less__one_0) ).

fof(c_0_438_439,axiom,
    ! [X10,X3] :
      ( ~ class_Ring__and__Field_Oidom(X3)
      | ~ class_Int_Onumber__ring(X3)
      | X10 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X10),c_HOL_Ozero__class_Ozero(X3)) ),
    file('<stdin>',cls_class__ringb_Oadd__r0__iff_1) ).

fof(c_0_439_440,axiom,
    ! [X10,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3)),X10) = X10 ),
    file('<stdin>',cls_class__semiring_Oadd__0_0) ).

fof(c_0_440_441,axiom,
    ! [X33,X3] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3)),X33) = X33 ),
    file('<stdin>',cls_comm__monoid__add_Omult__1_0) ).

fof(c_0_441_442,axiom,
    ! [X33,X3] :
      ( ~ class_OrderedGroup_Omonoid__add(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3)),X33) = X33 ),
    file('<stdin>',cls_add__0__left_0) ).

fof(c_0_442_443,axiom,
    ! [X33,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3)),X33) = X33 ),
    file('<stdin>',cls_class__semiring_Osemiring__rules_I5_J_0) ).

fof(c_0_443_444,axiom,
    ! [X20,X3] :
      ( ~ class_OrderedGroup_Omonoid__mult(X3)
      | c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X3),X20,X3) = c_HOL_Oone__class_Oone(X3) ),
    file('<stdin>',cls_power__one_0) ).

fof(c_0_444_445,axiom,
    ! [X10,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),X10,X3) = c_HOL_Ozero__class_Ozero(X3) ),
    file('<stdin>',cls_class__semiring_Omul__0_0) ).

fof(c_0_445_446,axiom,
    ! [X33,X3] :
      ( ~ class_Ring__and__Field_Omult__zero(X3)
      | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),X33,X3) = c_HOL_Ozero__class_Ozero(X3) ),
    file('<stdin>',cls_mult__zero__left_0) ).

fof(c_0_446_447,axiom,
    ! [X33,X3] :
      ( ~ class_Ring__and__Field_Omult__zero(X3)
      | c_HOL_Otimes__class_Otimes(X33,c_HOL_Ozero__class_Ozero(X3),X3) = c_HOL_Ozero__class_Ozero(X3) ),
    file('<stdin>',cls_mult__zero__right_0) ).

fof(c_0_447_448,axiom,
    ! [X35,X3] :
      ( ~ class_Ring__and__Field_Oring__no__zero__divisors(X3)
      | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),X35,X3) = c_HOL_Ozero__class_Ozero(X3) ),
    file('<stdin>',cls_mult__eq__0__iff_1) ).

fof(c_0_448_449,axiom,
    ! [X33,X3] :
      ( ~ class_Ring__and__Field_Oring__no__zero__divisors(X3)
      | c_HOL_Otimes__class_Otimes(X33,c_HOL_Ozero__class_Ozero(X3),X3) = c_HOL_Ozero__class_Ozero(X3) ),
    file('<stdin>',cls_mult__eq__0__iff_2) ).

fof(c_0_449_450,axiom,
    ! [X33,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_HOL_Otimes__class_Otimes(X33,c_HOL_Ozero__class_Ozero(X3),X3) = c_HOL_Ozero__class_Ozero(X3) ),
    file('<stdin>',cls_class__semiring_Osemiring__rules_I10_J_0) ).

fof(c_0_450_451,axiom,
    ! [X33,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),X33,X3) = c_HOL_Ozero__class_Ozero(X3) ),
    file('<stdin>',cls_class__semiring_Osemiring__rules_I9_J_0) ).

fof(c_0_451_452,axiom,
    ! [X33,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Odiv(X33,c_HOL_Ozero__class_Ozero(X3),X3) = c_HOL_Ozero__class_Ozero(X3) ),
    file('<stdin>',cls_div__by__0_0) ).

fof(c_0_452_453,axiom,
    ! [X33,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(X3),X33,X3) = c_HOL_Ozero__class_Ozero(X3) ),
    file('<stdin>',cls_div__0_0) ).

fof(c_0_453_454,axiom,
    ! [X33,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Omod(X33,c_HOL_Oone__class_Oone(X3),X3) = c_HOL_Ozero__class_Ozero(X3) ),
    file('<stdin>',cls_mod__by__1_0) ).

fof(c_0_454_455,axiom,
    ! [X33,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(X3),X33,X3) = c_HOL_Ozero__class_Ozero(X3) ),
    file('<stdin>',cls_mod__0_0) ).

fof(c_0_455_456,axiom,
    ! [X33,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Odiv(X33,X33,X3) = c_HOL_Oone__class_Oone(X3)
      | X33 = c_HOL_Ozero__class_Ozero(X3) ),
    file('<stdin>',cls_div__self_0) ).

fof(c_0_456_457,axiom,
    ! [X33,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X3),X33,X3) = X33 ),
    file('<stdin>',cls_class__semiring_Osemiring__rules_I11_J_0) ).

fof(c_0_457_458,axiom,
    ! [X33,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_HOL_Otimes__class_Otimes(X33,c_HOL_Oone__class_Oone(X3),X3) = X33 ),
    file('<stdin>',cls_class__semiring_Osemiring__rules_I12_J_0) ).

fof(c_0_458_459,axiom,
    ! [X33,X3] :
      ( ~ class_OrderedGroup_Omonoid__mult(X3)
      | c_HOL_Otimes__class_Otimes(X33,c_HOL_Oone__class_Oone(X3),X3) = X33 ),
    file('<stdin>',cls_mult__1__right_0) ).

fof(c_0_459_460,axiom,
    ! [X33,X3] :
      ( ~ class_OrderedGroup_Omonoid__mult(X3)
      | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X3),X33,X3) = X33 ),
    file('<stdin>',cls_mult__1__left_0) ).

fof(c_0_460_461,axiom,
    ! [X33,X3] :
      ( ~ class_OrderedGroup_Ocomm__monoid__mult(X3)
      | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X3),X33,X3) = X33 ),
    file('<stdin>',cls_mult__1_0) ).

fof(c_0_461_462,axiom,
    ! [X10,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X3),X10,X3) = X10 ),
    file('<stdin>',cls_class__semiring_Omul__1_0) ).

fof(c_0_462_463,axiom,
    ! [X33,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Odiv(X33,c_HOL_Oone__class_Oone(X3),X3) = X33 ),
    file('<stdin>',cls_div__by__1_0) ).

fof(c_0_463_464,axiom,
    ! [X33,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Omod(X33,c_HOL_Ozero__class_Ozero(X3),X3) = X33 ),
    file('<stdin>',cls_mod__by__0_0) ).

fof(c_0_464_465,axiom,
    ! [X33,X3] :
      ( ~ class_Power_Opower(X3)
      | c_Power_Opower__class_Opower(X33,c_HOL_Ozero__class_Ozero(tc_nat),X3) = c_HOL_Oone__class_Oone(X3) ),
    file('<stdin>',cls_power__0_0) ).

fof(c_0_465_466,axiom,
    ! [X10,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_Power_Opower__class_Opower(X10,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_466_467,axiom,
    ! [X33,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(X33,c_HOL_Ozero__class_Ozero(X3),X3) ),
    file('<stdin>',cls_dvd__0__right_0) ).

fof(c_0_467_468,axiom,
    ! [X33,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(X3),X33,X3) ),
    file('<stdin>',cls_one__dvd_0) ).

fof(c_0_468_469,axiom,
    ! [X33,X3] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),c_HOL_Ozero__class_Ozero(X3)) = X33 ),
    file('<stdin>',cls_comm__monoid__add_Omult__1__right_0) ).

fof(c_0_469_470,axiom,
    ! [X33,X3] :
      ( ~ class_OrderedGroup_Omonoid__add(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),c_HOL_Ozero__class_Ozero(X3)) = X33 ),
    file('<stdin>',cls_monoid__add__class_Oadd__0__right_0) ).

fof(c_0_470_471,axiom,
    ! [X33,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),c_HOL_Ozero__class_Ozero(X3)) = X33 ),
    file('<stdin>',cls_class__semiring_Osemiring__rules_I6_J_0) ).

fof(c_0_471_472,axiom,
    ! [X10,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_Power_Opower__class_Opower(X10,c_HOL_Oone__class_Oone(tc_nat),X3) = X10 ),
    file('<stdin>',cls_class__semiring_Osemiring__rules_I33_J_0) ).

fof(c_0_472_473,axiom,
    ! [X33,X3] :
      ( ~ class_OrderedGroup_Omonoid__mult(X3)
      | c_Power_Opower__class_Opower(X33,c_HOL_Oone__class_Oone(tc_nat),X3) = X33 ),
    file('<stdin>',cls_power__one__right_0) ).

fof(c_0_473_474,axiom,
    ! [X33,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Omod(X33,X33,X3) = c_HOL_Ozero__class_Ozero(X3) ),
    file('<stdin>',cls_mod__self_0) ).

fof(c_0_474_475,axiom,
    ! [X10,X3] :
      ( ~ class_OrderedGroup_Oab__semigroup__idem__mult(X3)
      | c_HOL_Otimes__class_Otimes(X10,X10,X3) = X10 ),
    file('<stdin>',cls_mult__idem_0) ).

fof(c_0_475_476,axiom,
    ! [X33,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(X33,X33,X3) ),
    file('<stdin>',cls_dvd__refl_0) ).

fof(c_0_476_477,axiom,
    ! [X20] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X20,tc_nat)
      | X20 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('<stdin>',cls_gr0I_0) ).

fof(c_0_477_478,axiom,
    ! [X20,X14,X3] :
      ( ~ class_Nat_Osemiring__char__0(X3)
      | c_Nat_Osemiring__1__class_Oof__nat(X14,X3) != c_Nat_Osemiring__1__class_Oof__nat(X20,X3)
      | X14 = X20 ),
    file('<stdin>',cls_of__nat__eq__iff_0) ).

fof(c_0_478_479,axiom,
    ! [X29,X7] :
      ( c_Lambda_Obeta(c_Lambda_OdB_OAbs(X7),c_Lambda_OdB_OAbs(X29))
      | ~ c_Lambda_Obeta(X7,X29) ),
    file('<stdin>',cls_abs_0) ).

fof(c_0_479_480,axiom,
    ! [X4,X5] :
      ( class_Orderings_Opreorder(tc_fun(X4,X5))
      | ~ class_Orderings_Opreorder(X5) ),
    file('<stdin>',clsarity_fun__Orderings_Opreorder) ).

fof(c_0_480_481,axiom,
    ! [X4,X5] :
      ( class_Orderings_Oorder(tc_fun(X4,X5))
      | ~ class_Orderings_Oorder(X5) ),
    file('<stdin>',clsarity_fun__Orderings_Oorder) ).

fof(c_0_481_482,axiom,
    ! [X3] :
      ( ~ class_Ring__and__Field_Osemiring__1(X3)
      | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),X3) = c_HOL_Oone__class_Oone(X3) ),
    file('<stdin>',cls_of__nat__1_0) ).

fof(c_0_482_483,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_483_484,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_484_485,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_485_486,axiom,
    ! [X60,X50] :
      ( c_Lambda_OdB_OAbs(X50) != c_Lambda_OdB_OAbs(X60)
      | X50 = X60 ),
    file('<stdin>',cls_dB_Osimps_I3_J_0) ).

fof(c_0_486_487,axiom,
    ! [X11,X12] :
      ( c_Lambda_OdB_OVar(X12) != c_Lambda_OdB_OVar(X11)
      | X12 = X11 ),
    file('<stdin>',cls_dB_Osimps_I1_J_0) ).

fof(c_0_487_488,axiom,
    ! [X11,X12] :
      ( c_Suc(X12) != c_Suc(X11)
      | X12 = X11 ),
    file('<stdin>',cls_nat_Oinject_0) ).

fof(c_0_488_489,axiom,
    ! [X9,X10] :
      ( c_Suc(X10) != c_Suc(X9)
      | X10 = X9 ),
    file('<stdin>',cls_Suc__inject_0) ).

fof(c_0_489_490,axiom,
    ! [X9] :
      ( X9 = c_Suc(c_ATP__Linkup_Osko__Nat__Xnat__Xexhaust__1__1(X9))
      | X9 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('<stdin>',cls_nat_Oexhaust_0) ).

fof(c_0_490_491,axiom,
    ! [X32] :
      ( X32 = c_Suc(c_ATP__Linkup_Osko__Nat__Xnat__Xnchotomy__1__1(X32))
      | X32 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('<stdin>',cls_nat_Onchotomy_0) ).

fof(c_0_491_492,axiom,
    ! [X20] :
      ( X20 = c_Suc(c_ATP__Linkup_Osko__Nat__Xnot0__implies__Suc__1__1(X20))
      | X20 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('<stdin>',cls_not0__implies__Suc_0) ).

fof(c_0_492_493,plain,
    ! [X26,X6,X21,X22,X28,X24] :
      ( c_Type_Otypings(X22,c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,X26,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),X21,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X6,tc_Lambda_OdB,tc_Lambda_OdB),X28)
      | ~ c_Type_Otypings(c_Type_Oshift(X22,X21,X24,tc_Type_Otype),X6,X28)
      | ~ c_Type_Otyping(X22,X26,X24) ),
    inference(fof_simplification,[status(thm)],[c_0_0]) ).

fof(c_0_493_494,plain,
    ! [X13,X7,X8] :
      ( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X8)),X7),X13,tc_Lambda_OdB,tc_Lambda_OdB)))
      | ~ hBOOL(hAPP(c_InductTermi_OIT,X7))
      | ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X8),X7),c_HOL_Ozero__class_Ozero(tc_nat)),X13,tc_Lambda_OdB,tc_Lambda_OdB))) ),
    inference(fof_simplification,[status(thm)],[c_0_1]) ).

fof(c_0_494_495,plain,
    ! [X54,X55,X47,X48,X49,X31] :
      ( ~ hBOOL(hAPP(X31,c_Lambda_OdB_OdB__case(X49,X48,X47,hAPP(hAPP(c_Lambda_OdB_OApp,X55),X54),t_a)))
      | hBOOL(hAPP(X31,hAPP(hAPP(X48,X55),X54))) ),
    inference(fof_simplification,[status(thm)],[c_0_2]) ).

fof(c_0_495_496,plain,
    ! [X47,X48,X49,X16,X18,X31] :
      ( ~ hBOOL(hAPP(X31,c_Lambda_OdB_OdB__case(X49,X48,X47,hAPP(hAPP(c_Lambda_OdB_OApp,X18),X16),t_a)))
      | hBOOL(hAPP(X31,hAPP(hAPP(X48,X18),X16))) ),
    inference(fof_simplification,[status(thm)],[c_0_3]) ).

fof(c_0_496_497,plain,
    ! [X6,X21,X22,X23,X24] :
      ( X24 = X23
      | ~ c_Type_Otyping(X22,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X21),X6,tc_Lambda_OdB,tc_Lambda_OdB),X23)
      | ~ c_Type_Otyping(X22,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X21),X6,tc_Lambda_OdB,tc_Lambda_OdB),X24) ),
    inference(fof_simplification,[status(thm)],[c_0_4]) ).

fof(c_0_497_498,plain,
    ! [X51,X47,X48,X49,X31] :
      ( ~ hBOOL(hAPP(X31,c_Lambda_OdB_OdB__case(X49,X48,X47,c_Lambda_OdB_OVar(X51),t_a)))
      | hBOOL(hAPP(X31,hAPP(X49,X51))) ),
    inference(fof_simplification,[status(thm)],[c_0_5]) ).

fof(c_0_498_499,plain,
    ! [X12,X47,X48,X49,X31] :
      ( ~ hBOOL(hAPP(X31,c_Lambda_OdB_OdB__case(X49,X48,X47,c_Lambda_OdB_OVar(X12),t_a)))
      | hBOOL(hAPP(X31,hAPP(X49,X12))) ),
    inference(fof_simplification,[status(thm)],[c_0_6]) ).

fof(c_0_499_500,plain,
    ! [X47,X48,X49,X50,X31] :
      ( ~ hBOOL(hAPP(X31,c_Lambda_OdB_OdB__case(X49,X48,X47,c_Lambda_OdB_OAbs(X50),t_a)))
      | hBOOL(hAPP(X31,hAPP(X47,X50))) ),
    inference(fof_simplification,[status(thm)],[c_0_7]) ).

fof(c_0_500_501,plain,
    ! [X46,X47,X48,X49,X31] :
      ( ~ hBOOL(hAPP(X31,c_Lambda_OdB_OdB__case(X49,X48,X47,c_Lambda_OdB_OAbs(X46),t_a)))
      | hBOOL(hAPP(X31,hAPP(X47,X46))) ),
    inference(fof_simplification,[status(thm)],[c_0_8]) ).

fof(c_0_501_502,plain,
    ! [X6,X21,X22,X23,X28] :
      ( c_Type_Otypings(c_Type_Oshift(X22,X21,X23,tc_Type_Otype),c_List_Omap(c_COMBC(c_Lambda_Olift,X21,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X6,tc_Lambda_OdB,tc_Lambda_OdB),X28)
      | ~ c_Type_Otypings(X22,X6,X28) ),
    inference(fof_simplification,[status(thm)],[c_0_9]) ).

fof(c_0_502_503,plain,
    ! [X6] :
      ( c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X6,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)
      | ~ c_List_Olistsp(c_InductTermi_OIT,X6,tc_Lambda_OdB) ),
    inference(fof_simplification,[status(thm)],[c_0_10]) ).

fof(c_0_503_504,plain,
    ! [X32,X19,X20] :
      ( X32 = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X20),c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(X20,X19,X32),tc_Lambda_OdB,tc_Lambda_OdB)
      | ~ c_Lambda_Obeta(c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X20),X19,tc_Lambda_OdB,tc_Lambda_OdB),X32) ),
    inference(fof_simplification,[status(thm)],[c_0_11]) ).

fof(c_0_504_505,plain,
    ! [X19,X20] :
      ( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X20),X19,tc_Lambda_OdB,tc_Lambda_OdB)))
      | ~ c_List_Olistsp(c_InductTermi_OIT,X19,tc_Lambda_OdB) ),
    inference(fof_simplification,[status(thm)],[c_0_12]) ).

fof(c_0_505_506,plain,
    ! [X13,X7,X8] :
      ( c_Lambda_Obeta(c_List_Ofoldl(c_Lambda_OdB_OApp,X8,X13,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,X7,X13,tc_Lambda_OdB,tc_Lambda_OdB))
      | ~ c_Lambda_Obeta(X8,X7) ),
    inference(fof_simplification,[status(thm)],[c_0_13]) ).

fof(c_0_506_507,axiom,
    ! [X13,X7,X19,X8] :
      ( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X8),X19,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X7),X13,tc_Lambda_OdB,tc_Lambda_OdB)
      | X8 = X7 ),
    c_0_14 ).

fof(c_0_507_508,axiom,
    ! [X13,X7,X19,X8] :
      ( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X8),X19,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X7),X13,tc_Lambda_OdB,tc_Lambda_OdB)
      | X19 = X13 ),
    c_0_15 ).

fof(c_0_508_509,axiom,
    ! [X13,X19,X20,X14] :
      ( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X14),X19,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X20),X13,tc_Lambda_OdB,tc_Lambda_OdB)
      | X14 = X20 ),
    c_0_16 ).

fof(c_0_509_510,axiom,
    ! [X13,X19,X20,X14] :
      ( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X14),X19,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X20),X13,tc_Lambda_OdB,tc_Lambda_OdB)
      | X19 = X13 ),
    c_0_17 ).

fof(c_0_510_511,plain,
    ! [X30,X9,X10,X3] :
      ( ~ class_OrderedGroup_Osemigroup__add(X3)
      | c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X10),X9),X30,X3,X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X10),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),X9,X30,X3,X3)) ),
    inference(fof_simplification,[status(thm)],[c_0_18]) ).

fof(c_0_511_512,axiom,
    ! [X6,X7,X8] :
      ( c_List_Ofoldl(c_Lambda_OdB_OApp,X8,X6,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,X7,X6,tc_Lambda_OdB,tc_Lambda_OdB)
      | X8 = X7 ),
    c_0_19 ).

fof(c_0_512_513,plain,
    ! [X30,X10,X3] :
      ( ~ class_OrderedGroup_Omonoid__add(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X10),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3),X30,X3,X3)) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),X10,X30,X3,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_20]) ).

fof(c_0_513_514,plain,
    ! [X25,X27,X21,X31] :
      ( ~ c_HOL_Oord__class_Oless(X27,X25,tc_nat)
      | X25 = c_HOL_Ozero__class_Ozero(tc_nat)
      | ~ hBOOL(hAPP(X31,c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X25,X21,tc_nat)),X27),X25,tc_nat)))
      | hBOOL(hAPP(X31,X27)) ),
    inference(fof_simplification,[status(thm)],[c_0_21]) ).

fof(c_0_514_515,plain,
    ! [X25,X27,X21,X31] :
      ( ~ c_HOL_Oord__class_Oless(X27,X25,tc_nat)
      | X25 = c_HOL_Ozero__class_Ozero(tc_nat)
      | ~ hBOOL(hAPP(X31,c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X25,X21,tc_nat)),X27),X25,tc_nat)))
      | hBOOL(hAPP(X31,X21)) ),
    inference(fof_simplification,[status(thm)],[c_0_22]) ).

fof(c_0_515_516,plain,
    ! [X37,X35,X33,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(X35,c_Divides_Odiv__class_Odiv(X33,X35,X3),X3)),c_Divides_Odiv__class_Omod(X33,X35,X3))),X37) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X37) ),
    inference(fof_simplification,[status(thm)],[c_0_23]) ).

fof(c_0_516_517,plain,
    ! [X37,X35,X33,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X33,X35,X3),X35,X3)),c_Divides_Odiv__class_Omod(X33,X35,X3))),X37) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X37) ),
    inference(fof_simplification,[status(thm)],[c_0_24]) ).

fof(c_0_517_518,plain,
    ! [X32,X26,X29,X27,X21] :
      ( hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,X29),hAPP(hAPP(c_Lambda_Olift,X32),X21)),c_Suc(X27))),hAPP(hAPP(hAPP(c_Lambda_Osubst,X26),X32),X27)),X21) = hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,X29),X26),X21)),X32),X27)
      | ~ c_HOL_Oord__class_Oless(X21,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X27),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_25]) ).

fof(c_0_518_519,axiom,
    ! [X29,X7,X8] :
      ( hAPP(hAPP(c_Lambda_OdB_OApp,X8),X7) != c_List_Ofoldl(c_Lambda_OdB_OApp,X29,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)
      | hAPP(hAPP(c_Lambda_OdB_OApp,X8),X7) = X29 ),
    c_0_26 ).

fof(c_0_519_520,axiom,
    ! [X13,X7,X8] :
      ( c_List_Ofoldl(c_Lambda_OdB_OApp,X7,X13,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X8)
      | X7 = c_Lambda_OdB_OAbs(X8) ),
    c_0_27 ).

fof(c_0_520_521,axiom,
    ! [X13,X7,X8] :
      ( c_Lambda_OdB_OAbs(X8) != c_List_Ofoldl(c_Lambda_OdB_OApp,X7,X13,tc_Lambda_OdB,tc_Lambda_OdB)
      | c_Lambda_OdB_OAbs(X8) = X7 ),
    c_0_28 ).

fof(c_0_521_522,axiom,
    ! [X13,X7,X14] :
      ( c_Lambda_OdB_OVar(X14) != c_List_Ofoldl(c_Lambda_OdB_OApp,X7,X13,tc_Lambda_OdB,tc_Lambda_OdB)
      | c_Lambda_OdB_OVar(X14) = X7 ),
    c_0_29 ).

fof(c_0_522_523,plain,
    ! [X29,X7,X27,X21] :
      ( hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(hAPP(c_Lambda_Osubst,X29),X7),X27)),X21) = hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,X29),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X21),c_HOL_Oone__class_Oone(tc_nat)))),hAPP(hAPP(c_Lambda_Olift,X7),X21)),X27)
      | ~ c_HOL_Oord__class_Oless(X27,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X21),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_30]) ).

fof(c_0_523_524,plain,
    ! [X20,X14,X34,X3] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
      | c_Finite__Set_Osetsum(X34,c_SetInterval_Oord__class_OatLeastLessThan(X14,c_Suc(X20),tc_nat),tc_nat,X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_Finite__Set_Osetsum(X34,c_SetInterval_Oord__class_OatLeastLessThan(X14,X20,tc_nat),tc_nat,X3)),hAPP(X34,X20))
      | c_HOL_Oord__class_Oless(X20,X14,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_31]) ).

fof(c_0_524_525,axiom,
    ! [X13,X7,X8] :
      ( c_Lambda_OdB_OAbs(X8) != c_List_Ofoldl(c_Lambda_OdB_OApp,X7,X13,tc_Lambda_OdB,tc_Lambda_OdB)
      | X13 = c_List_Olist_ONil(tc_Lambda_OdB) ),
    c_0_32 ).

fof(c_0_525_526,axiom,
    ! [X13,X7,X8] :
      ( c_List_Ofoldl(c_Lambda_OdB_OApp,X7,X13,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X8)
      | X13 = c_List_Olist_ONil(tc_Lambda_OdB) ),
    c_0_33 ).

fof(c_0_526_527,axiom,
    ! [X13,X7,X14] :
      ( c_Lambda_OdB_OVar(X14) != c_List_Ofoldl(c_Lambda_OdB_OApp,X7,X13,tc_Lambda_OdB,tc_Lambda_OdB)
      | X13 = c_List_Olist_ONil(tc_Lambda_OdB) ),
    c_0_34 ).

fof(c_0_527_528,plain,
    ! [X8,X42,X37,X35] :
      ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X35,c_Divides_Odiv__class_Omod(X42,X37,tc_nat),tc_nat)),X8),c_HOL_Otimes__class_Otimes(X35,X37,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X8,X35,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X37,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_35]) ).

fof(c_0_528_529,plain,
    ! [X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(X3),X3)),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(X3),X3)),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_36]) ).

fof(c_0_529_530,plain,
    ! [X22,X37,X35,X33,X3] :
      ( ~ class_Ring__and__Field_Osemiring(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(X33,X22,X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(X35,X22,X3)),X37)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X35),X22,X3)),X37) ),
    inference(fof_simplification,[status(thm)],[c_0_37]) ).

fof(c_0_530_531,plain,
    ! [X9,X10,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(X10,X10,X3)),c_HOL_Otimes__class_Otimes(X9,X9,X3)),c_HOL_Ozero__class_Ozero(X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_38]) ).

fof(c_0_531_532,plain,
    ! [X20,X14,X34,X3] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
      | c_Finite__Set_Osetsum(X34,c_SetInterval_Oord__class_OatLeastLessThan(X14,X20,tc_nat),tc_nat,X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(X34,X14)),c_Finite__Set_Osetsum(X34,c_SetInterval_Oord__class_OatLeastLessThan(c_Suc(X14),X20,tc_nat),tc_nat,X3))
      | ~ c_HOL_Oord__class_Oless(X14,X20,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_39]) ).

fof(c_0_532_533,plain,
    ! [X29,X7,X27,X21] :
      ( hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(hAPP(c_Lambda_Osubst,X29),X7),X27)),X21) = hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,X29),X21)),hAPP(hAPP(c_Lambda_Olift,X7),X21)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X27),c_HOL_Oone__class_Oone(tc_nat)))
      | ~ c_HOL_Oord__class_Oless(X21,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X27),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_40]) ).

fof(c_0_533_534,plain,
    ! [X36,X9,X10,X56,X3] :
      ( ~ class_Ring__and__Field_Oidom(X3)
      | ~ class_Int_Onumber__ring(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(X56,X9,X3)),c_HOL_Otimes__class_Otimes(X10,X36,X3)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(X56,X36,X3)),c_HOL_Otimes__class_Otimes(X10,X9,X3))
      | X9 = X36
      | X56 = X10 ),
    inference(fof_simplification,[status(thm)],[c_0_41]) ).

fof(c_0_534_535,plain,
    ! [X44,X37,X35,X33,X3] :
      ( ~ class_Ring__and__Field_Oidom(X3)
      | ~ class_Int_Onumber__ring(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(X33,X37,X3)),c_HOL_Otimes__class_Otimes(X35,X44,X3)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(X33,X44,X3)),c_HOL_Otimes__class_Otimes(X35,X37,X3))
      | X37 = X44
      | X33 = X35 ),
    inference(fof_simplification,[status(thm)],[c_0_42]) ).

fof(c_0_535_536,plain,
    ! [X26,X29,X21,X62,X23,X24] :
      ( ~ c_Type_Otyping(X62,X26,X23)
      | ~ c_Type_Otyping(c_Type_Oshift(X62,X21,X23,tc_Type_Otype),X29,X24)
      | c_Type_Otyping(X62,hAPP(hAPP(hAPP(c_Lambda_Osubst,X29),X26),X21),X24) ),
    inference(fof_simplification,[status(thm)],[c_0_43]) ).

fof(c_0_536_537,axiom,
    ! [X44,X37,X35,X33] :
      ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X33,X37,tc_nat)),c_HOL_Otimes__class_Otimes(X35,X44,tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X33,X44,tc_nat)),c_HOL_Otimes__class_Otimes(X35,X37,tc_nat))
      | X37 = X44
      | X33 = X35 ),
    c_0_44 ).

fof(c_0_537_538,axiom,
    ! [X36,X9,X10,X56] :
      ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X56,X9,tc_nat)),c_HOL_Otimes__class_Otimes(X10,X36,tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X56,X36,tc_nat)),c_HOL_Otimes__class_Otimes(X10,X9,tc_nat))
      | X9 = X36
      | X56 = X10 ),
    c_0_45 ).

fof(c_0_538_539,plain,
    ! [X37,X35,X33,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X35),X37,X3) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_Divides_Odiv__class_Omod(X33,X37,X3)),c_Divides_Odiv__class_Omod(X35,X37,X3)),X37,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_46]) ).

fof(c_0_539_540,plain,
    ! [X9,X10,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(X10,X10,X3)),c_HOL_Otimes__class_Otimes(X9,X9,X3)),X3)
      | X10 = c_HOL_Ozero__class_Ozero(X3) ),
    inference(fof_simplification,[status(thm)],[c_0_47]) ).

fof(c_0_540_541,plain,
    ! [X9,X10,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(X10,X10,X3)),c_HOL_Otimes__class_Otimes(X9,X9,X3)),X3)
      | X9 = c_HOL_Ozero__class_Ozero(X3) ),
    inference(fof_simplification,[status(thm)],[c_0_48]) ).

fof(c_0_541_542,plain,
    ! [X35,X33,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(X35,c_Divides_Odiv__class_Odiv(X33,X35,X3),X3)),c_Divides_Odiv__class_Omod(X33,X35,X3)) = X33 ),
    inference(fof_simplification,[status(thm)],[c_0_49]) ).

fof(c_0_542_543,plain,
    ! [X35,X33,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X33,X35,X3),X35,X3)),c_Divides_Odiv__class_Omod(X33,X35,X3)) = X33 ),
    inference(fof_simplification,[status(thm)],[c_0_50]) ).

fof(c_0_543_544,plain,
    ! [X35,X33,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | X33 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X33,X35,X3),X35,X3)),c_Divides_Odiv__class_Omod(X33,X35,X3)) ),
    inference(fof_simplification,[status(thm)],[c_0_51]) ).

fof(c_0_544_545,plain,
    ! [X25,X34,X3] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
      | hAPP(X34,c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Ozero__class_Ozero(X3)
      | c_Finite__Set_Osetsum(X34,c_SetInterval_Oord__class_OatLeastLessThan(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X25,tc_nat),tc_nat,X3) = c_Finite__Set_Osetsum(X34,c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),X25,tc_nat),tc_nat,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_52]) ).

fof(c_0_545_546,plain,
    ! [X36,X9,X10,X3] :
      ( ~ class_Ring__and__Field_Oidom(X3)
      | ~ class_Int_Onumber__ring(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(X10,X9,X3)),c_HOL_Otimes__class_Otimes(X10,X36,X3)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(X10,X36,X3)),c_HOL_Otimes__class_Otimes(X10,X9,X3)) ),
    inference(fof_simplification,[status(thm)],[c_0_53]) ).

fof(c_0_546_547,plain,
    ! [X10,X44,X37,X3] :
      ( ~ class_Ring__and__Field_Oidom(X3)
      | ~ class_Int_Onumber__ring(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(X10,X37,X3)),c_HOL_Otimes__class_Otimes(X10,X44,X3)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(X10,X44,X3)),c_HOL_Otimes__class_Otimes(X10,X37,X3)) ),
    inference(fof_simplification,[status(thm)],[c_0_54]) ).

fof(c_0_547_548,plain,
    ! [X37,X35,X33,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X33,X35,X3),X37,X3) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X33,X37,X3),c_Divides_Odiv__class_Omod(X35,X37,X3),X3),X37,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_55]) ).

fof(c_0_548_549,plain,
    ! [X37,X35,X33,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X35),X37,X3) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_Divides_Odiv__class_Omod(X33,X37,X3)),X35),X37,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_56]) ).

fof(c_0_549_550,plain,
    ! [X37,X35,X33,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_Divides_Odiv__class_Omod(X33,X37,X3)),X35),X37,X3) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X35),X37,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_57]) ).

fof(c_0_550_551,plain,
    ! [X44,X37,X35,X33,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),X33),X35)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X37),X44)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X37)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X35),X44)) ),
    inference(fof_simplification,[status(thm)],[c_0_58]) ).

fof(c_0_551_552,plain,
    ! [X36,X9,X10,X56,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X10,X9,X3),c_Divides_Odiv__class_Odiv(X56,X36,X3),X3) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X10,X56,X3),c_HOL_Otimes__class_Otimes(X9,X36,X3),X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X36,X56,X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X9,X10,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_59]) ).

fof(c_0_552_553,plain,
    ! [X36,X9,X10,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X10),X9),X36,X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_Divides_Odiv__class_Odiv(X10,X36,X3)),c_Divides_Odiv__class_Odiv(X9,X36,X3))
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X36,X9,X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X36,X10,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_60]) ).

fof(c_0_553_554,plain,
    ! [X29,X21,X22,X23,X24] :
      ( c_Type_Otyping(c_Type_Oshift(X22,X21,X23,tc_Type_Otype),hAPP(hAPP(c_Lambda_Olift,X29),X21),X24)
      | ~ c_Type_Otyping(X22,X29,X24) ),
    inference(fof_simplification,[status(thm)],[c_0_61]) ).

fof(c_0_554_555,plain,
    ! [X20,X33,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X33,c_Power_Opower__class_Opower(X33,X20,X3),X3),c_Power_Opower__class_Opower(X33,X20,X3),X3)
      | ~ c_HOL_Oord__class_Oless(X33,c_HOL_Oone__class_Oone(X3),X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X33,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_62]) ).

fof(c_0_555_556,plain,
    ! [X20,X14] :
      ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X20,tc_nat)
      | c_HOL_Oord__class_Oless(X14,c_HOL_Otimes__class_Otimes(X20,c_Suc(c_Divides_Odiv__class_Odiv(X14,X20,tc_nat)),tc_nat),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_63]) ).

fof(c_0_556_557,plain,
    ! [X37,X58,X35,X59,X33,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Omod(X35,X37,X3) != c_Divides_Odiv__class_Omod(X58,X37,X3)
      | c_Divides_Odiv__class_Omod(X33,X37,X3) != c_Divides_Odiv__class_Omod(X59,X37,X3)
      | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X33,X35,X3),X37,X3) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X59,X58,X3),X37,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_64]) ).

fof(c_0_557_558,plain,
    ! [X37,X58,X35,X59,X33,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Omod(X35,X37,X3) != c_Divides_Odiv__class_Omod(X58,X37,X3)
      | c_Divides_Odiv__class_Omod(X33,X37,X3) != c_Divides_Odiv__class_Omod(X59,X37,X3)
      | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X35),X37,X3) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X59),X58),X37,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_65]) ).

fof(c_0_558_559,plain,
    ! [X37,X35,X33,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(X35,X37,X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(X35,X33,X3),c_Divides_Odiv__class_Odiv(X37,X33,X3),X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X33,X37,X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X33,X35,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_66]) ).

fof(c_0_559_560,plain,
    ! [X38,X39,X41,X40,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X40,X41,X3),c_HOL_Otimes__class_Otimes(X39,X38,X3),X3) = c_HOL_Otimes__class_Otimes(X40,c_HOL_Otimes__class_Otimes(X41,c_HOL_Otimes__class_Otimes(X39,X38,X3),X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_67]) ).

fof(c_0_560_561,plain,
    ! [X38,X39,X41,X40,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X40,X41,X3),c_HOL_Otimes__class_Otimes(X39,X38,X3),X3) = c_HOL_Otimes__class_Otimes(X39,c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X40,X41,X3),X38,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_68]) ).

fof(c_0_561_562,plain,
    ! [X27,X21,X22,X24,X3] :
      ( hAPP(c_Type_Oshift(X22,X21,X24,X3),X27) = hAPP(X22,X27)
      | ~ c_HOL_Oord__class_Oless(X27,X21,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_69]) ).

fof(c_0_562_563,plain,
    ! [X9,X10,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(X10,X10,X3)),c_HOL_Otimes__class_Otimes(X9,X9,X3)) != c_HOL_Ozero__class_Ozero(X3)
      | X9 = c_HOL_Ozero__class_Ozero(X3) ),
    inference(fof_simplification,[status(thm)],[c_0_70]) ).

fof(c_0_563_564,plain,
    ! [X9,X10,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(X10,X10,X3)),c_HOL_Otimes__class_Otimes(X9,X9,X3)) != c_HOL_Ozero__class_Ozero(X3)
      | X10 = c_HOL_Ozero__class_Ozero(X3) ),
    inference(fof_simplification,[status(thm)],[c_0_71]) ).

fof(c_0_564_565,plain,
    ! [X29,X25,X21] :
      ( hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_Olift,X29),X21)),c_Suc(X25)) = hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_Olift,X29),X25)),X21)
      | ~ c_HOL_Oord__class_Oless(X21,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X25),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_72]) ).

fof(c_0_565_566,plain,
    ! [X35,X33,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_Divides_Odiv__class_Omod(X33,X35,X3)),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X33,X35,X3),X35,X3)) = X33 ),
    inference(fof_simplification,[status(thm)],[c_0_73]) ).

fof(c_0_566_567,plain,
    ! [X20,X33,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X33,X20,X3),c_HOL_Otimes__class_Otimes(X33,c_Power_Opower__class_Opower(X33,X20,X3),X3),X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X33,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_74]) ).

fof(c_0_567_568,plain,
    ! [X37,X35,X33,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_HOL_Oord__class_Oless(X35,X33,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X37,X33,X3),c_HOL_Otimes__class_Otimes(X37,X35,X3),X3)
      | ~ c_HOL_Oord__class_Oless(X37,c_HOL_Ozero__class_Ozero(X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_75]) ).

fof(c_0_568_569,plain,
    ! [X37,X35,X33,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_HOL_Oord__class_Oless(X33,X35,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X37,X33,X3),c_HOL_Otimes__class_Otimes(X37,X35,X3),X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X37,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_76]) ).

fof(c_0_569_570,plain,
    ! [X9,X10,X35,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_HOL_Oord__class_Oless(X10,X9,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X35,X10,X3),c_Power_Opower__class_Opower(X35,X9,X3),X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X35,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_77]) ).

fof(c_0_570_571,plain,
    ! [X20,X14,X33,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_HOL_Oord__class_Oless(X14,X20,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X33,X14,X3),c_Power_Opower__class_Opower(X33,X20,X3),X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X33,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_78]) ).

fof(c_0_571_572,axiom,
    ! [X9,X55,X46,X10,X20] :
      ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X10),c_HOL_Otimes__class_Otimes(X20,X46,tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X9),c_HOL_Otimes__class_Otimes(X20,X55,tc_nat))
      | c_Divides_Odiv__class_Omod(X10,X20,tc_nat) = c_Divides_Odiv__class_Omod(X9,X20,tc_nat) ),
    c_0_79 ).

fof(c_0_572_573,plain,
    ! [X20,X14,X25] :
      ( c_HOL_Oord__class_Oless(X14,X20,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X25,X14,tc_nat),c_HOL_Otimes__class_Otimes(X25,X20,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X25,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_80]) ).

fof(c_0_573_574,plain,
    ! [X20,X14,X21] :
      ( c_HOL_Oord__class_Oless(X14,X20,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X21,X14,tc_nat),c_Power_Opower__class_Opower(X21,X20,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X21,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_81]) ).

fof(c_0_574_575,plain,
    ! [X20,X14,X25] :
      ( c_Ring__and__Field_Odvd__class_Odvd(X14,X20,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X25,X14,tc_nat),c_HOL_Otimes__class_Otimes(X25,X20,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X25,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_82]) ).

fof(c_0_575_576,plain,
    ! [X20,X14,X25] :
      ( c_Ring__and__Field_Odvd__class_Odvd(X14,X20,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X25,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X25,X14,tc_nat),c_HOL_Otimes__class_Otimes(X25,X20,tc_nat),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_83]) ).

fof(c_0_576_577,plain,
    ! [X20,X33,X45,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X33,X45,X3),c_Power_Opower__class_Opower(X33,X20,X3),X3)
      | ~ c_HOL_Oord__class_Oless(X33,c_HOL_Oone__class_Oone(X3),X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X33,X3)
      | ~ c_HOL_Oord__class_Oless(X20,X45,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_84]) ).

fof(c_0_577_578,plain,
    ! [X37,X35,X33,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_HOL_Oord__class_Oless(X37,c_HOL_Ozero__class_Ozero(X3),X3)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X37,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X37,X33,X3),c_HOL_Otimes__class_Otimes(X37,X35,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_85]) ).

fof(c_0_578_579,plain,
    ! [X37,X35,X33,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_HOL_Oord__class_Oless(X37,c_HOL_Ozero__class_Ozero(X3),X3)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X37,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X33,X37,X3),c_HOL_Otimes__class_Otimes(X35,X37,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_86]) ).

fof(c_0_579_580,plain,
    ! [X37,X35,X33,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_HOL_Oord__class_Oless(X37,c_HOL_Ozero__class_Ozero(X3),X3)
      | c_HOL_Oord__class_Oless(X33,X35,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X33,X37,X3),c_HOL_Otimes__class_Otimes(X35,X37,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_87]) ).

fof(c_0_580_581,plain,
    ! [X37,X35,X33,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_HOL_Oord__class_Oless(X35,X33,X3)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X37,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X33,X37,X3),c_HOL_Otimes__class_Otimes(X35,X37,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_88]) ).

fof(c_0_581_582,plain,
    ! [X37,X35,X33,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_HOL_Oord__class_Oless(X37,c_HOL_Ozero__class_Ozero(X3),X3)
      | c_HOL_Oord__class_Oless(X33,X35,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X37,X33,X3),c_HOL_Otimes__class_Otimes(X37,X35,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_89]) ).

fof(c_0_582_583,plain,
    ! [X37,X35,X33,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_HOL_Oord__class_Oless(X35,X33,X3)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X37,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X37,X33,X3),c_HOL_Otimes__class_Otimes(X37,X35,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_90]) ).

fof(c_0_583_584,plain,
    ! [X37,X35,X33,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X33,X37,X3),X35,X3),X37,X3) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X33,X35,X3),X37,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_91]) ).

fof(c_0_584_585,plain,
    ! [X37,X35,X33,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X33,X35,X3),X37,X3) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X33,X37,X3),X35,X3),X37,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_92]) ).

fof(c_0_585_586,plain,
    ! [X37,X35,X33,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X33,X35,X3),X37,X3) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X33,c_Divides_Odiv__class_Omod(X35,X37,X3),X3),X37,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_93]) ).

fof(c_0_586_587,plain,
    ! [X38,X39,X41,X40,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X40,X41,X3),c_HOL_Otimes__class_Otimes(X39,X38,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X40,X39,X3),c_HOL_Otimes__class_Otimes(X41,X38,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_94]) ).

fof(c_0_587_588,plain,
    ! [X37,X35,X33,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),c_HOL_Otimes__class_Otimes(X35,X37,X3)),X35,X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X37),c_Divides_Odiv__class_Odiv(X33,X35,X3))
      | X35 = c_HOL_Ozero__class_Ozero(X3) ),
    inference(fof_simplification,[status(thm)],[c_0_95]) ).

fof(c_0_588_589,plain,
    ! [X37,X35,X33,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),c_HOL_Otimes__class_Otimes(X37,X35,X3)),X35,X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X37),c_Divides_Odiv__class_Odiv(X33,X35,X3))
      | X35 = c_HOL_Ozero__class_Ozero(X3) ),
    inference(fof_simplification,[status(thm)],[c_0_96]) ).

fof(c_0_589_590,plain,
    ! [X37,X35,X33,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_HOL_Oord__class_Oless(X35,X33,X3)
      | c_HOL_Oord__class_Oless(X33,X35,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X37,X33,X3),c_HOL_Otimes__class_Otimes(X37,X35,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_97]) ).

fof(c_0_590_591,plain,
    ! [X37,X35,X33,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_HOL_Oord__class_Oless(X35,X33,X3)
      | c_HOL_Oord__class_Oless(X33,X35,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X33,X37,X3),c_HOL_Otimes__class_Otimes(X35,X37,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_98]) ).

fof(c_0_591_592,plain,
    ! [X14,X35,X33,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(X33,X14,X3)),c_HOL_Otimes__class_Otimes(X35,X14,X3)) = c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X35),X14,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_99]) ).

fof(c_0_592_593,plain,
    ! [X37,X35,X33,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X35),X37,X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(X33,X37,X3)),c_HOL_Otimes__class_Otimes(X35,X37,X3)) ),
    inference(fof_simplification,[status(thm)],[c_0_100]) ).

fof(c_0_593_594,plain,
    ! [X37,X35,X33,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring(X3)
      | c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X35),X37,X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(X33,X37,X3)),c_HOL_Otimes__class_Otimes(X35,X37,X3)) ),
    inference(fof_simplification,[status(thm)],[c_0_101]) ).

fof(c_0_594_595,plain,
    ! [X36,X9,X10,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_HOL_Otimes__class_Otimes(X10,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X9),X36),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(X10,X9,X3)),c_HOL_Otimes__class_Otimes(X10,X36,X3)) ),
    inference(fof_simplification,[status(thm)],[c_0_102]) ).

fof(c_0_595_596,plain,
    ! [X37,X35,X33,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(X35,X33,X3),c_Divides_Odiv__class_Odiv(X37,X33,X3),X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X35,X37,X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X33,X37,X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X33,X35,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_103]) ).

fof(c_0_596_597,plain,
    ! [X37,X35,X33,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X35),X37,X3) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),c_Divides_Odiv__class_Omod(X35,X37,X3)),X37,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_104]) ).

fof(c_0_597_598,plain,
    ! [X37,X35,X33,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),c_Divides_Odiv__class_Omod(X35,X37,X3)),X37,X3) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X35),X37,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_105]) ).

fof(c_0_598_599,plain,
    ! [X9,X10,X20,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Power_Opower__class_Opower(c_Divides_Odiv__class_Odiv(X10,X9,X3),X20,X3) = c_Divides_Odiv__class_Odiv(c_Power_Opower__class_Opower(X10,X20,X3),c_Power_Opower__class_Opower(X9,X20,X3),X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X9,X10,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_106]) ).

fof(c_0_599_600,plain,
    ! [X10,X8,X44,X37,X3] :
      ( ~ class_Ring__and__Field_Oidom(X3)
      | ~ class_Int_Onumber__ring(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X10),c_HOL_Otimes__class_Otimes(X8,X37,X3)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X10),c_HOL_Otimes__class_Otimes(X8,X44,X3))
      | X37 = X44
      | X8 = c_HOL_Ozero__class_Ozero(X3) ),
    inference(fof_simplification,[status(thm)],[c_0_107]) ).

fof(c_0_600_601,plain,
    ! [X37,X35,X33,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),X33),X35)),X37) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X37)),X35) ),
    inference(fof_simplification,[status(thm)],[c_0_108]) ).

fof(c_0_601_602,plain,
    ! [X20,X14,X25] :
      ( c_HOL_Oord__class_Oless(X14,X20,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X25),X14,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X25),X20,tc_nat),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_109]) ).

fof(c_0_602_603,plain,
    ! [X37,X35,X33,X3] :
      ( ~ class_Ring__and__Field_Oidom(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(X33,X35,X3)
      | X37 = c_HOL_Ozero__class_Ozero(X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X37,X33,X3),c_HOL_Otimes__class_Otimes(X37,X35,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_110]) ).

fof(c_0_603_604,plain,
    ! [X37,X35,X33,X3] :
      ( ~ class_Ring__and__Field_Oidom(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(X33,X35,X3)
      | X37 = c_HOL_Ozero__class_Ozero(X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X33,X37,X3),c_HOL_Otimes__class_Otimes(X35,X37,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_111]) ).

fof(c_0_604_605,plain,
    ! [X20,X33,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),c_HOL_Otimes__class_Otimes(X33,c_Power_Opower__class_Opower(X33,X20,X3),X3),X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X33,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_112]) ).

fof(c_0_605_606,axiom,
    ! [X10,X8,X44,X37] :
      ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X10),c_HOL_Otimes__class_Otimes(X8,X37,tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X10),c_HOL_Otimes__class_Otimes(X8,X44,tc_nat))
      | X37 = X44
      | X8 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    c_0_113 ).

fof(c_0_606_607,plain,
    ! [X37,X35,X33,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
      | c_HOL_Oord__class_Oless(X33,X35,X3)
      | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X37),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X35),X37),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_114]) ).

fof(c_0_607_608,plain,
    ! [X37,X35,X33,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
      | c_HOL_Oord__class_Oless(X33,X35,X3)
      | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X37),X33),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X37),X35),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_115]) ).

fof(c_0_608_609,plain,
    ! [X20,X14,X25] :
      ( c_Ring__and__Field_Odvd__class_Odvd(X14,X20,tc_nat)
      | X25 = c_HOL_Ozero__class_Ozero(tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X25,X14,tc_nat),c_HOL_Otimes__class_Otimes(X25,X20,tc_nat),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_116]) ).

fof(c_0_609_610,plain,
    ! [X20,X14,X25] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X25,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X25,X14,tc_nat),c_HOL_Otimes__class_Otimes(X25,X20,tc_nat),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_117]) ).

fof(c_0_610_611,plain,
    ! [X20,X14,X25] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X25,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X14,X25,tc_nat),c_HOL_Otimes__class_Otimes(X20,X25,tc_nat),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_118]) ).

fof(c_0_611_612,plain,
    ! [X20,X14,X25] :
      ( c_HOL_Oord__class_Oless(X14,X20,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X25,X14,tc_nat),c_HOL_Otimes__class_Otimes(X25,X20,tc_nat),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_119]) ).

fof(c_0_612_613,plain,
    ! [X20,X14,X25] :
      ( c_HOL_Oord__class_Oless(X14,X20,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X14,X25,tc_nat),c_HOL_Otimes__class_Otimes(X20,X25,tc_nat),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_120]) ).

fof(c_0_613_614,plain,
    ! [X37,X35,X33,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X37,X33,X3),c_HOL_Otimes__class_Otimes(X37,X35,X3),X3)
      | ~ c_HOL_Oord__class_Oless(X35,X33,X3)
      | ~ c_HOL_Oord__class_Oless(X37,c_HOL_Ozero__class_Ozero(X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_121]) ).

fof(c_0_614_615,plain,
    ! [X37,X35,X33,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X37,X33,X3),c_HOL_Otimes__class_Otimes(X37,X35,X3),X3)
      | ~ c_HOL_Oord__class_Oless(X33,X35,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X37,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_122]) ).

fof(c_0_615_616,plain,
    ! [X37,X35,X33,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X37,X33,X3),c_HOL_Otimes__class_Otimes(X37,X35,X3),X3)
      | ~ c_HOL_Oord__class_Oless(X37,c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_HOL_Oord__class_Oless(X35,X33,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_123]) ).

fof(c_0_616_617,plain,
    ! [X37,X35,X33,X3] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X37,X33,X3),c_HOL_Otimes__class_Otimes(X37,X35,X3),X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X37,X3)
      | ~ c_HOL_Oord__class_Oless(X33,X35,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_124]) ).

fof(c_0_617_618,plain,
    ! [X37,X35,X33,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X37,X33,X3),c_HOL_Otimes__class_Otimes(X37,X35,X3),X3)
      | ~ c_HOL_Oord__class_Oless(X33,X35,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X37,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_125]) ).

fof(c_0_618_619,plain,
    ! [X37,X35,X33,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X37,X33,X3),c_HOL_Otimes__class_Otimes(X37,X35,X3),X3)
      | ~ c_HOL_Oord__class_Oless(X35,X33,X3)
      | ~ c_HOL_Oord__class_Oless(X37,c_HOL_Ozero__class_Ozero(X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_126]) ).

fof(c_0_619_620,plain,
    ! [X37,X35,X33,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X33,X37,X3),c_HOL_Otimes__class_Otimes(X35,X37,X3),X3)
      | ~ c_HOL_Oord__class_Oless(X37,c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_HOL_Oord__class_Oless(X35,X33,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_127]) ).

fof(c_0_620_621,plain,
    ! [X37,X35,X33,X3] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X33,X37,X3),c_HOL_Otimes__class_Otimes(X35,X37,X3),X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X37,X3)
      | ~ c_HOL_Oord__class_Oless(X33,X35,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_128]) ).

fof(c_0_621_622,plain,
    ! [X37,X35,X33,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X33,X37,X3),c_HOL_Otimes__class_Otimes(X35,X37,X3),X3)
      | ~ c_HOL_Oord__class_Oless(X33,X35,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X37,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_129]) ).

fof(c_0_622_623,plain,
    ! [X37,X35,X33,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X33,X37,X3),c_HOL_Otimes__class_Otimes(X35,X37,X3),X3)
      | ~ c_HOL_Oord__class_Oless(X35,X33,X3)
      | ~ c_HOL_Oord__class_Oless(X37,c_HOL_Ozero__class_Ozero(X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_130]) ).

fof(c_0_623_624,plain,
    ! [X37,X35,X33,X3] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X37,X33,X3),c_HOL_Otimes__class_Otimes(X37,X35,X3),X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X37,X3)
      | ~ c_HOL_Oord__class_Oless(X33,X35,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_131]) ).

fof(c_0_624_625,plain,
    ! [X20,X14,X34,X3] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
      | c_Finite__Set_Osetsum(X34,c_SetInterval_Oord__class_OatLeastLessThan(X14,c_Suc(X20),tc_nat),tc_nat,X3) = c_HOL_Ozero__class_Ozero(X3)
      | ~ c_HOL_Oord__class_Oless(X20,X14,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_132]) ).

fof(c_0_625_626,plain,
    ! [X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(X3),X3)),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(X3),X3)) = c_HOL_Ozero__class_Ozero(X3) ),
    inference(fof_simplification,[status(thm)],[c_0_133]) ).

fof(c_0_626_627,plain,
    ! [X9,X10,X35,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X35,X10,X3),c_Power_Opower__class_Opower(X35,X9,X3),X3)
      | ~ c_HOL_Oord__class_Oless(X10,X9,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X35,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_134]) ).

fof(c_0_627_628,plain,
    ! [X20,X33,X45,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X33,X20,X3),c_Power_Opower__class_Opower(X33,X45,X3),X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X33,X3)
      | ~ c_HOL_Oord__class_Oless(X20,X45,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_135]) ).

fof(c_0_628_629,plain,
    ! [X44,X37,X35,X33,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X33,X37,X3),c_HOL_Otimes__class_Otimes(X35,X44,X3),X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X37,X44,X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X33,X35,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_136]) ).

fof(c_0_629_630,plain,
    ! [X14,X33,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Otimes__class_Otimes(X33,X14,X3)),X14) = c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),c_HOL_Oone__class_Oone(X3)),X14,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_137]) ).

fof(c_0_630_631,plain,
    ! [X35,X33,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X35),X33),X35,X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_Divides_Odiv__class_Odiv(X33,X35,X3)),c_HOL_Oone__class_Oone(X3))
      | X35 = c_HOL_Ozero__class_Ozero(X3) ),
    inference(fof_simplification,[status(thm)],[c_0_138]) ).

fof(c_0_631_632,plain,
    ! [X35,X33,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X35),X35,X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_Divides_Odiv__class_Odiv(X33,X35,X3)),c_HOL_Oone__class_Oone(X3))
      | X35 = c_HOL_Ozero__class_Ozero(X3) ),
    inference(fof_simplification,[status(thm)],[c_0_139]) ).

fof(c_0_632_633,plain,
    ! [X44,X37,X35,X33,X3] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X37),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X35),X44),X3)
      | ~ c_HOL_Oord__class_Oless(X37,X44,X3)
      | ~ c_HOL_Oord__class_Oless(X33,X35,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_140]) ).

fof(c_0_633_634,plain,
    ! [X20,X35,X33,X3] :
      ( ~ class_OrderedGroup_Ocomm__monoid__mult(X3)
      | c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X33,X35,X3),X20,X3) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X33,X20,X3),c_Power_Opower__class_Opower(X35,X20,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_141]) ).

fof(c_0_634_635,plain,
    ! [X9,X10,X42,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X10,X9,X3),X42,X3) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X10,X42,X3),c_Power_Opower__class_Opower(X9,X42,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_142]) ).

fof(c_0_635_636,plain,
    ! [X37,X35,X33,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X33,X37,X3),c_HOL_Otimes__class_Otimes(X35,X37,X3),X3) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X33,X35,X3),X37,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_143]) ).

fof(c_0_636_637,plain,
    ! [X37,X35,X33,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X37,X33,X3),c_HOL_Otimes__class_Otimes(X37,X35,X3),X3) = c_HOL_Otimes__class_Otimes(X37,c_Divides_Odiv__class_Omod(X33,X35,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_144]) ).

fof(c_0_637_638,plain,
    ! [X20,X14,X25] :
      ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X14,X25,tc_nat),c_HOL_Otimes__class_Otimes(X20,X25,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X14,X20,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X25,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_145]) ).

fof(c_0_638_639,plain,
    ! [X20,X14,X25] :
      ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X25,X14,tc_nat),c_HOL_Otimes__class_Otimes(X25,X20,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X14,X20,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X25,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_146]) ).

fof(c_0_639_640,plain,
    ! [X25,X27,X21] :
      ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X25,X21,tc_nat),c_HOL_Otimes__class_Otimes(X25,X27,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X25,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X21,X27,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_147]) ).

fof(c_0_640_641,plain,
    ! [X25,X27,X21] :
      ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X21,X25,tc_nat),c_HOL_Otimes__class_Otimes(X27,X25,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X25,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X21,X27,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_148]) ).

fof(c_0_641_642,plain,
    ! [X20,X14,X25] :
      ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X25,X14,tc_nat),c_HOL_Otimes__class_Otimes(X25,X20,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X14,X20,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X25,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_149]) ).

fof(c_0_642_643,plain,
    ! [X20,X14,X25] :
      ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X25,X14,tc_nat),c_HOL_Otimes__class_Otimes(X25,X20,tc_nat),tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X14,X20,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X25,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_150]) ).

fof(c_0_643_644,plain,
    ! [X37,X35,X33,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),c_HOL_Otimes__class_Otimes(X37,X35,X3)),X35,X3) = c_Divides_Odiv__class_Omod(X33,X35,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_151]) ).

fof(c_0_644_645,plain,
    ! [X37,X35,X33,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),c_HOL_Otimes__class_Otimes(X35,X37,X3)),X35,X3) = c_Divides_Odiv__class_Omod(X33,X35,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_152]) ).

fof(c_0_645_646,plain,
    ! [X20,X31] :
      ( ~ hBOOL(hAPP(X31,c_Divides_Odiv__class_Odiv(X20,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)))
      | hBOOL(hAPP(X31,c_HOL_Ozero__class_Ozero(tc_nat))) ),
    inference(fof_simplification,[status(thm)],[c_0_153]) ).

fof(c_0_646_647,plain,
    ! [X35,X33,X3] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X35,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X33,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X35,X33,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_154]) ).

fof(c_0_647_648,plain,
    ! [X35,X33,X3] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X35,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X33,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X33,X35,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_155]) ).

fof(c_0_648_649,plain,
    ! [X20,X31] :
      ( ~ hBOOL(hAPP(X31,c_Divides_Odiv__class_Omod(X20,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)))
      | hBOOL(hAPP(X31,X20)) ),
    inference(fof_simplification,[status(thm)],[c_0_156]) ).

fof(c_0_649_650,plain,
    ! [X20,X14,X25] :
      ( c_HOL_Oord__class_Oless(X14,X20,tc_nat)
      | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X25),X14),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X25),X20),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_157]) ).

fof(c_0_650_651,plain,
    ! [X20,X14,X33,X3] :
      ( ~ class_OrderedGroup_Omonoid__mult(X3)
      | c_Power_Opower__class_Opower(X33,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X20),X3) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X33,X14,X3),c_Power_Opower__class_Opower(X33,X20,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_158]) ).

fof(c_0_651_652,plain,
    ! [X10,X42,X61,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X10,X61,X3),c_Power_Opower__class_Opower(X10,X42,X3),X3) = c_Power_Opower__class_Opower(X10,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X61),X42),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_159]) ).

fof(c_0_652_653,plain,
    ! [X37,X35,X33,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),X33),X35)),X37) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X35),X37)) ),
    inference(fof_simplification,[status(thm)],[c_0_160]) ).

fof(c_0_653_654,plain,
    ! [X44,X37,X33,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X37),X44)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X37)),X44) ),
    inference(fof_simplification,[status(thm)],[c_0_161]) ).

fof(c_0_654_655,plain,
    ! [X37,X35,X33,X3] :
      ( ~ class_OrderedGroup_Oab__semigroup__add(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X35)),X37) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X35),X37)) ),
    inference(fof_simplification,[status(thm)],[c_0_162]) ).

fof(c_0_655_656,plain,
    ! [X37,X35,X33,X3] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X35)),X37) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X35),X37)) ),
    inference(fof_simplification,[status(thm)],[c_0_163]) ).

fof(c_0_656_657,plain,
    ! [X36,X9,X10,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X10),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X9),X36)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X10),X9)),X36) ),
    inference(fof_simplification,[status(thm)],[c_0_164]) ).

fof(c_0_657_658,plain,
    ! [X37,X35,X33,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X35,X33,X3),X37,X3) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X35,X37,X3),X33,X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X33,X35,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_165]) ).

fof(c_0_658_659,plain,
    ! [X20,X14,X25,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(X25,X14,X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X25,X20,X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X25,c_Divides_Odiv__class_Omod(X14,X20,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_166]) ).

fof(c_0_659_660,plain,
    ! [X20,X14,X25,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(X25,X14,X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X25,c_Divides_Odiv__class_Omod(X14,X20,X3),X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X25,X20,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_167]) ).

fof(c_0_660_661,plain,
    ! [X20,X14,X25] :
      ( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X25,X14,tc_nat),c_HOL_Otimes__class_Otimes(X25,X20,tc_nat),tc_nat) = c_Divides_Odiv__class_Odiv(X14,X20,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X25,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_168]) ).

fof(c_0_661_662,plain,
    ! [X57,X25,X27,X21] :
      ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X21),X25),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X27),X57),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X25,X57,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X21,X27,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_169]) ).

fof(c_0_662_663,axiom,
    ! [X52,X34,X53,X3] :
      ( c_List_Omap(X34,X52,X53,X3) != c_List_Olist_ONil(X3)
      | X52 = c_List_Olist_ONil(X53) ),
    c_0_170 ).

fof(c_0_663_664,axiom,
    ! [X52,X34,X53,X3] :
      ( c_List_Olist_ONil(X3) != c_List_Omap(X34,X52,X53,X3)
      | X52 = c_List_Olist_ONil(X53) ),
    c_0_171 ).

fof(c_0_664_665,plain,
    ! [X36,X9,X10,X26,X3] :
      ( ~ class_OrderedGroup_Oab__group__add(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X10),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X9),X36)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X9),X26)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X10),X36) = X26 ),
    inference(fof_simplification,[status(thm)],[c_0_172]) ).

fof(c_0_665_666,plain,
    ! [X20,X33,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X33,c_Suc(X20),X3),c_HOL_Oone__class_Oone(X3),X3)
      | ~ c_HOL_Oord__class_Oless(X33,c_HOL_Oone__class_Oone(X3),X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X33,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_173]) ).

fof(c_0_666_667,plain,
    ! [X29,X7,X8,X21] :
      ( c_Lambda_Obeta(hAPP(hAPP(hAPP(c_Lambda_Osubst,X8),X29),X21),hAPP(hAPP(hAPP(c_Lambda_Osubst,X7),X29),X21))
      | ~ c_Lambda_Obeta(X8,X7) ),
    inference(fof_simplification,[status(thm)],[c_0_174]) ).

fof(c_0_667_668,plain,
    ! [X20,X14] :
      ( c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X14,X20,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X14,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X20,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_175]) ).

fof(c_0_668_669,plain,
    ! [X20,X14,X25] :
      ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X25),X14,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X25),X20,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X14,X20,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_176]) ).

fof(c_0_669_670,plain,
    ! [X20,X14,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),c_HOL_Otimes__class_Otimes(X14,X20,X3),X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X20,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X14,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_177]) ).

fof(c_0_670_671,plain,
    ! [X35,X33,X3] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X33,X35,X3),X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X35,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X33,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_178]) ).

fof(c_0_671_672,plain,
    ! [X35,X33,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X33,X35,X3),X3)
      | ~ c_HOL_Oord__class_Oless(X35,c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_HOL_Oord__class_Oless(X33,c_HOL_Ozero__class_Ozero(X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_179]) ).

fof(c_0_672_673,plain,
    ! [X35,X33,X3] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X35,X33,X3),c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_HOL_Oord__class_Oless(X35,c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X33,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_180]) ).

fof(c_0_673_674,plain,
    ! [X35,X33,X3] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X33,X35,X3),c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_HOL_Oord__class_Oless(X35,c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X33,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_181]) ).

fof(c_0_674_675,plain,
    ! [X35,X33,X3] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X33,X35,X3),c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X35,X3)
      | ~ c_HOL_Oord__class_Oless(X33,c_HOL_Ozero__class_Ozero(X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_182]) ).

fof(c_0_675_676,plain,
    ! [X20,X14] :
      ( c_HOL_Oord__class_Oless(X20,c_HOL_Otimes__class_Otimes(X20,X14,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X14,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X20,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_183]) ).

fof(c_0_676_677,plain,
    ! [X20,X14] :
      ( c_HOL_Oord__class_Oless(X20,c_HOL_Otimes__class_Otimes(X14,X20,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X14,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X20,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_184]) ).

fof(c_0_677_678,plain,
    ! [X35,X33,X3] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X35),c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_HOL_Oord__class_Oless(X35,c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_HOL_Oord__class_Oless(X33,c_HOL_Ozero__class_Ozero(X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_185]) ).

fof(c_0_678_679,plain,
    ! [X35,X33,X3] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X35),X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X35,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X33,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_186]) ).

fof(c_0_679_680,plain,
    ! [X37,X35,X33,X3] :
      ( ~ class_Ring__and__Field_Oidom(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X33,X37,X3),c_HOL_Otimes__class_Otimes(X35,X37,X3),X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X33,X35,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_187]) ).

fof(c_0_680_681,plain,
    ! [X37,X35,X33,X3] :
      ( ~ class_Ring__and__Field_Oidom(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X37,X33,X3),c_HOL_Otimes__class_Otimes(X37,X35,X3),X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X33,X35,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_188]) ).

fof(c_0_681_682,plain,
    ! [X9,X10,X20,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(X10,X20,X3),c_Power_Opower__class_Opower(X9,X20,X3),X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X10,X9,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_189]) ).

fof(c_0_682_683,plain,
    ! [X20,X33,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),c_Power_Opower__class_Opower(X33,X20,X3),X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X20,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X33,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_190]) ).

fof(c_0_683_684,plain,
    ! [X36,X9,X10] :
      ( ~ c_Ring__and__Field_Odvd__class_Odvd(X36,X10,tc_nat)
      | c_Ring__and__Field_Odvd__class_Odvd(X36,X9,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X9,X36,tc_nat)
      | c_Ring__and__Field_Odvd__class_Odvd(X9,X10,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X10,X9,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_191]) ).

fof(c_0_684_685,plain,
    ! [X14,X25] :
      ( c_Divides_Odiv__class_Omod(c_Suc(c_HOL_Otimes__class_Otimes(X25,X14,tc_nat)),X25,tc_nat) = c_HOL_Oone__class_Oone(tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X25,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_192]) ).

fof(c_0_685_686,plain,
    ! [X37,X35,X33,X3] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X37),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X35),X37),X3)
      | ~ c_HOL_Oord__class_Oless(X33,X35,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_193]) ).

fof(c_0_686_687,plain,
    ! [X37,X35,X33,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X37),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X35),X37),X3)
      | ~ c_HOL_Oord__class_Oless(X33,X35,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_194]) ).

fof(c_0_687_688,plain,
    ! [X37,X35,X33,X3] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X37),X33),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X37),X35),X3)
      | ~ c_HOL_Oord__class_Oless(X33,X35,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_195]) ).

fof(c_0_688_689,plain,
    ! [X37,X35,X33,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X37),X33),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X37),X35),X3)
      | ~ c_HOL_Oord__class_Oless(X33,X35,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_196]) ).

fof(c_0_689_690,plain,
    ! [X37,X35,X33,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_HOL_Oord__class_Oless(X35,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X37),X3)
      | ~ c_HOL_Oord__class_Oless(X35,X37,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X33,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_197]) ).

fof(c_0_690_691,plain,
    ! [X20,X14,X25] :
      ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X25,X14,tc_nat),c_HOL_Otimes__class_Otimes(X25,X20,tc_nat),tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X14,X20,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_198]) ).

fof(c_0_691_692,plain,
    ! [X20,X14] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X20,tc_nat)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X14,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X20),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_199]) ).

fof(c_0_692_693,plain,
    ! [X20,X14,X25,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(X25,c_Divides_Odiv__class_Omod(X14,X20,X3),X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X25,X14,X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X25,X20,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_200]) ).

fof(c_0_693_694,plain,
    ! [X20,X14,X25,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(X25,c_Divides_Odiv__class_Omod(X14,X20,X3),X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X25,X20,X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X25,X14,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_201]) ).

fof(c_0_694_695,plain,
    ! [X20,X14] :
      ( X20 = c_HOL_Oone__class_Oone(tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X14,X20,tc_nat),X14,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X14,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_202]) ).

fof(c_0_695_696,plain,
    ! [X20,X14] :
      ( X20 = c_HOL_Oone__class_Oone(tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X20,X14,tc_nat),X14,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X14,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_203]) ).

fof(c_0_696_697,plain,
    ! [X20,X14] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X14,X20,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X20,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X14,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_204]) ).

fof(c_0_697_698,plain,
    ! [X37,X35,X33,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(X33,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X35),X37),X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X33,X37,X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X33,X35,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_205]) ).

fof(c_0_698_699,plain,
    ! [X37,X35,X33,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X37,X33,X3),c_HOL_Otimes__class_Otimes(X37,X35,X3),X3) = c_Divides_Odiv__class_Odiv(X33,X35,X3)
      | X37 = c_HOL_Ozero__class_Ozero(X3) ),
    inference(fof_simplification,[status(thm)],[c_0_206]) ).

fof(c_0_699_700,plain,
    ! [X37,X35,X33,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X33,X37,X3),c_HOL_Otimes__class_Otimes(X35,X37,X3),X3) = c_Divides_Odiv__class_Odiv(X33,X35,X3)
      | X37 = c_HOL_Ozero__class_Ozero(X3) ),
    inference(fof_simplification,[status(thm)],[c_0_207]) ).

fof(c_0_700_701,plain,
    ! [X14,X33,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X14),c_HOL_Otimes__class_Otimes(X33,X14,X3)) = c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),c_HOL_Oone__class_Oone(X3)),X14,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_208]) ).

fof(c_0_701_702,plain,
    ! [X20,X14] :
      ( c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Odiv(X14,X20,tc_nat),X14,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X14,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X20,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_209]) ).

fof(c_0_702_703,plain,
    ! [X20,X33,X3] :
      ( ~ class_OrderedGroup_Omonoid__mult(X3)
      | c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X33,X20,X3),X33,X3) = c_HOL_Otimes__class_Otimes(X33,c_Power_Opower__class_Opower(X33,X20,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_210]) ).

fof(c_0_703_704,plain,
    ! [X37,X35,X33,X3] :
      ( ~ class_OrderedGroup_Oab__semigroup__mult(X3)
      | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X33,X35,X3),X37,X3) = c_HOL_Otimes__class_Otimes(X33,c_HOL_Otimes__class_Otimes(X35,X37,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_211]) ).

fof(c_0_704_705,plain,
    ! [X39,X41,X40,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X40,X41,X3),X39,X3) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X40,X39,X3),X41,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_212]) ).

fof(c_0_705_706,plain,
    ! [X39,X41,X40,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X40,X41,X3),X39,X3) = c_HOL_Otimes__class_Otimes(X40,c_HOL_Otimes__class_Otimes(X41,X39,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_213]) ).

fof(c_0_706_707,plain,
    ! [X38,X39,X40,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_HOL_Otimes__class_Otimes(X40,c_HOL_Otimes__class_Otimes(X39,X38,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X40,X39,X3),X38,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_214]) ).

fof(c_0_707_708,plain,
    ! [X38,X39,X40,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_HOL_Otimes__class_Otimes(X40,c_HOL_Otimes__class_Otimes(X39,X38,X3),X3) = c_HOL_Otimes__class_Otimes(X39,c_HOL_Otimes__class_Otimes(X40,X38,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_215]) ).

fof(c_0_708_709,plain,
    ! [X36,X9,X10,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_HOL_Otimes__class_Otimes(X10,c_HOL_Otimes__class_Otimes(X9,X36,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X10,X9,X3),X36,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_216]) ).

fof(c_0_709_710,plain,
    ! [X36,X9,X10] :
      ( c_Ring__and__Field_Odvd__class_Odvd(X10,X36,tc_nat)
      | c_Ring__and__Field_Odvd__class_Odvd(X36,X9,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X9,X36,tc_nat)
      | c_Ring__and__Field_Odvd__class_Odvd(X9,X10,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X10,X9,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_217]) ).

fof(c_0_710_711,plain,
    ! [X10,X42,X61,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(X10,X61,X3),X42,X3) = c_Power_Opower__class_Opower(X10,c_HOL_Otimes__class_Otimes(X61,X42,tc_nat),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_218]) ).

fof(c_0_711_712,plain,
    ! [X20,X14,X33,X3] :
      ( ~ class_OrderedGroup_Omonoid__mult(X3)
      | c_Power_Opower__class_Opower(X33,c_HOL_Otimes__class_Otimes(X14,X20,tc_nat),X3) = c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(X33,X14,X3),X20,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_219]) ).

fof(c_0_712_713,plain,
    ! [X33,X3] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X33,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X33),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_220]) ).

fof(c_0_713_714,plain,
    ! [X33,X3] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
      | c_HOL_Oord__class_Oless(X33,c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X33),c_HOL_Ozero__class_Ozero(X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_221]) ).

fof(c_0_714_715,plain,
    ! [X33,X3] :
      ( ~ class_Ring__and__Field_Oordered__idom(X3)
      | c_HOL_Oord__class_Oless(X33,c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X33),c_HOL_Ozero__class_Ozero(X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_222]) ).

fof(c_0_715_716,axiom,
    ! [X20,X14,X25] :
      ( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X25,X14,tc_nat),c_HOL_Otimes__class_Otimes(X25,X20,tc_nat),tc_nat) = c_Divides_Odiv__class_Odiv(X14,X20,tc_nat)
      | X25 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    c_0_223 ).

fof(c_0_716_717,plain,
    ! [X25,X27,X21] :
      ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X21),X25),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X27),X25),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X21,X27,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_224]) ).

fof(c_0_717_718,plain,
    ! [X20,X14,X25] :
      ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X25),X14),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X25),X20),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X14,X20,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_225]) ).

fof(c_0_718_719,plain,
    ! [X37,X35,X33,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(X35,X37,X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X33,X35,X3),X37,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_226]) ).

fof(c_0_719_720,plain,
    ! [X37,X35,X33,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(X33,X37,X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X33,X35,X3),X37,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_227]) ).

fof(c_0_720_721,plain,
    ! [X44,X37,X33,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X37),X44)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X37),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X44)) ),
    inference(fof_simplification,[status(thm)],[c_0_228]) ).

fof(c_0_721_722,plain,
    ! [X37,X35,X33,X3] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X35),X37)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X35),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X37)) ),
    inference(fof_simplification,[status(thm)],[c_0_229]) ).

fof(c_0_722_723,plain,
    ! [X36,X9,X10,X3] :
      ( ~ class_OrderedGroup_Oab__group__add(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X10),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X9),X36)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X9),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X10),X36)) ),
    inference(fof_simplification,[status(thm)],[c_0_230]) ).

fof(c_0_723_724,plain,
    ! [X10,X20] :
      ( X20 = c_HOL_Ozero__class_Ozero(tc_nat)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X10,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Power_Opower__class_Opower(X10,X20,tc_nat),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_231]) ).

fof(c_0_724_725,plain,
    ! [X37,X35,X33,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X33,X35,X3),X37,X3) = c_Divides_Odiv__class_Omod(X33,X37,X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X37,X35,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_232]) ).

fof(c_0_725_726,plain,
    ! [X20,X14] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X20,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X14,X20,tc_nat),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_233]) ).

fof(c_0_726_727,plain,
    ! [X20,X14] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X14,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X14,X20,tc_nat),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_234]) ).

fof(c_0_727_728,plain,
    ! [X14,X31] :
      ( hBOOL(hAPP(X31,c_Divides_Odiv__class_Odiv(X14,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)))
      | ~ hBOOL(hAPP(X31,c_HOL_Ozero__class_Ozero(tc_nat))) ),
    inference(fof_simplification,[status(thm)],[c_0_235]) ).

fof(c_0_728_729,plain,
    ! [X20,X31] :
      ( ~ hBOOL(hAPP(X31,c_HOL_Ozero__class_Ozero(tc_nat)))
      | hBOOL(hAPP(X31,c_Divides_Odiv__class_Odiv(X20,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))) ),
    inference(fof_simplification,[status(thm)],[c_0_236]) ).

fof(c_0_729_730,plain,
    ! [X36,X9,X10] :
      ( ~ c_Ring__and__Field_Odvd__class_Odvd(X36,X10,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X9,X36,tc_nat)
      | c_Ring__and__Field_Odvd__class_Odvd(X9,X10,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X10,X9,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_237]) ).

fof(c_0_730_731,plain,
    ! [X36,X9,X10] :
      ( ~ c_Ring__and__Field_Odvd__class_Odvd(X36,X10,tc_nat)
      | c_Ring__and__Field_Odvd__class_Odvd(X36,X9,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X9,X36,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X10,X9,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_238]) ).

fof(c_0_731_732,plain,
    ! [X35,X33,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),X33,X3),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),X35,X3),X3) = c_HOL_Ozero__class_Ozero(X3) ),
    inference(fof_simplification,[status(thm)],[c_0_239]) ).

fof(c_0_732_733,plain,
    ! [X35,X33,X3] :
      ( ~ class_Ring__and__Field_Oidom(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X33,c_HOL_Ozero__class_Ozero(X3),X3),c_HOL_Otimes__class_Otimes(X35,c_HOL_Ozero__class_Ozero(X3),X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_240]) ).

fof(c_0_733_734,plain,
    ! [X35,X33,X3] :
      ( ~ class_Ring__and__Field_Oidom(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),X33,X3),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),X35,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_241]) ).

fof(c_0_734_735,plain,
    ! [X20,X31] :
      ( ~ hBOOL(hAPP(X31,X20))
      | hBOOL(hAPP(X31,c_Divides_Odiv__class_Omod(X20,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))) ),
    inference(fof_simplification,[status(thm)],[c_0_242]) ).

fof(c_0_735_736,plain,
    ! [X20,X33,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),c_Power_Opower__class_Opower(X33,c_Suc(X20),X3),X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X33,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_243]) ).

fof(c_0_736_737,plain,
    ! [X20,X14,X57,X25] :
      ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X57) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X25),X20)
      | ~ c_HOL_Oord__class_Oless(X25,X57,tc_nat)
      | c_HOL_Oord__class_Oless(X14,X20,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_244]) ).

fof(c_0_737_738,plain,
    ! [X25,X27,X21] :
      ( c_HOL_Oord__class_Oless(X21,X25,tc_nat)
      | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X21),X27),X25,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_245]) ).

fof(c_0_738_739,plain,
    ! [X20,X25] :
      ( c_Ring__and__Field_Odvd__class_Odvd(X25,X20,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X25,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X20),X25),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_246]) ).

fof(c_0_739_740,plain,
    ! [X20,X14,X33,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_Power_Opower__class_Opower(X33,X14,X3) != c_Power_Opower__class_Opower(X33,X20,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X33,X3)
      | X14 = X20 ),
    inference(fof_simplification,[status(thm)],[c_0_247]) ).

fof(c_0_740_741,axiom,
    ! [X20,X14] :
      ( c_Divides_Odiv__class_Omod(c_Suc(X14),X20,tc_nat) = c_Suc(c_Divides_Odiv__class_Omod(X14,X20,tc_nat))
      | c_Suc(c_Divides_Odiv__class_Omod(X14,X20,tc_nat)) = X20 ),
    c_0_248 ).

fof(c_0_741_742,plain,
    ! [X36,X9,X10] :
      ( c_Ring__and__Field_Odvd__class_Odvd(X10,X36,tc_nat)
      | c_Ring__and__Field_Odvd__class_Odvd(X36,X9,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X9,X36,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X10,X9,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_249]) ).

fof(c_0_742_743,plain,
    ! [X36,X9,X10] :
      ( c_Ring__and__Field_Odvd__class_Odvd(X10,X36,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X9,X36,tc_nat)
      | c_Ring__and__Field_Odvd__class_Odvd(X9,X10,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X10,X9,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_250]) ).

fof(c_0_743_744,plain,
    ! [X33,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X33,X33,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_251]) ).

fof(c_0_744_745,plain,
    ! [X20,X33,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Power_Opower__class_Opower(X33,X20,X3),X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X33,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_252]) ).

fof(c_0_745_746,plain,
    ! [X33,X3] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X33),X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X33,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_253]) ).

fof(c_0_746_747,plain,
    ! [X33,X3] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X33),c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_HOL_Oord__class_Oless(X33,c_HOL_Ozero__class_Ozero(X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_254]) ).

fof(c_0_747_748,plain,
    ! [X33,X3] :
      ( ~ class_Ring__and__Field_Oordered__idom(X3)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X33),c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_HOL_Oord__class_Oless(X33,c_HOL_Ozero__class_Ozero(X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_255]) ).

fof(c_0_748_749,plain,
    ! [X20,X14,X25] :
      ( c_HOL_Otimes__class_Otimes(X25,X14,tc_nat) != c_HOL_Otimes__class_Otimes(X25,X20,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X25,tc_nat)
      | X14 = X20 ),
    inference(fof_simplification,[status(thm)],[c_0_256]) ).

fof(c_0_749_750,plain,
    ! [X10,X20,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(X10,c_Power_Opower__class_Opower(X10,X20,X3),X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X20,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_257]) ).

fof(c_0_750_751,plain,
    ! [X20,X14] :
      ( ~ c_Ring__and__Field_Odvd__class_Odvd(X20,X14,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X14,X20,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X14,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_258]) ).

fof(c_0_751_752,plain,
    ! [X35,X33,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X35,X33,X3),X33,X3) = X35
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X33,X35,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_259]) ).

fof(c_0_752_753,plain,
    ! [X35,X33,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_HOL_Otimes__class_Otimes(X33,c_Divides_Odiv__class_Odiv(X35,X33,X3),X3) = X35
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X33,X35,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_260]) ).

fof(c_0_753_754,plain,
    ! [X37,X35,X33,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(X33,c_HOL_Otimes__class_Otimes(X35,X37,X3),X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X33,X35,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_261]) ).

fof(c_0_754_755,plain,
    ! [X37,X35,X33,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(X33,c_HOL_Otimes__class_Otimes(X35,X37,X3),X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X33,X37,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_262]) ).

fof(c_0_755_756,plain,
    ! [X14,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X14),X14) = c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Oone__class_Oone(X3)),c_HOL_Oone__class_Oone(X3)),X14,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_263]) ).

fof(c_0_756_757,plain,
    ! [X14] :
      ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X14,tc_nat)
      | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X14,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X14,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_264]) ).

fof(c_0_757_758,plain,
    ! [X14] :
      ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X14,tc_nat)
      | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),X14,tc_nat),X14,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_265]) ).

fof(c_0_758_759,plain,
    ! [X10,X20] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Power_Opower__class_Opower(X10,X20,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X10,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_266]) ).

fof(c_0_759_760,plain,
    ! [X20,X14] :
      ( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X14,X20,tc_nat),X20,tc_nat) = X14
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X20,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_267]) ).

fof(c_0_760_761,plain,
    ! [X20,X14] :
      ( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X20,X14,tc_nat),X20,tc_nat) = X14
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X20,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_268]) ).

fof(c_0_761_762,plain,
    ! [X20,X14] :
      ( c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Omod(X14,X20,tc_nat),X20,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X20,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_269]) ).

fof(c_0_762_763,plain,
    ! [X20,X14,X3] :
      ( ~ class_Ring__and__Field_Osemiring__1(X3)
      | c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X20),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_Nat_Osemiring__1__class_Oof__nat(X14,X3)),c_Nat_Osemiring__1__class_Oof__nat(X20,X3)) ),
    inference(fof_simplification,[status(thm)],[c_0_270]) ).

fof(c_0_763_764,plain,
    ! [X20,X14] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X20),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X20,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_271]) ).

fof(c_0_764_765,plain,
    ! [X20,X14] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X20),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X14,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_272]) ).

fof(c_0_765_766,plain,
    ! [X36,X9,X10,X3] :
      ( ~ class_Orderings_Oorder(X3)
      | c_HOL_Oord__class_Oless(X36,X10,X3)
      | ~ c_HOL_Oord__class_Oless(X36,X9,X3)
      | ~ c_HOL_Oord__class_Oless(X9,X10,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_273]) ).

fof(c_0_766_767,plain,
    ! [X36,X9,X10,X3] :
      ( ~ class_Orderings_Opreorder(X3)
      | c_HOL_Oord__class_Oless(X10,X36,X3)
      | ~ c_HOL_Oord__class_Oless(X9,X36,X3)
      | ~ c_HOL_Oord__class_Oless(X10,X9,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_274]) ).

fof(c_0_767_768,plain,
    ! [X37,X35,X33,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(X33,X37,X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X35,X37,X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X33,X35,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_275]) ).

fof(c_0_768_769,axiom,
    ! [X20,X14] :
      ( c_Suc(c_Divides_Odiv__class_Omod(X14,X20,tc_nat)) != X20
      | c_Divides_Odiv__class_Omod(c_Suc(X14),X20,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ),
    c_0_276 ).

fof(c_0_769_770,plain,
    ! [X20,X14,X3] :
      ( ~ class_Ring__and__Field_Osemiring__1(X3)
      | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Otimes__class_Otimes(X14,X20,tc_nat),X3) = c_HOL_Otimes__class_Otimes(c_Nat_Osemiring__1__class_Oof__nat(X14,X3),c_Nat_Osemiring__1__class_Oof__nat(X20,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_277]) ).

fof(c_0_770,plain,
    ! [X10,X42,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_Power_Opower__class_Opower(X10,c_Suc(X42),X3) = c_HOL_Otimes__class_Otimes(X10,c_Power_Opower__class_Opower(X10,X42,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_278]) ).

fof(c_0_771,plain,
    ! [X10,X20,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_Power_Opower__class_Opower(X10,c_Suc(X20),X3) = c_HOL_Otimes__class_Otimes(X10,c_Power_Opower__class_Opower(X10,X20,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_279]) ).

fof(c_0_772,plain,
    ! [X20,X33,X3] :
      ( ~ class_Power_Opower(X3)
      | c_Power_Opower__class_Opower(X33,c_Suc(X20),X3) = c_HOL_Otimes__class_Otimes(X33,c_Power_Opower__class_Opower(X33,X20,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_280]) ).

fof(c_0_773,plain,
    ! [X20,X33,X3] :
      ( ~ class_OrderedGroup_Omonoid__mult(X3)
      | c_Power_Opower__class_Opower(X33,c_Suc(X20),X3) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X33,X20,X3),X33,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_281]) ).

fof(c_0_774,plain,
    ! [X10,X42,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_HOL_Otimes__class_Otimes(X10,c_Power_Opower__class_Opower(X10,X42,X3),X3) = c_Power_Opower__class_Opower(X10,c_Suc(X42),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_282]) ).

fof(c_0_775,plain,
    ! [X10,X42,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X10,X42,X3),X10,X3) = c_Power_Opower__class_Opower(X10,c_Suc(X42),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_283]) ).

fof(c_0_776,plain,
    ! [X20,X14,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_HOL_Oord__class_Oless(X14,X20,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X14,X3),c_Nat_Osemiring__1__class_Oof__nat(X20,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_284]) ).

fof(c_0_777,plain,
    ! [X20,X14] :
      ( c_Divides_Odiv__class_Odiv(X14,X20,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
      | ~ c_HOL_Oord__class_Oless(X14,X20,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X20,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_285]) ).

fof(c_0_778,plain,
    ! [X36,X9,X10] :
      ( c_HOL_Oord__class_Oless(X10,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X9),X36),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X10,X9,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_286]) ).

fof(c_0_779,plain,
    ! [X36,X9,X10] :
      ( c_HOL_Oord__class_Oless(X10,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X9),X36),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X10,X36,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_287]) ).

fof(c_0_780,plain,
    ! [X14,X27,X21] :
      ( c_HOL_Oord__class_Oless(X21,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X27),X14),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X21,X27,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_288]) ).

fof(c_0_781,plain,
    ! [X14,X27,X21] :
      ( c_HOL_Oord__class_Oless(X21,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X27),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X21,X27,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_289]) ).

fof(c_0_782,plain,
    ! [X20,X25] :
      ( c_Ring__and__Field_Odvd__class_Odvd(X25,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X20),X25),tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X25,X20,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_290]) ).

fof(c_0_783,plain,
    ! [X25,X27,X21] :
      ( c_HOL_Oord__class_Oless(c_Suc(X21),X25,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X27,X25,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X21,X27,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_291]) ).

fof(c_0_784,plain,
    ! [X35,X33,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X33,X35,X3),X35,X3) = c_Divides_Odiv__class_Omod(X33,X35,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_292]) ).

fof(c_0_785,plain,
    ! [X9,X10,X3] :
      ( ~ class_OrderedGroup_Oab__semigroup__idem__mult(X3)
      | c_HOL_Otimes__class_Otimes(X10,c_HOL_Otimes__class_Otimes(X10,X9,X3),X3) = c_HOL_Otimes__class_Otimes(X10,X9,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_293]) ).

fof(c_0_786,plain,
    ! [X36,X9,X10] :
      ( c_Ring__and__Field_Odvd__class_Odvd(X10,X36,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X9,X36,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X10,X9,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_294]) ).

fof(c_0_787,plain,
    ! [X35,X33,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X35),X35,X3) = c_Divides_Odiv__class_Omod(X33,X35,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_295]) ).

fof(c_0_788,plain,
    ! [X35,X33,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X35),X33),X35,X3) = c_Divides_Odiv__class_Omod(X33,X35,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_296]) ).

fof(c_0_789,plain,
    ! [X29,X21] :
      ( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_Olift,X29),X21)))
      | ~ hBOOL(hAPP(c_InductTermi_OIT,X29)) ),
    inference(fof_simplification,[status(thm)],[c_0_297]) ).

fof(c_0_790,plain,
    ! [X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Oone__class_Oone(X3)),c_HOL_Oone__class_Oone(X3)),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_298]) ).

fof(c_0_791,plain,
    ! [X20,X14,X3] :
      ( ~ class_Ring__and__Field_Osemiring__1(X3)
      | c_Nat_Osemiring__1__class_Oof__nat(c_Power_Opower__class_Opower(X14,X20,tc_nat),X3) = c_Power_Opower__class_Opower(c_Nat_Osemiring__1__class_Oof__nat(X14,X3),X20,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_299]) ).

fof(c_0_792,axiom,
    ! [X25,X21] :
      ( hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(X21)),X25) = c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X21),c_HOL_Oone__class_Oone(tc_nat)))
      | c_HOL_Oord__class_Oless(X21,X25,tc_nat) ),
    c_0_300 ).

fof(c_0_793,plain,
    ! [X20,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X20,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Nat_Osemiring__1__class_Oof__nat(X20,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_301]) ).

fof(c_0_794,plain,
    ! [X26,X27,X21] :
      ( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X27)),X26),X21) = c_Lambda_OdB_OVar(X27)
      | ~ c_HOL_Oord__class_Oless(X27,X21,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_302]) ).

fof(c_0_795,plain,
    ! [X20,X14,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X14,X3),c_Nat_Osemiring__1__class_Oof__nat(X20,X3),X3)
      | ~ c_HOL_Oord__class_Oless(X14,X20,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_303]) ).

fof(c_0_796,plain,
    ! [X12,X31] :
      ( hBOOL(hAPP(X31,X12))
      | ~ hBOOL(hAPP(X31,c_Suc(v_sko__List__Xlexn__Xinduct__1(X31))))
      | ~ hBOOL(hAPP(X31,c_HOL_Ozero__class_Ozero(tc_nat))) ),
    inference(fof_simplification,[status(thm)],[c_0_304]) ).

fof(c_0_797,plain,
    ! [X20,X31] :
      ( hBOOL(hAPP(X31,X20))
      | ~ hBOOL(hAPP(X31,c_Suc(c_ATP__Linkup_Osko__Nat__Xnat__induct__1__1(X31))))
      | ~ hBOOL(hAPP(X31,c_HOL_Ozero__class_Ozero(tc_nat))) ),
    inference(fof_simplification,[status(thm)],[c_0_305]) ).

fof(c_0_798,plain,
    ! [X12,X31] :
      ( hBOOL(hAPP(X31,X12))
      | ~ hBOOL(hAPP(X31,c_Suc(v_sko__List__Xreplicate__Xinduct__1(X31))))
      | ~ hBOOL(hAPP(X31,c_HOL_Ozero__class_Ozero(tc_nat))) ),
    inference(fof_simplification,[status(thm)],[c_0_306]) ).

fof(c_0_799,plain,
    ! [X12,X31] :
      ( hBOOL(hAPP(X31,X12))
      | ~ hBOOL(hAPP(X31,c_Suc(v_sko__List__Xupt__Xinduct__1(X31))))
      | ~ hBOOL(hAPP(X31,c_HOL_Ozero__class_Ozero(tc_nat))) ),
    inference(fof_simplification,[status(thm)],[c_0_307]) ).

fof(c_0_800,plain,
    ! [X12,X31] :
      ( hBOOL(hAPP(X31,X12))
      | ~ hBOOL(hAPP(X31,c_Suc(v_sko__Nat__Xnat__Xinduct__1(X31))))
      | ~ hBOOL(hAPP(X31,c_HOL_Ozero__class_Ozero(tc_nat))) ),
    inference(fof_simplification,[status(thm)],[c_0_308]) ).

fof(c_0_801,plain,
    ! [X12,X31] :
      ( hBOOL(hAPP(X31,X12))
      | ~ hBOOL(hAPP(X31,c_Suc(v_sko__Nat__Xnat__Xinducts__1(X31))))
      | ~ hBOOL(hAPP(X31,c_HOL_Ozero__class_Ozero(tc_nat))) ),
    inference(fof_simplification,[status(thm)],[c_0_309]) ).

fof(c_0_802,axiom,
    ! [X20,X14,X31] :
      ( hBOOL(hAPP(hAPP(X31,X20),X14))
      | c_HOL_Oord__class_Oless(X20,X14,tc_nat)
      | X14 = X20
      | c_HOL_Oord__class_Oless(X14,X20,tc_nat) ),
    c_0_310 ).

fof(c_0_803,axiom,
    ! [X20,X14,X25] :
      ( c_HOL_Otimes__class_Otimes(c_Suc(X25),X14,tc_nat) != c_HOL_Otimes__class_Otimes(c_Suc(X25),X20,tc_nat)
      | X14 = X20 ),
    c_0_311 ).

fof(c_0_804,plain,
    ! [X20,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(X3),c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X3),X20,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_312]) ).

fof(c_0_805,plain,
    ! [X20,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Nat_Osemiring__1__class_Oof__nat(X20,X3),X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X20,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_313]) ).

fof(c_0_806,plain,
    ! [X36,X9,X10,X3] :
      ( ~ class_Ring__and__Field_Oidom(X3)
      | ~ class_Int_Onumber__ring(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X10),X9) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X10),X36)
      | X9 = X36 ),
    inference(fof_simplification,[status(thm)],[c_0_314]) ).

fof(c_0_807,plain,
    ! [X7,X8,X21] :
      ( c_Lambda_Obeta(hAPP(hAPP(c_Lambda_Olift,X8),X21),hAPP(hAPP(c_Lambda_Olift,X7),X21))
      | ~ c_Lambda_Obeta(X8,X7) ),
    inference(fof_simplification,[status(thm)],[c_0_315]) ).

fof(c_0_808,plain,
    ! [X26,X29,X7] :
      ( c_Lambda_Obeta(hAPP(hAPP(c_Lambda_OdB_OApp,X26),X7),hAPP(hAPP(c_Lambda_OdB_OApp,X26),X29))
      | ~ c_Lambda_Obeta(X7,X29) ),
    inference(fof_simplification,[status(thm)],[c_0_316]) ).

fof(c_0_809,plain,
    ! [X26,X29,X7] :
      ( c_Lambda_Obeta(hAPP(hAPP(c_Lambda_OdB_OApp,X7),X26),hAPP(hAPP(c_Lambda_OdB_OApp,X29),X26))
      | ~ c_Lambda_Obeta(X7,X29) ),
    inference(fof_simplification,[status(thm)],[c_0_317]) ).

fof(c_0_810,plain,
    ! [X35,X33,X3] :
      ( ~ class_Orderings_Oorder(X3)
      | ~ c_HOL_Oord__class_Oless(X33,X35,X3)
      | ~ c_HOL_Oord__class_Oless(X35,X33,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_318]) ).

fof(c_0_811,plain,
    ! [X9,X10,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | ~ c_HOL_Oord__class_Oless(X10,X9,X3)
      | ~ c_HOL_Oord__class_Oless(X9,X10,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_319]) ).

fof(c_0_812,plain,
    ! [X9,X10,X3] :
      ( ~ class_Orderings_Opreorder(X3)
      | ~ c_HOL_Oord__class_Oless(X9,X10,X3)
      | ~ c_HOL_Oord__class_Oless(X10,X9,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_320]) ).

fof(c_0_813,plain,
    ! [X35,X33,X3] :
      ( ~ class_Orderings_Opreorder(X3)
      | ~ c_HOL_Oord__class_Oless(X35,X33,X3)
      | ~ c_HOL_Oord__class_Oless(X33,X35,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_321]) ).

fof(c_0_814,plain,
    ! [X20,X14] :
      ( ~ c_HOL_Oord__class_Oless(X14,X20,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X20,c_Suc(X14),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_322]) ).

fof(c_0_815,plain,
    ! [X33,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_HOL_Oord__class_Oless(X33,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),c_HOL_Oone__class_Oone(X3)),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_323]) ).

fof(c_0_816,plain,
    ! [X35,X33,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X33,X35,X3),X35,X3) = X33
      | X35 = c_HOL_Ozero__class_Ozero(X3) ),
    inference(fof_simplification,[status(thm)],[c_0_324]) ).

fof(c_0_817,plain,
    ! [X35,X33,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X35,X33,X3),X35,X3) = X33
      | X35 = c_HOL_Ozero__class_Ozero(X3) ),
    inference(fof_simplification,[status(thm)],[c_0_325]) ).

fof(c_0_818,plain,
    ! [X37,X35,X33,X3] :
      ( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X35) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X37)
      | X35 = X37 ),
    inference(fof_simplification,[status(thm)],[c_0_326]) ).

fof(c_0_819,plain,
    ! [X37,X35,X33,X3] :
      ( ~ class_OrderedGroup_Ocancel__semigroup__add(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X35) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X37)
      | X35 = X37 ),
    inference(fof_simplification,[status(thm)],[c_0_327]) ).

fof(c_0_820,plain,
    ! [X37,X35,X33,X3] :
      ( ~ class_OrderedGroup_Ocancel__semigroup__add(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X35),X33) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X37),X33)
      | X35 = X37 ),
    inference(fof_simplification,[status(thm)],[c_0_328]) ).

fof(c_0_821,plain,
    ! [X35,X33,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Omod(X33,X35,X3),X35,X3) = c_HOL_Ozero__class_Ozero(X3) ),
    inference(fof_simplification,[status(thm)],[c_0_329]) ).

fof(c_0_822,axiom,
    ! [X20,X14,X25] :
      ( c_HOL_Otimes__class_Otimes(X14,X25,tc_nat) != c_HOL_Otimes__class_Otimes(X20,X25,tc_nat)
      | X25 = c_HOL_Ozero__class_Ozero(tc_nat)
      | X14 = X20 ),
    c_0_330 ).

fof(c_0_823,axiom,
    ! [X20,X14,X25] :
      ( c_HOL_Otimes__class_Otimes(X25,X14,tc_nat) != c_HOL_Otimes__class_Otimes(X25,X20,tc_nat)
      | X25 = c_HOL_Ozero__class_Ozero(tc_nat)
      | X14 = X20 ),
    c_0_331 ).

fof(c_0_824,axiom,
    ! [X20,X14,X25] :
      ( c_HOL_Otimes__class_Otimes(X25,X14,tc_nat) != c_HOL_Otimes__class_Otimes(X25,X20,tc_nat)
      | X14 = X20
      | X25 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    c_0_332 ).

fof(c_0_825,plain,
    ! [X35,X33,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X33,X35,X3),X35,X3) = c_HOL_Ozero__class_Ozero(X3) ),
    inference(fof_simplification,[status(thm)],[c_0_333]) ).

fof(c_0_826,plain,
    ! [X35,X33,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X35,X33,X3),X35,X3) = c_HOL_Ozero__class_Ozero(X3) ),
    inference(fof_simplification,[status(thm)],[c_0_334]) ).

fof(c_0_827,plain,
    ! [X9,X10] :
      ( X10 = X9
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X9,X10,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X10,X9,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_335]) ).

fof(c_0_828,plain,
    ! [X9,X10] :
      ( X10 = X9
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X9,X10,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X10,X9,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_336]) ).

fof(c_0_829,plain,
    ! [X9,X10] :
      ( ~ c_Ring__and__Field_Odvd__class_Odvd(X9,X10,tc_nat)
      | X10 = X9
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X10,X9,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_337]) ).

fof(c_0_830,plain,
    ! [X20,X14] :
      ( X14 = X20
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X20,X14,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X14,X20,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_338]) ).

fof(c_0_831,plain,
    ! [X9,X10] :
      ( X10 = X9
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X10,X9,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X9,X10,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_339]) ).

fof(c_0_832,plain,
    ! [X35,X33] :
      ( ~ c_Ring__and__Field_Odvd__class_Odvd(X35,X33,tc_nat)
      | X33 = X35
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X33,X35,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_340]) ).

fof(c_0_833,plain,
    ! [X35,X33] :
      ( ~ c_Ring__and__Field_Odvd__class_Odvd(X35,X33,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X33,X35,tc_nat)
      | X33 = X35 ),
    inference(fof_simplification,[status(thm)],[c_0_341]) ).

fof(c_0_834,axiom,
    ! [X7,X25,X21] :
      ( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X21)),X7),X25) = c_Lambda_OdB_OVar(X21)
      | X21 = X25
      | c_HOL_Oord__class_Oless(X25,X21,tc_nat) ),
    c_0_342 ).

fof(c_0_835,plain,
    ! [X35,X33,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(X33,c_HOL_Otimes__class_Otimes(X35,X33,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_343]) ).

fof(c_0_836,plain,
    ! [X35,X33,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(X33,c_HOL_Otimes__class_Otimes(X33,X35,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_344]) ).

fof(c_0_837,plain,
    ! [X25,X35,X3] :
      ( ~ class_Ring__and__Field_Odvd(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(X35,c_HOL_Otimes__class_Otimes(X35,X25,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_345]) ).

fof(c_0_838,axiom,
    ! [X10,X7] :
      ( c_HOL_Oord__class_Oless(X10,X10,tc_nat)
      | hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X10)),X7),X10) = X7 ),
    c_0_346 ).

fof(c_0_839,plain,
    ! [X43,X29,X22,X24] :
      ( c_Type_Otyping(X22,X43,X24)
      | ~ c_Lambda_Obeta(X29,X43)
      | ~ c_Type_Otyping(X22,X29,X24) ),
    inference(fof_simplification,[status(thm)],[c_0_347]) ).

fof(c_0_840,plain,
    ! [X20,X14] :
      ( c_HOL_Oord__class_Oless(X14,X20,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_Suc(X14),c_Suc(X20),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_348]) ).

fof(c_0_841,plain,
    ! [X35,X33,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Omod(X35,X33,X3) != c_HOL_Ozero__class_Ozero(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(X33,X35,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_349]) ).

fof(c_0_842,plain,
    ! [X35,X33,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Omod(X35,X33,X3) = c_HOL_Ozero__class_Ozero(X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X33,X35,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_350]) ).

fof(c_0_843,plain,
    ! [X25,X31] :
      ( hBOOL(hAPP(X31,c_HOL_Ozero__class_Ozero(tc_nat)))
      | ~ hBOOL(hAPP(X31,c_ATP__Linkup_Osko__Nat__Xzero__induct__1__1(X31)))
      | ~ hBOOL(hAPP(X31,X25)) ),
    inference(fof_simplification,[status(thm)],[c_0_351]) ).

fof(c_0_844,plain,
    ! [X25,X31] :
      ( hBOOL(hAPP(X31,c_HOL_Ozero__class_Ozero(tc_nat)))
      | hBOOL(hAPP(X31,c_Suc(c_ATP__Linkup_Osko__Nat__Xzero__induct__1__1(X31))))
      | ~ hBOOL(hAPP(X31,X25)) ),
    inference(fof_simplification,[status(thm)],[c_0_352]) ).

fof(c_0_845,plain,
    ! [X10,X20] :
      ( c_HOL_Oord__class_Oless(c_Suc(X10),c_Suc(X20),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X10,X20,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_353]) ).

fof(c_0_846,plain,
    ! [X20,X14] :
      ( c_HOL_Oord__class_Oless(c_Suc(X14),c_Suc(X20),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X14,X20,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_354]) ).

fof(c_0_847,plain,
    ! [X20,X14] :
      ( X20 = X14
      | ~ c_HOL_Oord__class_Oless(X20,c_Suc(X14),tc_nat)
      | c_HOL_Oord__class_Oless(X20,X14,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_355]) ).

fof(c_0_848,plain,
    ! [X20,X14] :
      ( X14 = X20
      | ~ c_HOL_Oord__class_Oless(X20,c_Suc(X14),tc_nat)
      | c_HOL_Oord__class_Oless(X20,X14,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_356]) ).

fof(c_0_849,plain,
    ! [X20,X14] :
      ( X14 = X20
      | c_HOL_Oord__class_Oless(X14,X20,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X14,c_Suc(X20),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_357]) ).

fof(c_0_850,plain,
    ! [X20,X14] :
      ( c_HOL_Oord__class_Oless(c_Suc(X14),X20,tc_nat)
      | c_Suc(X14) = X20
      | ~ c_HOL_Oord__class_Oless(X14,X20,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_358]) ).

fof(c_0_851,axiom,
    ! [X36,X9,X10] :
      ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X10),X9) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X10),X36)
      | X9 = X36 ),
    c_0_359 ).

fof(c_0_852,axiom,
    ! [X20,X14,X25] :
      ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X25) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X20),X25)
      | X14 = X20 ),
    c_0_360 ).

fof(c_0_853,axiom,
    ! [X20,X14,X25] :
      ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X25),X14) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X25),X20)
      | X14 = X20 ),
    c_0_361 ).

fof(c_0_854,plain,
    ! [X20,X14] :
      ( c_HOL_Oord__class_Oless(X14,X20,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_Suc(X14),X20,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_362]) ).

fof(c_0_855,plain,
    ! [X14,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X14,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_363]) ).

fof(c_0_856,plain,
    ! [X20,X14] :
      ( c_HOL_Oord__class_Oless(X14,c_Suc(X20),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X14,X20,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_364]) ).

fof(c_0_857,plain,
    ! [X20,X14] :
      ( c_Divides_Odiv__class_Odiv(X14,X20,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
      | ~ c_HOL_Oord__class_Oless(X14,X20,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_365]) ).

fof(c_0_858,plain,
    ! [X20,X14] :
      ( c_Divides_Odiv__class_Omod(X14,X20,tc_nat) = X14
      | ~ c_HOL_Oord__class_Oless(X14,X20,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_366]) ).

fof(c_0_859,plain,
    ! [X25,X21] :
      ( hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(X21)),X25) = c_Lambda_OdB_OVar(X21)
      | ~ c_HOL_Oord__class_Oless(X21,X25,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_367]) ).

fof(c_0_860,plain,
    ! [X12,X31] :
      ( hBOOL(hAPP(X31,X12))
      | hBOOL(hAPP(X31,v_sko__List__Xlexn__Xinduct__1(X31)))
      | ~ hBOOL(hAPP(X31,c_HOL_Ozero__class_Ozero(tc_nat))) ),
    inference(fof_simplification,[status(thm)],[c_0_368]) ).

fof(c_0_861,plain,
    ! [X20,X31] :
      ( hBOOL(hAPP(X31,X20))
      | hBOOL(hAPP(X31,c_ATP__Linkup_Osko__Nat__Xnat__induct__1__1(X31)))
      | ~ hBOOL(hAPP(X31,c_HOL_Ozero__class_Ozero(tc_nat))) ),
    inference(fof_simplification,[status(thm)],[c_0_369]) ).

fof(c_0_862,plain,
    ! [X12,X31] :
      ( hBOOL(hAPP(X31,X12))
      | hBOOL(hAPP(X31,v_sko__List__Xreplicate__Xinduct__1(X31)))
      | ~ hBOOL(hAPP(X31,c_HOL_Ozero__class_Ozero(tc_nat))) ),
    inference(fof_simplification,[status(thm)],[c_0_370]) ).

fof(c_0_863,plain,
    ! [X12,X31] :
      ( hBOOL(hAPP(X31,X12))
      | hBOOL(hAPP(X31,v_sko__Nat__Xnat__Xinducts__1(X31)))
      | ~ hBOOL(hAPP(X31,c_HOL_Ozero__class_Ozero(tc_nat))) ),
    inference(fof_simplification,[status(thm)],[c_0_371]) ).

fof(c_0_864,plain,
    ! [X12,X31] :
      ( hBOOL(hAPP(X31,X12))
      | hBOOL(hAPP(X31,v_sko__Nat__Xnat__Xinduct__1(X31)))
      | ~ hBOOL(hAPP(X31,c_HOL_Ozero__class_Ozero(tc_nat))) ),
    inference(fof_simplification,[status(thm)],[c_0_372]) ).

fof(c_0_865,plain,
    ! [X12,X31] :
      ( hBOOL(hAPP(X31,X12))
      | hBOOL(hAPP(X31,v_sko__List__Xupt__Xinduct__1(X31)))
      | ~ hBOOL(hAPP(X31,c_HOL_Ozero__class_Ozero(tc_nat))) ),
    inference(fof_simplification,[status(thm)],[c_0_373]) ).

fof(c_0_866,plain,
    ! [X20,X33,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(X33,X20,X3) != c_HOL_Ozero__class_Ozero(X3)
      | X33 = c_HOL_Ozero__class_Ozero(X3) ),
    inference(fof_simplification,[status(thm)],[c_0_374]) ).

fof(c_0_867,plain,
    ! [X33,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(X33,c_HOL_Ozero__class_Ozero(tc_nat),X3) != c_HOL_Ozero__class_Ozero(X3) ),
    inference(fof_simplification,[status(thm)],[c_0_375]) ).

fof(c_0_868,axiom,
    ! [X7,X25,X21] :
      ( c_Lambda_Osubstn(c_Lambda_OdB_OVar(X21),X7,X25) = c_Lambda_OdB_OVar(X21)
      | X21 = X25
      | c_HOL_Oord__class_Oless(X25,X21,tc_nat) ),
    c_0_376 ).

fof(c_0_869,plain,
    ! [X9,X10,X3] :
      ( ~ class_Ring__and__Field_Oordered__idom(X3)
      | c_HOL_Oord__class_Oless(X9,X10,X3)
      | c_HOL_Oord__class_Oless(X10,X9,X3)
      | X10 = X9 ),
    inference(fof_simplification,[status(thm)],[c_0_377]) ).

fof(c_0_870,plain,
    ! [X9,X10,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | X10 = X9
      | c_HOL_Oord__class_Oless(X9,X10,X3)
      | c_HOL_Oord__class_Oless(X10,X9,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_378]) ).

fof(c_0_871,plain,
    ! [X9,X10,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_HOL_Oord__class_Oless(X9,X10,X3)
      | c_HOL_Oord__class_Oless(X10,X9,X3)
      | X10 = X9 ),
    inference(fof_simplification,[status(thm)],[c_0_379]) ).

fof(c_0_872,plain,
    ! [X9,X10,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_HOL_Oord__class_Oless(X9,X10,X3)
      | X10 = X9
      | c_HOL_Oord__class_Oless(X10,X9,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_380]) ).

fof(c_0_873,plain,
    ! [X9,X10,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | X10 = X9
      | c_HOL_Oord__class_Oless(X10,X9,X3)
      | c_HOL_Oord__class_Oless(X9,X10,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_381]) ).

fof(c_0_874,axiom,
    ! [X15,X16,X17,X18] :
      ( hAPP(hAPP(c_Lambda_OdB_OApp,X18),X16) != hAPP(hAPP(c_Lambda_OdB_OApp,X17),X15)
      | X18 = X17 ),
    c_0_382 ).

fof(c_0_875,axiom,
    ! [X15,X16,X17,X18] :
      ( hAPP(hAPP(c_Lambda_OdB_OApp,X18),X16) != hAPP(hAPP(c_Lambda_OdB_OApp,X17),X15)
      | X16 = X15 ),
    c_0_383 ).

fof(c_0_876,plain,
    ! [X14,X3] :
      ( ~ class_Ring__and__Field_Osemiring__1(X3)
      | c_Nat_Osemiring__1__class_Oof__nat(c_Suc(X14),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Oone__class_Oone(X3)),c_Nat_Osemiring__1__class_Oof__nat(X14,X3)) ),
    inference(fof_simplification,[status(thm)],[c_0_384]) ).

fof(c_0_877,plain,
    ! [X35,X33,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_HOL_Otimes__class_Otimes(X33,X35,X3) = c_HOL_Otimes__class_Otimes(X35,X33,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_385]) ).

fof(c_0_878,plain,
    ! [X9,X10,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_HOL_Otimes__class_Otimes(X10,X9,X3) = c_HOL_Otimes__class_Otimes(X9,X10,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_386]) ).

fof(c_0_879,axiom,
    ! [X10] :
      ( c_HOL_Oord__class_Oless(X10,X10,tc_nat)
      | c_HOL_Oord__class_Oless(X10,c_Suc(X10),tc_nat) ),
    c_0_387 ).

fof(c_0_880,axiom,
    ! [X20,X14] :
      ( c_HOL_Oord__class_Oless(X20,c_Suc(X14),tc_nat)
      | c_HOL_Oord__class_Oless(X14,X20,tc_nat) ),
    c_0_388 ).

fof(c_0_881,plain,
    ! [X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_389]) ).

fof(c_0_882,plain,
    ! [X37,X33,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X37) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X37),X33) ),
    inference(fof_simplification,[status(thm)],[c_0_390]) ).

fof(c_0_883,plain,
    ! [X35,X33,X3] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X35) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X35),X33) ),
    inference(fof_simplification,[status(thm)],[c_0_391]) ).

fof(c_0_884,plain,
    ! [X9,X10,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X10),X9) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X9),X10) ),
    inference(fof_simplification,[status(thm)],[c_0_392]) ).

fof(c_0_885,plain,
    ! [X14] :
      ( X14 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X14,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_393]) ).

fof(c_0_886,plain,
    ! [X21,X22,X24] :
      ( hAPP(X22,X21) = X24
      | ~ c_Type_Otyping(X22,c_Lambda_OdB_OVar(X21),X24) ),
    inference(fof_simplification,[status(thm)],[c_0_394]) ).

fof(c_0_887,plain,
    ! [X35,X33,X3] :
      ( ~ class_Ring__and__Field_Ono__zero__divisors(X3)
      | c_HOL_Otimes__class_Otimes(X33,X35,X3) != c_HOL_Ozero__class_Ozero(X3)
      | X33 = c_HOL_Ozero__class_Ozero(X3)
      | X35 = c_HOL_Ozero__class_Ozero(X3) ),
    inference(fof_simplification,[status(thm)],[c_0_395]) ).

fof(c_0_888,plain,
    ! [X35,X33,X3] :
      ( ~ class_Ring__and__Field_Ono__zero__divisors(X3)
      | c_HOL_Otimes__class_Otimes(X33,X35,X3) != c_HOL_Ozero__class_Ozero(X3)
      | X35 = c_HOL_Ozero__class_Ozero(X3)
      | X33 = c_HOL_Ozero__class_Ozero(X3) ),
    inference(fof_simplification,[status(thm)],[c_0_396]) ).

fof(c_0_889,plain,
    ! [X35,X33,X3] :
      ( ~ class_Ring__and__Field_Oring__no__zero__divisors(X3)
      | c_HOL_Otimes__class_Otimes(X33,X35,X3) != c_HOL_Ozero__class_Ozero(X3)
      | X35 = c_HOL_Ozero__class_Ozero(X3)
      | X33 = c_HOL_Ozero__class_Ozero(X3) ),
    inference(fof_simplification,[status(thm)],[c_0_397]) ).

fof(c_0_890,axiom,
    ! [X20,X14] :
      ( c_HOL_Oord__class_Oless(X20,X14,tc_nat)
      | c_HOL_Oord__class_Oless(X14,X20,tc_nat)
      | X14 = X20 ),
    c_0_398 ).

fof(c_0_891,axiom,
    ! [X9,X10] :
      ( c_HOL_Oord__class_Oless(X9,X10,tc_nat)
      | c_HOL_Oord__class_Oless(X10,X9,tc_nat)
      | X10 = X9 ),
    c_0_399 ).

fof(c_0_892,plain,
    ! [X33,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | X33 = c_HOL_Ozero__class_Ozero(X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(X3),X33,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_400]) ).

fof(c_0_893,axiom,
    ! [X10,X14] :
      ( c_Power_Opower__class_Opower(X10,X14,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X10 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X14 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    c_0_401 ).

fof(c_0_894,plain,
    ! [X20] :
      ( X20 = c_HOL_Ozero__class_Ozero(tc_nat)
      | ~ c_HOL_Oord__class_Oless(X20,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_402]) ).

fof(c_0_895,plain,
    ! [X20,X33,X3] :
      ( ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X3)
      | c_Power_Opower__class_Opower(X33,X20,X3) != c_HOL_Ozero__class_Ozero(X3)
      | X33 = c_HOL_Ozero__class_Ozero(X3) ),
    inference(fof_simplification,[status(thm)],[c_0_403]) ).

fof(c_0_896,plain,
    ! [X10,X33,X3] :
      ( ~ class_Ring__and__Field_Oidom(X3)
      | ~ class_Int_Onumber__ring(X3)
      | X10 != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X10),X33)
      | X33 = c_HOL_Ozero__class_Ozero(X3) ),
    inference(fof_simplification,[status(thm)],[c_0_404]) ).

fof(c_0_897,axiom,
    ! [X20,X14] :
      ( c_HOL_Otimes__class_Otimes(X14,X20,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X20 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    c_0_405 ).

fof(c_0_898,axiom,
    ! [X20,X14] :
      ( c_HOL_Otimes__class_Otimes(X14,X20,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X14 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    c_0_406 ).

fof(c_0_899,plain,
    ! [X33,X3] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X33) != c_HOL_Ozero__class_Ozero(X3)
      | X33 = c_HOL_Ozero__class_Ozero(X3) ),
    inference(fof_simplification,[status(thm)],[c_0_407]) ).

fof(c_0_900,axiom,
    ! [X20,X14] :
      ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X20) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X20 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X14 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    c_0_408 ).

fof(c_0_901,axiom,
    ! [X20,X14] :
      ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X20)
      | X20 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X14 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    c_0_409 ).

fof(c_0_902,plain,
    ! [X20,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),X20,X3) = c_HOL_Ozero__class_Ozero(X3)
      | X20 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_410]) ).

fof(c_0_903,axiom,
    ! [X20,X14] :
      ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X20)
      | X20 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X20 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    c_0_411 ).

fof(c_0_904,axiom,
    ! [X20,X14] :
      ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X20)
      | X14 = c_HOL_Ozero__class_Ozero(tc_nat)
      | X14 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    c_0_412 ).

fof(c_0_905,axiom,
    ! [X20,X14] :
      ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X20) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X20 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X20 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    c_0_413 ).

fof(c_0_906,axiom,
    ! [X20,X14] :
      ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X20) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X14 = c_HOL_Ozero__class_Ozero(tc_nat)
      | X14 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    c_0_414 ).

fof(c_0_907,axiom,
    ! [X20,X14] :
      ( c_HOL_Otimes__class_Otimes(X14,X20,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
      | X20 = c_HOL_Ozero__class_Ozero(tc_nat)
      | X14 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    c_0_415 ).

fof(c_0_908,plain,
    ! [X10,X3] :
      ( ~ class_Orderings_Oorder(X3)
      | ~ c_HOL_Oord__class_Oless(X10,X10,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_416]) ).

fof(c_0_909,plain,
    ! [X10,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | ~ c_HOL_Oord__class_Oless(X10,X10,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_417]) ).

fof(c_0_910,plain,
    ! [X10,X3] :
      ( ~ class_Orderings_Opreorder(X3)
      | ~ c_HOL_Oord__class_Oless(X10,X10,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_418]) ).

fof(c_0_911,axiom,
    ! [X20,X14] :
      ( X14 != c_HOL_Otimes__class_Otimes(X14,X20,tc_nat)
      | X14 = c_HOL_Ozero__class_Ozero(tc_nat)
      | X20 = c_HOL_Oone__class_Oone(tc_nat) ),
    c_0_419 ).

fof(c_0_912,plain,
    ! [X14] :
      ( X14 = c_HOL_Oone__class_Oone(tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X14,c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_420]) ).

fof(c_0_913,axiom,
    ! [X20,X14] :
      ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X20) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X14 = c_HOL_Ozero__class_Ozero(tc_nat)
      | X20 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    c_0_421 ).

fof(c_0_914,axiom,
    ! [X20,X14] :
      ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X20)
      | X14 = c_HOL_Ozero__class_Ozero(tc_nat)
      | X20 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    c_0_422 ).

fof(c_0_915,axiom,
    ! [X20,X14] :
      ( c_HOL_Otimes__class_Otimes(X14,X20,tc_nat) != c_HOL_Oone__class_Oone(tc_nat)
      | X14 = c_HOL_Oone__class_Oone(tc_nat) ),
    c_0_423 ).

fof(c_0_916,axiom,
    ! [X20,X14] :
      ( c_HOL_Otimes__class_Otimes(X14,X20,tc_nat) != c_HOL_Oone__class_Oone(tc_nat)
      | X20 = c_HOL_Oone__class_Oone(tc_nat) ),
    c_0_424 ).

fof(c_0_917,axiom,
    ! [X20,X14] :
      ( c_HOL_Oone__class_Oone(tc_nat) != c_HOL_Otimes__class_Otimes(X14,X20,tc_nat)
      | X14 = c_HOL_Oone__class_Oone(tc_nat) ),
    c_0_425 ).

fof(c_0_918,axiom,
    ! [X20,X14] :
      ( c_HOL_Oone__class_Oone(tc_nat) != c_HOL_Otimes__class_Otimes(X14,X20,tc_nat)
      | X20 = c_HOL_Oone__class_Oone(tc_nat) ),
    c_0_426 ).

fof(c_0_919,plain,
    ! [X1,X2,X3] :
      ( X2 = X1
      | ~ c_fequal(X2,X1,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_427]) ).

fof(c_0_920,plain,
    ! [X20,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(X20),X3) = c_HOL_Ozero__class_Ozero(X3) ),
    inference(fof_simplification,[status(thm)],[c_0_428]) ).

fof(c_0_921,plain,
    ! [X20,X3] :
      ( ~ class_Ring__and__Field_Osemiring__0(X3)
      | ~ class_Power_Opower(X3)
      | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X3),X20,X3) = c_HOL_Ozero__class_Ozero(X3)
      | X20 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_429]) ).

fof(c_0_922,plain,
    ! [X8] :
      ( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(X8)))
      | ~ hBOOL(hAPP(c_InductTermi_OIT,X8)) ),
    inference(fof_simplification,[status(thm)],[c_0_430]) ).

fof(c_0_923,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_431]) ).

fof(c_0_924,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_432]) ).

fof(c_0_925,axiom,
    ! [X20,X14] :
      ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X20) != c_HOL_Ozero__class_Ozero(tc_nat)
      | X20 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    c_0_433 ).

fof(c_0_926,axiom,
    ! [X20,X14] :
      ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X20) != c_HOL_Ozero__class_Ozero(tc_nat)
      | X14 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    c_0_434 ).

fof(c_0_927,axiom,
    ! [X10,X33] :
      ( X10 != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X10),X33)
      | X33 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    c_0_435 ).

fof(c_0_928,axiom,
    ! [X20,X14] :
      ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X20) != X14
      | X20 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    c_0_436 ).

fof(c_0_929,plain,
    ! [X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oone__class_Oone(X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_437]) ).

fof(c_0_930,plain,
    ! [X10,X3] :
      ( ~ class_Ring__and__Field_Oidom(X3)
      | ~ class_Int_Onumber__ring(X3)
      | X10 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X10),c_HOL_Ozero__class_Ozero(X3)) ),
    inference(fof_simplification,[status(thm)],[c_0_438]) ).

fof(c_0_931,plain,
    ! [X10,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3)),X10) = X10 ),
    inference(fof_simplification,[status(thm)],[c_0_439]) ).

fof(c_0_932,plain,
    ! [X33,X3] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3)),X33) = X33 ),
    inference(fof_simplification,[status(thm)],[c_0_440]) ).

fof(c_0_933,plain,
    ! [X33,X3] :
      ( ~ class_OrderedGroup_Omonoid__add(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3)),X33) = X33 ),
    inference(fof_simplification,[status(thm)],[c_0_441]) ).

fof(c_0_934,plain,
    ! [X33,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3)),X33) = X33 ),
    inference(fof_simplification,[status(thm)],[c_0_442]) ).

fof(c_0_935,plain,
    ! [X20,X3] :
      ( ~ class_OrderedGroup_Omonoid__mult(X3)
      | c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X3),X20,X3) = c_HOL_Oone__class_Oone(X3) ),
    inference(fof_simplification,[status(thm)],[c_0_443]) ).

fof(c_0_936,plain,
    ! [X10,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),X10,X3) = c_HOL_Ozero__class_Ozero(X3) ),
    inference(fof_simplification,[status(thm)],[c_0_444]) ).

fof(c_0_937,plain,
    ! [X33,X3] :
      ( ~ class_Ring__and__Field_Omult__zero(X3)
      | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),X33,X3) = c_HOL_Ozero__class_Ozero(X3) ),
    inference(fof_simplification,[status(thm)],[c_0_445]) ).

fof(c_0_938,plain,
    ! [X33,X3] :
      ( ~ class_Ring__and__Field_Omult__zero(X3)
      | c_HOL_Otimes__class_Otimes(X33,c_HOL_Ozero__class_Ozero(X3),X3) = c_HOL_Ozero__class_Ozero(X3) ),
    inference(fof_simplification,[status(thm)],[c_0_446]) ).

fof(c_0_939,plain,
    ! [X35,X3] :
      ( ~ class_Ring__and__Field_Oring__no__zero__divisors(X3)
      | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),X35,X3) = c_HOL_Ozero__class_Ozero(X3) ),
    inference(fof_simplification,[status(thm)],[c_0_447]) ).

fof(c_0_940,plain,
    ! [X33,X3] :
      ( ~ class_Ring__and__Field_Oring__no__zero__divisors(X3)
      | c_HOL_Otimes__class_Otimes(X33,c_HOL_Ozero__class_Ozero(X3),X3) = c_HOL_Ozero__class_Ozero(X3) ),
    inference(fof_simplification,[status(thm)],[c_0_448]) ).

fof(c_0_941,plain,
    ! [X33,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_HOL_Otimes__class_Otimes(X33,c_HOL_Ozero__class_Ozero(X3),X3) = c_HOL_Ozero__class_Ozero(X3) ),
    inference(fof_simplification,[status(thm)],[c_0_449]) ).

fof(c_0_942,plain,
    ! [X33,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),X33,X3) = c_HOL_Ozero__class_Ozero(X3) ),
    inference(fof_simplification,[status(thm)],[c_0_450]) ).

fof(c_0_943,plain,
    ! [X33,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Odiv(X33,c_HOL_Ozero__class_Ozero(X3),X3) = c_HOL_Ozero__class_Ozero(X3) ),
    inference(fof_simplification,[status(thm)],[c_0_451]) ).

fof(c_0_944,plain,
    ! [X33,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(X3),X33,X3) = c_HOL_Ozero__class_Ozero(X3) ),
    inference(fof_simplification,[status(thm)],[c_0_452]) ).

fof(c_0_945,plain,
    ! [X33,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Omod(X33,c_HOL_Oone__class_Oone(X3),X3) = c_HOL_Ozero__class_Ozero(X3) ),
    inference(fof_simplification,[status(thm)],[c_0_453]) ).

fof(c_0_946,plain,
    ! [X33,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(X3),X33,X3) = c_HOL_Ozero__class_Ozero(X3) ),
    inference(fof_simplification,[status(thm)],[c_0_454]) ).

fof(c_0_947,plain,
    ! [X33,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Odiv(X33,X33,X3) = c_HOL_Oone__class_Oone(X3)
      | X33 = c_HOL_Ozero__class_Ozero(X3) ),
    inference(fof_simplification,[status(thm)],[c_0_455]) ).

fof(c_0_948,plain,
    ! [X33,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X3),X33,X3) = X33 ),
    inference(fof_simplification,[status(thm)],[c_0_456]) ).

fof(c_0_949,plain,
    ! [X33,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_HOL_Otimes__class_Otimes(X33,c_HOL_Oone__class_Oone(X3),X3) = X33 ),
    inference(fof_simplification,[status(thm)],[c_0_457]) ).

fof(c_0_950,plain,
    ! [X33,X3] :
      ( ~ class_OrderedGroup_Omonoid__mult(X3)
      | c_HOL_Otimes__class_Otimes(X33,c_HOL_Oone__class_Oone(X3),X3) = X33 ),
    inference(fof_simplification,[status(thm)],[c_0_458]) ).

fof(c_0_951,plain,
    ! [X33,X3] :
      ( ~ class_OrderedGroup_Omonoid__mult(X3)
      | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X3),X33,X3) = X33 ),
    inference(fof_simplification,[status(thm)],[c_0_459]) ).

fof(c_0_952,plain,
    ! [X33,X3] :
      ( ~ class_OrderedGroup_Ocomm__monoid__mult(X3)
      | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X3),X33,X3) = X33 ),
    inference(fof_simplification,[status(thm)],[c_0_460]) ).

fof(c_0_953,plain,
    ! [X10,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X3),X10,X3) = X10 ),
    inference(fof_simplification,[status(thm)],[c_0_461]) ).

fof(c_0_954,plain,
    ! [X33,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Odiv(X33,c_HOL_Oone__class_Oone(X3),X3) = X33 ),
    inference(fof_simplification,[status(thm)],[c_0_462]) ).

fof(c_0_955,plain,
    ! [X33,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Omod(X33,c_HOL_Ozero__class_Ozero(X3),X3) = X33 ),
    inference(fof_simplification,[status(thm)],[c_0_463]) ).

fof(c_0_956,plain,
    ! [X33,X3] :
      ( ~ class_Power_Opower(X3)
      | c_Power_Opower__class_Opower(X33,c_HOL_Ozero__class_Ozero(tc_nat),X3) = c_HOL_Oone__class_Oone(X3) ),
    inference(fof_simplification,[status(thm)],[c_0_464]) ).

fof(c_0_957,plain,
    ! [X10,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_Power_Opower__class_Opower(X10,c_HOL_Ozero__class_Ozero(tc_nat),X3) = c_HOL_Oone__class_Oone(X3) ),
    inference(fof_simplification,[status(thm)],[c_0_465]) ).

fof(c_0_958,plain,
    ! [X33,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(X33,c_HOL_Ozero__class_Ozero(X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_466]) ).

fof(c_0_959,plain,
    ! [X33,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(X3),X33,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_467]) ).

fof(c_0_960,plain,
    ! [X33,X3] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),c_HOL_Ozero__class_Ozero(X3)) = X33 ),
    inference(fof_simplification,[status(thm)],[c_0_468]) ).

fof(c_0_961,plain,
    ! [X33,X3] :
      ( ~ class_OrderedGroup_Omonoid__add(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),c_HOL_Ozero__class_Ozero(X3)) = X33 ),
    inference(fof_simplification,[status(thm)],[c_0_469]) ).

fof(c_0_962,plain,
    ! [X33,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),c_HOL_Ozero__class_Ozero(X3)) = X33 ),
    inference(fof_simplification,[status(thm)],[c_0_470]) ).

fof(c_0_963,plain,
    ! [X10,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_Power_Opower__class_Opower(X10,c_HOL_Oone__class_Oone(tc_nat),X3) = X10 ),
    inference(fof_simplification,[status(thm)],[c_0_471]) ).

fof(c_0_964,plain,
    ! [X33,X3] :
      ( ~ class_OrderedGroup_Omonoid__mult(X3)
      | c_Power_Opower__class_Opower(X33,c_HOL_Oone__class_Oone(tc_nat),X3) = X33 ),
    inference(fof_simplification,[status(thm)],[c_0_472]) ).

fof(c_0_965,plain,
    ! [X33,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Omod(X33,X33,X3) = c_HOL_Ozero__class_Ozero(X3) ),
    inference(fof_simplification,[status(thm)],[c_0_473]) ).

fof(c_0_966,plain,
    ! [X10,X3] :
      ( ~ class_OrderedGroup_Oab__semigroup__idem__mult(X3)
      | c_HOL_Otimes__class_Otimes(X10,X10,X3) = X10 ),
    inference(fof_simplification,[status(thm)],[c_0_474]) ).

fof(c_0_967,plain,
    ! [X33,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(X33,X33,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_475]) ).

fof(c_0_968,axiom,
    ! [X20] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X20,tc_nat)
      | X20 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    c_0_476 ).

fof(c_0_969,plain,
    ! [X20,X14,X3] :
      ( ~ class_Nat_Osemiring__char__0(X3)
      | c_Nat_Osemiring__1__class_Oof__nat(X14,X3) != c_Nat_Osemiring__1__class_Oof__nat(X20,X3)
      | X14 = X20 ),
    inference(fof_simplification,[status(thm)],[c_0_477]) ).

fof(c_0_970,plain,
    ! [X29,X7] :
      ( c_Lambda_Obeta(c_Lambda_OdB_OAbs(X7),c_Lambda_OdB_OAbs(X29))
      | ~ c_Lambda_Obeta(X7,X29) ),
    inference(fof_simplification,[status(thm)],[c_0_478]) ).

fof(c_0_971,plain,
    ! [X4,X5] :
      ( class_Orderings_Opreorder(tc_fun(X4,X5))
      | ~ class_Orderings_Opreorder(X5) ),
    inference(fof_simplification,[status(thm)],[c_0_479]) ).

fof(c_0_972,plain,
    ! [X4,X5] :
      ( class_Orderings_Oorder(tc_fun(X4,X5))
      | ~ class_Orderings_Oorder(X5) ),
    inference(fof_simplification,[status(thm)],[c_0_480]) ).

fof(c_0_973,plain,
    ! [X3] :
      ( ~ class_Ring__and__Field_Osemiring__1(X3)
      | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),X3) = c_HOL_Oone__class_Oone(X3) ),
    inference(fof_simplification,[status(thm)],[c_0_481]) ).

fof(c_0_974,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_482]) ).

fof(c_0_975,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_483]) ).

fof(c_0_976,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_484]) ).

fof(c_0_977,axiom,
    ! [X60,X50] :
      ( c_Lambda_OdB_OAbs(X50) != c_Lambda_OdB_OAbs(X60)
      | X50 = X60 ),
    c_0_485 ).

fof(c_0_978,axiom,
    ! [X11,X12] :
      ( c_Lambda_OdB_OVar(X12) != c_Lambda_OdB_OVar(X11)
      | X12 = X11 ),
    c_0_486 ).

fof(c_0_979,axiom,
    ! [X11,X12] :
      ( c_Suc(X12) != c_Suc(X11)
      | X12 = X11 ),
    c_0_487 ).

fof(c_0_980,axiom,
    ! [X9,X10] :
      ( c_Suc(X10) != c_Suc(X9)
      | X10 = X9 ),
    c_0_488 ).

fof(c_0_981,axiom,
    ! [X9] :
      ( X9 = c_Suc(c_ATP__Linkup_Osko__Nat__Xnat__Xexhaust__1__1(X9))
      | X9 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    c_0_489 ).

fof(c_0_982,axiom,
    ! [X32] :
      ( X32 = c_Suc(c_ATP__Linkup_Osko__Nat__Xnat__Xnchotomy__1__1(X32))
      | X32 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    c_0_490 ).

fof(c_0_983,axiom,
    ! [X20] :
      ( X20 = c_Suc(c_ATP__Linkup_Osko__Nat__Xnot0__implies__Suc__1__1(X20))
      | X20 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    c_0_491 ).

fof(c_0_984,plain,
    ! [X29,X30,X31,X32,X33,X34] :
      ( c_Type_Otypings(X32,c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,X29,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),X31,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X30,tc_Lambda_OdB,tc_Lambda_OdB),X33)
      | ~ c_Type_Otypings(c_Type_Oshift(X32,X31,X34,tc_Type_Otype),X30,X33)
      | ~ c_Type_Otyping(X32,X29,X34) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_492])])]) ).

fof(c_0_985,plain,
    ! [X14,X15,X16] :
      ( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X16)),X15),X14,tc_Lambda_OdB,tc_Lambda_OdB)))
      | ~ hBOOL(hAPP(c_InductTermi_OIT,X15))
      | ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X16),X15),c_HOL_Ozero__class_Ozero(tc_nat)),X14,tc_Lambda_OdB,tc_Lambda_OdB))) ),
    inference(variable_rename,[status(thm)],[c_0_493]) ).

fof(c_0_986,plain,
    ! [X56,X57,X58,X59,X60,X61] :
      ( ~ hBOOL(hAPP(X61,c_Lambda_OdB_OdB__case(X60,X59,X58,hAPP(hAPP(c_Lambda_OdB_OApp,X57),X56),t_a)))
      | hBOOL(hAPP(X61,hAPP(hAPP(X59,X57),X56))) ),
    inference(variable_rename,[status(thm)],[c_0_494]) ).

fof(c_0_987,plain,
    ! [X50,X51,X52,X53,X54,X55] :
      ( ~ hBOOL(hAPP(X55,c_Lambda_OdB_OdB__case(X52,X51,X50,hAPP(hAPP(c_Lambda_OdB_OApp,X54),X53),t_a)))
      | hBOOL(hAPP(X55,hAPP(hAPP(X51,X54),X53))) ),
    inference(variable_rename,[status(thm)],[c_0_495]) ).

fof(c_0_988,plain,
    ! [X25,X26,X27,X28,X29] :
      ( X29 = X28
      | ~ c_Type_Otyping(X27,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X26),X25,tc_Lambda_OdB,tc_Lambda_OdB),X28)
      | ~ c_Type_Otyping(X27,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X26),X25,tc_Lambda_OdB,tc_Lambda_OdB),X29) ),
    inference(variable_rename,[status(thm)],[c_0_496]) ).

fof(c_0_989,plain,
    ! [X52,X53,X54,X55,X56] :
      ( ~ hBOOL(hAPP(X56,c_Lambda_OdB_OdB__case(X55,X54,X53,c_Lambda_OdB_OVar(X52),t_a)))
      | hBOOL(hAPP(X56,hAPP(X55,X52))) ),
    inference(variable_rename,[status(thm)],[c_0_497]) ).

fof(c_0_990,plain,
    ! [X50,X51,X52,X53,X54] :
      ( ~ hBOOL(hAPP(X54,c_Lambda_OdB_OdB__case(X53,X52,X51,c_Lambda_OdB_OVar(X50),t_a)))
      | hBOOL(hAPP(X54,hAPP(X53,X50))) ),
    inference(variable_rename,[status(thm)],[c_0_498]) ).

fof(c_0_991,plain,
    ! [X51,X52,X53,X54,X55] :
      ( ~ hBOOL(hAPP(X55,c_Lambda_OdB_OdB__case(X53,X52,X51,c_Lambda_OdB_OAbs(X54),t_a)))
      | hBOOL(hAPP(X55,hAPP(X51,X54))) ),
    inference(variable_rename,[status(thm)],[c_0_499]) ).

fof(c_0_992,plain,
    ! [X50,X51,X52,X53,X54] :
      ( ~ hBOOL(hAPP(X54,c_Lambda_OdB_OdB__case(X53,X52,X51,c_Lambda_OdB_OAbs(X50),t_a)))
      | hBOOL(hAPP(X54,hAPP(X51,X50))) ),
    inference(variable_rename,[status(thm)],[c_0_500]) ).

fof(c_0_993,plain,
    ! [X29,X30,X31,X32,X33] :
      ( c_Type_Otypings(c_Type_Oshift(X31,X30,X32,tc_Type_Otype),c_List_Omap(c_COMBC(c_Lambda_Olift,X30,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X29,tc_Lambda_OdB,tc_Lambda_OdB),X33)
      | ~ c_Type_Otypings(X31,X29,X33) ),
    inference(variable_rename,[status(thm)],[c_0_501]) ).

fof(c_0_994,plain,
    ! [X7] :
      ( c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X7,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)
      | ~ c_List_Olistsp(c_InductTermi_OIT,X7,tc_Lambda_OdB) ),
    inference(variable_rename,[status(thm)],[c_0_502]) ).

fof(c_0_995,plain,
    ! [X33,X34,X35] :
      ( X33 = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X35),c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(X35,X34,X33),tc_Lambda_OdB,tc_Lambda_OdB)
      | ~ c_Lambda_Obeta(c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X35),X34,tc_Lambda_OdB,tc_Lambda_OdB),X33) ),
    inference(variable_rename,[status(thm)],[c_0_503]) ).

fof(c_0_996,plain,
    ! [X21,X22] :
      ( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X22),X21,tc_Lambda_OdB,tc_Lambda_OdB)))
      | ~ c_List_Olistsp(c_InductTermi_OIT,X21,tc_Lambda_OdB) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_504])])]) ).

fof(c_0_997,plain,
    ! [X14,X15,X16] :
      ( c_Lambda_Obeta(c_List_Ofoldl(c_Lambda_OdB_OApp,X16,X14,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,X15,X14,tc_Lambda_OdB,tc_Lambda_OdB))
      | ~ c_Lambda_Obeta(X16,X15) ),
    inference(variable_rename,[status(thm)],[c_0_505]) ).

fof(c_0_998,plain,
    ! [X20,X21,X22,X23] :
      ( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X23),X22,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X21),X20,tc_Lambda_OdB,tc_Lambda_OdB)
      | X23 = X21 ),
    inference(variable_rename,[status(thm)],[c_0_506]) ).

fof(c_0_999,plain,
    ! [X20,X21,X22,X23] :
      ( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X23),X22,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X21),X20,tc_Lambda_OdB,tc_Lambda_OdB)
      | X22 = X20 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_507])])]) ).

fof(c_0_1000,plain,
    ! [X21,X22,X23,X24] :
      ( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X24),X22,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X23),X21,tc_Lambda_OdB,tc_Lambda_OdB)
      | X24 = X23 ),
    inference(variable_rename,[status(thm)],[c_0_508]) ).

fof(c_0_1001,plain,
    ! [X21,X22,X23,X24] :
      ( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X24),X22,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X23),X21,tc_Lambda_OdB,tc_Lambda_OdB)
      | X22 = X21 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_509])])]) ).

fof(c_0_1002,plain,
    ! [X31,X32,X33,X34] :
      ( ~ class_OrderedGroup_Osemigroup__add(X34)
      | c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X34),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X34),X33),X32),X31,X34,X34) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X34),X33),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X34),X32,X31,X34,X34)) ),
    inference(variable_rename,[status(thm)],[c_0_510]) ).

fof(c_0_1003,plain,
    ! [X9,X10,X11] :
      ( c_List_Ofoldl(c_Lambda_OdB_OApp,X11,X9,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,X10,X9,tc_Lambda_OdB,tc_Lambda_OdB)
      | X11 = X10 ),
    inference(variable_rename,[status(thm)],[c_0_511]) ).

fof(c_0_1004,plain,
    ! [X31,X32,X33] :
      ( ~ class_OrderedGroup_Omonoid__add(X33)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X33),X32),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X33),c_HOL_Ozero__class_Ozero(X33),X31,X33,X33)) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X33),X32,X31,X33,X33) ),
    inference(variable_rename,[status(thm)],[c_0_512]) ).

fof(c_0_1005,plain,
    ! [X32,X33,X34,X35] :
      ( ~ c_HOL_Oord__class_Oless(X33,X32,tc_nat)
      | X32 = c_HOL_Ozero__class_Ozero(tc_nat)
      | ~ hBOOL(hAPP(X35,c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X32,X34,tc_nat)),X33),X32,tc_nat)))
      | hBOOL(hAPP(X35,X33)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_513])])]) ).

fof(c_0_1006,plain,
    ! [X32,X33,X34,X35] :
      ( ~ c_HOL_Oord__class_Oless(X33,X32,tc_nat)
      | X32 = c_HOL_Ozero__class_Ozero(tc_nat)
      | ~ hBOOL(hAPP(X35,c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X32,X34,tc_nat)),X33),X32,tc_nat)))
      | hBOOL(hAPP(X35,X34)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_514])])]) ).

fof(c_0_1007,plain,
    ! [X38,X39,X40,X41] :
      ( ~ class_Divides_Osemiring__div(X41)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X41),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X41),c_HOL_Otimes__class_Otimes(X39,c_Divides_Odiv__class_Odiv(X40,X39,X41),X41)),c_Divides_Odiv__class_Omod(X40,X39,X41))),X38) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X41),X40),X38) ),
    inference(variable_rename,[status(thm)],[c_0_515]) ).

fof(c_0_1008,plain,
    ! [X38,X39,X40,X41] :
      ( ~ class_Divides_Osemiring__div(X41)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X41),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X41),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X40,X39,X41),X39,X41)),c_Divides_Odiv__class_Omod(X40,X39,X41))),X38) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X41),X40),X38) ),
    inference(variable_rename,[status(thm)],[c_0_516]) ).

fof(c_0_1009,plain,
    ! [X33,X34,X35,X36,X37] :
      ( hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,X35),hAPP(hAPP(c_Lambda_Olift,X33),X37)),c_Suc(X36))),hAPP(hAPP(hAPP(c_Lambda_Osubst,X34),X33),X36)),X37) = hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,X35),X34),X37)),X33),X36)
      | ~ c_HOL_Oord__class_Oless(X37,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X36),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_517]) ).

fof(c_0_1010,plain,
    ! [X30,X31,X32] :
      ( hAPP(hAPP(c_Lambda_OdB_OApp,X32),X31) != c_List_Ofoldl(c_Lambda_OdB_OApp,X30,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)
      | hAPP(hAPP(c_Lambda_OdB_OApp,X32),X31) = X30 ),
    inference(variable_rename,[status(thm)],[c_0_518]) ).

fof(c_0_1011,plain,
    ! [X14,X15,X16] :
      ( c_List_Ofoldl(c_Lambda_OdB_OApp,X15,X14,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X16)
      | X15 = c_Lambda_OdB_OAbs(X16) ),
    inference(variable_rename,[status(thm)],[c_0_519]) ).

fof(c_0_1012,plain,
    ! [X14,X15,X16] :
      ( c_Lambda_OdB_OAbs(X16) != c_List_Ofoldl(c_Lambda_OdB_OApp,X15,X14,tc_Lambda_OdB,tc_Lambda_OdB)
      | c_Lambda_OdB_OAbs(X16) = X15 ),
    inference(variable_rename,[status(thm)],[c_0_520]) ).

fof(c_0_1013,plain,
    ! [X15,X16,X17] :
      ( c_Lambda_OdB_OVar(X17) != c_List_Ofoldl(c_Lambda_OdB_OApp,X16,X15,tc_Lambda_OdB,tc_Lambda_OdB)
      | c_Lambda_OdB_OVar(X17) = X16 ),
    inference(variable_rename,[status(thm)],[c_0_521]) ).

fof(c_0_1014,plain,
    ! [X30,X31,X32,X33] :
      ( hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(hAPP(c_Lambda_Osubst,X30),X31),X32)),X33) = hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,X30),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X33),c_HOL_Oone__class_Oone(tc_nat)))),hAPP(hAPP(c_Lambda_Olift,X31),X33)),X32)
      | ~ c_HOL_Oord__class_Oless(X32,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X33),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_522]) ).

fof(c_0_1015,plain,
    ! [X35,X36,X37,X38] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X38)
      | c_Finite__Set_Osetsum(X37,c_SetInterval_Oord__class_OatLeastLessThan(X36,c_Suc(X35),tc_nat),tc_nat,X38) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X38),c_Finite__Set_Osetsum(X37,c_SetInterval_Oord__class_OatLeastLessThan(X36,X35,tc_nat),tc_nat,X38)),hAPP(X37,X35))
      | c_HOL_Oord__class_Oless(X35,X36,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_523]) ).

fof(c_0_1016,plain,
    ! [X14,X15,X16] :
      ( c_Lambda_OdB_OAbs(X16) != c_List_Ofoldl(c_Lambda_OdB_OApp,X15,X14,tc_Lambda_OdB,tc_Lambda_OdB)
      | X14 = c_List_Olist_ONil(tc_Lambda_OdB) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_524])])]) ).

fof(c_0_1017,plain,
    ! [X14,X15,X16] :
      ( c_List_Ofoldl(c_Lambda_OdB_OApp,X15,X14,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X16)
      | X14 = c_List_Olist_ONil(tc_Lambda_OdB) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_525])])]) ).

fof(c_0_1018,plain,
    ! [X15,X16,X17] :
      ( c_Lambda_OdB_OVar(X17) != c_List_Ofoldl(c_Lambda_OdB_OApp,X16,X15,tc_Lambda_OdB,tc_Lambda_OdB)
      | X15 = c_List_Olist_ONil(tc_Lambda_OdB) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_526])])]) ).

fof(c_0_1019,plain,
    ! [X43,X44,X45,X46] :
      ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X46,c_Divides_Odiv__class_Omod(X44,X45,tc_nat),tc_nat)),X43),c_HOL_Otimes__class_Otimes(X46,X45,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X43,X46,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X45,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_527]) ).

fof(c_0_1020,plain,
    ! [X4] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X4),c_HOL_Ozero__class_Ozero(X4),X4)),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X4),c_HOL_Ozero__class_Ozero(X4),X4)),X4) ),
    inference(variable_rename,[status(thm)],[c_0_528]) ).

fof(c_0_1021,plain,
    ! [X38,X39,X40,X41,X42] :
      ( ~ class_Ring__and__Field_Osemiring(X42)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X42),c_HOL_Otimes__class_Otimes(X41,X38,X42)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X42),c_HOL_Otimes__class_Otimes(X40,X38,X42)),X39)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X42),c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X42),X41),X40),X38,X42)),X39) ),
    inference(variable_rename,[status(thm)],[c_0_529]) ).

fof(c_0_1022,plain,
    ! [X11,X12,X13] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X13)
      | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X13),c_HOL_Otimes__class_Otimes(X12,X12,X13)),c_HOL_Otimes__class_Otimes(X11,X11,X13)),c_HOL_Ozero__class_Ozero(X13),X13) ),
    inference(variable_rename,[status(thm)],[c_0_530]) ).

fof(c_0_1023,plain,
    ! [X35,X36,X37,X38] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X38)
      | c_Finite__Set_Osetsum(X37,c_SetInterval_Oord__class_OatLeastLessThan(X36,X35,tc_nat),tc_nat,X38) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X38),hAPP(X37,X36)),c_Finite__Set_Osetsum(X37,c_SetInterval_Oord__class_OatLeastLessThan(c_Suc(X36),X35,tc_nat),tc_nat,X38))
      | ~ c_HOL_Oord__class_Oless(X36,X35,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_531]) ).

fof(c_0_1024,plain,
    ! [X30,X31,X32,X33] :
      ( hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(hAPP(c_Lambda_Osubst,X30),X31),X32)),X33) = hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,X30),X33)),hAPP(hAPP(c_Lambda_Olift,X31),X33)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X32),c_HOL_Oone__class_Oone(tc_nat)))
      | ~ c_HOL_Oord__class_Oless(X33,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X32),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_532]) ).

fof(c_0_1025,plain,
    ! [X57,X58,X59,X60,X61] :
      ( ~ class_Ring__and__Field_Oidom(X61)
      | ~ class_Int_Onumber__ring(X61)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X61),c_HOL_Otimes__class_Otimes(X60,X58,X61)),c_HOL_Otimes__class_Otimes(X59,X57,X61)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X61),c_HOL_Otimes__class_Otimes(X60,X57,X61)),c_HOL_Otimes__class_Otimes(X59,X58,X61))
      | X58 = X57
      | X60 = X59 ),
    inference(variable_rename,[status(thm)],[c_0_533]) ).

fof(c_0_1026,plain,
    ! [X45,X46,X47,X48,X49] :
      ( ~ class_Ring__and__Field_Oidom(X49)
      | ~ class_Int_Onumber__ring(X49)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X49),c_HOL_Otimes__class_Otimes(X48,X46,X49)),c_HOL_Otimes__class_Otimes(X47,X45,X49)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X49),c_HOL_Otimes__class_Otimes(X48,X45,X49)),c_HOL_Otimes__class_Otimes(X47,X46,X49))
      | X46 = X45
      | X48 = X47 ),
    inference(variable_rename,[status(thm)],[c_0_534]) ).

fof(c_0_1027,plain,
    ! [X63,X64,X65,X66,X67,X68] :
      ( ~ c_Type_Otyping(X66,X63,X67)
      | ~ c_Type_Otyping(c_Type_Oshift(X66,X65,X67,tc_Type_Otype),X64,X68)
      | c_Type_Otyping(X66,hAPP(hAPP(hAPP(c_Lambda_Osubst,X64),X63),X65),X68) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_535])])]) ).

fof(c_0_1028,plain,
    ! [X45,X46,X47,X48] :
      ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X48,X46,tc_nat)),c_HOL_Otimes__class_Otimes(X47,X45,tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X48,X45,tc_nat)),c_HOL_Otimes__class_Otimes(X47,X46,tc_nat))
      | X46 = X45
      | X48 = X47 ),
    inference(variable_rename,[status(thm)],[c_0_536]) ).

fof(c_0_1029,plain,
    ! [X57,X58,X59,X60] :
      ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X60,X58,tc_nat)),c_HOL_Otimes__class_Otimes(X59,X57,tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X60,X57,tc_nat)),c_HOL_Otimes__class_Otimes(X59,X58,tc_nat))
      | X58 = X57
      | X60 = X59 ),
    inference(variable_rename,[status(thm)],[c_0_537]) ).

fof(c_0_1030,plain,
    ! [X38,X39,X40,X41] :
      ( ~ class_Divides_Osemiring__div(X41)
      | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X41),X40),X39),X38,X41) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X41),c_Divides_Odiv__class_Omod(X40,X38,X41)),c_Divides_Odiv__class_Omod(X39,X38,X41)),X38,X41) ),
    inference(variable_rename,[status(thm)],[c_0_538]) ).

fof(c_0_1031,plain,
    ! [X11,X12,X13] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X13)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X13),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X13),c_HOL_Otimes__class_Otimes(X12,X12,X13)),c_HOL_Otimes__class_Otimes(X11,X11,X13)),X13)
      | X12 = c_HOL_Ozero__class_Ozero(X13) ),
    inference(variable_rename,[status(thm)],[c_0_539]) ).

fof(c_0_1032,plain,
    ! [X11,X12,X13] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X13)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X13),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X13),c_HOL_Otimes__class_Otimes(X12,X12,X13)),c_HOL_Otimes__class_Otimes(X11,X11,X13)),X13)
      | X11 = c_HOL_Ozero__class_Ozero(X13) ),
    inference(variable_rename,[status(thm)],[c_0_540]) ).

fof(c_0_1033,plain,
    ! [X36,X37,X38] :
      ( ~ class_Divides_Osemiring__div(X38)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X38),c_HOL_Otimes__class_Otimes(X36,c_Divides_Odiv__class_Odiv(X37,X36,X38),X38)),c_Divides_Odiv__class_Omod(X37,X36,X38)) = X37 ),
    inference(variable_rename,[status(thm)],[c_0_541]) ).

fof(c_0_1034,plain,
    ! [X36,X37,X38] :
      ( ~ class_Divides_Osemiring__div(X38)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X38),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X37,X36,X38),X36,X38)),c_Divides_Odiv__class_Omod(X37,X36,X38)) = X37 ),
    inference(variable_rename,[status(thm)],[c_0_542]) ).

fof(c_0_1035,plain,
    ! [X36,X37,X38] :
      ( ~ class_Divides_Osemiring__div(X38)
      | X37 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X38),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X37,X36,X38),X36,X38)),c_Divides_Odiv__class_Omod(X37,X36,X38)) ),
    inference(variable_rename,[status(thm)],[c_0_543]) ).

fof(c_0_1036,plain,
    ! [X35,X36,X37] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X37)
      | hAPP(X36,c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Ozero__class_Ozero(X37)
      | c_Finite__Set_Osetsum(X36,c_SetInterval_Oord__class_OatLeastLessThan(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X35,tc_nat),tc_nat,X37) = c_Finite__Set_Osetsum(X36,c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),X35,tc_nat),tc_nat,X37) ),
    inference(variable_rename,[status(thm)],[c_0_544]) ).

fof(c_0_1037,plain,
    ! [X37,X38,X39,X40] :
      ( ~ class_Ring__and__Field_Oidom(X40)
      | ~ class_Int_Onumber__ring(X40)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X40),c_HOL_Otimes__class_Otimes(X39,X38,X40)),c_HOL_Otimes__class_Otimes(X39,X37,X40)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X40),c_HOL_Otimes__class_Otimes(X39,X37,X40)),c_HOL_Otimes__class_Otimes(X39,X38,X40)) ),
    inference(variable_rename,[status(thm)],[c_0_545]) ).

fof(c_0_1038,plain,
    ! [X45,X46,X47,X48] :
      ( ~ class_Ring__and__Field_Oidom(X48)
      | ~ class_Int_Onumber__ring(X48)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X48),c_HOL_Otimes__class_Otimes(X45,X47,X48)),c_HOL_Otimes__class_Otimes(X45,X46,X48)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X48),c_HOL_Otimes__class_Otimes(X45,X46,X48)),c_HOL_Otimes__class_Otimes(X45,X47,X48)) ),
    inference(variable_rename,[status(thm)],[c_0_546]) ).

fof(c_0_1039,plain,
    ! [X38,X39,X40,X41] :
      ( ~ class_Divides_Osemiring__div(X41)
      | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X40,X39,X41),X38,X41) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X40,X38,X41),c_Divides_Odiv__class_Omod(X39,X38,X41),X41),X38,X41) ),
    inference(variable_rename,[status(thm)],[c_0_547]) ).

fof(c_0_1040,plain,
    ! [X38,X39,X40,X41] :
      ( ~ class_Divides_Osemiring__div(X41)
      | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X41),X40),X39),X38,X41) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X41),c_Divides_Odiv__class_Omod(X40,X38,X41)),X39),X38,X41) ),
    inference(variable_rename,[status(thm)],[c_0_548]) ).

fof(c_0_1041,plain,
    ! [X38,X39,X40,X41] :
      ( ~ class_Divides_Osemiring__div(X41)
      | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X41),c_Divides_Odiv__class_Omod(X40,X38,X41)),X39),X38,X41) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X41),X40),X39),X38,X41) ),
    inference(variable_rename,[status(thm)],[c_0_549]) ).

fof(c_0_1042,plain,
    ! [X45,X46,X47,X48,X49] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X49)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X49),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X49),X48),X47)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X49),X46),X45)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X49),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X49),X48),X46)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X49),X47),X45)) ),
    inference(variable_rename,[status(thm)],[c_0_550]) ).

fof(c_0_1043,plain,
    ! [X57,X58,X59,X60,X61] :
      ( ~ class_Divides_Osemiring__div(X61)
      | c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X59,X58,X61),c_Divides_Odiv__class_Odiv(X60,X57,X61),X61) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X59,X60,X61),c_HOL_Otimes__class_Otimes(X58,X57,X61),X61)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X57,X60,X61)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X58,X59,X61) ),
    inference(variable_rename,[status(thm)],[c_0_551]) ).

fof(c_0_1044,plain,
    ! [X37,X38,X39,X40] :
      ( ~ class_Divides_Osemiring__div(X40)
      | c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X40),X39),X38),X37,X40) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X40),c_Divides_Odiv__class_Odiv(X39,X37,X40)),c_Divides_Odiv__class_Odiv(X38,X37,X40))
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X37,X38,X40)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X37,X39,X40) ),
    inference(variable_rename,[status(thm)],[c_0_552]) ).

fof(c_0_1045,plain,
    ! [X30,X31,X32,X33,X34] :
      ( c_Type_Otyping(c_Type_Oshift(X32,X31,X33,tc_Type_Otype),hAPP(hAPP(c_Lambda_Olift,X30),X31),X34)
      | ~ c_Type_Otyping(X32,X30,X34) ),
    inference(variable_rename,[status(thm)],[c_0_553]) ).

fof(c_0_1046,plain,
    ! [X34,X35,X36] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X36)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X35,c_Power_Opower__class_Opower(X35,X34,X36),X36),c_Power_Opower__class_Opower(X35,X34,X36),X36)
      | ~ c_HOL_Oord__class_Oless(X35,c_HOL_Oone__class_Oone(X36),X36)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X36),X35,X36) ),
    inference(variable_rename,[status(thm)],[c_0_554]) ).

fof(c_0_1047,plain,
    ! [X21,X22] :
      ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X21,tc_nat)
      | c_HOL_Oord__class_Oless(X22,c_HOL_Otimes__class_Otimes(X21,c_Suc(c_Divides_Odiv__class_Odiv(X22,X21,tc_nat)),tc_nat),tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_555])])]) ).

fof(c_0_1048,plain,
    ! [X60,X61,X62,X63,X64,X65] :
      ( ~ class_Divides_Osemiring__div(X65)
      | c_Divides_Odiv__class_Omod(X62,X60,X65) != c_Divides_Odiv__class_Omod(X61,X60,X65)
      | c_Divides_Odiv__class_Omod(X64,X60,X65) != c_Divides_Odiv__class_Omod(X63,X60,X65)
      | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X64,X62,X65),X60,X65) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X63,X61,X65),X60,X65) ),
    inference(variable_rename,[status(thm)],[c_0_556]) ).

fof(c_0_1049,plain,
    ! [X60,X61,X62,X63,X64,X65] :
      ( ~ class_Divides_Osemiring__div(X65)
      | c_Divides_Odiv__class_Omod(X62,X60,X65) != c_Divides_Odiv__class_Omod(X61,X60,X65)
      | c_Divides_Odiv__class_Omod(X64,X60,X65) != c_Divides_Odiv__class_Omod(X63,X60,X65)
      | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X65),X64),X62),X60,X65) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X65),X63),X61),X60,X65) ),
    inference(variable_rename,[status(thm)],[c_0_557]) ).

fof(c_0_1050,plain,
    ! [X38,X39,X40,X41] :
      ( ~ class_Divides_Osemiring__div(X41)
      | c_Ring__and__Field_Odvd__class_Odvd(X39,X38,X41)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(X39,X40,X41),c_Divides_Odiv__class_Odiv(X38,X40,X41),X41)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X40,X38,X41)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X40,X39,X41) ),
    inference(variable_rename,[status(thm)],[c_0_558]) ).

fof(c_0_1051,plain,
    ! [X42,X43,X44,X45,X46] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X46)
      | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X45,X44,X46),c_HOL_Otimes__class_Otimes(X43,X42,X46),X46) = c_HOL_Otimes__class_Otimes(X45,c_HOL_Otimes__class_Otimes(X44,c_HOL_Otimes__class_Otimes(X43,X42,X46),X46),X46) ),
    inference(variable_rename,[status(thm)],[c_0_559]) ).

fof(c_0_1052,plain,
    ! [X42,X43,X44,X45,X46] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X46)
      | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X45,X44,X46),c_HOL_Otimes__class_Otimes(X43,X42,X46),X46) = c_HOL_Otimes__class_Otimes(X43,c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X45,X44,X46),X42,X46),X46) ),
    inference(variable_rename,[status(thm)],[c_0_560]) ).

fof(c_0_1053,plain,
    ! [X28,X29,X30,X31,X32] :
      ( hAPP(c_Type_Oshift(X30,X29,X31,X32),X28) = hAPP(X30,X28)
      | ~ c_HOL_Oord__class_Oless(X28,X29,tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_561])])]) ).

fof(c_0_1054,plain,
    ! [X11,X12,X13] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X13)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X13),c_HOL_Otimes__class_Otimes(X12,X12,X13)),c_HOL_Otimes__class_Otimes(X11,X11,X13)) != c_HOL_Ozero__class_Ozero(X13)
      | X11 = c_HOL_Ozero__class_Ozero(X13) ),
    inference(variable_rename,[status(thm)],[c_0_562]) ).

fof(c_0_1055,plain,
    ! [X11,X12,X13] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X13)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X13),c_HOL_Otimes__class_Otimes(X12,X12,X13)),c_HOL_Otimes__class_Otimes(X11,X11,X13)) != c_HOL_Ozero__class_Ozero(X13)
      | X12 = c_HOL_Ozero__class_Ozero(X13) ),
    inference(variable_rename,[status(thm)],[c_0_563]) ).

fof(c_0_1056,plain,
    ! [X30,X31,X32] :
      ( hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_Olift,X30),X32)),c_Suc(X31)) = hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_Olift,X30),X31)),X32)
      | ~ c_HOL_Oord__class_Oless(X32,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X31),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_564]) ).

fof(c_0_1057,plain,
    ! [X36,X37,X38] :
      ( ~ class_Divides_Osemiring__div(X38)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X38),c_Divides_Odiv__class_Omod(X37,X36,X38)),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X37,X36,X38),X36,X38)) = X37 ),
    inference(variable_rename,[status(thm)],[c_0_565]) ).

fof(c_0_1058,plain,
    ! [X34,X35,X36] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X36)
      | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X35,X34,X36),c_HOL_Otimes__class_Otimes(X35,c_Power_Opower__class_Opower(X35,X34,X36),X36),X36)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X36),X35,X36) ),
    inference(variable_rename,[status(thm)],[c_0_566]) ).

fof(c_0_1059,plain,
    ! [X38,X39,X40,X41] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X41)
      | c_HOL_Oord__class_Oless(X39,X40,X41)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X38,X40,X41),c_HOL_Otimes__class_Otimes(X38,X39,X41),X41)
      | ~ c_HOL_Oord__class_Oless(X38,c_HOL_Ozero__class_Ozero(X41),X41) ),
    inference(variable_rename,[status(thm)],[c_0_567]) ).

fof(c_0_1060,plain,
    ! [X38,X39,X40,X41] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X41)
      | c_HOL_Oord__class_Oless(X40,X39,X41)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X38,X40,X41),c_HOL_Otimes__class_Otimes(X38,X39,X41),X41)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X41),X38,X41) ),
    inference(variable_rename,[status(thm)],[c_0_568]) ).

fof(c_0_1061,plain,
    ! [X36,X37,X38,X39] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X39)
      | c_HOL_Oord__class_Oless(X37,X36,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X38,X37,X39),c_Power_Opower__class_Opower(X38,X36,X39),X39)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X39),X38,X39) ),
    inference(variable_rename,[status(thm)],[c_0_569]) ).

fof(c_0_1062,plain,
    ! [X34,X35,X36,X37] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X37)
      | c_HOL_Oord__class_Oless(X35,X34,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X36,X35,X37),c_Power_Opower__class_Opower(X36,X34,X37),X37)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X37),X36,X37) ),
    inference(variable_rename,[status(thm)],[c_0_570]) ).

fof(c_0_1063,plain,
    ! [X56,X57,X58,X59,X60] :
      ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X59),c_HOL_Otimes__class_Otimes(X60,X58,tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X56),c_HOL_Otimes__class_Otimes(X60,X57,tc_nat))
      | c_Divides_Odiv__class_Omod(X59,X60,tc_nat) = c_Divides_Odiv__class_Omod(X56,X60,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_571]) ).

fof(c_0_1064,plain,
    ! [X26,X27,X28] :
      ( c_HOL_Oord__class_Oless(X27,X26,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X28,X27,tc_nat),c_HOL_Otimes__class_Otimes(X28,X26,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X28,tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_572])])]) ).

fof(c_0_1065,plain,
    ! [X22,X23,X24] :
      ( c_HOL_Oord__class_Oless(X23,X22,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X24,X23,tc_nat),c_Power_Opower__class_Opower(X24,X22,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X24,tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_573])])]) ).

fof(c_0_1066,plain,
    ! [X26,X27,X28] :
      ( c_Ring__and__Field_Odvd__class_Odvd(X27,X26,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X28,X27,tc_nat),c_HOL_Otimes__class_Otimes(X28,X26,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X28,tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_574])])]) ).

fof(c_0_1067,plain,
    ! [X26,X27,X28] :
      ( c_Ring__and__Field_Odvd__class_Odvd(X27,X26,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X28,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X28,X27,tc_nat),c_HOL_Otimes__class_Otimes(X28,X26,tc_nat),tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_575])])]) ).

fof(c_0_1068,plain,
    ! [X46,X47,X48,X49] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X49)
      | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X47,X48,X49),c_Power_Opower__class_Opower(X47,X46,X49),X49)
      | ~ c_HOL_Oord__class_Oless(X47,c_HOL_Oone__class_Oone(X49),X49)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X49),X47,X49)
      | ~ c_HOL_Oord__class_Oless(X46,X48,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_576]) ).

fof(c_0_1069,plain,
    ! [X38,X39,X40,X41] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X41)
      | c_HOL_Oord__class_Oless(X38,c_HOL_Ozero__class_Ozero(X41),X41)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X41),X38,X41)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X38,X40,X41),c_HOL_Otimes__class_Otimes(X38,X39,X41),X41) ),
    inference(variable_rename,[status(thm)],[c_0_577]) ).

fof(c_0_1070,plain,
    ! [X38,X39,X40,X41] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X41)
      | c_HOL_Oord__class_Oless(X38,c_HOL_Ozero__class_Ozero(X41),X41)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X41),X38,X41)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X40,X38,X41),c_HOL_Otimes__class_Otimes(X39,X38,X41),X41) ),
    inference(variable_rename,[status(thm)],[c_0_578]) ).

fof(c_0_1071,plain,
    ! [X38,X39,X40,X41] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X41)
      | c_HOL_Oord__class_Oless(X38,c_HOL_Ozero__class_Ozero(X41),X41)
      | c_HOL_Oord__class_Oless(X40,X39,X41)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X40,X38,X41),c_HOL_Otimes__class_Otimes(X39,X38,X41),X41) ),
    inference(variable_rename,[status(thm)],[c_0_579]) ).

fof(c_0_1072,plain,
    ! [X38,X39,X40,X41] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X41)
      | c_HOL_Oord__class_Oless(X39,X40,X41)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X41),X38,X41)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X40,X38,X41),c_HOL_Otimes__class_Otimes(X39,X38,X41),X41) ),
    inference(variable_rename,[status(thm)],[c_0_580]) ).

fof(c_0_1073,plain,
    ! [X38,X39,X40,X41] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X41)
      | c_HOL_Oord__class_Oless(X38,c_HOL_Ozero__class_Ozero(X41),X41)
      | c_HOL_Oord__class_Oless(X40,X39,X41)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X38,X40,X41),c_HOL_Otimes__class_Otimes(X38,X39,X41),X41) ),
    inference(variable_rename,[status(thm)],[c_0_581]) ).

fof(c_0_1074,plain,
    ! [X38,X39,X40,X41] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X41)
      | c_HOL_Oord__class_Oless(X39,X40,X41)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X41),X38,X41)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X38,X40,X41),c_HOL_Otimes__class_Otimes(X38,X39,X41),X41) ),
    inference(variable_rename,[status(thm)],[c_0_582]) ).

fof(c_0_1075,plain,
    ! [X38,X39,X40,X41] :
      ( ~ class_Divides_Osemiring__div(X41)
      | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X40,X38,X41),X39,X41),X38,X41) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X40,X39,X41),X38,X41) ),
    inference(variable_rename,[status(thm)],[c_0_583]) ).

fof(c_0_1076,plain,
    ! [X38,X39,X40,X41] :
      ( ~ class_Divides_Osemiring__div(X41)
      | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X40,X39,X41),X38,X41) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X40,X38,X41),X39,X41),X38,X41) ),
    inference(variable_rename,[status(thm)],[c_0_584]) ).

fof(c_0_1077,plain,
    ! [X38,X39,X40,X41] :
      ( ~ class_Divides_Osemiring__div(X41)
      | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X40,X39,X41),X38,X41) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X40,c_Divides_Odiv__class_Omod(X39,X38,X41),X41),X38,X41) ),
    inference(variable_rename,[status(thm)],[c_0_585]) ).

fof(c_0_1078,plain,
    ! [X42,X43,X44,X45,X46] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X46)
      | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X45,X44,X46),c_HOL_Otimes__class_Otimes(X43,X42,X46),X46) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X45,X43,X46),c_HOL_Otimes__class_Otimes(X44,X42,X46),X46) ),
    inference(variable_rename,[status(thm)],[c_0_586]) ).

fof(c_0_1079,plain,
    ! [X38,X39,X40,X41] :
      ( ~ class_Divides_Osemiring__div(X41)
      | c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X41),X40),c_HOL_Otimes__class_Otimes(X39,X38,X41)),X39,X41) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X41),X38),c_Divides_Odiv__class_Odiv(X40,X39,X41))
      | X39 = c_HOL_Ozero__class_Ozero(X41) ),
    inference(variable_rename,[status(thm)],[c_0_587]) ).

fof(c_0_1080,plain,
    ! [X38,X39,X40,X41] :
      ( ~ class_Divides_Osemiring__div(X41)
      | c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X41),X40),c_HOL_Otimes__class_Otimes(X38,X39,X41)),X39,X41) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X41),X38),c_Divides_Odiv__class_Odiv(X40,X39,X41))
      | X39 = c_HOL_Ozero__class_Ozero(X41) ),
    inference(variable_rename,[status(thm)],[c_0_588]) ).

fof(c_0_1081,plain,
    ! [X38,X39,X40,X41] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X41)
      | c_HOL_Oord__class_Oless(X39,X40,X41)
      | c_HOL_Oord__class_Oless(X40,X39,X41)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X38,X40,X41),c_HOL_Otimes__class_Otimes(X38,X39,X41),X41) ),
    inference(variable_rename,[status(thm)],[c_0_589]) ).

fof(c_0_1082,plain,
    ! [X38,X39,X40,X41] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X41)
      | c_HOL_Oord__class_Oless(X39,X40,X41)
      | c_HOL_Oord__class_Oless(X40,X39,X41)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X40,X38,X41),c_HOL_Otimes__class_Otimes(X39,X38,X41),X41) ),
    inference(variable_rename,[status(thm)],[c_0_590]) ).

fof(c_0_1083,plain,
    ! [X36,X37,X38,X39] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X39),c_HOL_Otimes__class_Otimes(X38,X36,X39)),c_HOL_Otimes__class_Otimes(X37,X36,X39)) = c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X39),X38),X37),X36,X39) ),
    inference(variable_rename,[status(thm)],[c_0_591]) ).

fof(c_0_1084,plain,
    ! [X38,X39,X40,X41] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X41)
      | c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X41),X40),X39),X38,X41) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X41),c_HOL_Otimes__class_Otimes(X40,X38,X41)),c_HOL_Otimes__class_Otimes(X39,X38,X41)) ),
    inference(variable_rename,[status(thm)],[c_0_592]) ).

fof(c_0_1085,plain,
    ! [X38,X39,X40,X41] :
      ( ~ class_Ring__and__Field_Ocomm__semiring(X41)
      | c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X41),X40),X39),X38,X41) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X41),c_HOL_Otimes__class_Otimes(X40,X38,X41)),c_HOL_Otimes__class_Otimes(X39,X38,X41)) ),
    inference(variable_rename,[status(thm)],[c_0_593]) ).

fof(c_0_1086,plain,
    ! [X37,X38,X39,X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X40)
      | c_HOL_Otimes__class_Otimes(X39,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X40),X38),X37),X40) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X40),c_HOL_Otimes__class_Otimes(X39,X38,X40)),c_HOL_Otimes__class_Otimes(X39,X37,X40)) ),
    inference(variable_rename,[status(thm)],[c_0_594]) ).

fof(c_0_1087,plain,
    ! [X38,X39,X40,X41] :
      ( ~ class_Divides_Osemiring__div(X41)
      | c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(X39,X40,X41),c_Divides_Odiv__class_Odiv(X38,X40,X41),X41)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X39,X38,X41)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X40,X38,X41)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X40,X39,X41) ),
    inference(variable_rename,[status(thm)],[c_0_595]) ).

fof(c_0_1088,plain,
    ! [X38,X39,X40,X41] :
      ( ~ class_Divides_Osemiring__div(X41)
      | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X41),X40),X39),X38,X41) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X41),X40),c_Divides_Odiv__class_Omod(X39,X38,X41)),X38,X41) ),
    inference(variable_rename,[status(thm)],[c_0_596]) ).

fof(c_0_1089,plain,
    ! [X38,X39,X40,X41] :
      ( ~ class_Divides_Osemiring__div(X41)
      | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X41),X40),c_Divides_Odiv__class_Omod(X39,X38,X41)),X38,X41) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X41),X40),X39),X38,X41) ),
    inference(variable_rename,[status(thm)],[c_0_597]) ).

fof(c_0_1090,plain,
    ! [X21,X22,X23,X24] :
      ( ~ class_Divides_Osemiring__div(X24)
      | c_Power_Opower__class_Opower(c_Divides_Odiv__class_Odiv(X22,X21,X24),X23,X24) = c_Divides_Odiv__class_Odiv(c_Power_Opower__class_Opower(X22,X23,X24),c_Power_Opower__class_Opower(X21,X23,X24),X24)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X21,X22,X24) ),
    inference(variable_rename,[status(thm)],[c_0_598]) ).

fof(c_0_1091,plain,
    ! [X45,X46,X47,X48,X49] :
      ( ~ class_Ring__and__Field_Oidom(X49)
      | ~ class_Int_Onumber__ring(X49)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X49),X45),c_HOL_Otimes__class_Otimes(X46,X48,X49)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X49),X45),c_HOL_Otimes__class_Otimes(X46,X47,X49))
      | X48 = X47
      | X46 = c_HOL_Ozero__class_Ozero(X49) ),
    inference(variable_rename,[status(thm)],[c_0_599]) ).

fof(c_0_1092,plain,
    ! [X38,X39,X40,X41] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X41)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X41),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X41),X40),X39)),X38) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X41),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X41),X40),X38)),X39) ),
    inference(variable_rename,[status(thm)],[c_0_600]) ).

fof(c_0_1093,plain,
    ! [X26,X27,X28] :
      ( c_HOL_Oord__class_Oless(X27,X26,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X28),X27,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X28),X26,tc_nat),tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_601])])]) ).

fof(c_0_1094,plain,
    ! [X38,X39,X40,X41] :
      ( ~ class_Ring__and__Field_Oidom(X41)
      | c_Ring__and__Field_Odvd__class_Odvd(X40,X39,X41)
      | X38 = c_HOL_Ozero__class_Ozero(X41)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X38,X40,X41),c_HOL_Otimes__class_Otimes(X38,X39,X41),X41) ),
    inference(variable_rename,[status(thm)],[c_0_602]) ).

fof(c_0_1095,plain,
    ! [X38,X39,X40,X41] :
      ( ~ class_Ring__and__Field_Oidom(X41)
      | c_Ring__and__Field_Odvd__class_Odvd(X40,X39,X41)
      | X38 = c_HOL_Ozero__class_Ozero(X41)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X40,X38,X41),c_HOL_Otimes__class_Otimes(X39,X38,X41),X41) ),
    inference(variable_rename,[status(thm)],[c_0_603]) ).

fof(c_0_1096,plain,
    ! [X34,X35,X36] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X36)
      | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X36),c_HOL_Otimes__class_Otimes(X35,c_Power_Opower__class_Opower(X35,X34,X36),X36),X36)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X36),X35,X36) ),
    inference(variable_rename,[status(thm)],[c_0_604]) ).

fof(c_0_1097,plain,
    ! [X45,X46,X47,X48] :
      ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X45),c_HOL_Otimes__class_Otimes(X46,X48,tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X45),c_HOL_Otimes__class_Otimes(X46,X47,tc_nat))
      | X48 = X47
      | X46 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_605]) ).

fof(c_0_1098,plain,
    ! [X38,X39,X40,X41] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X41)
      | c_HOL_Oord__class_Oless(X40,X39,X41)
      | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X41),X40),X38),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X41),X39),X38),X41) ),
    inference(variable_rename,[status(thm)],[c_0_606]) ).

fof(c_0_1099,plain,
    ! [X38,X39,X40,X41] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X41)
      | c_HOL_Oord__class_Oless(X40,X39,X41)
      | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X41),X38),X40),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X41),X38),X39),X41) ),
    inference(variable_rename,[status(thm)],[c_0_607]) ).

fof(c_0_1100,plain,
    ! [X26,X27,X28] :
      ( c_Ring__and__Field_Odvd__class_Odvd(X27,X26,tc_nat)
      | X28 = c_HOL_Ozero__class_Ozero(tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X28,X27,tc_nat),c_HOL_Otimes__class_Otimes(X28,X26,tc_nat),tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_608])])]) ).

fof(c_0_1101,plain,
    ! [X26,X27,X28] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X28,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X28,X27,tc_nat),c_HOL_Otimes__class_Otimes(X28,X26,tc_nat),tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_609]) ).

fof(c_0_1102,plain,
    ! [X26,X27,X28] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X28,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X27,X28,tc_nat),c_HOL_Otimes__class_Otimes(X26,X28,tc_nat),tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_610]) ).

fof(c_0_1103,plain,
    ! [X26,X27,X28] :
      ( c_HOL_Oord__class_Oless(X27,X26,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X28,X27,tc_nat),c_HOL_Otimes__class_Otimes(X28,X26,tc_nat),tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_611])])]) ).

fof(c_0_1104,plain,
    ! [X26,X27,X28] :
      ( c_HOL_Oord__class_Oless(X27,X26,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X27,X28,tc_nat),c_HOL_Otimes__class_Otimes(X26,X28,tc_nat),tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_612])])]) ).

fof(c_0_1105,plain,
    ! [X38,X39,X40,X41] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X41)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X38,X40,X41),c_HOL_Otimes__class_Otimes(X38,X39,X41),X41)
      | ~ c_HOL_Oord__class_Oless(X39,X40,X41)
      | ~ c_HOL_Oord__class_Oless(X38,c_HOL_Ozero__class_Ozero(X41),X41) ),
    inference(variable_rename,[status(thm)],[c_0_613]) ).

fof(c_0_1106,plain,
    ! [X38,X39,X40,X41] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X41)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X38,X40,X41),c_HOL_Otimes__class_Otimes(X38,X39,X41),X41)
      | ~ c_HOL_Oord__class_Oless(X40,X39,X41)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X41),X38,X41) ),
    inference(variable_rename,[status(thm)],[c_0_614]) ).

fof(c_0_1107,plain,
    ! [X38,X39,X40,X41] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X41)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X38,X40,X41),c_HOL_Otimes__class_Otimes(X38,X39,X41),X41)
      | ~ c_HOL_Oord__class_Oless(X38,c_HOL_Ozero__class_Ozero(X41),X41)
      | ~ c_HOL_Oord__class_Oless(X39,X40,X41) ),
    inference(variable_rename,[status(thm)],[c_0_615]) ).

fof(c_0_1108,plain,
    ! [X38,X39,X40,X41] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X41)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X38,X40,X41),c_HOL_Otimes__class_Otimes(X38,X39,X41),X41)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X41),X38,X41)
      | ~ c_HOL_Oord__class_Oless(X40,X39,X41) ),
    inference(variable_rename,[status(thm)],[c_0_616]) ).

fof(c_0_1109,plain,
    ! [X38,X39,X40,X41] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X41)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X38,X40,X41),c_HOL_Otimes__class_Otimes(X38,X39,X41),X41)
      | ~ c_HOL_Oord__class_Oless(X40,X39,X41)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X41),X38,X41) ),
    inference(variable_rename,[status(thm)],[c_0_617]) ).

fof(c_0_1110,plain,
    ! [X38,X39,X40,X41] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X41)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X38,X40,X41),c_HOL_Otimes__class_Otimes(X38,X39,X41),X41)
      | ~ c_HOL_Oord__class_Oless(X39,X40,X41)
      | ~ c_HOL_Oord__class_Oless(X38,c_HOL_Ozero__class_Ozero(X41),X41) ),
    inference(variable_rename,[status(thm)],[c_0_618]) ).

fof(c_0_1111,plain,
    ! [X38,X39,X40,X41] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X41)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X40,X38,X41),c_HOL_Otimes__class_Otimes(X39,X38,X41),X41)
      | ~ c_HOL_Oord__class_Oless(X38,c_HOL_Ozero__class_Ozero(X41),X41)
      | ~ c_HOL_Oord__class_Oless(X39,X40,X41) ),
    inference(variable_rename,[status(thm)],[c_0_619]) ).

fof(c_0_1112,plain,
    ! [X38,X39,X40,X41] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X41)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X40,X38,X41),c_HOL_Otimes__class_Otimes(X39,X38,X41),X41)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X41),X38,X41)
      | ~ c_HOL_Oord__class_Oless(X40,X39,X41) ),
    inference(variable_rename,[status(thm)],[c_0_620]) ).

fof(c_0_1113,plain,
    ! [X38,X39,X40,X41] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X41)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X40,X38,X41),c_HOL_Otimes__class_Otimes(X39,X38,X41),X41)
      | ~ c_HOL_Oord__class_Oless(X40,X39,X41)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X41),X38,X41) ),
    inference(variable_rename,[status(thm)],[c_0_621]) ).

fof(c_0_1114,plain,
    ! [X38,X39,X40,X41] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X41)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X40,X38,X41),c_HOL_Otimes__class_Otimes(X39,X38,X41),X41)
      | ~ c_HOL_Oord__class_Oless(X39,X40,X41)
      | ~ c_HOL_Oord__class_Oless(X38,c_HOL_Ozero__class_Ozero(X41),X41) ),
    inference(variable_rename,[status(thm)],[c_0_622]) ).

fof(c_0_1115,plain,
    ! [X38,X39,X40,X41] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X41)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X38,X40,X41),c_HOL_Otimes__class_Otimes(X38,X39,X41),X41)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X41),X38,X41)
      | ~ c_HOL_Oord__class_Oless(X40,X39,X41) ),
    inference(variable_rename,[status(thm)],[c_0_623]) ).

fof(c_0_1116,plain,
    ! [X35,X36,X37,X38] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X38)
      | c_Finite__Set_Osetsum(X37,c_SetInterval_Oord__class_OatLeastLessThan(X36,c_Suc(X35),tc_nat),tc_nat,X38) = c_HOL_Ozero__class_Ozero(X38)
      | ~ c_HOL_Oord__class_Oless(X35,X36,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_624]) ).

fof(c_0_1117,plain,
    ! [X4] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X4),c_HOL_Ozero__class_Ozero(X4),X4)),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X4),c_HOL_Ozero__class_Ozero(X4),X4)) = c_HOL_Ozero__class_Ozero(X4) ),
    inference(variable_rename,[status(thm)],[c_0_625]) ).

fof(c_0_1118,plain,
    ! [X36,X37,X38,X39] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X39)
      | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X38,X37,X39),c_Power_Opower__class_Opower(X38,X36,X39),X39)
      | ~ c_HOL_Oord__class_Oless(X37,X36,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X39),X38,X39) ),
    inference(variable_rename,[status(thm)],[c_0_626]) ).

fof(c_0_1119,plain,
    ! [X46,X47,X48,X49] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X49)
      | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X47,X46,X49),c_Power_Opower__class_Opower(X47,X48,X49),X49)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X49),X47,X49)
      | ~ c_HOL_Oord__class_Oless(X46,X48,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_627]) ).

fof(c_0_1120,plain,
    ! [X45,X46,X47,X48,X49] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X49)
      | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X48,X46,X49),c_HOL_Otimes__class_Otimes(X47,X45,X49),X49)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X46,X45,X49)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X48,X47,X49) ),
    inference(variable_rename,[status(thm)],[c_0_628]) ).

fof(c_0_1121,plain,
    ! [X34,X35,X36] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X36)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X36),c_HOL_Otimes__class_Otimes(X35,X34,X36)),X34) = c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X36),X35),c_HOL_Oone__class_Oone(X36)),X34,X36) ),
    inference(variable_rename,[status(thm)],[c_0_629]) ).

fof(c_0_1122,plain,
    ! [X36,X37,X38] :
      ( ~ class_Divides_Osemiring__div(X38)
      | c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X38),X36),X37),X36,X38) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X38),c_Divides_Odiv__class_Odiv(X37,X36,X38)),c_HOL_Oone__class_Oone(X38))
      | X36 = c_HOL_Ozero__class_Ozero(X38) ),
    inference(variable_rename,[status(thm)],[c_0_630]) ).

fof(c_0_1123,plain,
    ! [X36,X37,X38] :
      ( ~ class_Divides_Osemiring__div(X38)
      | c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X38),X37),X36),X36,X38) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X38),c_Divides_Odiv__class_Odiv(X37,X36,X38)),c_HOL_Oone__class_Oone(X38))
      | X36 = c_HOL_Ozero__class_Ozero(X38) ),
    inference(variable_rename,[status(thm)],[c_0_631]) ).

fof(c_0_1124,plain,
    ! [X45,X46,X47,X48,X49] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X49)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X49),X48),X46),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X49),X47),X45),X49)
      | ~ c_HOL_Oord__class_Oless(X46,X45,X49)
      | ~ c_HOL_Oord__class_Oless(X48,X47,X49) ),
    inference(variable_rename,[status(thm)],[c_0_632]) ).

fof(c_0_1125,plain,
    ! [X36,X37,X38,X39] :
      ( ~ class_OrderedGroup_Ocomm__monoid__mult(X39)
      | c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X38,X37,X39),X36,X39) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X38,X36,X39),c_Power_Opower__class_Opower(X37,X36,X39),X39) ),
    inference(variable_rename,[status(thm)],[c_0_633]) ).

fof(c_0_1126,plain,
    ! [X43,X44,X45,X46] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X46)
      | c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X44,X43,X46),X45,X46) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X44,X45,X46),c_Power_Opower__class_Opower(X43,X45,X46),X46) ),
    inference(variable_rename,[status(thm)],[c_0_634]) ).

fof(c_0_1127,plain,
    ! [X38,X39,X40,X41] :
      ( ~ class_Divides_Osemiring__div(X41)
      | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X40,X38,X41),c_HOL_Otimes__class_Otimes(X39,X38,X41),X41) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X40,X39,X41),X38,X41) ),
    inference(variable_rename,[status(thm)],[c_0_635]) ).

fof(c_0_1128,plain,
    ! [X38,X39,X40,X41] :
      ( ~ class_Divides_Osemiring__div(X41)
      | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X38,X40,X41),c_HOL_Otimes__class_Otimes(X38,X39,X41),X41) = c_HOL_Otimes__class_Otimes(X38,c_Divides_Odiv__class_Omod(X40,X39,X41),X41) ),
    inference(variable_rename,[status(thm)],[c_0_636]) ).

fof(c_0_1129,plain,
    ! [X26,X27,X28] :
      ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X27,X28,tc_nat),c_HOL_Otimes__class_Otimes(X26,X28,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X27,X26,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X28,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_637]) ).

fof(c_0_1130,plain,
    ! [X26,X27,X28] :
      ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X28,X27,tc_nat),c_HOL_Otimes__class_Otimes(X28,X26,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X27,X26,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X28,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_638]) ).

fof(c_0_1131,plain,
    ! [X28,X29,X30] :
      ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X28,X30,tc_nat),c_HOL_Otimes__class_Otimes(X28,X29,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X28,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X30,X29,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_639]) ).

fof(c_0_1132,plain,
    ! [X28,X29,X30] :
      ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X30,X28,tc_nat),c_HOL_Otimes__class_Otimes(X29,X28,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X28,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X30,X29,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_640]) ).

fof(c_0_1133,plain,
    ! [X26,X27,X28] :
      ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X28,X27,tc_nat),c_HOL_Otimes__class_Otimes(X28,X26,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X27,X26,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X28,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_641]) ).

fof(c_0_1134,plain,
    ! [X26,X27,X28] :
      ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X28,X27,tc_nat),c_HOL_Otimes__class_Otimes(X28,X26,tc_nat),tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X27,X26,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X28,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_642]) ).

fof(c_0_1135,plain,
    ! [X38,X39,X40,X41] :
      ( ~ class_Divides_Osemiring__div(X41)
      | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X41),X40),c_HOL_Otimes__class_Otimes(X38,X39,X41)),X39,X41) = c_Divides_Odiv__class_Omod(X40,X39,X41) ),
    inference(variable_rename,[status(thm)],[c_0_643]) ).

fof(c_0_1136,plain,
    ! [X38,X39,X40,X41] :
      ( ~ class_Divides_Osemiring__div(X41)
      | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X41),X40),c_HOL_Otimes__class_Otimes(X39,X38,X41)),X39,X41) = c_Divides_Odiv__class_Omod(X40,X39,X41) ),
    inference(variable_rename,[status(thm)],[c_0_644]) ).

fof(c_0_1137,plain,
    ! [X32,X33] :
      ( ~ hBOOL(hAPP(X33,c_Divides_Odiv__class_Odiv(X32,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)))
      | hBOOL(hAPP(X33,c_HOL_Ozero__class_Ozero(tc_nat))) ),
    inference(variable_rename,[status(thm)],[c_0_645]) ).

fof(c_0_1138,plain,
    ! [X36,X37,X38] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X38)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X38),X36,X38)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X38),X37,X38)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X38),c_HOL_Otimes__class_Otimes(X36,X37,X38),X38) ),
    inference(variable_rename,[status(thm)],[c_0_646]) ).

fof(c_0_1139,plain,
    ! [X36,X37,X38] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X38)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X38),X36,X38)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X38),X37,X38)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X38),c_HOL_Otimes__class_Otimes(X37,X36,X38),X38) ),
    inference(variable_rename,[status(thm)],[c_0_647]) ).

fof(c_0_1140,plain,
    ! [X32,X33] :
      ( ~ hBOOL(hAPP(X33,c_Divides_Odiv__class_Omod(X32,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)))
      | hBOOL(hAPP(X33,X32)) ),
    inference(variable_rename,[status(thm)],[c_0_648]) ).

fof(c_0_1141,plain,
    ! [X26,X27,X28] :
      ( c_HOL_Oord__class_Oless(X27,X26,tc_nat)
      | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X28),X27),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X28),X26),tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_649])])]) ).

fof(c_0_1142,plain,
    ! [X34,X35,X36,X37] :
      ( ~ class_OrderedGroup_Omonoid__mult(X37)
      | c_Power_Opower__class_Opower(X36,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X35),X34),X37) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X36,X35,X37),c_Power_Opower__class_Opower(X36,X34,X37),X37) ),
    inference(variable_rename,[status(thm)],[c_0_650]) ).

fof(c_0_1143,plain,
    ! [X62,X63,X64,X65] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X65)
      | c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X62,X64,X65),c_Power_Opower__class_Opower(X62,X63,X65),X65) = c_Power_Opower__class_Opower(X62,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X64),X63),X65) ),
    inference(variable_rename,[status(thm)],[c_0_651]) ).

fof(c_0_1144,plain,
    ! [X38,X39,X40,X41] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X41)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X41),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X41),X40),X39)),X38) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X41),X40),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X41),X39),X38)) ),
    inference(variable_rename,[status(thm)],[c_0_652]) ).

fof(c_0_1145,plain,
    ! [X45,X46,X47,X48] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X48)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X48),X47),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X48),X46),X45)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X48),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X48),X47),X46)),X45) ),
    inference(variable_rename,[status(thm)],[c_0_653]) ).

fof(c_0_1146,plain,
    ! [X38,X39,X40,X41] :
      ( ~ class_OrderedGroup_Oab__semigroup__add(X41)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X41),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X41),X40),X39)),X38) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X41),X40),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X41),X39),X38)) ),
    inference(variable_rename,[status(thm)],[c_0_654]) ).

fof(c_0_1147,plain,
    ! [X38,X39,X40,X41] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X41)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X41),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X41),X40),X39)),X38) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X41),X40),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X41),X39),X38)) ),
    inference(variable_rename,[status(thm)],[c_0_655]) ).

fof(c_0_1148,plain,
    ! [X37,X38,X39,X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X40)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X40),X39),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X40),X38),X37)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X40),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X40),X39),X38)),X37) ),
    inference(variable_rename,[status(thm)],[c_0_656]) ).

fof(c_0_1149,plain,
    ! [X38,X39,X40,X41] :
      ( ~ class_Divides_Osemiring__div(X41)
      | c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X39,X40,X41),X38,X41) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X39,X38,X41),X40,X41)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X40,X39,X41) ),
    inference(variable_rename,[status(thm)],[c_0_657]) ).

fof(c_0_1150,plain,
    ! [X26,X27,X28,X29] :
      ( ~ class_Divides_Osemiring__div(X29)
      | c_Ring__and__Field_Odvd__class_Odvd(X28,X27,X29)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X28,X26,X29)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X28,c_Divides_Odiv__class_Omod(X27,X26,X29),X29) ),
    inference(variable_rename,[status(thm)],[c_0_658]) ).

fof(c_0_1151,plain,
    ! [X26,X27,X28,X29] :
      ( ~ class_Divides_Osemiring__div(X29)
      | c_Ring__and__Field_Odvd__class_Odvd(X28,X27,X29)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X28,c_Divides_Odiv__class_Omod(X27,X26,X29),X29)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X28,X26,X29) ),
    inference(variable_rename,[status(thm)],[c_0_659]) ).

fof(c_0_1152,plain,
    ! [X26,X27,X28] :
      ( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X28,X27,tc_nat),c_HOL_Otimes__class_Otimes(X28,X26,tc_nat),tc_nat) = c_Divides_Odiv__class_Odiv(X27,X26,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X28,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_660]) ).

fof(c_0_1153,plain,
    ! [X58,X59,X60,X61] :
      ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X61),X59),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X60),X58),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X59,X58,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X61,X60,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_661]) ).

fof(c_0_1154,plain,
    ! [X54,X55,X56,X57] :
      ( c_List_Omap(X55,X54,X56,X57) != c_List_Olist_ONil(X57)
      | X54 = c_List_Olist_ONil(X56) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_662])])]) ).

fof(c_0_1155,plain,
    ! [X54,X55,X56,X57] :
      ( c_List_Olist_ONil(X57) != c_List_Omap(X55,X54,X56,X57)
      | X54 = c_List_Olist_ONil(X56) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_663])])]) ).

fof(c_0_1156,plain,
    ! [X37,X38,X39,X40,X41] :
      ( ~ class_OrderedGroup_Oab__group__add(X41)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X41),X39),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X41),X38),X37)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X41),X38),X40)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X41),X39),X37) = X40 ),
    inference(variable_rename,[status(thm)],[c_0_664]) ).

fof(c_0_1157,plain,
    ! [X34,X35,X36] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X36)
      | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X35,c_Suc(X34),X36),c_HOL_Oone__class_Oone(X36),X36)
      | ~ c_HOL_Oord__class_Oless(X35,c_HOL_Oone__class_Oone(X36),X36)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X36),X35,X36) ),
    inference(variable_rename,[status(thm)],[c_0_665]) ).

fof(c_0_1158,plain,
    ! [X30,X31,X32,X33] :
      ( c_Lambda_Obeta(hAPP(hAPP(hAPP(c_Lambda_Osubst,X32),X30),X33),hAPP(hAPP(hAPP(c_Lambda_Osubst,X31),X30),X33))
      | ~ c_Lambda_Obeta(X32,X31) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_666])])]) ).

fof(c_0_1159,plain,
    ! [X21,X22] :
      ( c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X22,X21,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X22,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X21,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_667]) ).

fof(c_0_1160,plain,
    ! [X26,X27,X28] :
      ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X28),X27,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X28),X26,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X27,X26,tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_668])])]) ).

fof(c_0_1161,plain,
    ! [X21,X22,X23] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X23)
      | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X23),c_HOL_Otimes__class_Otimes(X22,X21,X23),X23)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X23),X21,X23)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X23),X22,X23) ),
    inference(variable_rename,[status(thm)],[c_0_669]) ).

fof(c_0_1162,plain,
    ! [X36,X37,X38] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X38)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X38),c_HOL_Otimes__class_Otimes(X37,X36,X38),X38)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X38),X36,X38)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X38),X37,X38) ),
    inference(variable_rename,[status(thm)],[c_0_670]) ).

fof(c_0_1163,plain,
    ! [X36,X37,X38] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X38)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X38),c_HOL_Otimes__class_Otimes(X37,X36,X38),X38)
      | ~ c_HOL_Oord__class_Oless(X36,c_HOL_Ozero__class_Ozero(X38),X38)
      | ~ c_HOL_Oord__class_Oless(X37,c_HOL_Ozero__class_Ozero(X38),X38) ),
    inference(variable_rename,[status(thm)],[c_0_671]) ).

fof(c_0_1164,plain,
    ! [X36,X37,X38] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X38)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X36,X37,X38),c_HOL_Ozero__class_Ozero(X38),X38)
      | ~ c_HOL_Oord__class_Oless(X36,c_HOL_Ozero__class_Ozero(X38),X38)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X38),X37,X38) ),
    inference(variable_rename,[status(thm)],[c_0_672]) ).

fof(c_0_1165,plain,
    ! [X36,X37,X38] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X38)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X37,X36,X38),c_HOL_Ozero__class_Ozero(X38),X38)
      | ~ c_HOL_Oord__class_Oless(X36,c_HOL_Ozero__class_Ozero(X38),X38)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X38),X37,X38) ),
    inference(variable_rename,[status(thm)],[c_0_673]) ).

fof(c_0_1166,plain,
    ! [X36,X37,X38] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X38)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X37,X36,X38),c_HOL_Ozero__class_Ozero(X38),X38)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X38),X36,X38)
      | ~ c_HOL_Oord__class_Oless(X37,c_HOL_Ozero__class_Ozero(X38),X38) ),
    inference(variable_rename,[status(thm)],[c_0_674]) ).

fof(c_0_1167,plain,
    ! [X21,X22] :
      ( c_HOL_Oord__class_Oless(X21,c_HOL_Otimes__class_Otimes(X21,X22,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X22,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X21,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_675]) ).

fof(c_0_1168,plain,
    ! [X21,X22] :
      ( c_HOL_Oord__class_Oless(X21,c_HOL_Otimes__class_Otimes(X22,X21,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X22,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X21,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_676]) ).

fof(c_0_1169,plain,
    ! [X36,X37,X38] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X38)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X38),X37),X36),c_HOL_Ozero__class_Ozero(X38),X38)
      | ~ c_HOL_Oord__class_Oless(X36,c_HOL_Ozero__class_Ozero(X38),X38)
      | ~ c_HOL_Oord__class_Oless(X37,c_HOL_Ozero__class_Ozero(X38),X38) ),
    inference(variable_rename,[status(thm)],[c_0_677]) ).

fof(c_0_1170,plain,
    ! [X36,X37,X38] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X38)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X38),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X38),X37),X36),X38)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X38),X36,X38)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X38),X37,X38) ),
    inference(variable_rename,[status(thm)],[c_0_678]) ).

fof(c_0_1171,plain,
    ! [X38,X39,X40,X41] :
      ( ~ class_Ring__and__Field_Oidom(X41)
      | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X40,X38,X41),c_HOL_Otimes__class_Otimes(X39,X38,X41),X41)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X40,X39,X41) ),
    inference(variable_rename,[status(thm)],[c_0_679]) ).

fof(c_0_1172,plain,
    ! [X38,X39,X40,X41] :
      ( ~ class_Ring__and__Field_Oidom(X41)
      | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X38,X40,X41),c_HOL_Otimes__class_Otimes(X38,X39,X41),X41)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X40,X39,X41) ),
    inference(variable_rename,[status(thm)],[c_0_680]) ).

fof(c_0_1173,plain,
    ! [X21,X22,X23,X24] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X24)
      | c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(X22,X23,X24),c_Power_Opower__class_Opower(X21,X23,X24),X24)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X22,X21,X24) ),
    inference(variable_rename,[status(thm)],[c_0_681]) ).

fof(c_0_1174,plain,
    ! [X34,X35,X36] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X36)
      | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X36),c_Power_Opower__class_Opower(X35,X34,X36),X36)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X34,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X36),X35,X36) ),
    inference(variable_rename,[status(thm)],[c_0_682]) ).

fof(c_0_1175,plain,
    ! [X37,X38,X39] :
      ( ~ c_Ring__and__Field_Odvd__class_Odvd(X37,X39,tc_nat)
      | c_Ring__and__Field_Odvd__class_Odvd(X37,X38,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X38,X37,tc_nat)
      | c_Ring__and__Field_Odvd__class_Odvd(X38,X39,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X39,X38,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_683]) ).

fof(c_0_1176,plain,
    ! [X26,X27] :
      ( c_Divides_Odiv__class_Omod(c_Suc(c_HOL_Otimes__class_Otimes(X27,X26,tc_nat)),X27,tc_nat) = c_HOL_Oone__class_Oone(tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X27,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_684]) ).

fof(c_0_1177,plain,
    ! [X38,X39,X40,X41] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X41)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X41),X40),X38),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X41),X39),X38),X41)
      | ~ c_HOL_Oord__class_Oless(X40,X39,X41) ),
    inference(variable_rename,[status(thm)],[c_0_685]) ).

fof(c_0_1178,plain,
    ! [X38,X39,X40,X41] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X41)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X41),X40),X38),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X41),X39),X38),X41)
      | ~ c_HOL_Oord__class_Oless(X40,X39,X41) ),
    inference(variable_rename,[status(thm)],[c_0_686]) ).

fof(c_0_1179,plain,
    ! [X38,X39,X40,X41] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X41)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X41),X38),X40),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X41),X38),X39),X41)
      | ~ c_HOL_Oord__class_Oless(X40,X39,X41) ),
    inference(variable_rename,[status(thm)],[c_0_687]) ).

fof(c_0_1180,plain,
    ! [X38,X39,X40,X41] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X41)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X41),X38),X40),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X41),X38),X39),X41)
      | ~ c_HOL_Oord__class_Oless(X40,X39,X41) ),
    inference(variable_rename,[status(thm)],[c_0_688]) ).

fof(c_0_1181,plain,
    ! [X38,X39,X40,X41] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X41)
      | c_HOL_Oord__class_Oless(X39,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X41),X40),X38),X41)
      | ~ c_HOL_Oord__class_Oless(X39,X38,X41)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X41),X40,X41) ),
    inference(variable_rename,[status(thm)],[c_0_689]) ).

fof(c_0_1182,plain,
    ! [X26,X27,X28] :
      ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X28,X27,tc_nat),c_HOL_Otimes__class_Otimes(X28,X26,tc_nat),tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X27,X26,tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_690])])]) ).

fof(c_0_1183,plain,
    ! [X21,X22] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X21,tc_nat)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X22,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X21),tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_691])])]) ).

fof(c_0_1184,plain,
    ! [X26,X27,X28,X29] :
      ( ~ class_Divides_Osemiring__div(X29)
      | c_Ring__and__Field_Odvd__class_Odvd(X28,c_Divides_Odiv__class_Omod(X27,X26,X29),X29)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X28,X27,X29)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X28,X26,X29) ),
    inference(variable_rename,[status(thm)],[c_0_692]) ).

fof(c_0_1185,plain,
    ! [X26,X27,X28,X29] :
      ( ~ class_Divides_Osemiring__div(X29)
      | c_Ring__and__Field_Odvd__class_Odvd(X28,c_Divides_Odiv__class_Omod(X27,X26,X29),X29)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X28,X26,X29)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X28,X27,X29) ),
    inference(variable_rename,[status(thm)],[c_0_693]) ).

fof(c_0_1186,plain,
    ! [X21,X22] :
      ( X21 = c_HOL_Oone__class_Oone(tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X22,X21,tc_nat),X22,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X22,tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_694])])]) ).

fof(c_0_1187,plain,
    ! [X21,X22] :
      ( X21 = c_HOL_Oone__class_Oone(tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X21,X22,tc_nat),X22,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X22,tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_695])])]) ).

fof(c_0_1188,plain,
    ! [X21,X22] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X22,X21,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X21,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X22,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_696]) ).

fof(c_0_1189,plain,
    ! [X38,X39,X40,X41] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X41)
      | c_Ring__and__Field_Odvd__class_Odvd(X40,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X41),X39),X38),X41)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X40,X38,X41)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X40,X39,X41) ),
    inference(variable_rename,[status(thm)],[c_0_697]) ).

fof(c_0_1190,plain,
    ! [X38,X39,X40,X41] :
      ( ~ class_Divides_Osemiring__div(X41)
      | c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X38,X40,X41),c_HOL_Otimes__class_Otimes(X38,X39,X41),X41) = c_Divides_Odiv__class_Odiv(X40,X39,X41)
      | X38 = c_HOL_Ozero__class_Ozero(X41) ),
    inference(variable_rename,[status(thm)],[c_0_698]) ).

fof(c_0_1191,plain,
    ! [X38,X39,X40,X41] :
      ( ~ class_Divides_Osemiring__div(X41)
      | c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X40,X38,X41),c_HOL_Otimes__class_Otimes(X39,X38,X41),X41) = c_Divides_Odiv__class_Odiv(X40,X39,X41)
      | X38 = c_HOL_Ozero__class_Ozero(X41) ),
    inference(variable_rename,[status(thm)],[c_0_699]) ).

fof(c_0_1192,plain,
    ! [X34,X35,X36] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X36)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X36),X34),c_HOL_Otimes__class_Otimes(X35,X34,X36)) = c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X36),X35),c_HOL_Oone__class_Oone(X36)),X34,X36) ),
    inference(variable_rename,[status(thm)],[c_0_700]) ).

fof(c_0_1193,plain,
    ! [X21,X22] :
      ( c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Odiv(X22,X21,tc_nat),X22,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X22,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X21,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_701]) ).

fof(c_0_1194,plain,
    ! [X34,X35,X36] :
      ( ~ class_OrderedGroup_Omonoid__mult(X36)
      | c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X35,X34,X36),X35,X36) = c_HOL_Otimes__class_Otimes(X35,c_Power_Opower__class_Opower(X35,X34,X36),X36) ),
    inference(variable_rename,[status(thm)],[c_0_702]) ).

fof(c_0_1195,plain,
    ! [X38,X39,X40,X41] :
      ( ~ class_OrderedGroup_Oab__semigroup__mult(X41)
      | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X40,X39,X41),X38,X41) = c_HOL_Otimes__class_Otimes(X40,c_HOL_Otimes__class_Otimes(X39,X38,X41),X41) ),
    inference(variable_rename,[status(thm)],[c_0_703]) ).

fof(c_0_1196,plain,
    ! [X42,X43,X44,X45] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X45)
      | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X44,X43,X45),X42,X45) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X44,X42,X45),X43,X45) ),
    inference(variable_rename,[status(thm)],[c_0_704]) ).

fof(c_0_1197,plain,
    ! [X42,X43,X44,X45] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X45)
      | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X44,X43,X45),X42,X45) = c_HOL_Otimes__class_Otimes(X44,c_HOL_Otimes__class_Otimes(X43,X42,X45),X45) ),
    inference(variable_rename,[status(thm)],[c_0_705]) ).

fof(c_0_1198,plain,
    ! [X41,X42,X43,X44] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X44)
      | c_HOL_Otimes__class_Otimes(X43,c_HOL_Otimes__class_Otimes(X42,X41,X44),X44) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X43,X42,X44),X41,X44) ),
    inference(variable_rename,[status(thm)],[c_0_706]) ).

fof(c_0_1199,plain,
    ! [X41,X42,X43,X44] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X44)
      | c_HOL_Otimes__class_Otimes(X43,c_HOL_Otimes__class_Otimes(X42,X41,X44),X44) = c_HOL_Otimes__class_Otimes(X42,c_HOL_Otimes__class_Otimes(X43,X41,X44),X44) ),
    inference(variable_rename,[status(thm)],[c_0_707]) ).

fof(c_0_1200,plain,
    ! [X37,X38,X39,X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X40)
      | c_HOL_Otimes__class_Otimes(X39,c_HOL_Otimes__class_Otimes(X38,X37,X40),X40) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X39,X38,X40),X37,X40) ),
    inference(variable_rename,[status(thm)],[c_0_708]) ).

fof(c_0_1201,plain,
    ! [X37,X38,X39] :
      ( c_Ring__and__Field_Odvd__class_Odvd(X39,X37,tc_nat)
      | c_Ring__and__Field_Odvd__class_Odvd(X37,X38,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X38,X37,tc_nat)
      | c_Ring__and__Field_Odvd__class_Odvd(X38,X39,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X39,X38,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_709]) ).

fof(c_0_1202,plain,
    ! [X62,X63,X64,X65] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X65)
      | c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(X62,X64,X65),X63,X65) = c_Power_Opower__class_Opower(X62,c_HOL_Otimes__class_Otimes(X64,X63,tc_nat),X65) ),
    inference(variable_rename,[status(thm)],[c_0_710]) ).

fof(c_0_1203,plain,
    ! [X34,X35,X36,X37] :
      ( ~ class_OrderedGroup_Omonoid__mult(X37)
      | c_Power_Opower__class_Opower(X36,c_HOL_Otimes__class_Otimes(X35,X34,tc_nat),X37) = c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(X36,X35,X37),X34,X37) ),
    inference(variable_rename,[status(thm)],[c_0_711]) ).

fof(c_0_1204,plain,
    ! [X34,X35] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X35)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X35),X34,X35)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X35),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X35),X34),X34),X35) ),
    inference(variable_rename,[status(thm)],[c_0_712]) ).

fof(c_0_1205,plain,
    ! [X34,X35] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X35)
      | c_HOL_Oord__class_Oless(X34,c_HOL_Ozero__class_Ozero(X35),X35)
      | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X35),X34),X34),c_HOL_Ozero__class_Ozero(X35),X35) ),
    inference(variable_rename,[status(thm)],[c_0_713]) ).

fof(c_0_1206,plain,
    ! [X34,X35] :
      ( ~ class_Ring__and__Field_Oordered__idom(X35)
      | c_HOL_Oord__class_Oless(X34,c_HOL_Ozero__class_Ozero(X35),X35)
      | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X35),X34),X34),c_HOL_Ozero__class_Ozero(X35),X35) ),
    inference(variable_rename,[status(thm)],[c_0_714]) ).

fof(c_0_1207,plain,
    ! [X26,X27,X28] :
      ( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X28,X27,tc_nat),c_HOL_Otimes__class_Otimes(X28,X26,tc_nat),tc_nat) = c_Divides_Odiv__class_Odiv(X27,X26,tc_nat)
      | X28 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_715]) ).

fof(c_0_1208,plain,
    ! [X28,X29,X30] :
      ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X30),X28),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X29),X28),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X30,X29,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_716]) ).

fof(c_0_1209,plain,
    ! [X26,X27,X28] :
      ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X28),X27),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X28),X26),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X27,X26,tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_717])])]) ).

fof(c_0_1210,plain,
    ! [X38,X39,X40,X41] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X41)
      | c_Ring__and__Field_Odvd__class_Odvd(X39,X38,X41)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X40,X39,X41),X38,X41) ),
    inference(variable_rename,[status(thm)],[c_0_718]) ).

fof(c_0_1211,plain,
    ! [X38,X39,X40,X41] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X41)
      | c_Ring__and__Field_Odvd__class_Odvd(X40,X38,X41)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X40,X39,X41),X38,X41) ),
    inference(variable_rename,[status(thm)],[c_0_719]) ).

fof(c_0_1212,plain,
    ! [X45,X46,X47,X48] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X48)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X48),X47),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X48),X46),X45)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X48),X46),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X48),X47),X45)) ),
    inference(variable_rename,[status(thm)],[c_0_720]) ).

fof(c_0_1213,plain,
    ! [X38,X39,X40,X41] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X41)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X41),X40),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X41),X39),X38)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X41),X39),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X41),X40),X38)) ),
    inference(variable_rename,[status(thm)],[c_0_721]) ).

fof(c_0_1214,plain,
    ! [X37,X38,X39,X40] :
      ( ~ class_OrderedGroup_Oab__group__add(X40)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X40),X39),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X40),X38),X37)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X40),X38),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X40),X39),X37)) ),
    inference(variable_rename,[status(thm)],[c_0_722]) ).

fof(c_0_1215,plain,
    ! [X21,X22] :
      ( X22 = c_HOL_Ozero__class_Ozero(tc_nat)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X21,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Power_Opower__class_Opower(X21,X22,tc_nat),tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_723]) ).

fof(c_0_1216,plain,
    ! [X38,X39,X40,X41] :
      ( ~ class_Divides_Osemiring__div(X41)
      | c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X40,X39,X41),X38,X41) = c_Divides_Odiv__class_Omod(X40,X38,X41)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X38,X39,X41) ),
    inference(variable_rename,[status(thm)],[c_0_724]) ).

fof(c_0_1217,plain,
    ! [X21,X22] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X21,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X22,X21,tc_nat),tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_725])])]) ).

fof(c_0_1218,plain,
    ! [X21,X22] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X22,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X22,X21,tc_nat),tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_726]) ).

fof(c_0_1219,plain,
    ! [X32,X33] :
      ( hBOOL(hAPP(X33,c_Divides_Odiv__class_Odiv(X32,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)))
      | ~ hBOOL(hAPP(X33,c_HOL_Ozero__class_Ozero(tc_nat))) ),
    inference(variable_rename,[status(thm)],[c_0_727]) ).

fof(c_0_1220,plain,
    ! [X32,X33] :
      ( ~ hBOOL(hAPP(X33,c_HOL_Ozero__class_Ozero(tc_nat)))
      | hBOOL(hAPP(X33,c_Divides_Odiv__class_Odiv(X32,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))) ),
    inference(variable_rename,[status(thm)],[c_0_728]) ).

fof(c_0_1221,plain,
    ! [X37,X38,X39] :
      ( ~ c_Ring__and__Field_Odvd__class_Odvd(X37,X39,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X38,X37,tc_nat)
      | c_Ring__and__Field_Odvd__class_Odvd(X38,X39,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X39,X38,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_729]) ).

fof(c_0_1222,plain,
    ! [X37,X38,X39] :
      ( ~ c_Ring__and__Field_Odvd__class_Odvd(X37,X39,tc_nat)
      | c_Ring__and__Field_Odvd__class_Odvd(X37,X38,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X38,X37,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X39,X38,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_730]) ).

fof(c_0_1223,plain,
    ! [X36,X37,X38] :
      ( ~ class_Divides_Osemiring__div(X38)
      | c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X38),X37,X38),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X38),X36,X38),X38) = c_HOL_Ozero__class_Ozero(X38) ),
    inference(variable_rename,[status(thm)],[c_0_731]) ).

fof(c_0_1224,plain,
    ! [X36,X37,X38] :
      ( ~ class_Ring__and__Field_Oidom(X38)
      | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X37,c_HOL_Ozero__class_Ozero(X38),X38),c_HOL_Otimes__class_Otimes(X36,c_HOL_Ozero__class_Ozero(X38),X38),X38) ),
    inference(variable_rename,[status(thm)],[c_0_732]) ).

fof(c_0_1225,plain,
    ! [X36,X37,X38] :
      ( ~ class_Ring__and__Field_Oidom(X38)
      | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X38),X37,X38),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X38),X36,X38),X38) ),
    inference(variable_rename,[status(thm)],[c_0_733]) ).

fof(c_0_1226,plain,
    ! [X32,X33] :
      ( ~ hBOOL(hAPP(X33,X32))
      | hBOOL(hAPP(X33,c_Divides_Odiv__class_Omod(X32,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))) ),
    inference(variable_rename,[status(thm)],[c_0_734]) ).

fof(c_0_1227,plain,
    ! [X34,X35,X36] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X36)
      | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X36),c_Power_Opower__class_Opower(X35,c_Suc(X34),X36),X36)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X36),X35,X36) ),
    inference(variable_rename,[status(thm)],[c_0_735]) ).

fof(c_0_1228,plain,
    ! [X58,X59,X60,X61] :
      ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X59),X60) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X61),X58)
      | ~ c_HOL_Oord__class_Oless(X61,X60,tc_nat)
      | c_HOL_Oord__class_Oless(X59,X58,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_736]) ).

fof(c_0_1229,plain,
    ! [X28,X29,X30] :
      ( c_HOL_Oord__class_Oless(X30,X28,tc_nat)
      | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X30),X29),X28,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_737]) ).

fof(c_0_1230,plain,
    ! [X26,X27] :
      ( c_Ring__and__Field_Odvd__class_Odvd(X27,X26,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X27,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X26),X27),tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_738]) ).

fof(c_0_1231,plain,
    ! [X34,X35,X36,X37] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X37)
      | c_Power_Opower__class_Opower(X36,X35,X37) != c_Power_Opower__class_Opower(X36,X34,X37)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X37),X36,X37)
      | X35 = X34 ),
    inference(variable_rename,[status(thm)],[c_0_739]) ).

fof(c_0_1232,plain,
    ! [X21,X22] :
      ( c_Divides_Odiv__class_Omod(c_Suc(X22),X21,tc_nat) = c_Suc(c_Divides_Odiv__class_Omod(X22,X21,tc_nat))
      | c_Suc(c_Divides_Odiv__class_Omod(X22,X21,tc_nat)) = X21 ),
    inference(variable_rename,[status(thm)],[c_0_740]) ).

fof(c_0_1233,plain,
    ! [X37,X38,X39] :
      ( c_Ring__and__Field_Odvd__class_Odvd(X39,X37,tc_nat)
      | c_Ring__and__Field_Odvd__class_Odvd(X37,X38,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X38,X37,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X39,X38,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_741]) ).

fof(c_0_1234,plain,
    ! [X37,X38,X39] :
      ( c_Ring__and__Field_Odvd__class_Odvd(X39,X37,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X38,X37,tc_nat)
      | c_Ring__and__Field_Odvd__class_Odvd(X38,X39,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X39,X38,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_742]) ).

fof(c_0_1235,plain,
    ! [X34,X35] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X35)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X34,X34,X35),c_HOL_Ozero__class_Ozero(X35),X35) ),
    inference(variable_rename,[status(thm)],[c_0_743]) ).

fof(c_0_1236,plain,
    ! [X34,X35,X36] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X36)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X36),c_Power_Opower__class_Opower(X35,X34,X36),X36)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X36),X35,X36) ),
    inference(variable_rename,[status(thm)],[c_0_744]) ).

fof(c_0_1237,plain,
    ! [X34,X35] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X35)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X35),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X35),X34),X34),X35)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X35),X34,X35) ),
    inference(variable_rename,[status(thm)],[c_0_745]) ).

fof(c_0_1238,plain,
    ! [X34,X35] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X35)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X35),X34),X34),c_HOL_Ozero__class_Ozero(X35),X35)
      | ~ c_HOL_Oord__class_Oless(X34,c_HOL_Ozero__class_Ozero(X35),X35) ),
    inference(variable_rename,[status(thm)],[c_0_746]) ).

fof(c_0_1239,plain,
    ! [X34,X35] :
      ( ~ class_Ring__and__Field_Oordered__idom(X35)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X35),X34),X34),c_HOL_Ozero__class_Ozero(X35),X35)
      | ~ c_HOL_Oord__class_Oless(X34,c_HOL_Ozero__class_Ozero(X35),X35) ),
    inference(variable_rename,[status(thm)],[c_0_747]) ).

fof(c_0_1240,plain,
    ! [X26,X27,X28] :
      ( c_HOL_Otimes__class_Otimes(X28,X27,tc_nat) != c_HOL_Otimes__class_Otimes(X28,X26,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X28,tc_nat)
      | X27 = X26 ),
    inference(variable_rename,[status(thm)],[c_0_748]) ).

fof(c_0_1241,plain,
    ! [X21,X22,X23] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X23)
      | c_Ring__and__Field_Odvd__class_Odvd(X21,c_Power_Opower__class_Opower(X21,X22,X23),X23)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X22,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_749]) ).

fof(c_0_1242,plain,
    ! [X21,X22] :
      ( ~ c_Ring__and__Field_Odvd__class_Odvd(X21,X22,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X22,X21,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X22,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_750]) ).

fof(c_0_1243,plain,
    ! [X36,X37,X38] :
      ( ~ class_Divides_Osemiring__div(X38)
      | c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X36,X37,X38),X37,X38) = X36
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X37,X36,X38) ),
    inference(variable_rename,[status(thm)],[c_0_751]) ).

fof(c_0_1244,plain,
    ! [X36,X37,X38] :
      ( ~ class_Divides_Osemiring__div(X38)
      | c_HOL_Otimes__class_Otimes(X37,c_Divides_Odiv__class_Odiv(X36,X37,X38),X38) = X36
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X37,X36,X38) ),
    inference(variable_rename,[status(thm)],[c_0_752]) ).

fof(c_0_1245,plain,
    ! [X38,X39,X40,X41] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X41)
      | c_Ring__and__Field_Odvd__class_Odvd(X40,c_HOL_Otimes__class_Otimes(X39,X38,X41),X41)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X40,X39,X41) ),
    inference(variable_rename,[status(thm)],[c_0_753]) ).

fof(c_0_1246,plain,
    ! [X38,X39,X40,X41] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X41)
      | c_Ring__and__Field_Odvd__class_Odvd(X40,c_HOL_Otimes__class_Otimes(X39,X38,X41),X41)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X40,X38,X41) ),
    inference(variable_rename,[status(thm)],[c_0_754]) ).

fof(c_0_1247,plain,
    ! [X15,X16] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X16)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X16),X15),X15) = c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X16),c_HOL_Oone__class_Oone(X16)),c_HOL_Oone__class_Oone(X16)),X15,X16) ),
    inference(variable_rename,[status(thm)],[c_0_755]) ).

fof(c_0_1248,plain,
    ! [X15] :
      ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X15,tc_nat)
      | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X15,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X15,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_756]) ).

fof(c_0_1249,plain,
    ! [X15] :
      ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X15,tc_nat)
      | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),X15,tc_nat),X15,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_757]) ).

fof(c_0_1250,plain,
    ! [X21,X22] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Power_Opower__class_Opower(X21,X22,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X21,tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_758])])]) ).

fof(c_0_1251,plain,
    ! [X21,X22] :
      ( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X22,X21,tc_nat),X21,tc_nat) = X22
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X21,tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_759])])]) ).

fof(c_0_1252,plain,
    ! [X21,X22] :
      ( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X21,X22,tc_nat),X21,tc_nat) = X22
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X21,tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_760])])]) ).

fof(c_0_1253,plain,
    ! [X21,X22] :
      ( c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Omod(X22,X21,tc_nat),X21,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X21,tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_761])])]) ).

fof(c_0_1254,plain,
    ! [X21,X22,X23] :
      ( ~ class_Ring__and__Field_Osemiring__1(X23)
      | c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X21),X23) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X23),c_Nat_Osemiring__1__class_Oof__nat(X22,X23)),c_Nat_Osemiring__1__class_Oof__nat(X21,X23)) ),
    inference(variable_rename,[status(thm)],[c_0_762]) ).

fof(c_0_1255,plain,
    ! [X21,X22] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X21),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X21,tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_763])])]) ).

fof(c_0_1256,plain,
    ! [X21,X22] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X21),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X22,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_764]) ).

fof(c_0_1257,plain,
    ! [X37,X38,X39,X40] :
      ( ~ class_Orderings_Oorder(X40)
      | c_HOL_Oord__class_Oless(X37,X39,X40)
      | ~ c_HOL_Oord__class_Oless(X37,X38,X40)
      | ~ c_HOL_Oord__class_Oless(X38,X39,X40) ),
    inference(variable_rename,[status(thm)],[c_0_765]) ).

fof(c_0_1258,plain,
    ! [X37,X38,X39,X40] :
      ( ~ class_Orderings_Opreorder(X40)
      | c_HOL_Oord__class_Oless(X39,X37,X40)
      | ~ c_HOL_Oord__class_Oless(X38,X37,X40)
      | ~ c_HOL_Oord__class_Oless(X39,X38,X40) ),
    inference(variable_rename,[status(thm)],[c_0_766]) ).

fof(c_0_1259,plain,
    ! [X38,X39,X40,X41] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X41)
      | c_Ring__and__Field_Odvd__class_Odvd(X40,X38,X41)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X39,X38,X41)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X40,X39,X41) ),
    inference(variable_rename,[status(thm)],[c_0_767]) ).

fof(c_0_1260,plain,
    ! [X21,X22] :
      ( c_Suc(c_Divides_Odiv__class_Omod(X22,X21,tc_nat)) != X21
      | c_Divides_Odiv__class_Omod(c_Suc(X22),X21,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_768]) ).

fof(c_0_1261,plain,
    ! [X21,X22,X23] :
      ( ~ class_Ring__and__Field_Osemiring__1(X23)
      | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Otimes__class_Otimes(X22,X21,tc_nat),X23) = c_HOL_Otimes__class_Otimes(c_Nat_Osemiring__1__class_Oof__nat(X22,X23),c_Nat_Osemiring__1__class_Oof__nat(X21,X23),X23) ),
    inference(variable_rename,[status(thm)],[c_0_769]) ).

fof(c_0_1262,plain,
    ! [X43,X44,X45] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X45)
      | c_Power_Opower__class_Opower(X43,c_Suc(X44),X45) = c_HOL_Otimes__class_Otimes(X43,c_Power_Opower__class_Opower(X43,X44,X45),X45) ),
    inference(variable_rename,[status(thm)],[c_0_770]) ).

fof(c_0_1263,plain,
    ! [X21,X22,X23] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X23)
      | c_Power_Opower__class_Opower(X21,c_Suc(X22),X23) = c_HOL_Otimes__class_Otimes(X21,c_Power_Opower__class_Opower(X21,X22,X23),X23) ),
    inference(variable_rename,[status(thm)],[c_0_771]) ).

fof(c_0_1264,plain,
    ! [X34,X35,X36] :
      ( ~ class_Power_Opower(X36)
      | c_Power_Opower__class_Opower(X35,c_Suc(X34),X36) = c_HOL_Otimes__class_Otimes(X35,c_Power_Opower__class_Opower(X35,X34,X36),X36) ),
    inference(variable_rename,[status(thm)],[c_0_772]) ).

fof(c_0_1265,plain,
    ! [X34,X35,X36] :
      ( ~ class_OrderedGroup_Omonoid__mult(X36)
      | c_Power_Opower__class_Opower(X35,c_Suc(X34),X36) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X35,X34,X36),X35,X36) ),
    inference(variable_rename,[status(thm)],[c_0_773]) ).

fof(c_0_1266,plain,
    ! [X43,X44,X45] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X45)
      | c_HOL_Otimes__class_Otimes(X43,c_Power_Opower__class_Opower(X43,X44,X45),X45) = c_Power_Opower__class_Opower(X43,c_Suc(X44),X45) ),
    inference(variable_rename,[status(thm)],[c_0_774]) ).

fof(c_0_1267,plain,
    ! [X43,X44,X45] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X45)
      | c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X43,X44,X45),X43,X45) = c_Power_Opower__class_Opower(X43,c_Suc(X44),X45) ),
    inference(variable_rename,[status(thm)],[c_0_775]) ).

fof(c_0_1268,plain,
    ! [X21,X22,X23] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X23)
      | c_HOL_Oord__class_Oless(X22,X21,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X22,X23),c_Nat_Osemiring__1__class_Oof__nat(X21,X23),X23) ),
    inference(variable_rename,[status(thm)],[c_0_776]) ).

fof(c_0_1269,plain,
    ! [X21,X22] :
      ( c_Divides_Odiv__class_Odiv(X22,X21,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
      | ~ c_HOL_Oord__class_Oless(X22,X21,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X21,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_777]) ).

fof(c_0_1270,plain,
    ! [X37,X38,X39] :
      ( c_HOL_Oord__class_Oless(X39,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X38),X37),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X39,X38,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_778]) ).

fof(c_0_1271,plain,
    ! [X37,X38,X39] :
      ( c_HOL_Oord__class_Oless(X39,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X38),X37),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X39,X37,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_779]) ).

fof(c_0_1272,plain,
    ! [X28,X29,X30] :
      ( c_HOL_Oord__class_Oless(X30,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X29),X28),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X30,X29,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_780]) ).

fof(c_0_1273,plain,
    ! [X28,X29,X30] :
      ( c_HOL_Oord__class_Oless(X30,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X28),X29),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X30,X29,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_781]) ).

fof(c_0_1274,plain,
    ! [X26,X27] :
      ( c_Ring__and__Field_Odvd__class_Odvd(X27,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X26),X27),tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X27,X26,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_782]) ).

fof(c_0_1275,plain,
    ! [X28,X29,X30] :
      ( c_HOL_Oord__class_Oless(c_Suc(X30),X28,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X29,X28,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X30,X29,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_783]) ).

fof(c_0_1276,plain,
    ! [X36,X37,X38] :
      ( ~ class_Divides_Osemiring__div(X38)
      | c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X37,X36,X38),X36,X38) = c_Divides_Odiv__class_Omod(X37,X36,X38) ),
    inference(variable_rename,[status(thm)],[c_0_784]) ).

fof(c_0_1277,plain,
    ! [X11,X12,X13] :
      ( ~ class_OrderedGroup_Oab__semigroup__idem__mult(X13)
      | c_HOL_Otimes__class_Otimes(X12,c_HOL_Otimes__class_Otimes(X12,X11,X13),X13) = c_HOL_Otimes__class_Otimes(X12,X11,X13) ),
    inference(variable_rename,[status(thm)],[c_0_785]) ).

fof(c_0_1278,plain,
    ! [X37,X38,X39] :
      ( c_Ring__and__Field_Odvd__class_Odvd(X39,X37,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X38,X37,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X39,X38,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_786]) ).

fof(c_0_1279,plain,
    ! [X36,X37,X38] :
      ( ~ class_Divides_Osemiring__div(X38)
      | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X38),X37),X36),X36,X38) = c_Divides_Odiv__class_Omod(X37,X36,X38) ),
    inference(variable_rename,[status(thm)],[c_0_787]) ).

fof(c_0_1280,plain,
    ! [X36,X37,X38] :
      ( ~ class_Divides_Osemiring__div(X38)
      | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X38),X36),X37),X36,X38) = c_Divides_Odiv__class_Omod(X37,X36,X38) ),
    inference(variable_rename,[status(thm)],[c_0_788]) ).

fof(c_0_1281,plain,
    ! [X30,X31] :
      ( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_Olift,X30),X31)))
      | ~ hBOOL(hAPP(c_InductTermi_OIT,X30)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_789])])]) ).

fof(c_0_1282,plain,
    ! [X4] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X4)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),c_HOL_Oone__class_Oone(X4)),c_HOL_Oone__class_Oone(X4)),X4) ),
    inference(variable_rename,[status(thm)],[c_0_790]) ).

fof(c_0_1283,plain,
    ! [X21,X22,X23] :
      ( ~ class_Ring__and__Field_Osemiring__1(X23)
      | c_Nat_Osemiring__1__class_Oof__nat(c_Power_Opower__class_Opower(X22,X21,tc_nat),X23) = c_Power_Opower__class_Opower(c_Nat_Osemiring__1__class_Oof__nat(X22,X23),X21,X23) ),
    inference(variable_rename,[status(thm)],[c_0_791]) ).

fof(c_0_1284,plain,
    ! [X26,X27] :
      ( hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(X27)),X26) = c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X27),c_HOL_Oone__class_Oone(tc_nat)))
      | c_HOL_Oord__class_Oless(X27,X26,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_792]) ).

fof(c_0_1285,plain,
    ! [X21,X22] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X22)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X21,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X22),c_Nat_Osemiring__1__class_Oof__nat(X21,X22),X22) ),
    inference(variable_rename,[status(thm)],[c_0_793]) ).

fof(c_0_1286,plain,
    ! [X28,X29,X30] :
      ( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X29)),X28),X30) = c_Lambda_OdB_OVar(X29)
      | ~ c_HOL_Oord__class_Oless(X29,X30,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_794]) ).

fof(c_0_1287,plain,
    ! [X21,X22,X23] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X23)
      | c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X22,X23),c_Nat_Osemiring__1__class_Oof__nat(X21,X23),X23)
      | ~ c_HOL_Oord__class_Oless(X22,X21,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_795]) ).

fof(c_0_1288,plain,
    ! [X32,X33] :
      ( hBOOL(hAPP(X33,X32))
      | ~ hBOOL(hAPP(X33,c_Suc(v_sko__List__Xlexn__Xinduct__1(X33))))
      | ~ hBOOL(hAPP(X33,c_HOL_Ozero__class_Ozero(tc_nat))) ),
    inference(variable_rename,[status(thm)],[c_0_796]) ).

fof(c_0_1289,plain,
    ! [X32,X33] :
      ( hBOOL(hAPP(X33,X32))
      | ~ hBOOL(hAPP(X33,c_Suc(c_ATP__Linkup_Osko__Nat__Xnat__induct__1__1(X33))))
      | ~ hBOOL(hAPP(X33,c_HOL_Ozero__class_Ozero(tc_nat))) ),
    inference(variable_rename,[status(thm)],[c_0_797]) ).

fof(c_0_1290,plain,
    ! [X32,X33] :
      ( hBOOL(hAPP(X33,X32))
      | ~ hBOOL(hAPP(X33,c_Suc(v_sko__List__Xreplicate__Xinduct__1(X33))))
      | ~ hBOOL(hAPP(X33,c_HOL_Ozero__class_Ozero(tc_nat))) ),
    inference(variable_rename,[status(thm)],[c_0_798]) ).

fof(c_0_1291,plain,
    ! [X32,X33] :
      ( hBOOL(hAPP(X33,X32))
      | ~ hBOOL(hAPP(X33,c_Suc(v_sko__List__Xupt__Xinduct__1(X33))))
      | ~ hBOOL(hAPP(X33,c_HOL_Ozero__class_Ozero(tc_nat))) ),
    inference(variable_rename,[status(thm)],[c_0_799]) ).

fof(c_0_1292,plain,
    ! [X32,X33] :
      ( hBOOL(hAPP(X33,X32))
      | ~ hBOOL(hAPP(X33,c_Suc(v_sko__Nat__Xnat__Xinduct__1(X33))))
      | ~ hBOOL(hAPP(X33,c_HOL_Ozero__class_Ozero(tc_nat))) ),
    inference(variable_rename,[status(thm)],[c_0_800]) ).

fof(c_0_1293,plain,
    ! [X32,X33] :
      ( hBOOL(hAPP(X33,X32))
      | ~ hBOOL(hAPP(X33,c_Suc(v_sko__Nat__Xnat__Xinducts__1(X33))))
      | ~ hBOOL(hAPP(X33,c_HOL_Ozero__class_Ozero(tc_nat))) ),
    inference(variable_rename,[status(thm)],[c_0_801]) ).

fof(c_0_1294,plain,
    ! [X32,X33,X34] :
      ( hBOOL(hAPP(hAPP(X34,X32),X33))
      | c_HOL_Oord__class_Oless(X32,X33,tc_nat)
      | X33 = X32
      | c_HOL_Oord__class_Oless(X33,X32,tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_802])])]) ).

fof(c_0_1295,plain,
    ! [X26,X27,X28] :
      ( c_HOL_Otimes__class_Otimes(c_Suc(X28),X27,tc_nat) != c_HOL_Otimes__class_Otimes(c_Suc(X28),X26,tc_nat)
      | X27 = X26 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_803])])]) ).

fof(c_0_1296,plain,
    ! [X21,X22] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X22)
      | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(X22),c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X22),X21,X22),X22) ),
    inference(variable_rename,[status(thm)],[c_0_804]) ).

fof(c_0_1297,plain,
    ! [X21,X22] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X22)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X22),c_Nat_Osemiring__1__class_Oof__nat(X21,X22),X22)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X21,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_805]) ).

fof(c_0_1298,plain,
    ! [X37,X38,X39,X40] :
      ( ~ class_Ring__and__Field_Oidom(X40)
      | ~ class_Int_Onumber__ring(X40)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X40),X39),X38) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X40),X39),X37)
      | X38 = X37 ),
    inference(variable_rename,[status(thm)],[c_0_806]) ).

fof(c_0_1299,plain,
    ! [X22,X23,X24] :
      ( c_Lambda_Obeta(hAPP(hAPP(c_Lambda_Olift,X23),X24),hAPP(hAPP(c_Lambda_Olift,X22),X24))
      | ~ c_Lambda_Obeta(X23,X22) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_807])])]) ).

fof(c_0_1300,plain,
    ! [X30,X31,X32] :
      ( c_Lambda_Obeta(hAPP(hAPP(c_Lambda_OdB_OApp,X30),X32),hAPP(hAPP(c_Lambda_OdB_OApp,X30),X31))
      | ~ c_Lambda_Obeta(X32,X31) ),
    inference(variable_rename,[status(thm)],[c_0_808]) ).

fof(c_0_1301,plain,
    ! [X30,X31,X32] :
      ( c_Lambda_Obeta(hAPP(hAPP(c_Lambda_OdB_OApp,X32),X30),hAPP(hAPP(c_Lambda_OdB_OApp,X31),X30))
      | ~ c_Lambda_Obeta(X32,X31) ),
    inference(variable_rename,[status(thm)],[c_0_809]) ).

fof(c_0_1302,plain,
    ! [X36,X37,X38] :
      ( ~ class_Orderings_Oorder(X38)
      | ~ c_HOL_Oord__class_Oless(X37,X36,X38)
      | ~ c_HOL_Oord__class_Oless(X36,X37,X38) ),
    inference(variable_rename,[status(thm)],[c_0_810]) ).

fof(c_0_1303,plain,
    ! [X11,X12,X13] :
      ( ~ class_Orderings_Olinorder(X13)
      | ~ c_HOL_Oord__class_Oless(X12,X11,X13)
      | ~ c_HOL_Oord__class_Oless(X11,X12,X13) ),
    inference(variable_rename,[status(thm)],[c_0_811]) ).

fof(c_0_1304,plain,
    ! [X11,X12,X13] :
      ( ~ class_Orderings_Opreorder(X13)
      | ~ c_HOL_Oord__class_Oless(X11,X12,X13)
      | ~ c_HOL_Oord__class_Oless(X12,X11,X13) ),
    inference(variable_rename,[status(thm)],[c_0_812]) ).

fof(c_0_1305,plain,
    ! [X36,X37,X38] :
      ( ~ class_Orderings_Opreorder(X38)
      | ~ c_HOL_Oord__class_Oless(X36,X37,X38)
      | ~ c_HOL_Oord__class_Oless(X37,X36,X38) ),
    inference(variable_rename,[status(thm)],[c_0_813]) ).

fof(c_0_1306,plain,
    ! [X21,X22] :
      ( ~ c_HOL_Oord__class_Oless(X22,X21,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X21,c_Suc(X22),tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_814]) ).

fof(c_0_1307,plain,
    ! [X34,X35] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X35)
      | c_HOL_Oord__class_Oless(X34,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X35),X34),c_HOL_Oone__class_Oone(X35)),X35) ),
    inference(variable_rename,[status(thm)],[c_0_815]) ).

fof(c_0_1308,plain,
    ! [X36,X37,X38] :
      ( ~ class_Divides_Osemiring__div(X38)
      | c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X37,X36,X38),X36,X38) = X37
      | X36 = c_HOL_Ozero__class_Ozero(X38) ),
    inference(variable_rename,[status(thm)],[c_0_816]) ).

fof(c_0_1309,plain,
    ! [X36,X37,X38] :
      ( ~ class_Divides_Osemiring__div(X38)
      | c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X36,X37,X38),X36,X38) = X37
      | X36 = c_HOL_Ozero__class_Ozero(X38) ),
    inference(variable_rename,[status(thm)],[c_0_817]) ).

fof(c_0_1310,plain,
    ! [X38,X39,X40,X41] :
      ( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X41)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X41),X40),X39) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X41),X40),X38)
      | X39 = X38 ),
    inference(variable_rename,[status(thm)],[c_0_818]) ).

fof(c_0_1311,plain,
    ! [X38,X39,X40,X41] :
      ( ~ class_OrderedGroup_Ocancel__semigroup__add(X41)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X41),X40),X39) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X41),X40),X38)
      | X39 = X38 ),
    inference(variable_rename,[status(thm)],[c_0_819]) ).

fof(c_0_1312,plain,
    ! [X38,X39,X40,X41] :
      ( ~ class_OrderedGroup_Ocancel__semigroup__add(X41)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X41),X39),X40) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X41),X38),X40)
      | X39 = X38 ),
    inference(variable_rename,[status(thm)],[c_0_820]) ).

fof(c_0_1313,plain,
    ! [X36,X37,X38] :
      ( ~ class_Divides_Osemiring__div(X38)
      | c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Omod(X37,X36,X38),X36,X38) = c_HOL_Ozero__class_Ozero(X38) ),
    inference(variable_rename,[status(thm)],[c_0_821]) ).

fof(c_0_1314,plain,
    ! [X26,X27,X28] :
      ( c_HOL_Otimes__class_Otimes(X27,X28,tc_nat) != c_HOL_Otimes__class_Otimes(X26,X28,tc_nat)
      | X28 = c_HOL_Ozero__class_Ozero(tc_nat)
      | X27 = X26 ),
    inference(variable_rename,[status(thm)],[c_0_822]) ).

fof(c_0_1315,plain,
    ! [X26,X27,X28] :
      ( c_HOL_Otimes__class_Otimes(X28,X27,tc_nat) != c_HOL_Otimes__class_Otimes(X28,X26,tc_nat)
      | X28 = c_HOL_Ozero__class_Ozero(tc_nat)
      | X27 = X26 ),
    inference(variable_rename,[status(thm)],[c_0_823]) ).

fof(c_0_1316,plain,
    ! [X26,X27,X28] :
      ( c_HOL_Otimes__class_Otimes(X28,X27,tc_nat) != c_HOL_Otimes__class_Otimes(X28,X26,tc_nat)
      | X27 = X26
      | X28 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_824]) ).

fof(c_0_1317,plain,
    ! [X36,X37,X38] :
      ( ~ class_Divides_Osemiring__div(X38)
      | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X37,X36,X38),X36,X38) = c_HOL_Ozero__class_Ozero(X38) ),
    inference(variable_rename,[status(thm)],[c_0_825]) ).

fof(c_0_1318,plain,
    ! [X36,X37,X38] :
      ( ~ class_Divides_Osemiring__div(X38)
      | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X36,X37,X38),X36,X38) = c_HOL_Ozero__class_Ozero(X38) ),
    inference(variable_rename,[status(thm)],[c_0_826]) ).

fof(c_0_1319,plain,
    ! [X11,X12] :
      ( X12 = X11
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X11,X12,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X12,X11,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_827]) ).

fof(c_0_1320,plain,
    ! [X11,X12] :
      ( X12 = X11
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X11,X12,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X12,X11,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_828]) ).

fof(c_0_1321,plain,
    ! [X11,X12] :
      ( ~ c_Ring__and__Field_Odvd__class_Odvd(X11,X12,tc_nat)
      | X12 = X11
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X12,X11,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_829]) ).

fof(c_0_1322,plain,
    ! [X21,X22] :
      ( X22 = X21
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X21,X22,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X22,X21,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_830]) ).

fof(c_0_1323,plain,
    ! [X11,X12] :
      ( X12 = X11
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X12,X11,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X11,X12,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_831]) ).

fof(c_0_1324,plain,
    ! [X36,X37] :
      ( ~ c_Ring__and__Field_Odvd__class_Odvd(X36,X37,tc_nat)
      | X37 = X36
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X37,X36,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_832]) ).

fof(c_0_1325,plain,
    ! [X36,X37] :
      ( ~ c_Ring__and__Field_Odvd__class_Odvd(X36,X37,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X37,X36,tc_nat)
      | X37 = X36 ),
    inference(variable_rename,[status(thm)],[c_0_833]) ).

fof(c_0_1326,plain,
    ! [X26,X27,X28] :
      ( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X28)),X26),X27) = c_Lambda_OdB_OVar(X28)
      | X28 = X27
      | c_HOL_Oord__class_Oless(X27,X28,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_834]) ).

fof(c_0_1327,plain,
    ! [X36,X37,X38] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X38)
      | c_Ring__and__Field_Odvd__class_Odvd(X37,c_HOL_Otimes__class_Otimes(X36,X37,X38),X38) ),
    inference(variable_rename,[status(thm)],[c_0_835]) ).

fof(c_0_1328,plain,
    ! [X36,X37,X38] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X38)
      | c_Ring__and__Field_Odvd__class_Odvd(X37,c_HOL_Otimes__class_Otimes(X37,X36,X38),X38) ),
    inference(variable_rename,[status(thm)],[c_0_836]) ).

fof(c_0_1329,plain,
    ! [X36,X37,X38] :
      ( ~ class_Ring__and__Field_Odvd(X38)
      | c_Ring__and__Field_Odvd__class_Odvd(X37,c_HOL_Otimes__class_Otimes(X37,X36,X38),X38) ),
    inference(variable_rename,[status(thm)],[c_0_837]) ).

fof(c_0_1330,plain,
    ! [X11,X12] :
      ( c_HOL_Oord__class_Oless(X11,X11,tc_nat)
      | hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X11)),X12),X11) = X12 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_838])])]) ).

fof(c_0_1331,plain,
    ! [X44,X45,X46,X47] :
      ( c_Type_Otyping(X46,X44,X47)
      | ~ c_Lambda_Obeta(X45,X44)
      | ~ c_Type_Otyping(X46,X45,X47) ),
    inference(variable_rename,[status(thm)],[c_0_839]) ).

fof(c_0_1332,plain,
    ! [X21,X22] :
      ( c_HOL_Oord__class_Oless(X22,X21,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_Suc(X22),c_Suc(X21),tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_840]) ).

fof(c_0_1333,plain,
    ! [X36,X37,X38] :
      ( ~ class_Divides_Osemiring__div(X38)
      | c_Divides_Odiv__class_Omod(X36,X37,X38) != c_HOL_Ozero__class_Ozero(X38)
      | c_Ring__and__Field_Odvd__class_Odvd(X37,X36,X38) ),
    inference(variable_rename,[status(thm)],[c_0_841]) ).

fof(c_0_1334,plain,
    ! [X36,X37,X38] :
      ( ~ class_Divides_Osemiring__div(X38)
      | c_Divides_Odiv__class_Omod(X36,X37,X38) = c_HOL_Ozero__class_Ozero(X38)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X37,X36,X38) ),
    inference(variable_rename,[status(thm)],[c_0_842]) ).

fof(c_0_1335,plain,
    ! [X32,X33] :
      ( hBOOL(hAPP(X33,c_HOL_Ozero__class_Ozero(tc_nat)))
      | ~ hBOOL(hAPP(X33,c_ATP__Linkup_Osko__Nat__Xzero__induct__1__1(X33)))
      | ~ hBOOL(hAPP(X33,X32)) ),
    inference(variable_rename,[status(thm)],[c_0_843]) ).

fof(c_0_1336,plain,
    ! [X32,X33] :
      ( hBOOL(hAPP(X33,c_HOL_Ozero__class_Ozero(tc_nat)))
      | hBOOL(hAPP(X33,c_Suc(c_ATP__Linkup_Osko__Nat__Xzero__induct__1__1(X33))))
      | ~ hBOOL(hAPP(X33,X32)) ),
    inference(variable_rename,[status(thm)],[c_0_844]) ).

fof(c_0_1337,plain,
    ! [X21,X22] :
      ( c_HOL_Oord__class_Oless(c_Suc(X21),c_Suc(X22),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X21,X22,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_845]) ).

fof(c_0_1338,plain,
    ! [X21,X22] :
      ( c_HOL_Oord__class_Oless(c_Suc(X22),c_Suc(X21),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X22,X21,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_846]) ).

fof(c_0_1339,plain,
    ! [X21,X22] :
      ( X21 = X22
      | ~ c_HOL_Oord__class_Oless(X21,c_Suc(X22),tc_nat)
      | c_HOL_Oord__class_Oless(X21,X22,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_847]) ).

fof(c_0_1340,plain,
    ! [X21,X22] :
      ( X22 = X21
      | ~ c_HOL_Oord__class_Oless(X21,c_Suc(X22),tc_nat)
      | c_HOL_Oord__class_Oless(X21,X22,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_848]) ).

fof(c_0_1341,plain,
    ! [X21,X22] :
      ( X22 = X21
      | c_HOL_Oord__class_Oless(X22,X21,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X22,c_Suc(X21),tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_849]) ).

fof(c_0_1342,plain,
    ! [X21,X22] :
      ( c_HOL_Oord__class_Oless(c_Suc(X22),X21,tc_nat)
      | c_Suc(X22) = X21
      | ~ c_HOL_Oord__class_Oless(X22,X21,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_850]) ).

fof(c_0_1343,plain,
    ! [X37,X38,X39] :
      ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X39),X38) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X39),X37)
      | X38 = X37 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_851])])]) ).

fof(c_0_1344,plain,
    ! [X26,X27,X28] :
      ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X27),X28) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X26),X28)
      | X27 = X26 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_852])])]) ).

fof(c_0_1345,plain,
    ! [X26,X27,X28] :
      ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X28),X27) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X28),X26)
      | X27 = X26 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_853])])]) ).

fof(c_0_1346,plain,
    ! [X21,X22] :
      ( c_HOL_Oord__class_Oless(X22,X21,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_Suc(X22),X21,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_854]) ).

fof(c_0_1347,plain,
    ! [X15,X16] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X16)
      | ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X15,X16),c_HOL_Ozero__class_Ozero(X16),X16) ),
    inference(variable_rename,[status(thm)],[c_0_855]) ).

fof(c_0_1348,plain,
    ! [X21,X22] :
      ( c_HOL_Oord__class_Oless(X22,c_Suc(X21),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X22,X21,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_856]) ).

fof(c_0_1349,plain,
    ! [X21,X22] :
      ( c_Divides_Odiv__class_Odiv(X22,X21,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
      | ~ c_HOL_Oord__class_Oless(X22,X21,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_857]) ).

fof(c_0_1350,plain,
    ! [X21,X22] :
      ( c_Divides_Odiv__class_Omod(X22,X21,tc_nat) = X22
      | ~ c_HOL_Oord__class_Oless(X22,X21,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_858]) ).

fof(c_0_1351,plain,
    ! [X26,X27] :
      ( hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(X27)),X26) = c_Lambda_OdB_OVar(X27)
      | ~ c_HOL_Oord__class_Oless(X27,X26,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_859]) ).

fof(c_0_1352,plain,
    ! [X32,X33] :
      ( hBOOL(hAPP(X33,X32))
      | hBOOL(hAPP(X33,v_sko__List__Xlexn__Xinduct__1(X33)))
      | ~ hBOOL(hAPP(X33,c_HOL_Ozero__class_Ozero(tc_nat))) ),
    inference(variable_rename,[status(thm)],[c_0_860]) ).

fof(c_0_1353,plain,
    ! [X32,X33] :
      ( hBOOL(hAPP(X33,X32))
      | hBOOL(hAPP(X33,c_ATP__Linkup_Osko__Nat__Xnat__induct__1__1(X33)))
      | ~ hBOOL(hAPP(X33,c_HOL_Ozero__class_Ozero(tc_nat))) ),
    inference(variable_rename,[status(thm)],[c_0_861]) ).

fof(c_0_1354,plain,
    ! [X32,X33] :
      ( hBOOL(hAPP(X33,X32))
      | hBOOL(hAPP(X33,v_sko__List__Xreplicate__Xinduct__1(X33)))
      | ~ hBOOL(hAPP(X33,c_HOL_Ozero__class_Ozero(tc_nat))) ),
    inference(variable_rename,[status(thm)],[c_0_862]) ).

fof(c_0_1355,plain,
    ! [X32,X33] :
      ( hBOOL(hAPP(X33,X32))
      | hBOOL(hAPP(X33,v_sko__Nat__Xnat__Xinducts__1(X33)))
      | ~ hBOOL(hAPP(X33,c_HOL_Ozero__class_Ozero(tc_nat))) ),
    inference(variable_rename,[status(thm)],[c_0_863]) ).

fof(c_0_1356,plain,
    ! [X32,X33] :
      ( hBOOL(hAPP(X33,X32))
      | hBOOL(hAPP(X33,v_sko__Nat__Xnat__Xinduct__1(X33)))
      | ~ hBOOL(hAPP(X33,c_HOL_Ozero__class_Ozero(tc_nat))) ),
    inference(variable_rename,[status(thm)],[c_0_864]) ).

fof(c_0_1357,plain,
    ! [X32,X33] :
      ( hBOOL(hAPP(X33,X32))
      | hBOOL(hAPP(X33,v_sko__List__Xupt__Xinduct__1(X33)))
      | ~ hBOOL(hAPP(X33,c_HOL_Ozero__class_Ozero(tc_nat))) ),
    inference(variable_rename,[status(thm)],[c_0_865]) ).

fof(c_0_1358,plain,
    ! [X34,X35,X36] :
      ( ~ class_Ring__and__Field_Ozero__neq__one(X36)
      | ~ class_Ring__and__Field_Ono__zero__divisors(X36)
      | ~ class_Ring__and__Field_Omult__zero(X36)
      | ~ class_Power_Opower(X36)
      | c_Power_Opower__class_Opower(X35,X34,X36) != c_HOL_Ozero__class_Ozero(X36)
      | X35 = c_HOL_Ozero__class_Ozero(X36) ),
    inference(variable_rename,[status(thm)],[c_0_866]) ).

fof(c_0_1359,plain,
    ! [X34,X35] :
      ( ~ class_Ring__and__Field_Ozero__neq__one(X35)
      | ~ class_Ring__and__Field_Ono__zero__divisors(X35)
      | ~ class_Ring__and__Field_Omult__zero(X35)
      | ~ class_Power_Opower(X35)
      | c_Power_Opower__class_Opower(X34,c_HOL_Ozero__class_Ozero(tc_nat),X35) != c_HOL_Ozero__class_Ozero(X35) ),
    inference(variable_rename,[status(thm)],[c_0_867]) ).

fof(c_0_1360,plain,
    ! [X26,X27,X28] :
      ( c_Lambda_Osubstn(c_Lambda_OdB_OVar(X28),X26,X27) = c_Lambda_OdB_OVar(X28)
      | X28 = X27
      | c_HOL_Oord__class_Oless(X27,X28,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_868]) ).

fof(c_0_1361,plain,
    ! [X11,X12,X13] :
      ( ~ class_Ring__and__Field_Oordered__idom(X13)
      | c_HOL_Oord__class_Oless(X11,X12,X13)
      | c_HOL_Oord__class_Oless(X12,X11,X13)
      | X12 = X11 ),
    inference(variable_rename,[status(thm)],[c_0_869]) ).

fof(c_0_1362,plain,
    ! [X11,X12,X13] :
      ( ~ class_Orderings_Olinorder(X13)
      | X12 = X11
      | c_HOL_Oord__class_Oless(X11,X12,X13)
      | c_HOL_Oord__class_Oless(X12,X11,X13) ),
    inference(variable_rename,[status(thm)],[c_0_870]) ).

fof(c_0_1363,plain,
    ! [X11,X12,X13] :
      ( ~ class_Orderings_Olinorder(X13)
      | c_HOL_Oord__class_Oless(X11,X12,X13)
      | c_HOL_Oord__class_Oless(X12,X11,X13)
      | X12 = X11 ),
    inference(variable_rename,[status(thm)],[c_0_871]) ).

fof(c_0_1364,plain,
    ! [X11,X12,X13] :
      ( ~ class_Orderings_Olinorder(X13)
      | c_HOL_Oord__class_Oless(X11,X12,X13)
      | X12 = X11
      | c_HOL_Oord__class_Oless(X12,X11,X13) ),
    inference(variable_rename,[status(thm)],[c_0_872]) ).

fof(c_0_1365,plain,
    ! [X11,X12,X13] :
      ( ~ class_Orderings_Olinorder(X13)
      | X12 = X11
      | c_HOL_Oord__class_Oless(X12,X11,X13)
      | c_HOL_Oord__class_Oless(X11,X12,X13) ),
    inference(variable_rename,[status(thm)],[c_0_873]) ).

fof(c_0_1366,plain,
    ! [X19,X20,X21,X22] :
      ( hAPP(hAPP(c_Lambda_OdB_OApp,X22),X20) != hAPP(hAPP(c_Lambda_OdB_OApp,X21),X19)
      | X22 = X21 ),
    inference(variable_rename,[status(thm)],[c_0_874]) ).

fof(c_0_1367,plain,
    ! [X19,X20,X21,X22] :
      ( hAPP(hAPP(c_Lambda_OdB_OApp,X22),X20) != hAPP(hAPP(c_Lambda_OdB_OApp,X21),X19)
      | X20 = X19 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_875])])]) ).

fof(c_0_1368,plain,
    ! [X15,X16] :
      ( ~ class_Ring__and__Field_Osemiring__1(X16)
      | c_Nat_Osemiring__1__class_Oof__nat(c_Suc(X15),X16) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X16),c_HOL_Oone__class_Oone(X16)),c_Nat_Osemiring__1__class_Oof__nat(X15,X16)) ),
    inference(variable_rename,[status(thm)],[c_0_876]) ).

fof(c_0_1369,plain,
    ! [X36,X37,X38] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X38)
      | c_HOL_Otimes__class_Otimes(X37,X36,X38) = c_HOL_Otimes__class_Otimes(X36,X37,X38) ),
    inference(variable_rename,[status(thm)],[c_0_877]) ).

fof(c_0_1370,plain,
    ! [X11,X12,X13] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X13)
      | c_HOL_Otimes__class_Otimes(X12,X11,X13) = c_HOL_Otimes__class_Otimes(X11,X12,X13) ),
    inference(variable_rename,[status(thm)],[c_0_878]) ).

fof(c_0_1371,plain,
    ! [X11] :
      ( c_HOL_Oord__class_Oless(X11,X11,tc_nat)
      | c_HOL_Oord__class_Oless(X11,c_Suc(X11),tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_879]) ).

fof(c_0_1372,plain,
    ! [X21,X22] :
      ( c_HOL_Oord__class_Oless(X21,c_Suc(X22),tc_nat)
      | c_HOL_Oord__class_Oless(X22,X21,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_880]) ).

fof(c_0_1373,plain,
    ! [X4] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X4)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
    inference(variable_rename,[status(thm)],[c_0_881]) ).

fof(c_0_1374,plain,
    ! [X38,X39,X40] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X40)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X40),X39),X38) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X40),X38),X39) ),
    inference(variable_rename,[status(thm)],[c_0_882]) ).

fof(c_0_1375,plain,
    ! [X36,X37,X38] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X38)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X38),X37),X36) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X38),X36),X37) ),
    inference(variable_rename,[status(thm)],[c_0_883]) ).

fof(c_0_1376,plain,
    ! [X11,X12,X13] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X13)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X13),X12),X11) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X13),X11),X12) ),
    inference(variable_rename,[status(thm)],[c_0_884]) ).

fof(c_0_1377,plain,
    ! [X15] :
      ( X15 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X15,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_885]) ).

fof(c_0_1378,plain,
    ! [X25,X26,X27] :
      ( hAPP(X26,X25) = X27
      | ~ c_Type_Otyping(X26,c_Lambda_OdB_OVar(X25),X27) ),
    inference(variable_rename,[status(thm)],[c_0_886]) ).

fof(c_0_1379,plain,
    ! [X36,X37,X38] :
      ( ~ class_Ring__and__Field_Ono__zero__divisors(X38)
      | c_HOL_Otimes__class_Otimes(X37,X36,X38) != c_HOL_Ozero__class_Ozero(X38)
      | X37 = c_HOL_Ozero__class_Ozero(X38)
      | X36 = c_HOL_Ozero__class_Ozero(X38) ),
    inference(variable_rename,[status(thm)],[c_0_887]) ).

fof(c_0_1380,plain,
    ! [X36,X37,X38] :
      ( ~ class_Ring__and__Field_Ono__zero__divisors(X38)
      | c_HOL_Otimes__class_Otimes(X37,X36,X38) != c_HOL_Ozero__class_Ozero(X38)
      | X36 = c_HOL_Ozero__class_Ozero(X38)
      | X37 = c_HOL_Ozero__class_Ozero(X38) ),
    inference(variable_rename,[status(thm)],[c_0_888]) ).

fof(c_0_1381,plain,
    ! [X36,X37,X38] :
      ( ~ class_Ring__and__Field_Oring__no__zero__divisors(X38)
      | c_HOL_Otimes__class_Otimes(X37,X36,X38) != c_HOL_Ozero__class_Ozero(X38)
      | X36 = c_HOL_Ozero__class_Ozero(X38)
      | X37 = c_HOL_Ozero__class_Ozero(X38) ),
    inference(variable_rename,[status(thm)],[c_0_889]) ).

fof(c_0_1382,plain,
    ! [X21,X22] :
      ( c_HOL_Oord__class_Oless(X21,X22,tc_nat)
      | c_HOL_Oord__class_Oless(X22,X21,tc_nat)
      | X22 = X21 ),
    inference(variable_rename,[status(thm)],[c_0_890]) ).

fof(c_0_1383,plain,
    ! [X11,X12] :
      ( c_HOL_Oord__class_Oless(X11,X12,tc_nat)
      | c_HOL_Oord__class_Oless(X12,X11,tc_nat)
      | X12 = X11 ),
    inference(variable_rename,[status(thm)],[c_0_891]) ).

fof(c_0_1384,plain,
    ! [X34,X35] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X35)
      | X34 = c_HOL_Ozero__class_Ozero(X35)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(X35),X34,X35) ),
    inference(variable_rename,[status(thm)],[c_0_892]) ).

fof(c_0_1385,plain,
    ! [X15,X16] :
      ( c_Power_Opower__class_Opower(X15,X16,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X15 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X16 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_893]) ).

fof(c_0_1386,plain,
    ! [X21] :
      ( X21 = c_HOL_Ozero__class_Ozero(tc_nat)
      | ~ c_HOL_Oord__class_Oless(X21,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_894]) ).

fof(c_0_1387,plain,
    ! [X34,X35,X36] :
      ( ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X36)
      | c_Power_Opower__class_Opower(X35,X34,X36) != c_HOL_Ozero__class_Ozero(X36)
      | X35 = c_HOL_Ozero__class_Ozero(X36) ),
    inference(variable_rename,[status(thm)],[c_0_895]) ).

fof(c_0_1388,plain,
    ! [X34,X35,X36] :
      ( ~ class_Ring__and__Field_Oidom(X36)
      | ~ class_Int_Onumber__ring(X36)
      | X34 != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X36),X34),X35)
      | X35 = c_HOL_Ozero__class_Ozero(X36) ),
    inference(variable_rename,[status(thm)],[c_0_896]) ).

fof(c_0_1389,plain,
    ! [X21,X22] :
      ( c_HOL_Otimes__class_Otimes(X22,X21,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X21 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_897])])]) ).

fof(c_0_1390,plain,
    ! [X21,X22] :
      ( c_HOL_Otimes__class_Otimes(X22,X21,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X22 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    inference(variable_rename,[status(thm)],[c_0_898]) ).

fof(c_0_1391,plain,
    ! [X34,X35] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X35)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X35),X34),X34) != c_HOL_Ozero__class_Ozero(X35)
      | X34 = c_HOL_Ozero__class_Ozero(X35) ),
    inference(variable_rename,[status(thm)],[c_0_899]) ).

fof(c_0_1392,plain,
    ! [X21,X22] :
      ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X21) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X21 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X22 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    inference(variable_rename,[status(thm)],[c_0_900]) ).

fof(c_0_1393,plain,
    ! [X21,X22] :
      ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X21)
      | X21 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X22 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    inference(variable_rename,[status(thm)],[c_0_901]) ).

fof(c_0_1394,plain,
    ! [X21,X22] :
      ( ~ class_Ring__and__Field_Ozero__neq__one(X22)
      | ~ class_Ring__and__Field_Ono__zero__divisors(X22)
      | ~ class_Ring__and__Field_Omult__zero(X22)
      | ~ class_Power_Opower(X22)
      | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X22),X21,X22) = c_HOL_Ozero__class_Ozero(X22)
      | X21 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_902]) ).

fof(c_0_1395,plain,
    ! [X21,X22] :
      ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X21)
      | X21 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X21 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_903])])]) ).

fof(c_0_1396,plain,
    ! [X21,X22] :
      ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X21)
      | X22 = c_HOL_Ozero__class_Ozero(tc_nat)
      | X22 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    inference(variable_rename,[status(thm)],[c_0_904]) ).

fof(c_0_1397,plain,
    ! [X21,X22] :
      ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X21) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X21 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X21 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_905])])]) ).

fof(c_0_1398,plain,
    ! [X21,X22] :
      ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X21) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X22 = c_HOL_Ozero__class_Ozero(tc_nat)
      | X22 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    inference(variable_rename,[status(thm)],[c_0_906]) ).

fof(c_0_1399,plain,
    ! [X21,X22] :
      ( c_HOL_Otimes__class_Otimes(X22,X21,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
      | X21 = c_HOL_Ozero__class_Ozero(tc_nat)
      | X22 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_907]) ).

fof(c_0_1400,plain,
    ! [X11,X12] :
      ( ~ class_Orderings_Oorder(X12)
      | ~ c_HOL_Oord__class_Oless(X11,X11,X12) ),
    inference(variable_rename,[status(thm)],[c_0_908]) ).

fof(c_0_1401,plain,
    ! [X11,X12] :
      ( ~ class_Orderings_Olinorder(X12)
      | ~ c_HOL_Oord__class_Oless(X11,X11,X12) ),
    inference(variable_rename,[status(thm)],[c_0_909]) ).

fof(c_0_1402,plain,
    ! [X11,X12] :
      ( ~ class_Orderings_Opreorder(X12)
      | ~ c_HOL_Oord__class_Oless(X11,X11,X12) ),
    inference(variable_rename,[status(thm)],[c_0_910]) ).

fof(c_0_1403,plain,
    ! [X21,X22] :
      ( X22 != c_HOL_Otimes__class_Otimes(X22,X21,tc_nat)
      | X22 = c_HOL_Ozero__class_Ozero(tc_nat)
      | X21 = c_HOL_Oone__class_Oone(tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_911]) ).

fof(c_0_1404,plain,
    ! [X15] :
      ( X15 = c_HOL_Oone__class_Oone(tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X15,c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_912]) ).

fof(c_0_1405,plain,
    ! [X21,X22] :
      ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X21) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X22 = c_HOL_Ozero__class_Ozero(tc_nat)
      | X21 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_913]) ).

fof(c_0_1406,plain,
    ! [X21,X22] :
      ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X21)
      | X22 = c_HOL_Ozero__class_Ozero(tc_nat)
      | X21 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_914]) ).

fof(c_0_1407,plain,
    ! [X21,X22] :
      ( c_HOL_Otimes__class_Otimes(X22,X21,tc_nat) != c_HOL_Oone__class_Oone(tc_nat)
      | X22 = c_HOL_Oone__class_Oone(tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_915]) ).

fof(c_0_1408,plain,
    ! [X21,X22] :
      ( c_HOL_Otimes__class_Otimes(X22,X21,tc_nat) != c_HOL_Oone__class_Oone(tc_nat)
      | X21 = c_HOL_Oone__class_Oone(tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_916])])]) ).

fof(c_0_1409,plain,
    ! [X21,X22] :
      ( c_HOL_Oone__class_Oone(tc_nat) != c_HOL_Otimes__class_Otimes(X22,X21,tc_nat)
      | X22 = c_HOL_Oone__class_Oone(tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_917]) ).

fof(c_0_1410,plain,
    ! [X21,X22] :
      ( c_HOL_Oone__class_Oone(tc_nat) != c_HOL_Otimes__class_Otimes(X22,X21,tc_nat)
      | X21 = c_HOL_Oone__class_Oone(tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_918])])]) ).

fof(c_0_1411,plain,
    ! [X4,X5,X6] :
      ( X5 = X4
      | ~ c_fequal(X5,X4,X6) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_919])])]) ).

fof(c_0_1412,plain,
    ! [X21,X22] :
      ( ~ class_Ring__and__Field_Osemiring__0(X22)
      | ~ class_Power_Opower(X22)
      | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X22),c_Suc(X21),X22) = c_HOL_Ozero__class_Ozero(X22) ),
    inference(variable_rename,[status(thm)],[c_0_920]) ).

fof(c_0_1413,plain,
    ! [X21,X22] :
      ( ~ class_Ring__and__Field_Osemiring__0(X22)
      | ~ class_Power_Opower(X22)
      | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X22),X21,X22) = c_HOL_Ozero__class_Ozero(X22)
      | X21 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_921]) ).

fof(c_0_1414,plain,
    ! [X9] :
      ( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(X9)))
      | ~ hBOOL(hAPP(c_InductTermi_OIT,X9)) ),
    inference(variable_rename,[status(thm)],[c_0_922]) ).

fof(c_0_1415,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_923]) ).

fof(c_0_1416,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_924]) ).

fof(c_0_1417,plain,
    ! [X21,X22] :
      ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X21) != c_HOL_Ozero__class_Ozero(tc_nat)
      | X21 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_925])])]) ).

fof(c_0_1418,plain,
    ! [X21,X22] :
      ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X21) != c_HOL_Ozero__class_Ozero(tc_nat)
      | X22 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_926]) ).

fof(c_0_1419,plain,
    ! [X34,X35] :
      ( X34 != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X34),X35)
      | X35 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_927]) ).

fof(c_0_1420,plain,
    ! [X21,X22] :
      ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X21) != X22
      | X21 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_928])])]) ).

fof(c_0_1421,plain,
    ! [X4] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X4)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oone__class_Oone(X4),X4) ),
    inference(variable_rename,[status(thm)],[c_0_929]) ).

fof(c_0_1422,plain,
    ! [X11,X12] :
      ( ~ class_Ring__and__Field_Oidom(X12)
      | ~ class_Int_Onumber__ring(X12)
      | X11 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X12),X11),c_HOL_Ozero__class_Ozero(X12)) ),
    inference(variable_rename,[status(thm)],[c_0_930]) ).

fof(c_0_1423,plain,
    ! [X11,X12] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X12)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X12),c_HOL_Ozero__class_Ozero(X12)),X11) = X11 ),
    inference(variable_rename,[status(thm)],[c_0_931]) ).

fof(c_0_1424,plain,
    ! [X34,X35] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X35)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X35),c_HOL_Ozero__class_Ozero(X35)),X34) = X34 ),
    inference(variable_rename,[status(thm)],[c_0_932]) ).

fof(c_0_1425,plain,
    ! [X34,X35] :
      ( ~ class_OrderedGroup_Omonoid__add(X35)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X35),c_HOL_Ozero__class_Ozero(X35)),X34) = X34 ),
    inference(variable_rename,[status(thm)],[c_0_933]) ).

fof(c_0_1426,plain,
    ! [X34,X35] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X35)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X35),c_HOL_Ozero__class_Ozero(X35)),X34) = X34 ),
    inference(variable_rename,[status(thm)],[c_0_934]) ).

fof(c_0_1427,plain,
    ! [X21,X22] :
      ( ~ class_OrderedGroup_Omonoid__mult(X22)
      | c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X22),X21,X22) = c_HOL_Oone__class_Oone(X22) ),
    inference(variable_rename,[status(thm)],[c_0_935]) ).

fof(c_0_1428,plain,
    ! [X11,X12] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X12)
      | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X12),X11,X12) = c_HOL_Ozero__class_Ozero(X12) ),
    inference(variable_rename,[status(thm)],[c_0_936]) ).

fof(c_0_1429,plain,
    ! [X34,X35] :
      ( ~ class_Ring__and__Field_Omult__zero(X35)
      | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X35),X34,X35) = c_HOL_Ozero__class_Ozero(X35) ),
    inference(variable_rename,[status(thm)],[c_0_937]) ).

fof(c_0_1430,plain,
    ! [X34,X35] :
      ( ~ class_Ring__and__Field_Omult__zero(X35)
      | c_HOL_Otimes__class_Otimes(X34,c_HOL_Ozero__class_Ozero(X35),X35) = c_HOL_Ozero__class_Ozero(X35) ),
    inference(variable_rename,[status(thm)],[c_0_938]) ).

fof(c_0_1431,plain,
    ! [X36,X37] :
      ( ~ class_Ring__and__Field_Oring__no__zero__divisors(X37)
      | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X37),X36,X37) = c_HOL_Ozero__class_Ozero(X37) ),
    inference(variable_rename,[status(thm)],[c_0_939]) ).

fof(c_0_1432,plain,
    ! [X34,X35] :
      ( ~ class_Ring__and__Field_Oring__no__zero__divisors(X35)
      | c_HOL_Otimes__class_Otimes(X34,c_HOL_Ozero__class_Ozero(X35),X35) = c_HOL_Ozero__class_Ozero(X35) ),
    inference(variable_rename,[status(thm)],[c_0_940]) ).

fof(c_0_1433,plain,
    ! [X34,X35] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X35)
      | c_HOL_Otimes__class_Otimes(X34,c_HOL_Ozero__class_Ozero(X35),X35) = c_HOL_Ozero__class_Ozero(X35) ),
    inference(variable_rename,[status(thm)],[c_0_941]) ).

fof(c_0_1434,plain,
    ! [X34,X35] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X35)
      | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X35),X34,X35) = c_HOL_Ozero__class_Ozero(X35) ),
    inference(variable_rename,[status(thm)],[c_0_942]) ).

fof(c_0_1435,plain,
    ! [X34,X35] :
      ( ~ class_Divides_Osemiring__div(X35)
      | c_Divides_Odiv__class_Odiv(X34,c_HOL_Ozero__class_Ozero(X35),X35) = c_HOL_Ozero__class_Ozero(X35) ),
    inference(variable_rename,[status(thm)],[c_0_943]) ).

fof(c_0_1436,plain,
    ! [X34,X35] :
      ( ~ class_Divides_Osemiring__div(X35)
      | c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(X35),X34,X35) = c_HOL_Ozero__class_Ozero(X35) ),
    inference(variable_rename,[status(thm)],[c_0_944]) ).

fof(c_0_1437,plain,
    ! [X34,X35] :
      ( ~ class_Divides_Osemiring__div(X35)
      | c_Divides_Odiv__class_Omod(X34,c_HOL_Oone__class_Oone(X35),X35) = c_HOL_Ozero__class_Ozero(X35) ),
    inference(variable_rename,[status(thm)],[c_0_945]) ).

fof(c_0_1438,plain,
    ! [X34,X35] :
      ( ~ class_Divides_Osemiring__div(X35)
      | c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(X35),X34,X35) = c_HOL_Ozero__class_Ozero(X35) ),
    inference(variable_rename,[status(thm)],[c_0_946]) ).

fof(c_0_1439,plain,
    ! [X34,X35] :
      ( ~ class_Divides_Osemiring__div(X35)
      | c_Divides_Odiv__class_Odiv(X34,X34,X35) = c_HOL_Oone__class_Oone(X35)
      | X34 = c_HOL_Ozero__class_Ozero(X35) ),
    inference(variable_rename,[status(thm)],[c_0_947]) ).

fof(c_0_1440,plain,
    ! [X34,X35] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X35)
      | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X35),X34,X35) = X34 ),
    inference(variable_rename,[status(thm)],[c_0_948]) ).

fof(c_0_1441,plain,
    ! [X34,X35] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X35)
      | c_HOL_Otimes__class_Otimes(X34,c_HOL_Oone__class_Oone(X35),X35) = X34 ),
    inference(variable_rename,[status(thm)],[c_0_949]) ).

fof(c_0_1442,plain,
    ! [X34,X35] :
      ( ~ class_OrderedGroup_Omonoid__mult(X35)
      | c_HOL_Otimes__class_Otimes(X34,c_HOL_Oone__class_Oone(X35),X35) = X34 ),
    inference(variable_rename,[status(thm)],[c_0_950]) ).

fof(c_0_1443,plain,
    ! [X34,X35] :
      ( ~ class_OrderedGroup_Omonoid__mult(X35)
      | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X35),X34,X35) = X34 ),
    inference(variable_rename,[status(thm)],[c_0_951]) ).

fof(c_0_1444,plain,
    ! [X34,X35] :
      ( ~ class_OrderedGroup_Ocomm__monoid__mult(X35)
      | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X35),X34,X35) = X34 ),
    inference(variable_rename,[status(thm)],[c_0_952]) ).

fof(c_0_1445,plain,
    ! [X11,X12] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X12)
      | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X12),X11,X12) = X11 ),
    inference(variable_rename,[status(thm)],[c_0_953]) ).

fof(c_0_1446,plain,
    ! [X34,X35] :
      ( ~ class_Divides_Osemiring__div(X35)
      | c_Divides_Odiv__class_Odiv(X34,c_HOL_Oone__class_Oone(X35),X35) = X34 ),
    inference(variable_rename,[status(thm)],[c_0_954]) ).

fof(c_0_1447,plain,
    ! [X34,X35] :
      ( ~ class_Divides_Osemiring__div(X35)
      | c_Divides_Odiv__class_Omod(X34,c_HOL_Ozero__class_Ozero(X35),X35) = X34 ),
    inference(variable_rename,[status(thm)],[c_0_955]) ).

fof(c_0_1448,plain,
    ! [X34,X35] :
      ( ~ class_Power_Opower(X35)
      | c_Power_Opower__class_Opower(X34,c_HOL_Ozero__class_Ozero(tc_nat),X35) = c_HOL_Oone__class_Oone(X35) ),
    inference(variable_rename,[status(thm)],[c_0_956]) ).

fof(c_0_1449,plain,
    ! [X11,X12] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X12)
      | c_Power_Opower__class_Opower(X11,c_HOL_Ozero__class_Ozero(tc_nat),X12) = c_HOL_Oone__class_Oone(X12) ),
    inference(variable_rename,[status(thm)],[c_0_957]) ).

fof(c_0_1450,plain,
    ! [X34,X35] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X35)
      | c_Ring__and__Field_Odvd__class_Odvd(X34,c_HOL_Ozero__class_Ozero(X35),X35) ),
    inference(variable_rename,[status(thm)],[c_0_958]) ).

fof(c_0_1451,plain,
    ! [X34,X35] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X35)
      | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(X35),X34,X35) ),
    inference(variable_rename,[status(thm)],[c_0_959]) ).

fof(c_0_1452,plain,
    ! [X34,X35] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X35)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X35),X34),c_HOL_Ozero__class_Ozero(X35)) = X34 ),
    inference(variable_rename,[status(thm)],[c_0_960]) ).

fof(c_0_1453,plain,
    ! [X34,X35] :
      ( ~ class_OrderedGroup_Omonoid__add(X35)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X35),X34),c_HOL_Ozero__class_Ozero(X35)) = X34 ),
    inference(variable_rename,[status(thm)],[c_0_961]) ).

fof(c_0_1454,plain,
    ! [X34,X35] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X35)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X35),X34),c_HOL_Ozero__class_Ozero(X35)) = X34 ),
    inference(variable_rename,[status(thm)],[c_0_962]) ).

fof(c_0_1455,plain,
    ! [X11,X12] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X12)
      | c_Power_Opower__class_Opower(X11,c_HOL_Oone__class_Oone(tc_nat),X12) = X11 ),
    inference(variable_rename,[status(thm)],[c_0_963]) ).

fof(c_0_1456,plain,
    ! [X34,X35] :
      ( ~ class_OrderedGroup_Omonoid__mult(X35)
      | c_Power_Opower__class_Opower(X34,c_HOL_Oone__class_Oone(tc_nat),X35) = X34 ),
    inference(variable_rename,[status(thm)],[c_0_964]) ).

fof(c_0_1457,plain,
    ! [X34,X35] :
      ( ~ class_Divides_Osemiring__div(X35)
      | c_Divides_Odiv__class_Omod(X34,X34,X35) = c_HOL_Ozero__class_Ozero(X35) ),
    inference(variable_rename,[status(thm)],[c_0_965]) ).

fof(c_0_1458,plain,
    ! [X11,X12] :
      ( ~ class_OrderedGroup_Oab__semigroup__idem__mult(X12)
      | c_HOL_Otimes__class_Otimes(X11,X11,X12) = X11 ),
    inference(variable_rename,[status(thm)],[c_0_966]) ).

fof(c_0_1459,plain,
    ! [X34,X35] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X35)
      | c_Ring__and__Field_Odvd__class_Odvd(X34,X34,X35) ),
    inference(variable_rename,[status(thm)],[c_0_967]) ).

fof(c_0_1460,plain,
    ! [X21] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X21,tc_nat)
      | X21 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_968]) ).

fof(c_0_1461,plain,
    ! [X21,X22,X23] :
      ( ~ class_Nat_Osemiring__char__0(X23)
      | c_Nat_Osemiring__1__class_Oof__nat(X22,X23) != c_Nat_Osemiring__1__class_Oof__nat(X21,X23)
      | X22 = X21 ),
    inference(variable_rename,[status(thm)],[c_0_969]) ).

fof(c_0_1462,plain,
    ! [X30,X31] :
      ( c_Lambda_Obeta(c_Lambda_OdB_OAbs(X31),c_Lambda_OdB_OAbs(X30))
      | ~ c_Lambda_Obeta(X31,X30) ),
    inference(variable_rename,[status(thm)],[c_0_970]) ).

fof(c_0_1463,plain,
    ! [X6,X7] :
      ( class_Orderings_Opreorder(tc_fun(X6,X7))
      | ~ class_Orderings_Opreorder(X7) ),
    inference(variable_rename,[status(thm)],[c_0_971]) ).

fof(c_0_1464,plain,
    ! [X6,X7] :
      ( class_Orderings_Oorder(tc_fun(X6,X7))
      | ~ class_Orderings_Oorder(X7) ),
    inference(variable_rename,[status(thm)],[c_0_972]) ).

fof(c_0_1465,plain,
    ! [X4] :
      ( ~ class_Ring__and__Field_Osemiring__1(X4)
      | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),X4) = c_HOL_Oone__class_Oone(X4) ),
    inference(variable_rename,[status(thm)],[c_0_973]) ).

fof(c_0_1466,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_974]) ).

fof(c_0_1467,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_975]) ).

fof(c_0_1468,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_976]) ).

fof(c_0_1469,plain,
    ! [X61,X62] :
      ( c_Lambda_OdB_OAbs(X62) != c_Lambda_OdB_OAbs(X61)
      | X62 = X61 ),
    inference(variable_rename,[status(thm)],[c_0_977]) ).

fof(c_0_1470,plain,
    ! [X13,X14] :
      ( c_Lambda_OdB_OVar(X14) != c_Lambda_OdB_OVar(X13)
      | X14 = X13 ),
    inference(variable_rename,[status(thm)],[c_0_978]) ).

fof(c_0_1471,plain,
    ! [X13,X14] :
      ( c_Suc(X14) != c_Suc(X13)
      | X14 = X13 ),
    inference(variable_rename,[status(thm)],[c_0_979]) ).

fof(c_0_1472,plain,
    ! [X11,X12] :
      ( c_Suc(X12) != c_Suc(X11)
      | X12 = X11 ),
    inference(variable_rename,[status(thm)],[c_0_980]) ).

fof(c_0_1473,plain,
    ! [X10] :
      ( X10 = c_Suc(c_ATP__Linkup_Osko__Nat__Xnat__Xexhaust__1__1(X10))
      | X10 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_981]) ).

fof(c_0_1474,plain,
    ! [X33] :
      ( X33 = c_Suc(c_ATP__Linkup_Osko__Nat__Xnat__Xnchotomy__1__1(X33))
      | X33 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_982]) ).

fof(c_0_1475,plain,
    ! [X21] :
      ( X21 = c_Suc(c_ATP__Linkup_Osko__Nat__Xnot0__implies__Suc__1__1(X21))
      | X21 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_983]) ).

cnf(c_0_1476,plain,
    ( c_Type_Otypings(X1,c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,X2,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),X4,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X5,tc_Lambda_OdB,tc_Lambda_OdB),X6)
    | ~ c_Type_Otyping(X1,X2,X3)
    | ~ c_Type_Otypings(c_Type_Oshift(X1,X4,X3,tc_Type_Otype),X5,X6) ),
    inference(split_conjunct,[status(thm)],[c_0_984]) ).

cnf(c_0_1477,plain,
    ( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1)),X2),X3,tc_Lambda_OdB,tc_Lambda_OdB)))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X2),c_HOL_Ozero__class_Ozero(tc_nat)),X3,tc_Lambda_OdB,tc_Lambda_OdB)))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_985]) ).

cnf(c_0_1478,plain,
    ( hBOOL(hAPP(X1,hAPP(hAPP(X2,X3),X4)))
    | ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X5,X2,X6,hAPP(hAPP(c_Lambda_OdB_OApp,X3),X4),t_a))) ),
    inference(split_conjunct,[status(thm)],[c_0_986]) ).

cnf(c_0_1479,plain,
    ( hBOOL(hAPP(X1,hAPP(hAPP(X2,X3),X4)))
    | ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X5,X2,X6,hAPP(hAPP(c_Lambda_OdB_OApp,X3),X4),t_a))) ),
    inference(split_conjunct,[status(thm)],[c_0_987]) ).

cnf(c_0_1480,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_988]) ).

cnf(c_0_1481,plain,
    ( hBOOL(hAPP(X1,hAPP(X2,X3)))
    | ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X2,X4,X5,c_Lambda_OdB_OVar(X3),t_a))) ),
    inference(split_conjunct,[status(thm)],[c_0_989]) ).

cnf(c_0_1482,plain,
    ( hBOOL(hAPP(X1,hAPP(X2,X3)))
    | ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X2,X4,X5,c_Lambda_OdB_OVar(X3),t_a))) ),
    inference(split_conjunct,[status(thm)],[c_0_990]) ).

cnf(c_0_1483,plain,
    ( hBOOL(hAPP(X1,hAPP(X2,X3)))
    | ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X4,X5,X2,c_Lambda_OdB_OAbs(X3),t_a))) ),
    inference(split_conjunct,[status(thm)],[c_0_991]) ).

cnf(c_0_1484,plain,
    ( hBOOL(hAPP(X1,hAPP(X2,X3)))
    | ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X4,X5,X2,c_Lambda_OdB_OAbs(X3),t_a))) ),
    inference(split_conjunct,[status(thm)],[c_0_992]) ).

cnf(c_0_1485,plain,
    ( c_Type_Otypings(c_Type_Oshift(X1,X4,X5,tc_Type_Otype),c_List_Omap(c_COMBC(c_Lambda_Olift,X4,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X2,tc_Lambda_OdB,tc_Lambda_OdB),X3)
    | ~ c_Type_Otypings(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_993]) ).

cnf(c_0_1486,plain,
    ( c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X1,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)
    | ~ c_List_Olistsp(c_InductTermi_OIT,X1,tc_Lambda_OdB) ),
    inference(split_conjunct,[status(thm)],[c_0_994]) ).

cnf(c_0_1487,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)
    | ~ 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_995]) ).

cnf(c_0_1488,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_996]) ).

cnf(c_0_1489,plain,
    ( 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))
    | ~ c_Lambda_Obeta(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_997]) ).

cnf(c_0_1490,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_998]) ).

cnf(c_0_1491,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_999]) ).

cnf(c_0_1492,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_1000]) ).

cnf(c_0_1493,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_1001]) ).

cnf(c_0_1494,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_1002]) ).

cnf(c_0_1495,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_1003]) ).

cnf(c_0_1496,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_1004]) ).

cnf(c_0_1497,plain,
    ( hBOOL(hAPP(X1,X2))
    | X3 = c_HOL_Ozero__class_Ozero(tc_nat)
    | ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X3,X4,tc_nat)),X2),X3,tc_nat)))
    | ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1005]) ).

cnf(c_0_1498,plain,
    ( hBOOL(hAPP(X1,X2))
    | X3 = c_HOL_Ozero__class_Ozero(tc_nat)
    | ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat)),X4),X3,tc_nat)))
    | ~ c_HOL_Oord__class_Oless(X4,X3,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1006]) ).

cnf(c_0_1499,plain,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,c_Divides_Odiv__class_Odiv(X3,X2,X1),X1)),c_Divides_Odiv__class_Omod(X3,X2,X1))),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1007]) ).

cnf(c_0_1500,plain,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X3,X1),X3,X1)),c_Divides_Odiv__class_Omod(X2,X3,X1))),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1008]) ).

cnf(c_0_1501,plain,
    ( hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,X3),hAPP(hAPP(c_Lambda_Olift,X4),X1)),c_Suc(X2))),hAPP(hAPP(hAPP(c_Lambda_Osubst,X5),X4),X2)),X1) = hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,X3),X5),X1)),X4),X2)
    | ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1009]) ).

cnf(c_0_1502,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_1010]) ).

cnf(c_0_1503,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_1011]) ).

cnf(c_0_1504,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_1012]) ).

cnf(c_0_1505,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_1013]) ).

cnf(c_0_1506,plain,
    ( hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(hAPP(c_Lambda_Osubst,X3),X4),X1)),X2) = hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)))),hAPP(hAPP(c_Lambda_Olift,X4),X2)),X1)
    | ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1014]) ).

cnf(c_0_1507,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_Finite__Set_Osetsum(X3,c_SetInterval_Oord__class_OatLeastLessThan(X2,c_Suc(X1),tc_nat),tc_nat,X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),c_Finite__Set_Osetsum(X3,c_SetInterval_Oord__class_OatLeastLessThan(X2,X1,tc_nat),tc_nat,X4)),hAPP(X3,X1))
    | ~ class_OrderedGroup_Ocomm__monoid__add(X4) ),
    inference(split_conjunct,[status(thm)],[c_0_1015]) ).

cnf(c_0_1508,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_1016]) ).

cnf(c_0_1509,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_1017]) ).

cnf(c_0_1510,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_1018]) ).

cnf(c_0_1511,plain,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X3,c_Divides_Odiv__class_Omod(X4,X1,tc_nat),tc_nat)),X2),c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1019]) ).

cnf(c_0_1512,plain,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)),X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1020]) ).

cnf(c_0_1513,plain,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X4,X3,X1)),X5)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X3,X1)),X5)
    | ~ class_Ring__and__Field_Osemiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1021]) ).

cnf(c_0_1514,plain,
    ( ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X2,X1)),c_HOL_Otimes__class_Otimes(X3,X3,X1)),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1022]) ).

cnf(c_0_1515,plain,
    ( c_Finite__Set_Osetsum(X3,c_SetInterval_Oord__class_OatLeastLessThan(X1,X2,tc_nat),tc_nat,X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),hAPP(X3,X1)),c_Finite__Set_Osetsum(X3,c_SetInterval_Oord__class_OatLeastLessThan(c_Suc(X1),X2,tc_nat),tc_nat,X4))
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X4) ),
    inference(split_conjunct,[status(thm)],[c_0_1023]) ).

cnf(c_0_1516,plain,
    ( hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(hAPP(c_Lambda_Osubst,X3),X4),X2)),X1) = hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,X3),X1)),hAPP(hAPP(c_Lambda_Olift,X4),X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)))
    | ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1024]) ).

cnf(c_0_1517,plain,
    ( X1 = X2
    | X3 = X4
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_HOL_Otimes__class_Otimes(X1,X3,X5)),c_HOL_Otimes__class_Otimes(X2,X4,X5)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_HOL_Otimes__class_Otimes(X1,X4,X5)),c_HOL_Otimes__class_Otimes(X2,X3,X5))
    | ~ class_Int_Onumber__ring(X5)
    | ~ class_Ring__and__Field_Oidom(X5) ),
    inference(split_conjunct,[status(thm)],[c_0_1025]) ).

cnf(c_0_1518,plain,
    ( X1 = X2
    | X3 = X4
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_HOL_Otimes__class_Otimes(X1,X3,X5)),c_HOL_Otimes__class_Otimes(X2,X4,X5)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_HOL_Otimes__class_Otimes(X1,X4,X5)),c_HOL_Otimes__class_Otimes(X2,X3,X5))
    | ~ class_Int_Onumber__ring(X5)
    | ~ class_Ring__and__Field_Oidom(X5) ),
    inference(split_conjunct,[status(thm)],[c_0_1026]) ).

cnf(c_0_1519,plain,
    ( c_Type_Otyping(X1,hAPP(hAPP(hAPP(c_Lambda_Osubst,X2),X3),X4),X5)
    | ~ c_Type_Otyping(c_Type_Oshift(X1,X4,X6,tc_Type_Otype),X2,X5)
    | ~ c_Type_Otyping(X1,X3,X6) ),
    inference(split_conjunct,[status(thm)],[c_0_1027]) ).

cnf(c_0_1520,plain,
    ( X1 = X2
    | X3 = X4
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat)),c_HOL_Otimes__class_Otimes(X2,X4,tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X1,X4,tc_nat)),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat)) ),
    inference(split_conjunct,[status(thm)],[c_0_1028]) ).

cnf(c_0_1521,plain,
    ( X1 = X2
    | X3 = X4
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat)),c_HOL_Otimes__class_Otimes(X2,X4,tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X1,X4,tc_nat)),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat)) ),
    inference(split_conjunct,[status(thm)],[c_0_1029]) ).

cnf(c_0_1522,plain,
    ( c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X4,X1) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_Divides_Odiv__class_Omod(X2,X4,X1)),c_Divides_Odiv__class_Omod(X3,X4,X1)),X4,X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1030]) ).

cnf(c_0_1523,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(X2)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_HOL_Otimes__class_Otimes(X1,X1,X2)),c_HOL_Otimes__class_Otimes(X3,X3,X2)),X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1031]) ).

cnf(c_0_1524,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(X2)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_HOL_Otimes__class_Otimes(X3,X3,X2)),c_HOL_Otimes__class_Otimes(X1,X1,X2)),X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1032]) ).

cnf(c_0_1525,plain,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,c_Divides_Odiv__class_Odiv(X3,X2,X1),X1)),c_Divides_Odiv__class_Omod(X3,X2,X1)) = X3
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1033]) ).

cnf(c_0_1526,plain,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X3,X1),X3,X1)),c_Divides_Odiv__class_Omod(X2,X3,X1)) = X2
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1034]) ).

cnf(c_0_1527,plain,
    ( X1 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X1,X3,X2),X3,X2)),c_Divides_Odiv__class_Omod(X1,X3,X2))
    | ~ class_Divides_Osemiring__div(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1035]) ).

cnf(c_0_1528,plain,
    ( c_Finite__Set_Osetsum(X1,c_SetInterval_Oord__class_OatLeastLessThan(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat),tc_nat,X3) = c_Finite__Set_Osetsum(X1,c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat),tc_nat,X3)
    | hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Ozero__class_Ozero(X3)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1036]) ).

cnf(c_0_1529,plain,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1)),c_HOL_Otimes__class_Otimes(X2,X4,X1)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X4,X1)),c_HOL_Otimes__class_Otimes(X2,X3,X1))
    | ~ class_Int_Onumber__ring(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1037]) ).

cnf(c_0_1530,plain,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1)),c_HOL_Otimes__class_Otimes(X2,X4,X1)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X4,X1)),c_HOL_Otimes__class_Otimes(X2,X3,X1))
    | ~ class_Int_Onumber__ring(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1038]) ).

cnf(c_0_1531,plain,
    ( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X1,X4,X3),c_Divides_Odiv__class_Omod(X2,X4,X3),X3),X4,X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1039]) ).

cnf(c_0_1532,plain,
    ( c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X4,X1) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_Divides_Odiv__class_Omod(X2,X4,X1)),X3),X4,X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1040]) ).

cnf(c_0_1533,plain,
    ( c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_Divides_Odiv__class_Omod(X2,X3,X1)),X4),X3,X1) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X3,X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1041]) ).

cnf(c_0_1534,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_1042]) ).

cnf(c_0_1535,plain,
    ( c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X1,X3),c_Divides_Odiv__class_Odiv(X5,X4,X3),X3) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X2,X5,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X5,X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1043]) ).

cnf(c_0_1536,plain,
    ( c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4),X1,X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_Divides_Odiv__class_Odiv(X2,X1,X3)),c_Divides_Odiv__class_Odiv(X4,X1,X3))
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1044]) ).

cnf(c_0_1537,plain,
    ( c_Type_Otyping(c_Type_Oshift(X1,X4,X5,tc_Type_Otype),hAPP(hAPP(c_Lambda_Olift,X2),X4),X3)
    | ~ c_Type_Otyping(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1045]) ).

cnf(c_0_1538,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X3,X1),X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1046]) ).

cnf(c_0_1539,plain,
    ( c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,c_Suc(c_Divides_Odiv__class_Odiv(X1,X2,tc_nat)),tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1047]) ).

cnf(c_0_1540,plain,
    ( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X5,X6,X3),X4,X3)
    | c_Divides_Odiv__class_Omod(X1,X4,X3) != c_Divides_Odiv__class_Omod(X5,X4,X3)
    | c_Divides_Odiv__class_Omod(X2,X4,X3) != c_Divides_Odiv__class_Omod(X6,X4,X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1048]) ).

cnf(c_0_1541,plain,
    ( c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X4,X1) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X5),X6),X4,X1)
    | c_Divides_Odiv__class_Omod(X2,X4,X1) != c_Divides_Odiv__class_Omod(X5,X4,X1)
    | c_Divides_Odiv__class_Omod(X3,X4,X1) != c_Divides_Odiv__class_Omod(X6,X4,X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1049]) ).

cnf(c_0_1542,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(X2,X1,X3),c_Divides_Odiv__class_Odiv(X4,X1,X3),X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1050]) ).

cnf(c_0_1543,plain,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X5,X3),X3) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X4,X5,X3),X3),X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1051]) ).

cnf(c_0_1544,plain,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X5,X3),X3) = c_HOL_Otimes__class_Otimes(X4,c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),X5,X3),X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1052]) ).

cnf(c_0_1545,plain,
    ( hAPP(c_Type_Oshift(X3,X2,X4,X5),X1) = hAPP(X3,X1)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1053]) ).

cnf(c_0_1546,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(X2)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_HOL_Otimes__class_Otimes(X3,X3,X2)),c_HOL_Otimes__class_Otimes(X1,X1,X2)) != c_HOL_Ozero__class_Ozero(X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1054]) ).

cnf(c_0_1547,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(X2)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_HOL_Otimes__class_Otimes(X1,X1,X2)),c_HOL_Otimes__class_Otimes(X3,X3,X2)) != c_HOL_Ozero__class_Ozero(X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1055]) ).

cnf(c_0_1548,plain,
    ( hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_Olift,X3),X1)),c_Suc(X2)) = hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_Olift,X3),X2)),X1)
    | ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1056]) ).

cnf(c_0_1549,plain,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_Divides_Odiv__class_Omod(X2,X3,X1)),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X3,X1),X3,X1)) = X2
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1057]) ).

cnf(c_0_1550,plain,
    ( c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X3,X1),X1),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1058]) ).

cnf(c_0_1551,plain,
    ( c_HOL_Oord__class_Oless(X4,X3,X2)
    | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Otimes__class_Otimes(X1,X4,X2),X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1059]) ).

cnf(c_0_1552,plain,
    ( c_HOL_Oord__class_Oless(X3,X4,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1060]) ).

cnf(c_0_1553,plain,
    ( c_HOL_Oord__class_Oless(X3,X4,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
    | ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1061]) ).

cnf(c_0_1554,plain,
    ( c_HOL_Oord__class_Oless(X3,X4,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
    | ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1062]) ).

cnf(c_0_1555,plain,
    ( c_Divides_Odiv__class_Omod(X1,X2,tc_nat) = c_Divides_Odiv__class_Omod(X3,X2,tc_nat)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Otimes__class_Otimes(X2,X4,tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Otimes__class_Otimes(X2,X5,tc_nat)) ),
    inference(split_conjunct,[status(thm)],[c_0_1063]) ).

cnf(c_0_1556,plain,
    ( c_HOL_Oord__class_Oless(X2,X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1064]) ).

cnf(c_0_1557,plain,
    ( c_HOL_Oord__class_Oless(X2,X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X2,tc_nat),c_Power_Opower__class_Opower(X1,X3,tc_nat),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1065]) ).

cnf(c_0_1558,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1066]) ).

cnf(c_0_1559,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1067]) ).

cnf(c_0_1560,plain,
    ( c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X4,X2,X3),c_Power_Opower__class_Opower(X4,X1,X3),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
    | ~ c_HOL_Oord__class_Oless(X4,c_HOL_Oone__class_Oone(X3),X3)
    | ~ class_Ring__and__Field_Oordered__semidom(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1068]) ).

cnf(c_0_1561,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
    | c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1069]) ).

cnf(c_0_1562,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
    | c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1070]) ).

cnf(c_0_1563,plain,
    ( c_HOL_Oord__class_Oless(X1,X4,X3)
    | c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1071]) ).

cnf(c_0_1564,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
    | c_HOL_Oord__class_Oless(X4,X1,X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1072]) ).

cnf(c_0_1565,plain,
    ( c_HOL_Oord__class_Oless(X2,X4,X3)
    | c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1073]) ).

cnf(c_0_1566,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
    | c_HOL_Oord__class_Oless(X4,X2,X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1074]) ).

cnf(c_0_1567,plain,
    ( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X1,X2,X3),X4,X3),X2,X3) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X4,X3),X2,X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1075]) ).

cnf(c_0_1568,plain,
    ( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X1,X4,X3),X2,X3),X4,X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1076]) ).

cnf(c_0_1569,plain,
    ( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Omod(X2,X4,X3),X3),X4,X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1077]) ).

cnf(c_0_1570,plain,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X5,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1078]) ).

cnf(c_0_1571,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(X2)
    | c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),c_HOL_Otimes__class_Otimes(X1,X4,X2)),X1,X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X4),c_Divides_Odiv__class_Odiv(X3,X1,X2))
    | ~ class_Divides_Osemiring__div(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1079]) ).

cnf(c_0_1572,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(X2)
    | c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),c_HOL_Otimes__class_Otimes(X4,X1,X2)),X1,X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X4),c_Divides_Odiv__class_Odiv(X3,X1,X2))
    | ~ class_Divides_Osemiring__div(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1080]) ).

cnf(c_0_1573,plain,
    ( c_HOL_Oord__class_Oless(X2,X4,X3)
    | c_HOL_Oord__class_Oless(X4,X2,X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1081]) ).

cnf(c_0_1574,plain,
    ( c_HOL_Oord__class_Oless(X1,X4,X3)
    | c_HOL_Oord__class_Oless(X4,X1,X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1082]) ).

cnf(c_0_1575,plain,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1)),c_HOL_Otimes__class_Otimes(X4,X3,X1)) = c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X3,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1083]) ).

cnf(c_0_1576,plain,
    ( c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X4,X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X4,X1)),c_HOL_Otimes__class_Otimes(X3,X4,X1))
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1084]) ).

cnf(c_0_1577,plain,
    ( c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X4,X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X4,X1)),c_HOL_Otimes__class_Otimes(X3,X4,X1))
    | ~ class_Ring__and__Field_Ocomm__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1085]) ).

cnf(c_0_1578,plain,
    ( c_HOL_Otimes__class_Otimes(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),X4),X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_HOL_Otimes__class_Otimes(X1,X3,X2)),c_HOL_Otimes__class_Otimes(X1,X4,X2))
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1086]) ).

cnf(c_0_1579,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(X2,X1,X3),c_Divides_Odiv__class_Odiv(X4,X1,X3),X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1087]) ).

cnf(c_0_1580,plain,
    ( c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X4,X1) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_Divides_Odiv__class_Omod(X3,X4,X1)),X4,X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1088]) ).

cnf(c_0_1581,plain,
    ( c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_Divides_Odiv__class_Omod(X3,X4,X1)),X4,X1) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X4,X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1089]) ).

cnf(c_0_1582,plain,
    ( c_Power_Opower__class_Opower(c_Divides_Odiv__class_Odiv(X2,X1,X3),X4,X3) = c_Divides_Odiv__class_Odiv(c_Power_Opower__class_Opower(X2,X4,X3),c_Power_Opower__class_Opower(X1,X4,X3),X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1090]) ).

cnf(c_0_1583,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(X2)
    | X3 = X4
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X5),c_HOL_Otimes__class_Otimes(X1,X3,X2)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X5),c_HOL_Otimes__class_Otimes(X1,X4,X2))
    | ~ class_Int_Onumber__ring(X2)
    | ~ class_Ring__and__Field_Oidom(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1091]) ).

cnf(c_0_1584,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_1092]) ).

cnf(c_0_1585,plain,
    ( c_HOL_Oord__class_Oless(X2,X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X1),X2,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X1),X3,tc_nat),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1093]) ).

cnf(c_0_1586,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(X3)
    | c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
    | ~ class_Ring__and__Field_Oidom(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1094]) ).

cnf(c_0_1587,plain,
    ( X2 = c_HOL_Ozero__class_Ozero(X3)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
    | ~ class_Ring__and__Field_Oidom(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1095]) ).

cnf(c_0_1588,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X3,X1),X1),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1096]) ).

cnf(c_0_1589,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X2 = X3
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat)) ),
    inference(split_conjunct,[status(thm)],[c_0_1097]) ).

cnf(c_0_1590,plain,
    ( c_HOL_Oord__class_Oless(X2,X4,X1)
    | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3),X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1098]) ).

cnf(c_0_1591,plain,
    ( c_HOL_Oord__class_Oless(X3,X4,X1)
    | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1099]) ).

cnf(c_0_1592,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1100]) ).

cnf(c_0_1593,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1101]) ).

cnf(c_0_1594,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1102]) ).

cnf(c_0_1595,plain,
    ( c_HOL_Oord__class_Oless(X2,X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1103]) ).

cnf(c_0_1596,plain,
    ( c_HOL_Oord__class_Oless(X1,X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1104]) ).

cnf(c_0_1597,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
    | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_HOL_Oord__class_Oless(X3,X4,X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1105]) ).

cnf(c_0_1598,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_HOL_Oord__class_Oless(X3,X4,X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1106]) ).

cnf(c_0_1599,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X2,X3),c_HOL_Otimes__class_Otimes(X4,X1,X3),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1107]) ).

cnf(c_0_1600,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X1,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1108]) ).

cnf(c_0_1601,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_HOL_Oord__class_Oless(X3,X4,X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1109]) ).

cnf(c_0_1602,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
    | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_HOL_Oord__class_Oless(X3,X4,X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1110]) ).

cnf(c_0_1603,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X4,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1111]) ).

cnf(c_0_1604,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1112]) ).

cnf(c_0_1605,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X2,X1),c_HOL_Otimes__class_Otimes(X4,X2,X1),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_HOL_Oord__class_Oless(X3,X4,X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1113]) ).

cnf(c_0_1606,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X1,X2),c_HOL_Otimes__class_Otimes(X3,X1,X2),X2)
    | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_HOL_Oord__class_Oless(X3,X4,X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1114]) ).

cnf(c_0_1607,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X1,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1115]) ).

cnf(c_0_1608,plain,
    ( c_Finite__Set_Osetsum(X3,c_SetInterval_Oord__class_OatLeastLessThan(X2,c_Suc(X1),tc_nat),tc_nat,X4) = c_HOL_Ozero__class_Ozero(X4)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X4) ),
    inference(split_conjunct,[status(thm)],[c_0_1116]) ).

cnf(c_0_1609,plain,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1117]) ).

cnf(c_0_1610,plain,
    ( c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
    | ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1118]) ).

cnf(c_0_1611,plain,
    ( c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X4,X1,X3),c_Power_Opower__class_Opower(X4,X2,X3),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X4,X3)
    | ~ class_Ring__and__Field_Oordered__semidom(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1119]) ).

cnf(c_0_1612,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X5,X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1120]) ).

cnf(c_0_1613,plain,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1)),X3) = c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Oone__class_Oone(X1)),X3,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1121]) ).

cnf(c_0_1614,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(X2)
    | c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X3),X1,X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_Divides_Odiv__class_Odiv(X3,X1,X2)),c_HOL_Oone__class_Oone(X2))
    | ~ class_Divides_Osemiring__div(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1122]) ).

cnf(c_0_1615,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(X2)
    | c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),X1),X1,X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_Divides_Odiv__class_Odiv(X3,X1,X2)),c_HOL_Oone__class_Oone(X2))
    | ~ class_Divides_Osemiring__div(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1123]) ).

cnf(c_0_1616,plain,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X5),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X4,X5,X3)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1124]) ).

cnf(c_0_1617,plain,
    ( c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X4,X3),c_Power_Opower__class_Opower(X2,X4,X3),X3)
    | ~ class_OrderedGroup_Ocomm__monoid__mult(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1125]) ).

cnf(c_0_1618,plain,
    ( c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X4,X3),c_Power_Opower__class_Opower(X2,X4,X3),X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1126]) ).

cnf(c_0_1619,plain,
    ( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X1,X4,X3),X2,X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1127]) ).

cnf(c_0_1620,plain,
    ( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3) = c_HOL_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Omod(X2,X4,X3),X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1128]) ).

cnf(c_0_1621,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1129]) ).

cnf(c_0_1622,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1130]) ).

cnf(c_0_1623,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1131]) ).

cnf(c_0_1624,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1132]) ).

cnf(c_0_1625,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1133]) ).

cnf(c_0_1626,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1134]) ).

cnf(c_0_1627,plain,
    ( c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Otimes__class_Otimes(X3,X4,X1)),X4,X1) = c_Divides_Odiv__class_Omod(X2,X4,X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1135]) ).

cnf(c_0_1628,plain,
    ( c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Otimes__class_Otimes(X3,X4,X1)),X3,X1) = c_Divides_Odiv__class_Omod(X2,X3,X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1136]) ).

cnf(c_0_1629,plain,
    ( hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
    | ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))) ),
    inference(split_conjunct,[status(thm)],[c_0_1137]) ).

cnf(c_0_1630,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1138]) ).

cnf(c_0_1631,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1139]) ).

cnf(c_0_1632,plain,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))) ),
    inference(split_conjunct,[status(thm)],[c_0_1140]) ).

cnf(c_0_1633,plain,
    ( c_HOL_Oord__class_Oless(X2,X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1141]) ).

cnf(c_0_1634,plain,
    ( c_Power_Opower__class_Opower(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),X4) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X2,X4),c_Power_Opower__class_Opower(X1,X3,X4),X4)
    | ~ class_OrderedGroup_Omonoid__mult(X4) ),
    inference(split_conjunct,[status(thm)],[c_0_1142]) ).

cnf(c_0_1635,plain,
    ( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X4,X3),X3) = c_Power_Opower__class_Opower(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X4),X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1143]) ).

cnf(c_0_1636,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_1144]) ).

cnf(c_0_1637,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_1145]) ).

cnf(c_0_1638,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_1146]) ).

cnf(c_0_1639,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_1147]) ).

cnf(c_0_1640,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_1148]) ).

cnf(c_0_1641,plain,
    ( c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X1,X3),X4,X3) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X2,X4,X3),X1,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1149]) ).

cnf(c_0_1642,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X4)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_Divides_Odiv__class_Omod(X2,X3,X4),X4)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X3,X4)
    | ~ class_Divides_Osemiring__div(X4) ),
    inference(split_conjunct,[status(thm)],[c_0_1150]) ).

cnf(c_0_1643,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_Divides_Odiv__class_Omod(X4,X2,X3),X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1151]) ).

cnf(c_0_1644,plain,
    ( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) = c_Divides_Odiv__class_Odiv(X2,X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1152]) ).

cnf(c_0_1645,plain,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X4),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1153]) ).

cnf(c_0_1646,plain,
    ( X1 = c_List_Olist_ONil(X2)
    | c_List_Omap(X3,X1,X2,X4) != c_List_Olist_ONil(X4) ),
    inference(split_conjunct,[status(thm)],[c_0_1154]) ).

cnf(c_0_1647,plain,
    ( X1 = c_List_Olist_ONil(X2)
    | c_List_Olist_ONil(X3) != c_List_Omap(X4,X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1155]) ).

cnf(c_0_1648,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_1156]) ).

cnf(c_0_1649,plain,
    ( c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,c_Suc(X3),X1),c_HOL_Oone__class_Oone(X1),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1157]) ).

cnf(c_0_1650,plain,
    ( c_Lambda_Obeta(hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X3),X4),hAPP(hAPP(hAPP(c_Lambda_Osubst,X2),X3),X4))
    | ~ c_Lambda_Obeta(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1158]) ).

cnf(c_0_1651,plain,
    ( c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1159]) ).

cnf(c_0_1652,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X3),X1,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X3),X2,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1160]) ).

cnf(c_0_1653,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X3,X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1161]) ).

cnf(c_0_1654,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1162]) ).

cnf(c_0_1655,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
    | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1163]) ).

cnf(c_0_1656,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1164]) ).

cnf(c_0_1657,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1165]) ).

cnf(c_0_1658,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1166]) ).

cnf(c_0_1659,plain,
    ( c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1167]) ).

cnf(c_0_1660,plain,
    ( c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1168]) ).

cnf(c_0_1661,plain,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X3),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1169]) ).

cnf(c_0_1662,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1170]) ).

cnf(c_0_1663,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ class_Ring__and__Field_Oidom(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1171]) ).

cnf(c_0_1664,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X4,X1,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ class_Ring__and__Field_Oidom(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1172]) ).

cnf(c_0_1665,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(X1,X4,X3),c_Power_Opower__class_Opower(X2,X4,X3),X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1173]) ).

cnf(c_0_1666,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1174]) ).

cnf(c_0_1667,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X3,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1175]) ).

cnf(c_0_1668,plain,
    ( c_Divides_Odiv__class_Omod(c_Suc(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat)),X1,tc_nat) = c_HOL_Oone__class_Oone(tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1176]) ).

cnf(c_0_1669,plain,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1177]) ).

cnf(c_0_1670,plain,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1178]) ).

cnf(c_0_1671,plain,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1179]) ).

cnf(c_0_1672,plain,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1180]) ).

cnf(c_0_1673,plain,
    ( c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_HOL_Oord__class_Oless(X3,X4,X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1181]) ).

cnf(c_0_1674,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1182]) ).

cnf(c_0_1675,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1183]) ).

cnf(c_0_1676,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,c_Divides_Odiv__class_Omod(X4,X2,X3),X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1184]) ).

cnf(c_0_1677,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,c_Divides_Odiv__class_Omod(X2,X4,X3),X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1185]) ).

cnf(c_0_1678,plain,
    ( X2 = c_HOL_Oone__class_Oone(tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1186]) ).

cnf(c_0_1679,plain,
    ( X2 = c_HOL_Oone__class_Oone(tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),X1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1187]) ).

cnf(c_0_1680,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1188]) ).

cnf(c_0_1681,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4),X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1189]) ).

cnf(c_0_1682,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(X2)
    | c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Otimes__class_Otimes(X1,X4,X2),X2) = c_Divides_Odiv__class_Odiv(X3,X4,X2)
    | ~ class_Divides_Osemiring__div(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1190]) ).

cnf(c_0_1683,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(X2)
    | c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X3,X1,X2),c_HOL_Otimes__class_Otimes(X4,X1,X2),X2) = c_Divides_Odiv__class_Odiv(X3,X4,X2)
    | ~ class_Divides_Osemiring__div(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1191]) ).

cnf(c_0_1684,plain,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Otimes__class_Otimes(X3,X2,X1)) = c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),c_HOL_Oone__class_Oone(X1)),X2,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1192]) ).

cnf(c_0_1685,plain,
    ( c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Odiv(X2,X1,tc_nat),X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1193]) ).

cnf(c_0_1686,plain,
    ( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X2,X3),X1,X3) = c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X3),X3)
    | ~ class_OrderedGroup_Omonoid__mult(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1194]) ).

cnf(c_0_1687,plain,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
    | ~ class_OrderedGroup_Oab__semigroup__mult(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1195]) ).

cnf(c_0_1688,plain,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X4,X3),X2,X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1196]) ).

cnf(c_0_1689,plain,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1197]) ).

cnf(c_0_1690,plain,
    ( c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X4),X3,X4)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X4) ),
    inference(split_conjunct,[status(thm)],[c_0_1198]) ).

cnf(c_0_1691,plain,
    ( c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X1,X3,X4),X4)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X4) ),
    inference(split_conjunct,[status(thm)],[c_0_1199]) ).

cnf(c_0_1692,plain,
    ( c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X4),X3,X4)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X4) ),
    inference(split_conjunct,[status(thm)],[c_0_1200]) ).

cnf(c_0_1693,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X3,X2,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1201]) ).

cnf(c_0_1694,plain,
    ( c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(X1,X2,X3),X4,X3) = c_Power_Opower__class_Opower(X1,c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1202]) ).

cnf(c_0_1695,plain,
    ( c_Power_Opower__class_Opower(X1,c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X4) = c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(X1,X2,X4),X3,X4)
    | ~ class_OrderedGroup_Omonoid__mult(X4) ),
    inference(split_conjunct,[status(thm)],[c_0_1203]) ).

cnf(c_0_1696,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1204]) ).

cnf(c_0_1697,plain,
    ( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1205]) ).

cnf(c_0_1698,plain,
    ( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1206]) ).

cnf(c_0_1699,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) = c_Divides_Odiv__class_Odiv(X2,X3,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1207]) ).

cnf(c_0_1700,plain,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1208]) ).

cnf(c_0_1701,plain,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1209]) ).

cnf(c_0_1702,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1210]) ).

cnf(c_0_1703,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1211]) ).

cnf(c_0_1704,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_1212]) ).

cnf(c_0_1705,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_1213]) ).

cnf(c_0_1706,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_1214]) ).

cnf(c_0_1707,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | X2 = c_HOL_Ozero__class_Ozero(tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Power_Opower__class_Opower(X1,X2,tc_nat),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1215]) ).

cnf(c_0_1708,plain,
    ( c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X4,X2,X3),X1,X3) = c_Divides_Odiv__class_Omod(X4,X1,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1216]) ).

cnf(c_0_1709,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1217]) ).

cnf(c_0_1710,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1218]) ).

cnf(c_0_1711,plain,
    ( hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)))
    | ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
    inference(split_conjunct,[status(thm)],[c_0_1219]) ).

cnf(c_0_1712,plain,
    ( hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)))
    | ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
    inference(split_conjunct,[status(thm)],[c_0_1220]) ).

cnf(c_0_1713,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1221]) ).

cnf(c_0_1714,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X3,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1222]) ).

cnf(c_0_1715,plain,
    ( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X3,X1),X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1223]) ).

cnf(c_0_1716,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X2),X2),c_HOL_Otimes__class_Otimes(X3,c_HOL_Ozero__class_Ozero(X2),X2),X2)
    | ~ class_Ring__and__Field_Oidom(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1224]) ).

cnf(c_0_1717,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X3,X1),X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1225]) ).

cnf(c_0_1718,plain,
    ( hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)))
    | ~ hBOOL(hAPP(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_1226]) ).

cnf(c_0_1719,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_Power_Opower__class_Opower(X2,c_Suc(X3),X1),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1227]) ).

cnf(c_0_1720,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X4) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1228]) ).

cnf(c_0_1721,plain,
    ( c_HOL_Oord__class_Oless(X1,X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X3,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1229]) ).

cnf(c_0_1722,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1230]) ).

cnf(c_0_1723,plain,
    ( X1 = X2
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X4,X3)
    | c_Power_Opower__class_Opower(X4,X1,X3) != c_Power_Opower__class_Opower(X4,X2,X3)
    | ~ class_Ring__and__Field_Oordered__semidom(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1231]) ).

cnf(c_0_1724,plain,
    ( c_Suc(c_Divides_Odiv__class_Omod(X1,X2,tc_nat)) = X2
    | c_Divides_Odiv__class_Omod(c_Suc(X1),X2,tc_nat) = c_Suc(c_Divides_Odiv__class_Omod(X1,X2,tc_nat)) ),
    inference(split_conjunct,[status(thm)],[c_0_1232]) ).

cnf(c_0_1725,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X3,X2,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1233]) ).

cnf(c_0_1726,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1234]) ).

cnf(c_0_1727,plain,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1235]) ).

cnf(c_0_1728,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1236]) ).

cnf(c_0_1729,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1237]) ).

cnf(c_0_1730,plain,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X1),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1238]) ).

cnf(c_0_1731,plain,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X1),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1239]) ).

cnf(c_0_1732,plain,
    ( X1 = X2
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
    | c_HOL_Otimes__class_Otimes(X3,X1,tc_nat) != c_HOL_Otimes__class_Otimes(X3,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1240]) ).

cnf(c_0_1733,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X2,c_Power_Opower__class_Opower(X2,X1,X3),X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1241]) ).

cnf(c_0_1734,plain,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1242]) ).

cnf(c_0_1735,plain,
    ( c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X1,X3),X1,X3) = X2
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1243]) ).

cnf(c_0_1736,plain,
    ( c_HOL_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Odiv(X2,X1,X3),X3) = X2
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1244]) ).

cnf(c_0_1737,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1245]) ).

cnf(c_0_1738,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1246]) ).

cnf(c_0_1739,plain,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2) = c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Oone__class_Oone(X1)),c_HOL_Oone__class_Oone(X1)),X2,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1247]) ).

cnf(c_0_1740,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1248]) ).

cnf(c_0_1741,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat),X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1249]) ).

cnf(c_0_1742,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Power_Opower__class_Opower(X1,X2,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1250]) ).

cnf(c_0_1743,plain,
    ( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),X1,tc_nat) = X2
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1251]) ).

cnf(c_0_1744,plain,
    ( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X1,tc_nat) = X2
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1252]) ).

cnf(c_0_1745,plain,
    ( c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Omod(X2,X1,tc_nat),X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1253]) ).

cnf(c_0_1746,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_1254]) ).

cnf(c_0_1747,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1255]) ).

cnf(c_0_1748,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1256]) ).

cnf(c_0_1749,plain,
    ( c_HOL_Oord__class_Oless(X4,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X4,X1,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1257]) ).

cnf(c_0_1750,plain,
    ( c_HOL_Oord__class_Oless(X1,X4,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X2,X4,X3)
    | ~ class_Orderings_Opreorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1258]) ).

cnf(c_0_1751,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1259]) ).

cnf(c_0_1752,plain,
    ( c_Divides_Odiv__class_Omod(c_Suc(X1),X2,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_Suc(c_Divides_Odiv__class_Omod(X1,X2,tc_nat)) != X2 ),
    inference(split_conjunct,[status(thm)],[c_0_1260]) ).

cnf(c_0_1753,plain,
    ( c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X3) = c_HOL_Otimes__class_Otimes(c_Nat_Osemiring__1__class_Oof__nat(X1,X3),c_Nat_Osemiring__1__class_Oof__nat(X2,X3),X3)
    | ~ class_Ring__and__Field_Osemiring__1(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1261]) ).

cnf(c_0_1754,plain,
    ( c_Power_Opower__class_Opower(X1,c_Suc(X2),X3) = c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X3),X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1262]) ).

cnf(c_0_1755,plain,
    ( c_Power_Opower__class_Opower(X1,c_Suc(X2),X3) = c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X3),X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1263]) ).

cnf(c_0_1756,plain,
    ( c_Power_Opower__class_Opower(X1,c_Suc(X2),X3) = c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X3),X3)
    | ~ class_Power_Opower(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1264]) ).

cnf(c_0_1757,plain,
    ( c_Power_Opower__class_Opower(X1,c_Suc(X2),X3) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X2,X3),X1,X3)
    | ~ class_OrderedGroup_Omonoid__mult(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1265]) ).

cnf(c_0_1758,plain,
    ( c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X3),X3) = c_Power_Opower__class_Opower(X1,c_Suc(X2),X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1266]) ).

cnf(c_0_1759,plain,
    ( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X2,X3),X1,X3) = c_Power_Opower__class_Opower(X1,c_Suc(X2),X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1267]) ).

cnf(c_0_1760,plain,
    ( c_HOL_Oord__class_Oless(X1,X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_Nat_Osemiring__1__class_Oof__nat(X3,X2),X2)
    | ~ class_Ring__and__Field_Oordered__semidom(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1268]) ).

cnf(c_0_1761,plain,
    ( c_Divides_Odiv__class_Odiv(X2,X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1269]) ).

cnf(c_0_1762,plain,
    ( c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1270]) ).

cnf(c_0_1763,plain,
    ( c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1271]) ).

cnf(c_0_1764,plain,
    ( c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1272]) ).

cnf(c_0_1765,plain,
    ( c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1273]) ).

cnf(c_0_1766,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1),tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1274]) ).

cnf(c_0_1767,plain,
    ( c_HOL_Oord__class_Oless(c_Suc(X1),X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1275]) ).

cnf(c_0_1768,plain,
    ( c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X1,X2,X3),X2,X3) = c_Divides_Odiv__class_Omod(X1,X2,X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1276]) ).

cnf(c_0_1769,plain,
    ( c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X1,X2,X3),X3) = c_HOL_Otimes__class_Otimes(X1,X2,X3)
    | ~ class_OrderedGroup_Oab__semigroup__idem__mult(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1277]) ).

cnf(c_0_1770,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1278]) ).

cnf(c_0_1771,plain,
    ( c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X3,X1) = c_Divides_Odiv__class_Omod(X2,X3,X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1279]) ).

cnf(c_0_1772,plain,
    ( c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X2,X1) = c_Divides_Odiv__class_Omod(X3,X2,X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1280]) ).

cnf(c_0_1773,plain,
    ( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_Olift,X1),X2)))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_1281]) ).

cnf(c_0_1774,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Oone__class_Oone(X1)),c_HOL_Oone__class_Oone(X1)),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1282]) ).

cnf(c_0_1775,plain,
    ( c_Nat_Osemiring__1__class_Oof__nat(c_Power_Opower__class_Opower(X1,X2,tc_nat),X3) = c_Power_Opower__class_Opower(c_Nat_Osemiring__1__class_Oof__nat(X1,X3),X2,X3)
    | ~ class_Ring__and__Field_Osemiring__1(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1283]) ).

cnf(c_0_1776,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(X1)),X2) = c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat))) ),
    inference(split_conjunct,[status(thm)],[c_0_1284]) ).

cnf(c_0_1777,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1285]) ).

cnf(c_0_1778,plain,
    ( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X1)),X3),X2) = c_Lambda_OdB_OVar(X1)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1286]) ).

cnf(c_0_1779,plain,
    ( c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X3),c_Nat_Osemiring__1__class_Oof__nat(X2,X3),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ class_Ring__and__Field_Oordered__semidom(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1287]) ).

cnf(c_0_1780,plain,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
    | ~ hBOOL(hAPP(X1,c_Suc(v_sko__List__Xlexn__Xinduct__1(X1)))) ),
    inference(split_conjunct,[status(thm)],[c_0_1288]) ).

cnf(c_0_1781,plain,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
    | ~ hBOOL(hAPP(X1,c_Suc(c_ATP__Linkup_Osko__Nat__Xnat__induct__1__1(X1)))) ),
    inference(split_conjunct,[status(thm)],[c_0_1289]) ).

cnf(c_0_1782,plain,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
    | ~ hBOOL(hAPP(X1,c_Suc(v_sko__List__Xreplicate__Xinduct__1(X1)))) ),
    inference(split_conjunct,[status(thm)],[c_0_1290]) ).

cnf(c_0_1783,plain,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
    | ~ hBOOL(hAPP(X1,c_Suc(v_sko__List__Xupt__Xinduct__1(X1)))) ),
    inference(split_conjunct,[status(thm)],[c_0_1291]) ).

cnf(c_0_1784,plain,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
    | ~ hBOOL(hAPP(X1,c_Suc(v_sko__Nat__Xnat__Xinduct__1(X1)))) ),
    inference(split_conjunct,[status(thm)],[c_0_1292]) ).

cnf(c_0_1785,plain,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
    | ~ hBOOL(hAPP(X1,c_Suc(v_sko__Nat__Xnat__Xinducts__1(X1)))) ),
    inference(split_conjunct,[status(thm)],[c_0_1293]) ).

cnf(c_0_1786,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | X1 = X2
    | c_HOL_Oord__class_Oless(X2,X1,tc_nat)
    | hBOOL(hAPP(hAPP(X3,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_1294]) ).

cnf(c_0_1787,plain,
    ( X1 = X2
    | c_HOL_Otimes__class_Otimes(c_Suc(X3),X1,tc_nat) != c_HOL_Otimes__class_Otimes(c_Suc(X3),X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1295]) ).

cnf(c_0_1788,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(X1),c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X1),X2,X1),X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1296]) ).

cnf(c_0_1789,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_Nat_Osemiring__1__class_Oof__nat(X1,X2),X2)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | ~ class_Ring__and__Field_Oordered__semidom(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1297]) ).

cnf(c_0_1790,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_1298]) ).

cnf(c_0_1791,plain,
    ( c_Lambda_Obeta(hAPP(hAPP(c_Lambda_Olift,X1),X3),hAPP(hAPP(c_Lambda_Olift,X2),X3))
    | ~ c_Lambda_Obeta(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1299]) ).

cnf(c_0_1792,plain,
    ( c_Lambda_Obeta(hAPP(hAPP(c_Lambda_OdB_OApp,X3),X1),hAPP(hAPP(c_Lambda_OdB_OApp,X3),X2))
    | ~ c_Lambda_Obeta(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1300]) ).

cnf(c_0_1793,plain,
    ( c_Lambda_Obeta(hAPP(hAPP(c_Lambda_OdB_OApp,X1),X3),hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3))
    | ~ c_Lambda_Obeta(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1301]) ).

cnf(c_0_1794,plain,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X2,X1,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1302]) ).

cnf(c_0_1795,plain,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X2,X1,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1303]) ).

cnf(c_0_1796,plain,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X2,X1,X3)
    | ~ class_Orderings_Opreorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1304]) ).

cnf(c_0_1797,plain,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X2,X1,X3)
    | ~ class_Orderings_Opreorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1305]) ).

cnf(c_0_1798,plain,
    ( ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1306]) ).

cnf(c_0_1799,plain,
    ( c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),c_HOL_Oone__class_Oone(X2)),X2)
    | ~ class_Ring__and__Field_Oordered__semidom(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1307]) ).

cnf(c_0_1800,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(X2)
    | c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X3,X1,X2),X1,X2) = X3
    | ~ class_Divides_Osemiring__div(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1308]) ).

cnf(c_0_1801,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(X2)
    | c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X1,X3,X2),X1,X2) = X3
    | ~ class_Divides_Osemiring__div(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1309]) ).

cnf(c_0_1802,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_1310]) ).

cnf(c_0_1803,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_1311]) ).

cnf(c_0_1804,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_1312]) ).

cnf(c_0_1805,plain,
    ( c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Omod(X1,X2,X3),X2,X3) = c_HOL_Ozero__class_Ozero(X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1313]) ).

cnf(c_0_1806,plain,
    ( X1 = X2
    | X3 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_HOL_Otimes__class_Otimes(X1,X3,tc_nat) != c_HOL_Otimes__class_Otimes(X2,X3,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1314]) ).

cnf(c_0_1807,plain,
    ( X1 = X2
    | X3 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_HOL_Otimes__class_Otimes(X3,X1,tc_nat) != c_HOL_Otimes__class_Otimes(X3,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1315]) ).

cnf(c_0_1808,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X2 = X3
    | c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_HOL_Otimes__class_Otimes(X1,X3,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1316]) ).

cnf(c_0_1809,plain,
    ( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X3),X2,X3) = c_HOL_Ozero__class_Ozero(X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1317]) ).

cnf(c_0_1810,plain,
    ( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X3),X1,X3) = c_HOL_Ozero__class_Ozero(X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1318]) ).

cnf(c_0_1811,plain,
    ( X1 = X2
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1319]) ).

cnf(c_0_1812,plain,
    ( X1 = X2
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1320]) ).

cnf(c_0_1813,plain,
    ( X1 = X2
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1321]) ).

cnf(c_0_1814,plain,
    ( X1 = X2
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1322]) ).

cnf(c_0_1815,plain,
    ( X2 = X1
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1323]) ).

cnf(c_0_1816,plain,
    ( X1 = X2
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1324]) ).

cnf(c_0_1817,plain,
    ( X1 = X2
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1325]) ).

cnf(c_0_1818,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | X2 = X1
    | hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X2)),X3),X1) = c_Lambda_OdB_OVar(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1326]) ).

cnf(c_0_1819,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X2,X1,X3),X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1327]) ).

cnf(c_0_1820,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1328]) ).

cnf(c_0_1821,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
    | ~ class_Ring__and__Field_Odvd(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1329]) ).

cnf(c_0_1822,plain,
    ( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X1)),X2),X1) = X2
    | c_HOL_Oord__class_Oless(X1,X1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1330]) ).

cnf(c_0_1823,plain,
    ( c_Type_Otyping(X1,X4,X3)
    | ~ c_Type_Otyping(X1,X2,X3)
    | ~ c_Lambda_Obeta(X2,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_1331]) ).

cnf(c_0_1824,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X2),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1332]) ).

cnf(c_0_1825,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | c_Divides_Odiv__class_Omod(X2,X1,X3) != c_HOL_Ozero__class_Ozero(X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1333]) ).

cnf(c_0_1826,plain,
    ( c_Divides_Odiv__class_Omod(X2,X1,X3) = c_HOL_Ozero__class_Ozero(X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1334]) ).

cnf(c_0_1827,plain,
    ( hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
    | ~ hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Nat__Xzero__induct__1__1(X1))) ),
    inference(split_conjunct,[status(thm)],[c_0_1335]) ).

cnf(c_0_1828,plain,
    ( hBOOL(hAPP(X1,c_Suc(c_ATP__Linkup_Osko__Nat__Xzero__induct__1__1(X1))))
    | hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
    | ~ hBOOL(hAPP(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_1336]) ).

cnf(c_0_1829,plain,
    ( c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X2),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1337]) ).

cnf(c_0_1830,plain,
    ( c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X2),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1338]) ).

cnf(c_0_1831,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | X1 = X2
    | ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1339]) ).

cnf(c_0_1832,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | X2 = X1
    | ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1340]) ).

cnf(c_0_1833,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | X1 = X2
    | ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1341]) ).

cnf(c_0_1834,plain,
    ( c_Suc(X1) = X2
    | c_HOL_Oord__class_Oless(c_Suc(X1),X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1342]) ).

cnf(c_0_1835,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_1343]) ).

cnf(c_0_1836,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_1344]) ).

cnf(c_0_1837,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_1345]) ).

cnf(c_0_1838,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_Suc(X1),X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1346]) ).

cnf(c_0_1839,plain,
    ( ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_Ring__and__Field_Oordered__semidom(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1347]) ).

cnf(c_0_1840,plain,
    ( c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1348]) ).

cnf(c_0_1841,plain,
    ( c_Divides_Odiv__class_Odiv(X1,X2,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1349]) ).

cnf(c_0_1842,plain,
    ( c_Divides_Odiv__class_Omod(X1,X2,tc_nat) = X1
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1350]) ).

cnf(c_0_1843,plain,
    ( hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(X1)),X2) = c_Lambda_OdB_OVar(X1)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1351]) ).

cnf(c_0_1844,plain,
    ( hBOOL(hAPP(X1,v_sko__List__Xlexn__Xinduct__1(X1)))
    | hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
    inference(split_conjunct,[status(thm)],[c_0_1352]) ).

cnf(c_0_1845,plain,
    ( hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Nat__Xnat__induct__1__1(X1)))
    | hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
    inference(split_conjunct,[status(thm)],[c_0_1353]) ).

cnf(c_0_1846,plain,
    ( hBOOL(hAPP(X1,v_sko__List__Xreplicate__Xinduct__1(X1)))
    | hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
    inference(split_conjunct,[status(thm)],[c_0_1354]) ).

cnf(c_0_1847,plain,
    ( hBOOL(hAPP(X1,v_sko__Nat__Xnat__Xinducts__1(X1)))
    | hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
    inference(split_conjunct,[status(thm)],[c_0_1355]) ).

cnf(c_0_1848,plain,
    ( hBOOL(hAPP(X1,v_sko__Nat__Xnat__Xinduct__1(X1)))
    | hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
    inference(split_conjunct,[status(thm)],[c_0_1356]) ).

cnf(c_0_1849,plain,
    ( hBOOL(hAPP(X1,v_sko__List__Xupt__Xinduct__1(X1)))
    | hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
    inference(split_conjunct,[status(thm)],[c_0_1357]) ).

cnf(c_0_1850,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_1358]) ).

cnf(c_0_1851,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_1359]) ).

cnf(c_0_1852,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | X2 = X1
    | c_Lambda_Osubstn(c_Lambda_OdB_OVar(X2),X3,X1) = c_Lambda_OdB_OVar(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1360]) ).

cnf(c_0_1853,plain,
    ( X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X2,X1,X3)
    | ~ class_Ring__and__Field_Oordered__idom(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1361]) ).

cnf(c_0_1854,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X2,X1,X3)
    | X1 = X2
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1362]) ).

cnf(c_0_1855,plain,
    ( X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X2,X1,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1363]) ).

cnf(c_0_1856,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,X3)
    | X1 = X2
    | c_HOL_Oord__class_Oless(X2,X1,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1364]) ).

cnf(c_0_1857,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X2,X1,X3)
    | X2 = X1
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1365]) ).

cnf(c_0_1858,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_1366]) ).

cnf(c_0_1859,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_1367]) ).

cnf(c_0_1860,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_1368]) ).

cnf(c_0_1861,plain,
    ( c_HOL_Otimes__class_Otimes(X1,X2,X3) = c_HOL_Otimes__class_Otimes(X2,X1,X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1369]) ).

cnf(c_0_1862,plain,
    ( c_HOL_Otimes__class_Otimes(X1,X2,X3) = c_HOL_Otimes__class_Otimes(X2,X1,X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1370]) ).

cnf(c_0_1863,plain,
    ( c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat)
    | c_HOL_Oord__class_Oless(X1,X1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1371]) ).

cnf(c_0_1864,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(X2,c_Suc(X1),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1372]) ).

cnf(c_0_1865,plain,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1373]) ).

cnf(c_0_1866,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_1374]) ).

cnf(c_0_1867,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_1375]) ).

cnf(c_0_1868,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_1376]) ).

cnf(c_0_1869,plain,
    ( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1377]) ).

cnf(c_0_1870,plain,
    ( hAPP(X1,X2) = X3
    | ~ c_Type_Otyping(X1,c_Lambda_OdB_OVar(X2),X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1378]) ).

cnf(c_0_1871,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(X2)
    | X3 = c_HOL_Ozero__class_Ozero(X2)
    | c_HOL_Otimes__class_Otimes(X3,X1,X2) != c_HOL_Ozero__class_Ozero(X2)
    | ~ class_Ring__and__Field_Ono__zero__divisors(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1379]) ).

cnf(c_0_1872,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(X2)
    | X3 = c_HOL_Ozero__class_Ozero(X2)
    | c_HOL_Otimes__class_Otimes(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
    | ~ class_Ring__and__Field_Ono__zero__divisors(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1380]) ).

cnf(c_0_1873,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(X2)
    | X3 = c_HOL_Ozero__class_Ozero(X2)
    | c_HOL_Otimes__class_Otimes(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
    | ~ class_Ring__and__Field_Oring__no__zero__divisors(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1381]) ).

cnf(c_0_1874,plain,
    ( X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1382]) ).

cnf(c_0_1875,plain,
    ( X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1383]) ).

cnf(c_0_1876,plain,
    ( X2 = c_HOL_Ozero__class_Ozero(X1)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1384]) ).

cnf(c_0_1877,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | c_Power_Opower__class_Opower(X2,X1,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    inference(split_conjunct,[status(thm)],[c_0_1385]) ).

cnf(c_0_1878,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1386]) ).

cnf(c_0_1879,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_1387]) ).

cnf(c_0_1880,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_1388]) ).

cnf(c_0_1881,plain,
    ( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | c_HOL_Otimes__class_Otimes(X2,X1,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    inference(split_conjunct,[status(thm)],[c_0_1389]) ).

cnf(c_0_1882,plain,
    ( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    inference(split_conjunct,[status(thm)],[c_0_1390]) ).

cnf(c_0_1883,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_1391]) ).

cnf(c_0_1884,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_1392]) ).

cnf(c_0_1885,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_1393]) ).

cnf(c_0_1886,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_1394]) ).

cnf(c_0_1887,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_1395]) ).

cnf(c_0_1888,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_1396]) ).

cnf(c_0_1889,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_1397]) ).

cnf(c_0_1890,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_1398]) ).

cnf(c_0_1891,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X2 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1399]) ).

cnf(c_0_1892,plain,
    ( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
    | ~ class_Orderings_Oorder(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1400]) ).

cnf(c_0_1893,plain,
    ( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
    | ~ class_Orderings_Olinorder(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1401]) ).

cnf(c_0_1894,plain,
    ( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
    | ~ class_Orderings_Opreorder(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1402]) ).

cnf(c_0_1895,plain,
    ( X1 = c_HOL_Oone__class_Oone(tc_nat)
    | X2 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X2 != c_HOL_Otimes__class_Otimes(X2,X1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1403]) ).

cnf(c_0_1896,plain,
    ( X1 = c_HOL_Oone__class_Oone(tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1404]) ).

cnf(c_0_1897,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_1405]) ).

cnf(c_0_1898,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_1406]) ).

cnf(c_0_1899,plain,
    ( X1 = c_HOL_Oone__class_Oone(tc_nat)
    | c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_HOL_Oone__class_Oone(tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1407]) ).

cnf(c_0_1900,plain,
    ( X1 = c_HOL_Oone__class_Oone(tc_nat)
    | c_HOL_Otimes__class_Otimes(X2,X1,tc_nat) != c_HOL_Oone__class_Oone(tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1408]) ).

cnf(c_0_1901,plain,
    ( X1 = c_HOL_Oone__class_Oone(tc_nat)
    | c_HOL_Oone__class_Oone(tc_nat) != c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1409]) ).

cnf(c_0_1902,plain,
    ( X1 = c_HOL_Oone__class_Oone(tc_nat)
    | c_HOL_Oone__class_Oone(tc_nat) != c_HOL_Otimes__class_Otimes(X2,X1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1410]) ).

cnf(c_0_1903,plain,
    ( X1 = X2
    | ~ c_fequal(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1411]) ).

cnf(c_0_1904,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_1412]) ).

cnf(c_0_1905,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_1413]) ).

cnf(c_0_1906,plain,
    ( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(X1)))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_1414]) ).

cnf(c_0_1907,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_1415]) ).

cnf(c_0_1908,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_1416]) ).

cnf(c_0_1909,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_1417]) ).

cnf(c_0_1910,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_1418]) ).

cnf(c_0_1911,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_1419]) ).

cnf(c_0_1912,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_1420]) ).

cnf(c_0_1913,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oone__class_Oone(X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1421]) ).

cnf(c_0_1914,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_1422]) ).

cnf(c_0_1915,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_1423]) ).

cnf(c_0_1916,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_1424]) ).

cnf(c_0_1917,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_1425]) ).

cnf(c_0_1918,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_1426]) ).

cnf(c_0_1919,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_1427]) ).

cnf(c_0_1920,plain,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1428]) ).

cnf(c_0_1921,plain,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Omult__zero(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1429]) ).

cnf(c_0_1922,plain,
    ( c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X2),X2) = c_HOL_Ozero__class_Ozero(X2)
    | ~ class_Ring__and__Field_Omult__zero(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1430]) ).

cnf(c_0_1923,plain,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Oring__no__zero__divisors(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1431]) ).

cnf(c_0_1924,plain,
    ( c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X2),X2) = c_HOL_Ozero__class_Ozero(X2)
    | ~ class_Ring__and__Field_Oring__no__zero__divisors(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1432]) ).

cnf(c_0_1925,plain,
    ( c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X2),X2) = c_HOL_Ozero__class_Ozero(X2)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1433]) ).

cnf(c_0_1926,plain,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1434]) ).

cnf(c_0_1927,plain,
    ( c_Divides_Odiv__class_Odiv(X1,c_HOL_Ozero__class_Ozero(X2),X2) = c_HOL_Ozero__class_Ozero(X2)
    | ~ class_Divides_Osemiring__div(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1435]) ).

cnf(c_0_1928,plain,
    ( c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1436]) ).

cnf(c_0_1929,plain,
    ( c_Divides_Odiv__class_Omod(X1,c_HOL_Oone__class_Oone(X2),X2) = c_HOL_Ozero__class_Ozero(X2)
    | ~ class_Divides_Osemiring__div(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1437]) ).

cnf(c_0_1930,plain,
    ( c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1438]) ).

cnf(c_0_1931,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(X2)
    | c_Divides_Odiv__class_Odiv(X1,X1,X2) = c_HOL_Oone__class_Oone(X2)
    | ~ class_Divides_Osemiring__div(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1439]) ).

cnf(c_0_1932,plain,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X1),X2,X1) = X2
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1440]) ).

cnf(c_0_1933,plain,
    ( c_HOL_Otimes__class_Otimes(X1,c_HOL_Oone__class_Oone(X2),X2) = X1
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1441]) ).

cnf(c_0_1934,plain,
    ( c_HOL_Otimes__class_Otimes(X1,c_HOL_Oone__class_Oone(X2),X2) = X1
    | ~ class_OrderedGroup_Omonoid__mult(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1442]) ).

cnf(c_0_1935,plain,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X1),X2,X1) = X2
    | ~ class_OrderedGroup_Omonoid__mult(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1443]) ).

cnf(c_0_1936,plain,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X1),X2,X1) = X2
    | ~ class_OrderedGroup_Ocomm__monoid__mult(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1444]) ).

cnf(c_0_1937,plain,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X1),X2,X1) = X2
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1445]) ).

cnf(c_0_1938,plain,
    ( c_Divides_Odiv__class_Odiv(X1,c_HOL_Oone__class_Oone(X2),X2) = X1
    | ~ class_Divides_Osemiring__div(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1446]) ).

cnf(c_0_1939,plain,
    ( c_Divides_Odiv__class_Omod(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1
    | ~ class_Divides_Osemiring__div(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1447]) ).

cnf(c_0_1940,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_1448]) ).

cnf(c_0_1941,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_1449]) ).

cnf(c_0_1942,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1450]) ).

cnf(c_0_1943,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(X1),X2,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1451]) ).

cnf(c_0_1944,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_1452]) ).

cnf(c_0_1945,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_1453]) ).

cnf(c_0_1946,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_1454]) ).

cnf(c_0_1947,plain,
    ( c_Power_Opower__class_Opower(X1,c_HOL_Oone__class_Oone(tc_nat),X2) = X1
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1455]) ).

cnf(c_0_1948,plain,
    ( c_Power_Opower__class_Opower(X1,c_HOL_Oone__class_Oone(tc_nat),X2) = X1
    | ~ class_OrderedGroup_Omonoid__mult(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1456]) ).

cnf(c_0_1949,plain,
    ( c_Divides_Odiv__class_Omod(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
    | ~ class_Divides_Osemiring__div(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1457]) ).

cnf(c_0_1950,plain,
    ( c_HOL_Otimes__class_Otimes(X1,X1,X2) = X1
    | ~ class_OrderedGroup_Oab__semigroup__idem__mult(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1458]) ).

cnf(c_0_1951,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,X1,X2)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1459]) ).

cnf(c_0_1952,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1460]) ).

cnf(c_0_1953,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_1461]) ).

cnf(c_0_1954,plain,
    ( c_Lambda_Obeta(c_Lambda_OdB_OAbs(X1),c_Lambda_OdB_OAbs(X2))
    | ~ c_Lambda_Obeta(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1462]) ).

cnf(c_0_1955,plain,
    ( class_Orderings_Opreorder(tc_fun(X2,X1))
    | ~ class_Orderings_Opreorder(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1463]) ).

cnf(c_0_1956,plain,
    ( class_Orderings_Oorder(tc_fun(X2,X1))
    | ~ class_Orderings_Oorder(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1464]) ).

cnf(c_0_1957,plain,
    ( c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),X1) = c_HOL_Oone__class_Oone(X1)
    | ~ class_Ring__and__Field_Osemiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1465]) ).

cnf(c_0_1958,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_1466]) ).

cnf(c_0_1959,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_1467]) ).

cnf(c_0_1960,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_1468]) ).

cnf(c_0_1961,plain,
    ( X1 = X2
    | c_Lambda_OdB_OAbs(X1) != c_Lambda_OdB_OAbs(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1469]) ).

cnf(c_0_1962,plain,
    ( X1 = X2
    | c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OVar(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1470]) ).

cnf(c_0_1963,plain,
    ( X1 = X2
    | c_Suc(X1) != c_Suc(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1471]) ).

cnf(c_0_1964,plain,
    ( X1 = X2
    | c_Suc(X1) != c_Suc(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1472]) ).

cnf(c_0_1965,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X1 = c_Suc(c_ATP__Linkup_Osko__Nat__Xnat__Xexhaust__1__1(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_1473]) ).

cnf(c_0_1966,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X1 = c_Suc(c_ATP__Linkup_Osko__Nat__Xnat__Xnchotomy__1__1(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_1474]) ).

cnf(c_0_1967,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X1 = c_Suc(c_ATP__Linkup_Osko__Nat__Xnot0__implies__Suc__1__1(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_1475]) ).

cnf(c_0_1968,plain,
    ( c_Type_Otypings(X1,c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,X2,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),X4,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X5,tc_Lambda_OdB,tc_Lambda_OdB),X6)
    | ~ c_Type_Otyping(X1,X2,X3)
    | ~ c_Type_Otypings(c_Type_Oshift(X1,X4,X3,tc_Type_Otype),X5,X6) ),
    c_0_1476,
    [final] ).

cnf(c_0_1969,plain,
    ( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1)),X2),X3,tc_Lambda_OdB,tc_Lambda_OdB)))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X2),c_HOL_Ozero__class_Ozero(tc_nat)),X3,tc_Lambda_OdB,tc_Lambda_OdB)))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X2)) ),
    c_0_1477,
    [final] ).

cnf(c_0_1970,plain,
    ( hBOOL(hAPP(X1,hAPP(hAPP(X2,X3),X4)))
    | ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X5,X2,X6,hAPP(hAPP(c_Lambda_OdB_OApp,X3),X4),t_a))) ),
    c_0_1478,
    [final] ).

cnf(c_0_1971,plain,
    ( hBOOL(hAPP(X1,hAPP(hAPP(X2,X3),X4)))
    | ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X5,X2,X6,hAPP(hAPP(c_Lambda_OdB_OApp,X3),X4),t_a))) ),
    c_0_1479,
    [final] ).

cnf(c_0_1972,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_1480,
    [final] ).

cnf(c_0_1973,plain,
    ( hBOOL(hAPP(X1,hAPP(X2,X3)))
    | ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X2,X4,X5,c_Lambda_OdB_OVar(X3),t_a))) ),
    c_0_1481,
    [final] ).

cnf(c_0_1974,plain,
    ( hBOOL(hAPP(X1,hAPP(X2,X3)))
    | ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X2,X4,X5,c_Lambda_OdB_OVar(X3),t_a))) ),
    c_0_1482,
    [final] ).

cnf(c_0_1975,plain,
    ( hBOOL(hAPP(X1,hAPP(X2,X3)))
    | ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X4,X5,X2,c_Lambda_OdB_OAbs(X3),t_a))) ),
    c_0_1483,
    [final] ).

cnf(c_0_1976,plain,
    ( hBOOL(hAPP(X1,hAPP(X2,X3)))
    | ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X4,X5,X2,c_Lambda_OdB_OAbs(X3),t_a))) ),
    c_0_1484,
    [final] ).

cnf(c_0_1977,plain,
    ( c_Type_Otypings(c_Type_Oshift(X1,X4,X5,tc_Type_Otype),c_List_Omap(c_COMBC(c_Lambda_Olift,X4,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X2,tc_Lambda_OdB,tc_Lambda_OdB),X3)
    | ~ c_Type_Otypings(X1,X2,X3) ),
    c_0_1485,
    [final] ).

cnf(c_0_1978,plain,
    ( c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X1,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)
    | ~ c_List_Olistsp(c_InductTermi_OIT,X1,tc_Lambda_OdB) ),
    c_0_1486,
    [final] ).

cnf(c_0_1979,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
    | ~ 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_1487,
    [final] ).

cnf(c_0_1980,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_1488,
    [final] ).

cnf(c_0_1981,plain,
    ( 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))
    | ~ c_Lambda_Obeta(X1,X2) ),
    c_0_1489,
    [final] ).

cnf(c_0_1982,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_1490,
    [final] ).

cnf(c_0_1983,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_1491,
    [final] ).

cnf(c_0_1984,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_1492,
    [final] ).

cnf(c_0_1985,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_1493,
    [final] ).

cnf(c_0_1986,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_1494,
    [final] ).

cnf(c_0_1987,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_1495,
    [final] ).

cnf(c_0_1988,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_1496,
    [final] ).

cnf(c_0_1989,plain,
    ( hBOOL(hAPP(X1,X2))
    | X3 = c_HOL_Ozero__class_Ozero(tc_nat)
    | ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X3,X4,tc_nat)),X2),X3,tc_nat)))
    | ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
    c_0_1497,
    [final] ).

cnf(c_0_1990,plain,
    ( hBOOL(hAPP(X1,X2))
    | X3 = c_HOL_Ozero__class_Ozero(tc_nat)
    | ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat)),X4),X3,tc_nat)))
    | ~ c_HOL_Oord__class_Oless(X4,X3,tc_nat) ),
    c_0_1498,
    [final] ).

cnf(c_0_1991,plain,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,c_Divides_Odiv__class_Odiv(X3,X2,X1),X1)),c_Divides_Odiv__class_Omod(X3,X2,X1))),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)
    | ~ class_Divides_Osemiring__div(X1) ),
    c_0_1499,
    [final] ).

cnf(c_0_1992,plain,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X3,X1),X3,X1)),c_Divides_Odiv__class_Omod(X2,X3,X1))),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)
    | ~ class_Divides_Osemiring__div(X1) ),
    c_0_1500,
    [final] ).

cnf(c_0_1993,plain,
    ( hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,X3),hAPP(hAPP(c_Lambda_Olift,X4),X1)),c_Suc(X2))),hAPP(hAPP(hAPP(c_Lambda_Osubst,X5),X4),X2)),X1) = hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,X3),X5),X1)),X4),X2)
    | ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
    c_0_1501,
    [final] ).

cnf(c_0_1994,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_1502,
    [final] ).

cnf(c_0_1995,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_1503,
    [final] ).

cnf(c_0_1996,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_1504,
    [final] ).

cnf(c_0_1997,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_1505,
    [final] ).

cnf(c_0_1998,plain,
    ( hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)))),hAPP(hAPP(c_Lambda_Olift,X4),X2)),X1) = hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(hAPP(c_Lambda_Osubst,X3),X4),X1)),X2)
    | ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
    c_0_1506,
    [final] ).

cnf(c_0_1999,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),c_Finite__Set_Osetsum(X3,c_SetInterval_Oord__class_OatLeastLessThan(X2,X1,tc_nat),tc_nat,X4)),hAPP(X3,X1)) = c_Finite__Set_Osetsum(X3,c_SetInterval_Oord__class_OatLeastLessThan(X2,c_Suc(X1),tc_nat),tc_nat,X4)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X4) ),
    c_0_1507,
    [final] ).

cnf(c_0_2000,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_1508,
    [final] ).

cnf(c_0_2001,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_1509,
    [final] ).

cnf(c_0_2002,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_1510,
    [final] ).

cnf(c_0_2003,plain,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X3,c_Divides_Odiv__class_Omod(X4,X1,tc_nat),tc_nat)),X2),c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
    c_0_1511,
    [final] ).

cnf(c_0_2004,plain,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)),X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    c_0_1512,
    [final] ).

cnf(c_0_2005,plain,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X4,X3,X1)),X5)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X3,X1)),X5)
    | ~ class_Ring__and__Field_Osemiring(X1) ),
    c_0_1513,
    [final] ).

cnf(c_0_2006,plain,
    ( ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X2,X1)),c_HOL_Otimes__class_Otimes(X3,X3,X1)),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    c_0_1514,
    [final] ).

cnf(c_0_2007,plain,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),hAPP(X3,X1)),c_Finite__Set_Osetsum(X3,c_SetInterval_Oord__class_OatLeastLessThan(c_Suc(X1),X2,tc_nat),tc_nat,X4)) = c_Finite__Set_Osetsum(X3,c_SetInterval_Oord__class_OatLeastLessThan(X1,X2,tc_nat),tc_nat,X4)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X4) ),
    c_0_1515,
    [final] ).

cnf(c_0_2008,plain,
    ( hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,X3),X1)),hAPP(hAPP(c_Lambda_Olift,X4),X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat))) = hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(hAPP(c_Lambda_Osubst,X3),X4),X2)),X1)
    | ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
    c_0_1516,
    [final] ).

cnf(c_0_2009,plain,
    ( X1 = X2
    | X3 = X4
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_HOL_Otimes__class_Otimes(X1,X3,X5)),c_HOL_Otimes__class_Otimes(X2,X4,X5)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_HOL_Otimes__class_Otimes(X1,X4,X5)),c_HOL_Otimes__class_Otimes(X2,X3,X5))
    | ~ class_Int_Onumber__ring(X5)
    | ~ class_Ring__and__Field_Oidom(X5) ),
    c_0_1517,
    [final] ).

cnf(c_0_2010,plain,
    ( X1 = X2
    | X3 = X4
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_HOL_Otimes__class_Otimes(X1,X3,X5)),c_HOL_Otimes__class_Otimes(X2,X4,X5)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_HOL_Otimes__class_Otimes(X1,X4,X5)),c_HOL_Otimes__class_Otimes(X2,X3,X5))
    | ~ class_Int_Onumber__ring(X5)
    | ~ class_Ring__and__Field_Oidom(X5) ),
    c_0_1518,
    [final] ).

cnf(c_0_2011,plain,
    ( c_Type_Otyping(X1,hAPP(hAPP(hAPP(c_Lambda_Osubst,X2),X3),X4),X5)
    | ~ c_Type_Otyping(c_Type_Oshift(X1,X4,X6,tc_Type_Otype),X2,X5)
    | ~ c_Type_Otyping(X1,X3,X6) ),
    c_0_1519,
    [final] ).

cnf(c_0_2012,plain,
    ( X1 = X2
    | X3 = X4
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat)),c_HOL_Otimes__class_Otimes(X2,X4,tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X1,X4,tc_nat)),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat)) ),
    c_0_1520,
    [final] ).

cnf(c_0_2013,plain,
    ( X1 = X2
    | X3 = X4
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat)),c_HOL_Otimes__class_Otimes(X2,X4,tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X1,X4,tc_nat)),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat)) ),
    c_0_1521,
    [final] ).

cnf(c_0_2014,plain,
    ( c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_Divides_Odiv__class_Omod(X2,X4,X1)),c_Divides_Odiv__class_Omod(X3,X4,X1)),X4,X1) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X4,X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    c_0_1522,
    [final] ).

cnf(c_0_2015,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(X2)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_HOL_Otimes__class_Otimes(X1,X1,X2)),c_HOL_Otimes__class_Otimes(X3,X3,X2)),X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
    c_0_1523,
    [final] ).

cnf(c_0_2016,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(X2)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_HOL_Otimes__class_Otimes(X3,X3,X2)),c_HOL_Otimes__class_Otimes(X1,X1,X2)),X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
    c_0_1524,
    [final] ).

cnf(c_0_2017,plain,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,c_Divides_Odiv__class_Odiv(X3,X2,X1),X1)),c_Divides_Odiv__class_Omod(X3,X2,X1)) = X3
    | ~ class_Divides_Osemiring__div(X1) ),
    c_0_1525,
    [final] ).

cnf(c_0_2018,plain,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X3,X1),X3,X1)),c_Divides_Odiv__class_Omod(X2,X3,X1)) = X2
    | ~ class_Divides_Osemiring__div(X1) ),
    c_0_1526,
    [final] ).

cnf(c_0_2019,plain,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X1,X3,X2),X3,X2)),c_Divides_Odiv__class_Omod(X1,X3,X2)) = X1
    | ~ class_Divides_Osemiring__div(X2) ),
    c_0_1527,
    [final] ).

cnf(c_0_2020,plain,
    ( c_Finite__Set_Osetsum(X1,c_SetInterval_Oord__class_OatLeastLessThan(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat),tc_nat,X3) = c_Finite__Set_Osetsum(X1,c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat),tc_nat,X3)
    | hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Ozero__class_Ozero(X3)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X3) ),
    c_0_1528,
    [final] ).

cnf(c_0_2021,plain,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1)),c_HOL_Otimes__class_Otimes(X2,X4,X1)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X4,X1)),c_HOL_Otimes__class_Otimes(X2,X3,X1))
    | ~ class_Int_Onumber__ring(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    c_0_1529,
    [final] ).

cnf(c_0_2022,plain,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1)),c_HOL_Otimes__class_Otimes(X2,X4,X1)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X4,X1)),c_HOL_Otimes__class_Otimes(X2,X3,X1))
    | ~ class_Int_Onumber__ring(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    c_0_1530,
    [final] ).

cnf(c_0_2023,plain,
    ( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X1,X4,X3),c_Divides_Odiv__class_Omod(X2,X4,X3),X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    c_0_1531,
    [final] ).

cnf(c_0_2024,plain,
    ( c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_Divides_Odiv__class_Omod(X2,X4,X1)),X3),X4,X1) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X4,X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    c_0_1532,
    [final] ).

cnf(c_0_2025,plain,
    ( c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_Divides_Odiv__class_Omod(X2,X3,X1)),X4),X3,X1) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X3,X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    c_0_1533,
    [final] ).

cnf(c_0_2026,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_1534,
    [final] ).

cnf(c_0_2027,plain,
    ( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X2,X5,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X1,X3),c_Divides_Odiv__class_Odiv(X5,X4,X3),X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X5,X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    c_0_1535,
    [final] ).

cnf(c_0_2028,plain,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_Divides_Odiv__class_Odiv(X2,X1,X3)),c_Divides_Odiv__class_Odiv(X4,X1,X3)) = c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4),X1,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    c_0_1536,
    [final] ).

cnf(c_0_2029,plain,
    ( c_Type_Otyping(c_Type_Oshift(X1,X4,X5,tc_Type_Otype),hAPP(hAPP(c_Lambda_Olift,X2),X4),X3)
    | ~ c_Type_Otyping(X1,X2,X3) ),
    c_0_1537,
    [final] ).

cnf(c_0_2030,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X3,X1),X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_1538,
    [final] ).

cnf(c_0_2031,plain,
    ( c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,c_Suc(c_Divides_Odiv__class_Odiv(X1,X2,tc_nat)),tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
    c_0_1539,
    [final] ).

cnf(c_0_2032,plain,
    ( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X5,X6,X3),X4,X3)
    | c_Divides_Odiv__class_Omod(X1,X4,X3) != c_Divides_Odiv__class_Omod(X5,X4,X3)
    | c_Divides_Odiv__class_Omod(X2,X4,X3) != c_Divides_Odiv__class_Omod(X6,X4,X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    c_0_1540,
    [final] ).

cnf(c_0_2033,plain,
    ( c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X4,X1) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X5),X6),X4,X1)
    | c_Divides_Odiv__class_Omod(X2,X4,X1) != c_Divides_Odiv__class_Omod(X5,X4,X1)
    | c_Divides_Odiv__class_Omod(X3,X4,X1) != c_Divides_Odiv__class_Omod(X6,X4,X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    c_0_1541,
    [final] ).

cnf(c_0_2034,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(X2,X1,X3),c_Divides_Odiv__class_Odiv(X4,X1,X3),X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    c_0_1542,
    [final] ).

cnf(c_0_2035,plain,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X5,X3),X3) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X4,X5,X3),X3),X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    c_0_1543,
    [final] ).

cnf(c_0_2036,plain,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X5,X3),X3) = c_HOL_Otimes__class_Otimes(X4,c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),X5,X3),X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    c_0_1544,
    [final] ).

cnf(c_0_2037,plain,
    ( hAPP(c_Type_Oshift(X3,X2,X4,X5),X1) = hAPP(X3,X1)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    c_0_1545,
    [final] ).

cnf(c_0_2038,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(X2)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_HOL_Otimes__class_Otimes(X3,X3,X2)),c_HOL_Otimes__class_Otimes(X1,X1,X2)) != c_HOL_Ozero__class_Ozero(X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
    c_0_1546,
    [final] ).

cnf(c_0_2039,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(X2)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_HOL_Otimes__class_Otimes(X1,X1,X2)),c_HOL_Otimes__class_Otimes(X3,X3,X2)) != c_HOL_Ozero__class_Ozero(X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
    c_0_1547,
    [final] ).

cnf(c_0_2040,plain,
    ( hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_Olift,X3),X1)),c_Suc(X2)) = hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_Olift,X3),X2)),X1)
    | ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
    c_0_1548,
    [final] ).

cnf(c_0_2041,plain,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_Divides_Odiv__class_Omod(X2,X3,X1)),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X3,X1),X3,X1)) = X2
    | ~ class_Divides_Osemiring__div(X1) ),
    c_0_1549,
    [final] ).

cnf(c_0_2042,plain,
    ( c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X3,X1),X1),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_1550,
    [final] ).

cnf(c_0_2043,plain,
    ( c_HOL_Oord__class_Oless(X4,X3,X2)
    | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Otimes__class_Otimes(X1,X4,X2),X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
    c_0_1551,
    [final] ).

cnf(c_0_2044,plain,
    ( c_HOL_Oord__class_Oless(X3,X4,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    c_0_1552,
    [final] ).

cnf(c_0_2045,plain,
    ( c_HOL_Oord__class_Oless(X3,X4,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
    | ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_1553,
    [final] ).

cnf(c_0_2046,plain,
    ( c_HOL_Oord__class_Oless(X3,X4,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
    | ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_1554,
    [final] ).

cnf(c_0_2047,plain,
    ( c_Divides_Odiv__class_Omod(X1,X2,tc_nat) = c_Divides_Odiv__class_Omod(X3,X2,tc_nat)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Otimes__class_Otimes(X2,X4,tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Otimes__class_Otimes(X2,X5,tc_nat)) ),
    c_0_1555,
    [final] ).

cnf(c_0_2048,plain,
    ( c_HOL_Oord__class_Oless(X2,X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) ),
    c_0_1556,
    [final] ).

cnf(c_0_2049,plain,
    ( c_HOL_Oord__class_Oless(X2,X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X2,tc_nat),c_Power_Opower__class_Opower(X1,X3,tc_nat),tc_nat) ),
    c_0_1557,
    [final] ).

cnf(c_0_2050,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) ),
    c_0_1558,
    [final] ).

cnf(c_0_2051,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    c_0_1559,
    [final] ).

cnf(c_0_2052,plain,
    ( c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X4,X2,X3),c_Power_Opower__class_Opower(X4,X1,X3),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
    | ~ c_HOL_Oord__class_Oless(X4,c_HOL_Oone__class_Oone(X3),X3)
    | ~ class_Ring__and__Field_Oordered__semidom(X3) ),
    c_0_1560,
    [final] ).

cnf(c_0_2053,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
    | c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
    c_0_1561,
    [final] ).

cnf(c_0_2054,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
    | c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
    c_0_1562,
    [final] ).

cnf(c_0_2055,plain,
    ( c_HOL_Oord__class_Oless(X1,X4,X3)
    | c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
    c_0_1563,
    [final] ).

cnf(c_0_2056,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
    | c_HOL_Oord__class_Oless(X4,X1,X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
    c_0_1564,
    [final] ).

cnf(c_0_2057,plain,
    ( c_HOL_Oord__class_Oless(X2,X4,X3)
    | c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
    c_0_1565,
    [final] ).

cnf(c_0_2058,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
    | c_HOL_Oord__class_Oless(X4,X2,X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
    c_0_1566,
    [final] ).

cnf(c_0_2059,plain,
    ( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X1,X2,X3),X4,X3),X2,X3) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X4,X3),X2,X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    c_0_1567,
    [final] ).

cnf(c_0_2060,plain,
    ( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X1,X4,X3),X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    c_0_1568,
    [final] ).

cnf(c_0_2061,plain,
    ( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Omod(X2,X4,X3),X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    c_0_1569,
    [final] ).

cnf(c_0_2062,plain,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X5,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    c_0_1570,
    [final] ).

cnf(c_0_2063,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(X2)
    | c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),c_HOL_Otimes__class_Otimes(X1,X4,X2)),X1,X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X4),c_Divides_Odiv__class_Odiv(X3,X1,X2))
    | ~ class_Divides_Osemiring__div(X2) ),
    c_0_1571,
    [final] ).

cnf(c_0_2064,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(X2)
    | c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),c_HOL_Otimes__class_Otimes(X4,X1,X2)),X1,X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X4),c_Divides_Odiv__class_Odiv(X3,X1,X2))
    | ~ class_Divides_Osemiring__div(X2) ),
    c_0_1572,
    [final] ).

cnf(c_0_2065,plain,
    ( c_HOL_Oord__class_Oless(X2,X4,X3)
    | c_HOL_Oord__class_Oless(X4,X2,X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
    c_0_1573,
    [final] ).

cnf(c_0_2066,plain,
    ( c_HOL_Oord__class_Oless(X1,X4,X3)
    | c_HOL_Oord__class_Oless(X4,X1,X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
    c_0_1574,
    [final] ).

cnf(c_0_2067,plain,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1)),c_HOL_Otimes__class_Otimes(X4,X3,X1)) = c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X3,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    c_0_1575,
    [final] ).

cnf(c_0_2068,plain,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X4,X1)),c_HOL_Otimes__class_Otimes(X3,X4,X1)) = c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X4,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    c_0_1576,
    [final] ).

cnf(c_0_2069,plain,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X4,X1)),c_HOL_Otimes__class_Otimes(X3,X4,X1)) = c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X4,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring(X1) ),
    c_0_1577,
    [final] ).

cnf(c_0_2070,plain,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_HOL_Otimes__class_Otimes(X1,X3,X2)),c_HOL_Otimes__class_Otimes(X1,X4,X2)) = c_HOL_Otimes__class_Otimes(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),X4),X2)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ),
    c_0_1578,
    [final] ).

cnf(c_0_2071,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(X2,X1,X3),c_Divides_Odiv__class_Odiv(X4,X1,X3),X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    c_0_1579,
    [final] ).

cnf(c_0_2072,plain,
    ( c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_Divides_Odiv__class_Omod(X3,X4,X1)),X4,X1) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X4,X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    c_0_1580,
    [final] ).

cnf(c_0_2073,plain,
    ( c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_Divides_Odiv__class_Omod(X3,X4,X1)),X4,X1) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X4,X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    c_0_1581,
    [final] ).

cnf(c_0_2074,plain,
    ( c_Divides_Odiv__class_Odiv(c_Power_Opower__class_Opower(X2,X4,X3),c_Power_Opower__class_Opower(X1,X4,X3),X3) = c_Power_Opower__class_Opower(c_Divides_Odiv__class_Odiv(X2,X1,X3),X4,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    c_0_1582,
    [final] ).

cnf(c_0_2075,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(X2)
    | X3 = X4
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X5),c_HOL_Otimes__class_Otimes(X1,X3,X2)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X5),c_HOL_Otimes__class_Otimes(X1,X4,X2))
    | ~ class_Int_Onumber__ring(X2)
    | ~ class_Ring__and__Field_Oidom(X2) ),
    c_0_1583,
    [final] ).

cnf(c_0_2076,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_1584,
    [final] ).

cnf(c_0_2077,plain,
    ( c_HOL_Oord__class_Oless(X2,X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X1),X2,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X1),X3,tc_nat),tc_nat) ),
    c_0_1585,
    [final] ).

cnf(c_0_2078,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(X3)
    | c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
    | ~ class_Ring__and__Field_Oidom(X3) ),
    c_0_1586,
    [final] ).

cnf(c_0_2079,plain,
    ( X2 = c_HOL_Ozero__class_Ozero(X3)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
    | ~ class_Ring__and__Field_Oidom(X3) ),
    c_0_1587,
    [final] ).

cnf(c_0_2080,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X3,X1),X1),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_1588,
    [final] ).

cnf(c_0_2081,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X2 = X3
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat)) ),
    c_0_1589,
    [final] ).

cnf(c_0_2082,plain,
    ( c_HOL_Oord__class_Oless(X2,X4,X1)
    | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3),X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    c_0_1590,
    [final] ).

cnf(c_0_2083,plain,
    ( c_HOL_Oord__class_Oless(X3,X4,X1)
    | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    c_0_1591,
    [final] ).

cnf(c_0_2084,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) ),
    c_0_1592,
    [final] ).

cnf(c_0_2085,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) ),
    c_0_1593,
    [final] ).

cnf(c_0_2086,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat) ),
    c_0_1594,
    [final] ).

cnf(c_0_2087,plain,
    ( c_HOL_Oord__class_Oless(X2,X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) ),
    c_0_1595,
    [final] ).

cnf(c_0_2088,plain,
    ( c_HOL_Oord__class_Oless(X1,X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat) ),
    c_0_1596,
    [final] ).

cnf(c_0_2089,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
    | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_HOL_Oord__class_Oless(X3,X4,X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
    c_0_1597,
    [final] ).

cnf(c_0_2090,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_HOL_Oord__class_Oless(X3,X4,X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    c_0_1598,
    [final] ).

cnf(c_0_2091,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X2,X3),c_HOL_Otimes__class_Otimes(X4,X1,X3),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
    c_0_1599,
    [final] ).

cnf(c_0_2092,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X1,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
    c_0_1600,
    [final] ).

cnf(c_0_2093,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_HOL_Oord__class_Oless(X3,X4,X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    c_0_1601,
    [final] ).

cnf(c_0_2094,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
    | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_HOL_Oord__class_Oless(X3,X4,X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
    c_0_1602,
    [final] ).

cnf(c_0_2095,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X4,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
    c_0_1603,
    [final] ).

cnf(c_0_2096,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
    c_0_1604,
    [final] ).

cnf(c_0_2097,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X2,X1),c_HOL_Otimes__class_Otimes(X4,X2,X1),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_HOL_Oord__class_Oless(X3,X4,X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    c_0_1605,
    [final] ).

cnf(c_0_2098,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X1,X2),c_HOL_Otimes__class_Otimes(X3,X1,X2),X2)
    | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_HOL_Oord__class_Oless(X3,X4,X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
    c_0_1606,
    [final] ).

cnf(c_0_2099,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X1,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X3) ),
    c_0_1607,
    [final] ).

cnf(c_0_2100,plain,
    ( c_Finite__Set_Osetsum(X3,c_SetInterval_Oord__class_OatLeastLessThan(X2,c_Suc(X1),tc_nat),tc_nat,X4) = c_HOL_Ozero__class_Ozero(X4)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X4) ),
    c_0_1608,
    [final] ).

cnf(c_0_2101,plain,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    c_0_1609,
    [final] ).

cnf(c_0_2102,plain,
    ( c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
    | ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_1610,
    [final] ).

cnf(c_0_2103,plain,
    ( c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X4,X1,X3),c_Power_Opower__class_Opower(X4,X2,X3),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X4,X3)
    | ~ class_Ring__and__Field_Oordered__semidom(X3) ),
    c_0_1611,
    [final] ).

cnf(c_0_2104,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X5,X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    c_0_1612,
    [final] ).

cnf(c_0_2105,plain,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1)),X3) = c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Oone__class_Oone(X1)),X3,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    c_0_1613,
    [final] ).

cnf(c_0_2106,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(X2)
    | c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X3),X1,X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_Divides_Odiv__class_Odiv(X3,X1,X2)),c_HOL_Oone__class_Oone(X2))
    | ~ class_Divides_Osemiring__div(X2) ),
    c_0_1614,
    [final] ).

cnf(c_0_2107,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(X2)
    | c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),X1),X1,X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_Divides_Odiv__class_Odiv(X3,X1,X2)),c_HOL_Oone__class_Oone(X2))
    | ~ class_Divides_Osemiring__div(X2) ),
    c_0_1615,
    [final] ).

cnf(c_0_2108,plain,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X5),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X4,X5,X3)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
    c_0_1616,
    [final] ).

cnf(c_0_2109,plain,
    ( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X4,X3),c_Power_Opower__class_Opower(X2,X4,X3),X3) = c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
    | ~ class_OrderedGroup_Ocomm__monoid__mult(X3) ),
    c_0_1617,
    [final] ).

cnf(c_0_2110,plain,
    ( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X4,X3),c_Power_Opower__class_Opower(X2,X4,X3),X3) = c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    c_0_1618,
    [final] ).

cnf(c_0_2111,plain,
    ( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X1,X4,X3),X2,X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    c_0_1619,
    [final] ).

cnf(c_0_2112,plain,
    ( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3) = c_HOL_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Omod(X2,X4,X3),X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    c_0_1620,
    [final] ).

cnf(c_0_2113,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
    c_0_1621,
    [final] ).

cnf(c_0_2114,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
    c_0_1622,
    [final] ).

cnf(c_0_2115,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat) ),
    c_0_1623,
    [final] ).

cnf(c_0_2116,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat) ),
    c_0_1624,
    [final] ).

cnf(c_0_2117,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
    c_0_1625,
    [final] ).

cnf(c_0_2118,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat) ),
    c_0_1626,
    [final] ).

cnf(c_0_2119,plain,
    ( c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Otimes__class_Otimes(X3,X4,X1)),X4,X1) = c_Divides_Odiv__class_Omod(X2,X4,X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    c_0_1627,
    [final] ).

cnf(c_0_2120,plain,
    ( c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Otimes__class_Otimes(X3,X4,X1)),X3,X1) = c_Divides_Odiv__class_Omod(X2,X3,X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    c_0_1628,
    [final] ).

cnf(c_0_2121,plain,
    ( hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
    | ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))) ),
    c_0_1629,
    [final] ).

cnf(c_0_2122,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    c_0_1630,
    [final] ).

cnf(c_0_2123,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    c_0_1631,
    [final] ).

cnf(c_0_2124,plain,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))) ),
    c_0_1632,
    [final] ).

cnf(c_0_2125,plain,
    ( c_HOL_Oord__class_Oless(X2,X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),tc_nat) ),
    c_0_1633,
    [final] ).

cnf(c_0_2126,plain,
    ( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X2,X4),c_Power_Opower__class_Opower(X1,X3,X4),X4) = c_Power_Opower__class_Opower(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),X4)
    | ~ class_OrderedGroup_Omonoid__mult(X4) ),
    c_0_1634,
    [final] ).

cnf(c_0_2127,plain,
    ( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X4,X3),X3) = c_Power_Opower__class_Opower(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X4),X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    c_0_1635,
    [final] ).

cnf(c_0_2128,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_1636,
    [final] ).

cnf(c_0_2129,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_1637,
    [final] ).

cnf(c_0_2130,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_1638,
    [final] ).

cnf(c_0_2131,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_1639,
    [final] ).

cnf(c_0_2132,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_1640,
    [final] ).

cnf(c_0_2133,plain,
    ( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X2,X4,X3),X1,X3) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X1,X3),X4,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    c_0_1641,
    [final] ).

cnf(c_0_2134,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X4)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_Divides_Odiv__class_Omod(X2,X3,X4),X4)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X3,X4)
    | ~ class_Divides_Osemiring__div(X4) ),
    c_0_1642,
    [final] ).

cnf(c_0_2135,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_Divides_Odiv__class_Omod(X4,X2,X3),X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    c_0_1643,
    [final] ).

cnf(c_0_2136,plain,
    ( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) = c_Divides_Odiv__class_Odiv(X2,X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    c_0_1644,
    [final] ).

cnf(c_0_2137,plain,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X4),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat) ),
    c_0_1645,
    [final] ).

cnf(c_0_2138,plain,
    ( X1 = c_List_Olist_ONil(X2)
    | c_List_Omap(X3,X1,X2,X4) != c_List_Olist_ONil(X4) ),
    c_0_1646,
    [final] ).

cnf(c_0_2139,plain,
    ( X1 = c_List_Olist_ONil(X2)
    | c_List_Omap(X4,X1,X2,X3) != c_List_Olist_ONil(X3) ),
    c_0_1647,
    [final] ).

cnf(c_0_2140,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_1648,
    [final] ).

cnf(c_0_2141,plain,
    ( c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,c_Suc(X3),X1),c_HOL_Oone__class_Oone(X1),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_1649,
    [final] ).

cnf(c_0_2142,plain,
    ( c_Lambda_Obeta(hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X3),X4),hAPP(hAPP(hAPP(c_Lambda_Osubst,X2),X3),X4))
    | ~ c_Lambda_Obeta(X1,X2) ),
    c_0_1650,
    [final] ).

cnf(c_0_2143,plain,
    ( c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat) ),
    c_0_1651,
    [final] ).

cnf(c_0_2144,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X3),X1,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X3),X2,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    c_0_1652,
    [final] ).

cnf(c_0_2145,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X3,X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_1653,
    [final] ).

cnf(c_0_2146,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    c_0_1654,
    [final] ).

cnf(c_0_2147,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
    | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
    c_0_1655,
    [final] ).

cnf(c_0_2148,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    c_0_1656,
    [final] ).

cnf(c_0_2149,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    c_0_1657,
    [final] ).

cnf(c_0_2150,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X2) ),
    c_0_1658,
    [final] ).

cnf(c_0_2151,plain,
    ( c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat) ),
    c_0_1659,
    [final] ).

cnf(c_0_2152,plain,
    ( c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat) ),
    c_0_1660,
    [final] ).

cnf(c_0_2153,plain,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X3),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
    c_0_1661,
    [final] ).

cnf(c_0_2154,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
    c_0_1662,
    [final] ).

cnf(c_0_2155,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ class_Ring__and__Field_Oidom(X3) ),
    c_0_1663,
    [final] ).

cnf(c_0_2156,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X4,X1,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ class_Ring__and__Field_Oidom(X3) ),
    c_0_1664,
    [final] ).

cnf(c_0_2157,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(X1,X4,X3),c_Power_Opower__class_Opower(X2,X4,X3),X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    c_0_1665,
    [final] ).

cnf(c_0_2158,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_1666,
    [final] ).

cnf(c_0_2159,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X3,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X1,tc_nat) ),
    c_0_1667,
    [final] ).

cnf(c_0_2160,plain,
    ( c_Divides_Odiv__class_Omod(c_Suc(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat)),X1,tc_nat) = c_HOL_Oone__class_Oone(tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat) ),
    c_0_1668,
    [final] ).

cnf(c_0_2161,plain,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
    c_0_1669,
    [final] ).

cnf(c_0_2162,plain,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
    c_0_1670,
    [final] ).

cnf(c_0_2163,plain,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
    c_0_1671,
    [final] ).

cnf(c_0_2164,plain,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
    c_0_1672,
    [final] ).

cnf(c_0_2165,plain,
    ( c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_HOL_Oord__class_Oless(X3,X4,X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_1673,
    [final] ).

cnf(c_0_2166,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat) ),
    c_0_1674,
    [final] ).

cnf(c_0_2167,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),tc_nat) ),
    c_0_1675,
    [final] ).

cnf(c_0_2168,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,c_Divides_Odiv__class_Omod(X4,X2,X3),X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    c_0_1676,
    [final] ).

cnf(c_0_2169,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,c_Divides_Odiv__class_Omod(X2,X4,X3),X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    c_0_1677,
    [final] ).

cnf(c_0_2170,plain,
    ( X2 = c_HOL_Oone__class_Oone(tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X1,tc_nat) ),
    c_0_1678,
    [final] ).

cnf(c_0_2171,plain,
    ( X2 = c_HOL_Oone__class_Oone(tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),X1,tc_nat) ),
    c_0_1679,
    [final] ).

cnf(c_0_2172,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
    c_0_1680,
    [final] ).

cnf(c_0_2173,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4),X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    c_0_1681,
    [final] ).

cnf(c_0_2174,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(X2)
    | c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Otimes__class_Otimes(X1,X4,X2),X2) = c_Divides_Odiv__class_Odiv(X3,X4,X2)
    | ~ class_Divides_Osemiring__div(X2) ),
    c_0_1682,
    [final] ).

cnf(c_0_2175,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(X2)
    | c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X3,X1,X2),c_HOL_Otimes__class_Otimes(X4,X1,X2),X2) = c_Divides_Odiv__class_Odiv(X3,X4,X2)
    | ~ class_Divides_Osemiring__div(X2) ),
    c_0_1683,
    [final] ).

cnf(c_0_2176,plain,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Otimes__class_Otimes(X3,X2,X1)) = c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),c_HOL_Oone__class_Oone(X1)),X2,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    c_0_1684,
    [final] ).

cnf(c_0_2177,plain,
    ( c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Odiv(X2,X1,tc_nat),X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
    c_0_1685,
    [final] ).

cnf(c_0_2178,plain,
    ( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X2,X3),X1,X3) = c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X3),X3)
    | ~ class_OrderedGroup_Omonoid__mult(X3) ),
    c_0_1686,
    [final] ).

cnf(c_0_2179,plain,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
    | ~ class_OrderedGroup_Oab__semigroup__mult(X3) ),
    c_0_1687,
    [final] ).

cnf(c_0_2180,plain,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X4,X3),X2,X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    c_0_1688,
    [final] ).

cnf(c_0_2181,plain,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    c_0_1689,
    [final] ).

cnf(c_0_2182,plain,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X4),X3,X4) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X4) ),
    c_0_1690,
    [final] ).

cnf(c_0_2183,plain,
    ( c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X1,X3,X4),X4)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X4) ),
    c_0_1691,
    [final] ).

cnf(c_0_2184,plain,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X4),X3,X4) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X4) ),
    c_0_1692,
    [final] ).

cnf(c_0_2185,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X3,X2,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat) ),
    c_0_1693,
    [final] ).

cnf(c_0_2186,plain,
    ( c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(X1,X2,X3),X4,X3) = c_Power_Opower__class_Opower(X1,c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    c_0_1694,
    [final] ).

cnf(c_0_2187,plain,
    ( c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(X1,X2,X4),X3,X4) = c_Power_Opower__class_Opower(X1,c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X4)
    | ~ class_OrderedGroup_Omonoid__mult(X4) ),
    c_0_1695,
    [final] ).

cnf(c_0_2188,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
    c_0_1696,
    [final] ).

cnf(c_0_2189,plain,
    ( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
    c_0_1697,
    [final] ).

cnf(c_0_2190,plain,
    ( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_1698,
    [final] ).

cnf(c_0_2191,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) = c_Divides_Odiv__class_Odiv(X2,X3,tc_nat) ),
    c_0_1699,
    [final] ).

cnf(c_0_2192,plain,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    c_0_1700,
    [final] ).

cnf(c_0_2193,plain,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    c_0_1701,
    [final] ).

cnf(c_0_2194,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    c_0_1702,
    [final] ).

cnf(c_0_2195,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    c_0_1703,
    [final] ).

cnf(c_0_2196,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_1704,
    [final] ).

cnf(c_0_2197,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_1705,
    [final] ).

cnf(c_0_2198,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_1706,
    [final] ).

cnf(c_0_2199,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | X2 = c_HOL_Ozero__class_Ozero(tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Power_Opower__class_Opower(X1,X2,tc_nat),tc_nat) ),
    c_0_1707,
    [final] ).

cnf(c_0_2200,plain,
    ( c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X4,X2,X3),X1,X3) = c_Divides_Odiv__class_Omod(X4,X1,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    c_0_1708,
    [final] ).

cnf(c_0_2201,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) ),
    c_0_1709,
    [final] ).

cnf(c_0_2202,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) ),
    c_0_1710,
    [final] ).

cnf(c_0_2203,plain,
    ( hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)))
    | ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
    c_0_1711,
    [final] ).

cnf(c_0_2204,plain,
    ( hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)))
    | ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
    c_0_1712,
    [final] ).

cnf(c_0_2205,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X1,tc_nat) ),
    c_0_1713,
    [final] ).

cnf(c_0_2206,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X3,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X1,tc_nat) ),
    c_0_1714,
    [final] ).

cnf(c_0_2207,plain,
    ( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X3,X1),X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    c_0_1715,
    [final] ).

cnf(c_0_2208,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X2),X2),c_HOL_Otimes__class_Otimes(X3,c_HOL_Ozero__class_Ozero(X2),X2),X2)
    | ~ class_Ring__and__Field_Oidom(X2) ),
    c_0_1716,
    [final] ).

cnf(c_0_2209,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X3,X1),X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    c_0_1717,
    [final] ).

cnf(c_0_2210,plain,
    ( hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)))
    | ~ hBOOL(hAPP(X1,X2)) ),
    c_0_1718,
    [final] ).

cnf(c_0_2211,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_Power_Opower__class_Opower(X2,c_Suc(X3),X1),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_1719,
    [final] ).

cnf(c_0_2212,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X4) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2) ),
    c_0_1720,
    [final] ).

cnf(c_0_2213,plain,
    ( c_HOL_Oord__class_Oless(X1,X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X3,tc_nat) ),
    c_0_1721,
    [final] ).

cnf(c_0_2214,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1),tc_nat) ),
    c_0_1722,
    [final] ).

cnf(c_0_2215,plain,
    ( X1 = X2
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X4,X3)
    | c_Power_Opower__class_Opower(X4,X1,X3) != c_Power_Opower__class_Opower(X4,X2,X3)
    | ~ class_Ring__and__Field_Oordered__semidom(X3) ),
    c_0_1723,
    [final] ).

cnf(c_0_2216,plain,
    ( c_Suc(c_Divides_Odiv__class_Omod(X1,X2,tc_nat)) = X2
    | c_Suc(c_Divides_Odiv__class_Omod(X1,X2,tc_nat)) = c_Divides_Odiv__class_Omod(c_Suc(X1),X2,tc_nat) ),
    c_0_1724,
    [final] ).

cnf(c_0_2217,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X3,X2,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat) ),
    c_0_1725,
    [final] ).

cnf(c_0_2218,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat) ),
    c_0_1726,
    [final] ).

cnf(c_0_2219,plain,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
    c_0_1727,
    [final] ).

cnf(c_0_2220,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_1728,
    [final] ).

cnf(c_0_2221,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
    c_0_1729,
    [final] ).

cnf(c_0_2222,plain,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X1),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
    c_0_1730,
    [final] ).

cnf(c_0_2223,plain,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X1),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2) ),
    c_0_1731,
    [final] ).

cnf(c_0_2224,plain,
    ( X1 = X2
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
    | c_HOL_Otimes__class_Otimes(X3,X1,tc_nat) != c_HOL_Otimes__class_Otimes(X3,X2,tc_nat) ),
    c_0_1732,
    [final] ).

cnf(c_0_2225,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X2,c_Power_Opower__class_Opower(X2,X1,X3),X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    c_0_1733,
    [final] ).

cnf(c_0_2226,plain,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
    c_0_1734,
    [final] ).

cnf(c_0_2227,plain,
    ( c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X1,X3),X1,X3) = X2
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    c_0_1735,
    [final] ).

cnf(c_0_2228,plain,
    ( c_HOL_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Odiv(X2,X1,X3),X3) = X2
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    c_0_1736,
    [final] ).

cnf(c_0_2229,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    c_0_1737,
    [final] ).

cnf(c_0_2230,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    c_0_1738,
    [final] ).

cnf(c_0_2231,plain,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2) = c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Oone__class_Oone(X1)),c_HOL_Oone__class_Oone(X1)),X2,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    c_0_1739,
    [final] ).

cnf(c_0_2232,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    c_0_1740,
    [final] ).

cnf(c_0_2233,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat),X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    c_0_1741,
    [final] ).

cnf(c_0_2234,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Power_Opower__class_Opower(X1,X2,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    c_0_1742,
    [final] ).

cnf(c_0_2235,plain,
    ( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),X1,tc_nat) = X2
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    c_0_1743,
    [final] ).

cnf(c_0_2236,plain,
    ( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X1,tc_nat) = X2
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    c_0_1744,
    [final] ).

cnf(c_0_2237,plain,
    ( c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Omod(X2,X1,tc_nat),X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    c_0_1745,
    [final] ).

cnf(c_0_2238,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_1746,
    [final] ).

cnf(c_0_2239,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    c_0_1747,
    [final] ).

cnf(c_0_2240,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    c_0_1748,
    [final] ).

cnf(c_0_2241,plain,
    ( c_HOL_Oord__class_Oless(X4,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X4,X1,X3)
    | ~ class_Orderings_Oorder(X3) ),
    c_0_1749,
    [final] ).

cnf(c_0_2242,plain,
    ( c_HOL_Oord__class_Oless(X1,X4,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X2,X4,X3)
    | ~ class_Orderings_Opreorder(X3) ),
    c_0_1750,
    [final] ).

cnf(c_0_2243,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    c_0_1751,
    [final] ).

cnf(c_0_2244,plain,
    ( c_Divides_Odiv__class_Omod(c_Suc(X1),X2,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_Suc(c_Divides_Odiv__class_Omod(X1,X2,tc_nat)) != X2 ),
    c_0_1752,
    [final] ).

cnf(c_0_2245,plain,
    ( c_HOL_Otimes__class_Otimes(c_Nat_Osemiring__1__class_Oof__nat(X1,X3),c_Nat_Osemiring__1__class_Oof__nat(X2,X3),X3) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X3)
    | ~ class_Ring__and__Field_Osemiring__1(X3) ),
    c_0_1753,
    [final] ).

cnf(c_0_2246,plain,
    ( c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X3),X3) = c_Power_Opower__class_Opower(X1,c_Suc(X2),X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    c_0_1754,
    [final] ).

cnf(c_0_2247,plain,
    ( c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X3),X3) = c_Power_Opower__class_Opower(X1,c_Suc(X2),X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    c_0_1755,
    [final] ).

cnf(c_0_2248,plain,
    ( c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X3),X3) = c_Power_Opower__class_Opower(X1,c_Suc(X2),X3)
    | ~ class_Power_Opower(X3) ),
    c_0_1756,
    [final] ).

cnf(c_0_2249,plain,
    ( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X2,X3),X1,X3) = c_Power_Opower__class_Opower(X1,c_Suc(X2),X3)
    | ~ class_OrderedGroup_Omonoid__mult(X3) ),
    c_0_1757,
    [final] ).

cnf(c_0_2250,plain,
    ( c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X3),X3) = c_Power_Opower__class_Opower(X1,c_Suc(X2),X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    c_0_1758,
    [final] ).

cnf(c_0_2251,plain,
    ( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X2,X3),X1,X3) = c_Power_Opower__class_Opower(X1,c_Suc(X2),X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    c_0_1759,
    [final] ).

cnf(c_0_2252,plain,
    ( c_HOL_Oord__class_Oless(X1,X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_Nat_Osemiring__1__class_Oof__nat(X3,X2),X2)
    | ~ class_Ring__and__Field_Oordered__semidom(X2) ),
    c_0_1760,
    [final] ).

cnf(c_0_2253,plain,
    ( c_Divides_Odiv__class_Odiv(X2,X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
    c_0_1761,
    [final] ).

cnf(c_0_2254,plain,
    ( c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    c_0_1762,
    [final] ).

cnf(c_0_2255,plain,
    ( c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    c_0_1763,
    [final] ).

cnf(c_0_2256,plain,
    ( c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    c_0_1764,
    [final] ).

cnf(c_0_2257,plain,
    ( c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    c_0_1765,
    [final] ).

cnf(c_0_2258,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1),tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat) ),
    c_0_1766,
    [final] ).

cnf(c_0_2259,plain,
    ( c_HOL_Oord__class_Oless(c_Suc(X1),X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
    c_0_1767,
    [final] ).

cnf(c_0_2260,plain,
    ( c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X1,X2,X3),X2,X3) = c_Divides_Odiv__class_Omod(X1,X2,X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    c_0_1768,
    [final] ).

cnf(c_0_2261,plain,
    ( c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X1,X2,X3),X3) = c_HOL_Otimes__class_Otimes(X1,X2,X3)
    | ~ class_OrderedGroup_Oab__semigroup__idem__mult(X3) ),
    c_0_1769,
    [final] ).

cnf(c_0_2262,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat) ),
    c_0_1770,
    [final] ).

cnf(c_0_2263,plain,
    ( c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X3,X1) = c_Divides_Odiv__class_Omod(X2,X3,X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    c_0_1771,
    [final] ).

cnf(c_0_2264,plain,
    ( c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X2,X1) = c_Divides_Odiv__class_Omod(X3,X2,X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    c_0_1772,
    [final] ).

cnf(c_0_2265,plain,
    ( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_Olift,X1),X2)))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
    c_0_1773,
    [final] ).

cnf(c_0_2266,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Oone__class_Oone(X1)),c_HOL_Oone__class_Oone(X1)),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_1774,
    [final] ).

cnf(c_0_2267,plain,
    ( c_Power_Opower__class_Opower(c_Nat_Osemiring__1__class_Oof__nat(X1,X3),X2,X3) = c_Nat_Osemiring__1__class_Oof__nat(c_Power_Opower__class_Opower(X1,X2,tc_nat),X3)
    | ~ class_Ring__and__Field_Osemiring__1(X3) ),
    c_0_1775,
    [final] ).

cnf(c_0_2268,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(X1)),X2) = c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat))) ),
    c_0_1776,
    [final] ).

cnf(c_0_2269,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_1777,
    [final] ).

cnf(c_0_2270,plain,
    ( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X1)),X3),X2) = c_Lambda_OdB_OVar(X1)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    c_0_1778,
    [final] ).

cnf(c_0_2271,plain,
    ( c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X3),c_Nat_Osemiring__1__class_Oof__nat(X2,X3),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ class_Ring__and__Field_Oordered__semidom(X3) ),
    c_0_1779,
    [final] ).

cnf(c_0_2272,plain,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
    | ~ hBOOL(hAPP(X1,c_Suc(v_sko__List__Xlexn__Xinduct__1(X1)))) ),
    c_0_1780,
    [final] ).

cnf(c_0_2273,plain,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
    | ~ hBOOL(hAPP(X1,c_Suc(c_ATP__Linkup_Osko__Nat__Xnat__induct__1__1(X1)))) ),
    c_0_1781,
    [final] ).

cnf(c_0_2274,plain,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
    | ~ hBOOL(hAPP(X1,c_Suc(v_sko__List__Xreplicate__Xinduct__1(X1)))) ),
    c_0_1782,
    [final] ).

cnf(c_0_2275,plain,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
    | ~ hBOOL(hAPP(X1,c_Suc(v_sko__List__Xupt__Xinduct__1(X1)))) ),
    c_0_1783,
    [final] ).

cnf(c_0_2276,plain,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
    | ~ hBOOL(hAPP(X1,c_Suc(v_sko__Nat__Xnat__Xinduct__1(X1)))) ),
    c_0_1784,
    [final] ).

cnf(c_0_2277,plain,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
    | ~ hBOOL(hAPP(X1,c_Suc(v_sko__Nat__Xnat__Xinducts__1(X1)))) ),
    c_0_1785,
    [final] ).

cnf(c_0_2278,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | X1 = X2
    | c_HOL_Oord__class_Oless(X2,X1,tc_nat)
    | hBOOL(hAPP(hAPP(X3,X2),X1)) ),
    c_0_1786,
    [final] ).

cnf(c_0_2279,plain,
    ( X1 = X2
    | c_HOL_Otimes__class_Otimes(c_Suc(X3),X1,tc_nat) != c_HOL_Otimes__class_Otimes(c_Suc(X3),X2,tc_nat) ),
    c_0_1787,
    [final] ).

cnf(c_0_2280,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(X1),c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X1),X2,X1),X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    c_0_1788,
    [final] ).

cnf(c_0_2281,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_Nat_Osemiring__1__class_Oof__nat(X1,X2),X2)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | ~ class_Ring__and__Field_Oordered__semidom(X2) ),
    c_0_1789,
    [final] ).

cnf(c_0_2282,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_1790,
    [final] ).

cnf(c_0_2283,plain,
    ( c_Lambda_Obeta(hAPP(hAPP(c_Lambda_Olift,X1),X3),hAPP(hAPP(c_Lambda_Olift,X2),X3))
    | ~ c_Lambda_Obeta(X1,X2) ),
    c_0_1791,
    [final] ).

cnf(c_0_2284,plain,
    ( c_Lambda_Obeta(hAPP(hAPP(c_Lambda_OdB_OApp,X3),X1),hAPP(hAPP(c_Lambda_OdB_OApp,X3),X2))
    | ~ c_Lambda_Obeta(X1,X2) ),
    c_0_1792,
    [final] ).

cnf(c_0_2285,plain,
    ( c_Lambda_Obeta(hAPP(hAPP(c_Lambda_OdB_OApp,X1),X3),hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3))
    | ~ c_Lambda_Obeta(X1,X2) ),
    c_0_1793,
    [final] ).

cnf(c_0_2286,plain,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X2,X1,X3)
    | ~ class_Orderings_Oorder(X3) ),
    c_0_1794,
    [final] ).

cnf(c_0_2287,plain,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X2,X1,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_1795,
    [final] ).

cnf(c_0_2288,plain,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X2,X1,X3)
    | ~ class_Orderings_Opreorder(X3) ),
    c_0_1796,
    [final] ).

cnf(c_0_2289,plain,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X2,X1,X3)
    | ~ class_Orderings_Opreorder(X3) ),
    c_0_1797,
    [final] ).

cnf(c_0_2290,plain,
    ( ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
    c_0_1798,
    [final] ).

cnf(c_0_2291,plain,
    ( c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),c_HOL_Oone__class_Oone(X2)),X2)
    | ~ class_Ring__and__Field_Oordered__semidom(X2) ),
    c_0_1799,
    [final] ).

cnf(c_0_2292,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(X2)
    | c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X3,X1,X2),X1,X2) = X3
    | ~ class_Divides_Osemiring__div(X2) ),
    c_0_1800,
    [final] ).

cnf(c_0_2293,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(X2)
    | c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X1,X3,X2),X1,X2) = X3
    | ~ class_Divides_Osemiring__div(X2) ),
    c_0_1801,
    [final] ).

cnf(c_0_2294,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_1802,
    [final] ).

cnf(c_0_2295,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_1803,
    [final] ).

cnf(c_0_2296,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_1804,
    [final] ).

cnf(c_0_2297,plain,
    ( c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Omod(X1,X2,X3),X2,X3) = c_HOL_Ozero__class_Ozero(X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    c_0_1805,
    [final] ).

cnf(c_0_2298,plain,
    ( X1 = X2
    | X3 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_HOL_Otimes__class_Otimes(X1,X3,tc_nat) != c_HOL_Otimes__class_Otimes(X2,X3,tc_nat) ),
    c_0_1806,
    [final] ).

cnf(c_0_2299,plain,
    ( X1 = X2
    | X3 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_HOL_Otimes__class_Otimes(X3,X1,tc_nat) != c_HOL_Otimes__class_Otimes(X3,X2,tc_nat) ),
    c_0_1807,
    [final] ).

cnf(c_0_2300,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X2 = X3
    | c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_HOL_Otimes__class_Otimes(X1,X3,tc_nat) ),
    c_0_1808,
    [final] ).

cnf(c_0_2301,plain,
    ( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X3),X2,X3) = c_HOL_Ozero__class_Ozero(X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    c_0_1809,
    [final] ).

cnf(c_0_2302,plain,
    ( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X3),X1,X3) = c_HOL_Ozero__class_Ozero(X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    c_0_1810,
    [final] ).

cnf(c_0_2303,plain,
    ( X1 = X2
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
    c_0_1811,
    [final] ).

cnf(c_0_2304,plain,
    ( X1 = X2
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
    c_0_1812,
    [final] ).

cnf(c_0_2305,plain,
    ( X1 = X2
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
    c_0_1813,
    [final] ).

cnf(c_0_2306,plain,
    ( X1 = X2
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
    c_0_1814,
    [final] ).

cnf(c_0_2307,plain,
    ( X2 = X1
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
    c_0_1815,
    [final] ).

cnf(c_0_2308,plain,
    ( X1 = X2
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
    c_0_1816,
    [final] ).

cnf(c_0_2309,plain,
    ( X1 = X2
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
    c_0_1817,
    [final] ).

cnf(c_0_2310,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | X2 = X1
    | hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X2)),X3),X1) = c_Lambda_OdB_OVar(X2) ),
    c_0_1818,
    [final] ).

cnf(c_0_2311,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X2,X1,X3),X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    c_0_1819,
    [final] ).

cnf(c_0_2312,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    c_0_1820,
    [final] ).

cnf(c_0_2313,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
    | ~ class_Ring__and__Field_Odvd(X3) ),
    c_0_1821,
    [final] ).

cnf(c_0_2314,plain,
    ( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X1)),X2),X1) = X2
    | c_HOL_Oord__class_Oless(X1,X1,tc_nat) ),
    c_0_1822,
    [final] ).

cnf(c_0_2315,plain,
    ( c_Type_Otyping(X1,X4,X3)
    | ~ c_Type_Otyping(X1,X2,X3)
    | ~ c_Lambda_Obeta(X2,X4) ),
    c_0_1823,
    [final] ).

cnf(c_0_2316,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X2),tc_nat) ),
    c_0_1824,
    [final] ).

cnf(c_0_2317,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | c_Divides_Odiv__class_Omod(X2,X1,X3) != c_HOL_Ozero__class_Ozero(X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    c_0_1825,
    [final] ).

cnf(c_0_2318,plain,
    ( c_Divides_Odiv__class_Omod(X2,X1,X3) = c_HOL_Ozero__class_Ozero(X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    c_0_1826,
    [final] ).

cnf(c_0_2319,plain,
    ( hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
    | ~ hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Nat__Xzero__induct__1__1(X1))) ),
    c_0_1827,
    [final] ).

cnf(c_0_2320,plain,
    ( hBOOL(hAPP(X1,c_Suc(c_ATP__Linkup_Osko__Nat__Xzero__induct__1__1(X1))))
    | hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
    | ~ hBOOL(hAPP(X1,X2)) ),
    c_0_1828,
    [final] ).

cnf(c_0_2321,plain,
    ( c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X2),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    c_0_1829,
    [final] ).

cnf(c_0_2322,plain,
    ( c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X2),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    c_0_1830,
    [final] ).

cnf(c_0_2323,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | X1 = X2
    | ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
    c_0_1831,
    [final] ).

cnf(c_0_2324,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | X2 = X1
    | ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
    c_0_1832,
    [final] ).

cnf(c_0_2325,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | X1 = X2
    | ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
    c_0_1833,
    [final] ).

cnf(c_0_2326,plain,
    ( c_Suc(X1) = X2
    | c_HOL_Oord__class_Oless(c_Suc(X1),X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    c_0_1834,
    [final] ).

cnf(c_0_2327,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_1835,
    [final] ).

cnf(c_0_2328,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_1836,
    [final] ).

cnf(c_0_2329,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_1837,
    [final] ).

cnf(c_0_2330,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_Suc(X1),X2,tc_nat) ),
    c_0_1838,
    [final] ).

cnf(c_0_2331,plain,
    ( ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_Ring__and__Field_Oordered__semidom(X2) ),
    c_0_1839,
    [final] ).

cnf(c_0_2332,plain,
    ( c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    c_0_1840,
    [final] ).

cnf(c_0_2333,plain,
    ( c_Divides_Odiv__class_Odiv(X1,X2,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    c_0_1841,
    [final] ).

cnf(c_0_2334,plain,
    ( c_Divides_Odiv__class_Omod(X1,X2,tc_nat) = X1
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    c_0_1842,
    [final] ).

cnf(c_0_2335,plain,
    ( hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(X1)),X2) = c_Lambda_OdB_OVar(X1)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    c_0_1843,
    [final] ).

cnf(c_0_2336,plain,
    ( hBOOL(hAPP(X1,v_sko__List__Xlexn__Xinduct__1(X1)))
    | hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
    c_0_1844,
    [final] ).

cnf(c_0_2337,plain,
    ( hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Nat__Xnat__induct__1__1(X1)))
    | hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
    c_0_1845,
    [final] ).

cnf(c_0_2338,plain,
    ( hBOOL(hAPP(X1,v_sko__List__Xreplicate__Xinduct__1(X1)))
    | hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
    c_0_1846,
    [final] ).

cnf(c_0_2339,plain,
    ( hBOOL(hAPP(X1,v_sko__Nat__Xnat__Xinducts__1(X1)))
    | hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
    c_0_1847,
    [final] ).

cnf(c_0_2340,plain,
    ( hBOOL(hAPP(X1,v_sko__Nat__Xnat__Xinduct__1(X1)))
    | hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
    c_0_1848,
    [final] ).

cnf(c_0_2341,plain,
    ( hBOOL(hAPP(X1,v_sko__List__Xupt__Xinduct__1(X1)))
    | hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
    c_0_1849,
    [final] ).

cnf(c_0_2342,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_1850,
    [final] ).

cnf(c_0_2343,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_1851,
    [final] ).

cnf(c_0_2344,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | X2 = X1
    | c_Lambda_Osubstn(c_Lambda_OdB_OVar(X2),X3,X1) = c_Lambda_OdB_OVar(X2) ),
    c_0_1852,
    [final] ).

cnf(c_0_2345,plain,
    ( X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X2,X1,X3)
    | ~ class_Ring__and__Field_Oordered__idom(X3) ),
    c_0_1853,
    [final] ).

cnf(c_0_2346,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X2,X1,X3)
    | X1 = X2
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_1854,
    [final] ).

cnf(c_0_2347,plain,
    ( X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X2,X1,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_1855,
    [final] ).

cnf(c_0_2348,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,X3)
    | X1 = X2
    | c_HOL_Oord__class_Oless(X2,X1,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_1856,
    [final] ).

cnf(c_0_2349,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X2,X1,X3)
    | X2 = X1
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_1857,
    [final] ).

cnf(c_0_2350,plain,
    ( X1 = X2
    | hAPP(hAPP(c_Lambda_OdB_OApp,X1),X3) != hAPP(hAPP(c_Lambda_OdB_OApp,X2),X4) ),
    c_0_1858,
    [final] ).

cnf(c_0_2351,plain,
    ( X1 = X2
    | hAPP(hAPP(c_Lambda_OdB_OApp,X3),X1) != hAPP(hAPP(c_Lambda_OdB_OApp,X4),X2) ),
    c_0_1859,
    [final] ).

cnf(c_0_2352,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_1860,
    [final] ).

cnf(c_0_2353,plain,
    ( c_HOL_Otimes__class_Otimes(X1,X2,X3) = c_HOL_Otimes__class_Otimes(X2,X1,X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    c_0_1861,
    [final] ).

cnf(c_0_2354,plain,
    ( c_HOL_Otimes__class_Otimes(X1,X2,X3) = c_HOL_Otimes__class_Otimes(X2,X1,X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    c_0_1862,
    [final] ).

cnf(c_0_2355,plain,
    ( c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat)
    | c_HOL_Oord__class_Oless(X1,X1,tc_nat) ),
    c_0_1863,
    [final] ).

cnf(c_0_2356,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(X2,c_Suc(X1),tc_nat) ),
    c_0_1864,
    [final] ).

cnf(c_0_2357,plain,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_1865,
    [final] ).

cnf(c_0_2358,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_1866,
    [final] ).

cnf(c_0_2359,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_1867,
    [final] ).

cnf(c_0_2360,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_1868,
    [final] ).

cnf(c_0_2361,plain,
    ( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
    c_0_1869,
    [final] ).

cnf(c_0_2362,plain,
    ( hAPP(X1,X2) = X3
    | ~ c_Type_Otyping(X1,c_Lambda_OdB_OVar(X2),X3) ),
    c_0_1870,
    [final] ).

cnf(c_0_2363,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(X2)
    | X3 = c_HOL_Ozero__class_Ozero(X2)
    | c_HOL_Otimes__class_Otimes(X3,X1,X2) != c_HOL_Ozero__class_Ozero(X2)
    | ~ class_Ring__and__Field_Ono__zero__divisors(X2) ),
    c_0_1871,
    [final] ).

cnf(c_0_2364,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(X2)
    | X3 = c_HOL_Ozero__class_Ozero(X2)
    | c_HOL_Otimes__class_Otimes(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
    | ~ class_Ring__and__Field_Ono__zero__divisors(X2) ),
    c_0_1872,
    [final] ).

cnf(c_0_2365,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(X2)
    | X3 = c_HOL_Ozero__class_Ozero(X2)
    | c_HOL_Otimes__class_Otimes(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
    | ~ class_Ring__and__Field_Oring__no__zero__divisors(X2) ),
    c_0_1873,
    [final] ).

cnf(c_0_2366,plain,
    ( X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
    c_0_1874,
    [final] ).

cnf(c_0_2367,plain,
    ( X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
    c_0_1875,
    [final] ).

cnf(c_0_2368,plain,
    ( X2 = c_HOL_Ozero__class_Ozero(X1)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    c_0_1876,
    [final] ).

cnf(c_0_2369,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | c_Power_Opower__class_Opower(X2,X1,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    c_0_1877,
    [final] ).

cnf(c_0_2370,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
    c_0_1878,
    [final] ).

cnf(c_0_2371,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_1879,
    [final] ).

cnf(c_0_2372,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_1880,
    [final] ).

cnf(c_0_2373,plain,
    ( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | c_HOL_Otimes__class_Otimes(X2,X1,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    c_0_1881,
    [final] ).

cnf(c_0_2374,plain,
    ( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    c_0_1882,
    [final] ).

cnf(c_0_2375,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_1883,
    [final] ).

cnf(c_0_2376,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_1884,
    [final] ).

cnf(c_0_2377,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_1885,
    [final] ).

cnf(c_0_2378,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_1886,
    [final] ).

cnf(c_0_2379,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_1887,
    [final] ).

cnf(c_0_2380,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_1888,
    [final] ).

cnf(c_0_2381,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_1889,
    [final] ).

cnf(c_0_2382,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_1890,
    [final] ).

cnf(c_0_2383,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X2 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
    c_0_1891,
    [final] ).

cnf(c_0_2384,plain,
    ( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
    | ~ class_Orderings_Oorder(X2) ),
    c_0_1892,
    [final] ).

cnf(c_0_2385,plain,
    ( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
    | ~ class_Orderings_Olinorder(X2) ),
    c_0_1893,
    [final] ).

cnf(c_0_2386,plain,
    ( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
    | ~ class_Orderings_Opreorder(X2) ),
    c_0_1894,
    [final] ).

cnf(c_0_2387,plain,
    ( X1 = c_HOL_Oone__class_Oone(tc_nat)
    | X2 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_HOL_Otimes__class_Otimes(X2,X1,tc_nat) != X2 ),
    c_0_1895,
    [final] ).

cnf(c_0_2388,plain,
    ( X1 = c_HOL_Oone__class_Oone(tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
    c_0_1896,
    [final] ).

cnf(c_0_2389,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_1897,
    [final] ).

cnf(c_0_2390,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_1898,
    [final] ).

cnf(c_0_2391,plain,
    ( X1 = c_HOL_Oone__class_Oone(tc_nat)
    | c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_HOL_Oone__class_Oone(tc_nat) ),
    c_0_1899,
    [final] ).

cnf(c_0_2392,plain,
    ( X1 = c_HOL_Oone__class_Oone(tc_nat)
    | c_HOL_Otimes__class_Otimes(X2,X1,tc_nat) != c_HOL_Oone__class_Oone(tc_nat) ),
    c_0_1900,
    [final] ).

cnf(c_0_2393,plain,
    ( X1 = c_HOL_Oone__class_Oone(tc_nat)
    | c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_HOL_Oone__class_Oone(tc_nat) ),
    c_0_1901,
    [final] ).

cnf(c_0_2394,plain,
    ( X1 = c_HOL_Oone__class_Oone(tc_nat)
    | c_HOL_Otimes__class_Otimes(X2,X1,tc_nat) != c_HOL_Oone__class_Oone(tc_nat) ),
    c_0_1902,
    [final] ).

cnf(c_0_2395,plain,
    ( X1 = X2
    | ~ c_fequal(X1,X2,X3) ),
    c_0_1903,
    [final] ).

cnf(c_0_2396,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_1904,
    [final] ).

cnf(c_0_2397,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_1905,
    [final] ).

cnf(c_0_2398,plain,
    ( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(X1)))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
    c_0_1906,
    [final] ).

cnf(c_0_2399,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_1907,
    [final] ).

cnf(c_0_2400,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_1908,
    [final] ).

cnf(c_0_2401,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_1909,
    [final] ).

cnf(c_0_2402,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_1910,
    [final] ).

cnf(c_0_2403,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != X2 ),
    c_0_1911,
    [final] ).

cnf(c_0_2404,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) != X2 ),
    c_0_1912,
    [final] ).

cnf(c_0_2405,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oone__class_Oone(X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_1913,
    [final] ).

cnf(c_0_2406,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_1914,
    [final] ).

cnf(c_0_2407,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_1915,
    [final] ).

cnf(c_0_2408,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_1916,
    [final] ).

cnf(c_0_2409,plain,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
    | ~ class_OrderedGroup_Omonoid__add(X1) ),
    c_0_1917,
    [final] ).

cnf(c_0_2410,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_1918,
    [final] ).

cnf(c_0_2411,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_1919,
    [final] ).

cnf(c_0_2412,plain,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    c_0_1920,
    [final] ).

cnf(c_0_2413,plain,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Omult__zero(X1) ),
    c_0_1921,
    [final] ).

cnf(c_0_2414,plain,
    ( c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X2),X2) = c_HOL_Ozero__class_Ozero(X2)
    | ~ class_Ring__and__Field_Omult__zero(X2) ),
    c_0_1922,
    [final] ).

cnf(c_0_2415,plain,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Oring__no__zero__divisors(X1) ),
    c_0_1923,
    [final] ).

cnf(c_0_2416,plain,
    ( c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X2),X2) = c_HOL_Ozero__class_Ozero(X2)
    | ~ class_Ring__and__Field_Oring__no__zero__divisors(X2) ),
    c_0_1924,
    [final] ).

cnf(c_0_2417,plain,
    ( c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X2),X2) = c_HOL_Ozero__class_Ozero(X2)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ),
    c_0_1925,
    [final] ).

cnf(c_0_2418,plain,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    c_0_1926,
    [final] ).

cnf(c_0_2419,plain,
    ( c_Divides_Odiv__class_Odiv(X1,c_HOL_Ozero__class_Ozero(X2),X2) = c_HOL_Ozero__class_Ozero(X2)
    | ~ class_Divides_Osemiring__div(X2) ),
    c_0_1927,
    [final] ).

cnf(c_0_2420,plain,
    ( c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    c_0_1928,
    [final] ).

cnf(c_0_2421,plain,
    ( c_Divides_Odiv__class_Omod(X1,c_HOL_Oone__class_Oone(X2),X2) = c_HOL_Ozero__class_Ozero(X2)
    | ~ class_Divides_Osemiring__div(X2) ),
    c_0_1929,
    [final] ).

cnf(c_0_2422,plain,
    ( c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    c_0_1930,
    [final] ).

cnf(c_0_2423,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(X2)
    | c_Divides_Odiv__class_Odiv(X1,X1,X2) = c_HOL_Oone__class_Oone(X2)
    | ~ class_Divides_Osemiring__div(X2) ),
    c_0_1931,
    [final] ).

cnf(c_0_2424,plain,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X1),X2,X1) = X2
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    c_0_1932,
    [final] ).

cnf(c_0_2425,plain,
    ( c_HOL_Otimes__class_Otimes(X1,c_HOL_Oone__class_Oone(X2),X2) = X1
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ),
    c_0_1933,
    [final] ).

cnf(c_0_2426,plain,
    ( c_HOL_Otimes__class_Otimes(X1,c_HOL_Oone__class_Oone(X2),X2) = X1
    | ~ class_OrderedGroup_Omonoid__mult(X2) ),
    c_0_1934,
    [final] ).

cnf(c_0_2427,plain,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X1),X2,X1) = X2
    | ~ class_OrderedGroup_Omonoid__mult(X1) ),
    c_0_1935,
    [final] ).

cnf(c_0_2428,plain,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X1),X2,X1) = X2
    | ~ class_OrderedGroup_Ocomm__monoid__mult(X1) ),
    c_0_1936,
    [final] ).

cnf(c_0_2429,plain,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X1),X2,X1) = X2
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    c_0_1937,
    [final] ).

cnf(c_0_2430,plain,
    ( c_Divides_Odiv__class_Odiv(X1,c_HOL_Oone__class_Oone(X2),X2) = X1
    | ~ class_Divides_Osemiring__div(X2) ),
    c_0_1938,
    [final] ).

cnf(c_0_2431,plain,
    ( c_Divides_Odiv__class_Omod(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1
    | ~ class_Divides_Osemiring__div(X2) ),
    c_0_1939,
    [final] ).

cnf(c_0_2432,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_1940,
    [final] ).

cnf(c_0_2433,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_1941,
    [final] ).

cnf(c_0_2434,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ),
    c_0_1942,
    [final] ).

cnf(c_0_2435,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(X1),X2,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    c_0_1943,
    [final] ).

cnf(c_0_2436,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_1944,
    [final] ).

cnf(c_0_2437,plain,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = X2
    | ~ class_OrderedGroup_Omonoid__add(X1) ),
    c_0_1945,
    [final] ).

cnf(c_0_2438,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_1946,
    [final] ).

cnf(c_0_2439,plain,
    ( c_Power_Opower__class_Opower(X1,c_HOL_Oone__class_Oone(tc_nat),X2) = X1
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ),
    c_0_1947,
    [final] ).

cnf(c_0_2440,plain,
    ( c_Power_Opower__class_Opower(X1,c_HOL_Oone__class_Oone(tc_nat),X2) = X1
    | ~ class_OrderedGroup_Omonoid__mult(X2) ),
    c_0_1948,
    [final] ).

cnf(c_0_2441,plain,
    ( c_Divides_Odiv__class_Omod(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
    | ~ class_Divides_Osemiring__div(X2) ),
    c_0_1949,
    [final] ).

cnf(c_0_2442,plain,
    ( c_HOL_Otimes__class_Otimes(X1,X1,X2) = X1
    | ~ class_OrderedGroup_Oab__semigroup__idem__mult(X2) ),
    c_0_1950,
    [final] ).

cnf(c_0_2443,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,X1,X2)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ),
    c_0_1951,
    [final] ).

cnf(c_0_2444,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    c_0_1952,
    [final] ).

cnf(c_0_2445,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_1953,
    [final] ).

cnf(c_0_2446,plain,
    ( c_Lambda_Obeta(c_Lambda_OdB_OAbs(X1),c_Lambda_OdB_OAbs(X2))
    | ~ c_Lambda_Obeta(X1,X2) ),
    c_0_1954,
    [final] ).

cnf(c_0_2447,plain,
    ( class_Orderings_Opreorder(tc_fun(X2,X1))
    | ~ class_Orderings_Opreorder(X1) ),
    c_0_1955,
    [final] ).

cnf(c_0_2448,plain,
    ( class_Orderings_Oorder(tc_fun(X2,X1))
    | ~ class_Orderings_Oorder(X1) ),
    c_0_1956,
    [final] ).

cnf(c_0_2449,plain,
    ( c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),X1) = c_HOL_Oone__class_Oone(X1)
    | ~ class_Ring__and__Field_Osemiring__1(X1) ),
    c_0_1957,
    [final] ).

cnf(c_0_2450,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_1958,
    [final] ).

cnf(c_0_2451,plain,
    ( c_HOL_Oone__class_Oone(X1) != c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Ozero__neq__one(X1) ),
    c_0_1959,
    [final] ).

cnf(c_0_2452,plain,
    ( c_HOL_Oone__class_Oone(X1) != c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Ozero__neq__one(X1) ),
    c_0_1960,
    [final] ).

cnf(c_0_2453,plain,
    ( X1 = X2
    | c_Lambda_OdB_OAbs(X1) != c_Lambda_OdB_OAbs(X2) ),
    c_0_1961,
    [final] ).

cnf(c_0_2454,plain,
    ( X1 = X2
    | c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OVar(X2) ),
    c_0_1962,
    [final] ).

cnf(c_0_2455,plain,
    ( X1 = X2
    | c_Suc(X1) != c_Suc(X2) ),
    c_0_1963,
    [final] ).

cnf(c_0_2456,plain,
    ( X1 = X2
    | c_Suc(X1) != c_Suc(X2) ),
    c_0_1964,
    [final] ).

cnf(c_0_2457,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_Suc(c_ATP__Linkup_Osko__Nat__Xnat__Xexhaust__1__1(X1)) = X1 ),
    c_0_1965,
    [final] ).

cnf(c_0_2458,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_Suc(c_ATP__Linkup_Osko__Nat__Xnat__Xnchotomy__1__1(X1)) = X1 ),
    c_0_1966,
    [final] ).

cnf(c_0_2459,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_Suc(c_ATP__Linkup_Osko__Nat__Xnot0__implies__Suc__1__1(X1)) = X1 ),
    c_0_1967,
    [final] ).

% End CNF derivation
% Generating one_way clauses for all literals in the CNF.
cnf(c_0_1968_0,axiom,
    ( c_Type_Otypings(X1,c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,X2,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),X4,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X5,tc_Lambda_OdB,tc_Lambda_OdB),X6)
    | ~ c_Type_Otyping(X1,X2,X3)
    | ~ c_Type_Otypings(c_Type_Oshift(X1,X4,X3,tc_Type_Otype),X5,X6) ),
    inference(literals_permutation,[status(thm)],[c_0_1968]) ).

cnf(c_0_1968_1,axiom,
    ( ~ c_Type_Otyping(X1,X2,X3)
    | c_Type_Otypings(X1,c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,X2,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),X4,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X5,tc_Lambda_OdB,tc_Lambda_OdB),X6)
    | ~ c_Type_Otypings(c_Type_Oshift(X1,X4,X3,tc_Type_Otype),X5,X6) ),
    inference(literals_permutation,[status(thm)],[c_0_1968]) ).

cnf(c_0_1968_2,axiom,
    ( ~ c_Type_Otypings(c_Type_Oshift(X1,X4,X3,tc_Type_Otype),X5,X6)
    | ~ c_Type_Otyping(X1,X2,X3)
    | c_Type_Otypings(X1,c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,X2,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),X4,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X5,tc_Lambda_OdB,tc_Lambda_OdB),X6) ),
    inference(literals_permutation,[status(thm)],[c_0_1968]) ).

cnf(c_0_1969_0,axiom,
    ( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1)),X2),X3,tc_Lambda_OdB,tc_Lambda_OdB)))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X2),c_HOL_Ozero__class_Ozero(tc_nat)),X3,tc_Lambda_OdB,tc_Lambda_OdB)))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_1969]) ).

cnf(c_0_1969_1,axiom,
    ( ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X2),c_HOL_Ozero__class_Ozero(tc_nat)),X3,tc_Lambda_OdB,tc_Lambda_OdB)))
    | hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1)),X2),X3,tc_Lambda_OdB,tc_Lambda_OdB)))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_1969]) ).

cnf(c_0_1969_2,axiom,
    ( ~ hBOOL(hAPP(c_InductTermi_OIT,X2))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X2),c_HOL_Ozero__class_Ozero(tc_nat)),X3,tc_Lambda_OdB,tc_Lambda_OdB)))
    | hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1)),X2),X3,tc_Lambda_OdB,tc_Lambda_OdB))) ),
    inference(literals_permutation,[status(thm)],[c_0_1969]) ).

cnf(c_0_1970_0,axiom,
    ( hBOOL(hAPP(X1,hAPP(hAPP(X2,X3),X4)))
    | ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X5,X2,X6,hAPP(hAPP(c_Lambda_OdB_OApp,X3),X4),t_a))) ),
    inference(literals_permutation,[status(thm)],[c_0_1970]) ).

cnf(c_0_1970_1,axiom,
    ( ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X5,X2,X6,hAPP(hAPP(c_Lambda_OdB_OApp,X3),X4),t_a)))
    | hBOOL(hAPP(X1,hAPP(hAPP(X2,X3),X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_1970]) ).

cnf(c_0_1971_0,axiom,
    ( hBOOL(hAPP(X1,hAPP(hAPP(X2,X3),X4)))
    | ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X5,X2,X6,hAPP(hAPP(c_Lambda_OdB_OApp,X3),X4),t_a))) ),
    inference(literals_permutation,[status(thm)],[c_0_1971]) ).

cnf(c_0_1971_1,axiom,
    ( ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X5,X2,X6,hAPP(hAPP(c_Lambda_OdB_OApp,X3),X4),t_a)))
    | hBOOL(hAPP(X1,hAPP(hAPP(X2,X3),X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_1971]) ).

cnf(c_0_1972_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_1972]) ).

cnf(c_0_1972_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_1972]) ).

cnf(c_0_1972_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_1972]) ).

cnf(c_0_1973_0,axiom,
    ( hBOOL(hAPP(X1,hAPP(X2,X3)))
    | ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X2,X4,X5,c_Lambda_OdB_OVar(X3),t_a))) ),
    inference(literals_permutation,[status(thm)],[c_0_1973]) ).

cnf(c_0_1973_1,axiom,
    ( ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X2,X4,X5,c_Lambda_OdB_OVar(X3),t_a)))
    | hBOOL(hAPP(X1,hAPP(X2,X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_1973]) ).

cnf(c_0_1974_0,axiom,
    ( hBOOL(hAPP(X1,hAPP(X2,X3)))
    | ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X2,X4,X5,c_Lambda_OdB_OVar(X3),t_a))) ),
    inference(literals_permutation,[status(thm)],[c_0_1974]) ).

cnf(c_0_1974_1,axiom,
    ( ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X2,X4,X5,c_Lambda_OdB_OVar(X3),t_a)))
    | hBOOL(hAPP(X1,hAPP(X2,X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_1974]) ).

cnf(c_0_1975_0,axiom,
    ( hBOOL(hAPP(X1,hAPP(X2,X3)))
    | ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X4,X5,X2,c_Lambda_OdB_OAbs(X3),t_a))) ),
    inference(literals_permutation,[status(thm)],[c_0_1975]) ).

cnf(c_0_1975_1,axiom,
    ( ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X4,X5,X2,c_Lambda_OdB_OAbs(X3),t_a)))
    | hBOOL(hAPP(X1,hAPP(X2,X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_1975]) ).

cnf(c_0_1976_0,axiom,
    ( hBOOL(hAPP(X1,hAPP(X2,X3)))
    | ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X4,X5,X2,c_Lambda_OdB_OAbs(X3),t_a))) ),
    inference(literals_permutation,[status(thm)],[c_0_1976]) ).

cnf(c_0_1976_1,axiom,
    ( ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X4,X5,X2,c_Lambda_OdB_OAbs(X3),t_a)))
    | hBOOL(hAPP(X1,hAPP(X2,X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_1976]) ).

cnf(c_0_1977_0,axiom,
    ( c_Type_Otypings(c_Type_Oshift(X1,X4,X5,tc_Type_Otype),c_List_Omap(c_COMBC(c_Lambda_Olift,X4,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X2,tc_Lambda_OdB,tc_Lambda_OdB),X3)
    | ~ c_Type_Otypings(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1977]) ).

cnf(c_0_1977_1,axiom,
    ( ~ c_Type_Otypings(X1,X2,X3)
    | c_Type_Otypings(c_Type_Oshift(X1,X4,X5,tc_Type_Otype),c_List_Omap(c_COMBC(c_Lambda_Olift,X4,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X2,tc_Lambda_OdB,tc_Lambda_OdB),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_1977]) ).

cnf(c_0_1978_0,axiom,
    ( c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X1,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)
    | ~ c_List_Olistsp(c_InductTermi_OIT,X1,tc_Lambda_OdB) ),
    inference(literals_permutation,[status(thm)],[c_0_1978]) ).

cnf(c_0_1978_1,axiom,
    ( ~ c_List_Olistsp(c_InductTermi_OIT,X1,tc_Lambda_OdB)
    | c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X1,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB) ),
    inference(literals_permutation,[status(thm)],[c_0_1978]) ).

cnf(c_0_1979_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
    | ~ 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_1979]) ).

cnf(c_0_1979_1,axiom,
    ( ~ 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_1979]) ).

cnf(c_0_1980_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_1980]) ).

cnf(c_0_1980_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_1980]) ).

cnf(c_0_1981_0,axiom,
    ( 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))
    | ~ c_Lambda_Obeta(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1981]) ).

cnf(c_0_1981_1,axiom,
    ( ~ c_Lambda_Obeta(X1,X2)
    | 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_1981]) ).

cnf(c_0_1982_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_1982]) ).

cnf(c_0_1982_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_1982]) ).

cnf(c_0_1983_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_1983]) ).

cnf(c_0_1983_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_1983]) ).

cnf(c_0_1984_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_1984]) ).

cnf(c_0_1984_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_1984]) ).

cnf(c_0_1985_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_1985]) ).

cnf(c_0_1985_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_1985]) ).

cnf(c_0_1986_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_1986]) ).

cnf(c_0_1986_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_1986]) ).

cnf(c_0_1987_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_1987]) ).

cnf(c_0_1987_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_1987]) ).

cnf(c_0_1988_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_1988]) ).

cnf(c_0_1988_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_1988]) ).

cnf(c_0_1989_0,axiom,
    ( hBOOL(hAPP(X1,X2))
    | X3 = c_HOL_Ozero__class_Ozero(tc_nat)
    | ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X3,X4,tc_nat)),X2),X3,tc_nat)))
    | ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_1989]) ).

cnf(c_0_1989_1,axiom,
    ( X3 = c_HOL_Ozero__class_Ozero(tc_nat)
    | hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X3,X4,tc_nat)),X2),X3,tc_nat)))
    | ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_1989]) ).

cnf(c_0_1989_2,axiom,
    ( ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X3,X4,tc_nat)),X2),X3,tc_nat)))
    | X3 = c_HOL_Ozero__class_Ozero(tc_nat)
    | hBOOL(hAPP(X1,X2))
    | ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_1989]) ).

cnf(c_0_1989_3,axiom,
    ( ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat)
    | ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X3,X4,tc_nat)),X2),X3,tc_nat)))
    | X3 = c_HOL_Ozero__class_Ozero(tc_nat)
    | hBOOL(hAPP(X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_1989]) ).

cnf(c_0_1990_0,axiom,
    ( hBOOL(hAPP(X1,X2))
    | X3 = c_HOL_Ozero__class_Ozero(tc_nat)
    | ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat)),X4),X3,tc_nat)))
    | ~ c_HOL_Oord__class_Oless(X4,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_1990]) ).

cnf(c_0_1990_1,axiom,
    ( X3 = c_HOL_Ozero__class_Ozero(tc_nat)
    | hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat)),X4),X3,tc_nat)))
    | ~ c_HOL_Oord__class_Oless(X4,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_1990]) ).

cnf(c_0_1990_2,axiom,
    ( ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat)),X4),X3,tc_nat)))
    | X3 = c_HOL_Ozero__class_Ozero(tc_nat)
    | hBOOL(hAPP(X1,X2))
    | ~ c_HOL_Oord__class_Oless(X4,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_1990]) ).

cnf(c_0_1990_3,axiom,
    ( ~ c_HOL_Oord__class_Oless(X4,X3,tc_nat)
    | ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat)),X4),X3,tc_nat)))
    | X3 = c_HOL_Ozero__class_Ozero(tc_nat)
    | hBOOL(hAPP(X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_1990]) ).

cnf(c_0_1991_0,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,c_Divides_Odiv__class_Odiv(X3,X2,X1),X1)),c_Divides_Odiv__class_Omod(X3,X2,X1))),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1991]) ).

cnf(c_0_1991_1,axiom,
    ( ~ class_Divides_Osemiring__div(X1)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,c_Divides_Odiv__class_Odiv(X3,X2,X1),X1)),c_Divides_Odiv__class_Omod(X3,X2,X1))),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_1991]) ).

cnf(c_0_1992_0,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X3,X1),X3,X1)),c_Divides_Odiv__class_Omod(X2,X3,X1))),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1992]) ).

cnf(c_0_1992_1,axiom,
    ( ~ class_Divides_Osemiring__div(X1)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X3,X1),X3,X1)),c_Divides_Odiv__class_Omod(X2,X3,X1))),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_1992]) ).

cnf(c_0_1993_0,axiom,
    ( hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,X3),hAPP(hAPP(c_Lambda_Olift,X4),X1)),c_Suc(X2))),hAPP(hAPP(hAPP(c_Lambda_Osubst,X5),X4),X2)),X1) = hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,X3),X5),X1)),X4),X2)
    | ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_1993]) ).

cnf(c_0_1993_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),tc_nat)
    | hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,X3),hAPP(hAPP(c_Lambda_Olift,X4),X1)),c_Suc(X2))),hAPP(hAPP(hAPP(c_Lambda_Osubst,X5),X4),X2)),X1) = hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,X3),X5),X1)),X4),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1993]) ).

cnf(c_0_1994_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_1994]) ).

cnf(c_0_1994_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_1994]) ).

cnf(c_0_1995_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_1995]) ).

cnf(c_0_1995_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_1995]) ).

cnf(c_0_1996_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_1996]) ).

cnf(c_0_1996_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_1996]) ).

cnf(c_0_1997_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_1997]) ).

cnf(c_0_1997_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_1997]) ).

cnf(c_0_1998_0,axiom,
    ( hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)))),hAPP(hAPP(c_Lambda_Olift,X4),X2)),X1) = hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(hAPP(c_Lambda_Osubst,X3),X4),X1)),X2)
    | ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_1998]) ).

cnf(c_0_1998_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),tc_nat)
    | hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)))),hAPP(hAPP(c_Lambda_Olift,X4),X2)),X1) = hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(hAPP(c_Lambda_Osubst,X3),X4),X1)),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1998]) ).

cnf(c_0_1999_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),c_Finite__Set_Osetsum(X3,c_SetInterval_Oord__class_OatLeastLessThan(X2,X1,tc_nat),tc_nat,X4)),hAPP(X3,X1)) = c_Finite__Set_Osetsum(X3,c_SetInterval_Oord__class_OatLeastLessThan(X2,c_Suc(X1),tc_nat),tc_nat,X4)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_1999]) ).

cnf(c_0_1999_1,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),c_Finite__Set_Osetsum(X3,c_SetInterval_Oord__class_OatLeastLessThan(X2,X1,tc_nat),tc_nat,X4)),hAPP(X3,X1)) = c_Finite__Set_Osetsum(X3,c_SetInterval_Oord__class_OatLeastLessThan(X2,c_Suc(X1),tc_nat),tc_nat,X4)
    | c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_1999]) ).

cnf(c_0_1999_2,axiom,
    ( ~ class_OrderedGroup_Ocomm__monoid__add(X4)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),c_Finite__Set_Osetsum(X3,c_SetInterval_Oord__class_OatLeastLessThan(X2,X1,tc_nat),tc_nat,X4)),hAPP(X3,X1)) = c_Finite__Set_Osetsum(X3,c_SetInterval_Oord__class_OatLeastLessThan(X2,c_Suc(X1),tc_nat),tc_nat,X4)
    | c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_1999]) ).

cnf(c_0_2000_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_2000]) ).

cnf(c_0_2000_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_2000]) ).

cnf(c_0_2001_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_2001]) ).

cnf(c_0_2001_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_2001]) ).

cnf(c_0_2002_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_2002]) ).

cnf(c_0_2002_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_2002]) ).

cnf(c_0_2003_0,axiom,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X3,c_Divides_Odiv__class_Omod(X4,X1,tc_nat),tc_nat)),X2),c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2003]) ).

cnf(c_0_2003_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X3,c_Divides_Odiv__class_Omod(X4,X1,tc_nat),tc_nat)),X2),c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2003]) ).

cnf(c_0_2003_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X3,c_Divides_Odiv__class_Omod(X4,X1,tc_nat),tc_nat)),X2),c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2003]) ).

cnf(c_0_2004_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)),X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2004]) ).

cnf(c_0_2004_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2004]) ).

cnf(c_0_2005_0,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X4,X3,X1)),X5)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X3,X1)),X5)
    | ~ class_Ring__and__Field_Osemiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2005]) ).

cnf(c_0_2005_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring(X1)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X4,X3,X1)),X5)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X3,X1)),X5) ),
    inference(literals_permutation,[status(thm)],[c_0_2005]) ).

cnf(c_0_2006_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X2,X1)),c_HOL_Otimes__class_Otimes(X3,X3,X1)),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2006]) ).

cnf(c_0_2006_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X2,X1)),c_HOL_Otimes__class_Otimes(X3,X3,X1)),c_HOL_Ozero__class_Ozero(X1),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2006]) ).

cnf(c_0_2007_0,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),hAPP(X3,X1)),c_Finite__Set_Osetsum(X3,c_SetInterval_Oord__class_OatLeastLessThan(c_Suc(X1),X2,tc_nat),tc_nat,X4)) = c_Finite__Set_Osetsum(X3,c_SetInterval_Oord__class_OatLeastLessThan(X1,X2,tc_nat),tc_nat,X4)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_2007]) ).

cnf(c_0_2007_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),hAPP(X3,X1)),c_Finite__Set_Osetsum(X3,c_SetInterval_Oord__class_OatLeastLessThan(c_Suc(X1),X2,tc_nat),tc_nat,X4)) = c_Finite__Set_Osetsum(X3,c_SetInterval_Oord__class_OatLeastLessThan(X1,X2,tc_nat),tc_nat,X4)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_2007]) ).

cnf(c_0_2007_2,axiom,
    ( ~ class_OrderedGroup_Ocomm__monoid__add(X4)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),hAPP(X3,X1)),c_Finite__Set_Osetsum(X3,c_SetInterval_Oord__class_OatLeastLessThan(c_Suc(X1),X2,tc_nat),tc_nat,X4)) = c_Finite__Set_Osetsum(X3,c_SetInterval_Oord__class_OatLeastLessThan(X1,X2,tc_nat),tc_nat,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_2007]) ).

cnf(c_0_2008_0,axiom,
    ( hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,X3),X1)),hAPP(hAPP(c_Lambda_Olift,X4),X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat))) = hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(hAPP(c_Lambda_Osubst,X3),X4),X2)),X1)
    | ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2008]) ).

cnf(c_0_2008_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),tc_nat)
    | hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,X3),X1)),hAPP(hAPP(c_Lambda_Olift,X4),X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat))) = hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(hAPP(c_Lambda_Osubst,X3),X4),X2)),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2008]) ).

cnf(c_0_2009_0,axiom,
    ( X1 = X2
    | X3 = X4
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_HOL_Otimes__class_Otimes(X1,X3,X5)),c_HOL_Otimes__class_Otimes(X2,X4,X5)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_HOL_Otimes__class_Otimes(X1,X4,X5)),c_HOL_Otimes__class_Otimes(X2,X3,X5))
    | ~ class_Int_Onumber__ring(X5)
    | ~ class_Ring__and__Field_Oidom(X5) ),
    inference(literals_permutation,[status(thm)],[c_0_2009]) ).

cnf(c_0_2009_1,axiom,
    ( X3 = X4
    | X1 = X2
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_HOL_Otimes__class_Otimes(X1,X3,X5)),c_HOL_Otimes__class_Otimes(X2,X4,X5)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_HOL_Otimes__class_Otimes(X1,X4,X5)),c_HOL_Otimes__class_Otimes(X2,X3,X5))
    | ~ class_Int_Onumber__ring(X5)
    | ~ class_Ring__and__Field_Oidom(X5) ),
    inference(literals_permutation,[status(thm)],[c_0_2009]) ).

cnf(c_0_2009_2,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_HOL_Otimes__class_Otimes(X1,X3,X5)),c_HOL_Otimes__class_Otimes(X2,X4,X5)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_HOL_Otimes__class_Otimes(X1,X4,X5)),c_HOL_Otimes__class_Otimes(X2,X3,X5))
    | X3 = X4
    | X1 = X2
    | ~ class_Int_Onumber__ring(X5)
    | ~ class_Ring__and__Field_Oidom(X5) ),
    inference(literals_permutation,[status(thm)],[c_0_2009]) ).

cnf(c_0_2009_3,axiom,
    ( ~ class_Int_Onumber__ring(X5)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_HOL_Otimes__class_Otimes(X1,X3,X5)),c_HOL_Otimes__class_Otimes(X2,X4,X5)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_HOL_Otimes__class_Otimes(X1,X4,X5)),c_HOL_Otimes__class_Otimes(X2,X3,X5))
    | X3 = X4
    | X1 = X2
    | ~ class_Ring__and__Field_Oidom(X5) ),
    inference(literals_permutation,[status(thm)],[c_0_2009]) ).

cnf(c_0_2009_4,axiom,
    ( ~ class_Ring__and__Field_Oidom(X5)
    | ~ class_Int_Onumber__ring(X5)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_HOL_Otimes__class_Otimes(X1,X3,X5)),c_HOL_Otimes__class_Otimes(X2,X4,X5)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_HOL_Otimes__class_Otimes(X1,X4,X5)),c_HOL_Otimes__class_Otimes(X2,X3,X5))
    | X3 = X4
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_2009]) ).

cnf(c_0_2010_0,axiom,
    ( X1 = X2
    | X3 = X4
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_HOL_Otimes__class_Otimes(X1,X3,X5)),c_HOL_Otimes__class_Otimes(X2,X4,X5)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_HOL_Otimes__class_Otimes(X1,X4,X5)),c_HOL_Otimes__class_Otimes(X2,X3,X5))
    | ~ class_Int_Onumber__ring(X5)
    | ~ class_Ring__and__Field_Oidom(X5) ),
    inference(literals_permutation,[status(thm)],[c_0_2010]) ).

cnf(c_0_2010_1,axiom,
    ( X3 = X4
    | X1 = X2
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_HOL_Otimes__class_Otimes(X1,X3,X5)),c_HOL_Otimes__class_Otimes(X2,X4,X5)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_HOL_Otimes__class_Otimes(X1,X4,X5)),c_HOL_Otimes__class_Otimes(X2,X3,X5))
    | ~ class_Int_Onumber__ring(X5)
    | ~ class_Ring__and__Field_Oidom(X5) ),
    inference(literals_permutation,[status(thm)],[c_0_2010]) ).

cnf(c_0_2010_2,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_HOL_Otimes__class_Otimes(X1,X3,X5)),c_HOL_Otimes__class_Otimes(X2,X4,X5)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_HOL_Otimes__class_Otimes(X1,X4,X5)),c_HOL_Otimes__class_Otimes(X2,X3,X5))
    | X3 = X4
    | X1 = X2
    | ~ class_Int_Onumber__ring(X5)
    | ~ class_Ring__and__Field_Oidom(X5) ),
    inference(literals_permutation,[status(thm)],[c_0_2010]) ).

cnf(c_0_2010_3,axiom,
    ( ~ class_Int_Onumber__ring(X5)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_HOL_Otimes__class_Otimes(X1,X3,X5)),c_HOL_Otimes__class_Otimes(X2,X4,X5)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_HOL_Otimes__class_Otimes(X1,X4,X5)),c_HOL_Otimes__class_Otimes(X2,X3,X5))
    | X3 = X4
    | X1 = X2
    | ~ class_Ring__and__Field_Oidom(X5) ),
    inference(literals_permutation,[status(thm)],[c_0_2010]) ).

cnf(c_0_2010_4,axiom,
    ( ~ class_Ring__and__Field_Oidom(X5)
    | ~ class_Int_Onumber__ring(X5)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_HOL_Otimes__class_Otimes(X1,X3,X5)),c_HOL_Otimes__class_Otimes(X2,X4,X5)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_HOL_Otimes__class_Otimes(X1,X4,X5)),c_HOL_Otimes__class_Otimes(X2,X3,X5))
    | X3 = X4
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_2010]) ).

cnf(c_0_2011_0,axiom,
    ( c_Type_Otyping(X1,hAPP(hAPP(hAPP(c_Lambda_Osubst,X2),X3),X4),X5)
    | ~ c_Type_Otyping(c_Type_Oshift(X1,X4,X6,tc_Type_Otype),X2,X5)
    | ~ c_Type_Otyping(X1,X3,X6) ),
    inference(literals_permutation,[status(thm)],[c_0_2011]) ).

cnf(c_0_2011_1,axiom,
    ( ~ c_Type_Otyping(c_Type_Oshift(X1,X4,X6,tc_Type_Otype),X2,X5)
    | c_Type_Otyping(X1,hAPP(hAPP(hAPP(c_Lambda_Osubst,X2),X3),X4),X5)
    | ~ c_Type_Otyping(X1,X3,X6) ),
    inference(literals_permutation,[status(thm)],[c_0_2011]) ).

cnf(c_0_2011_2,axiom,
    ( ~ c_Type_Otyping(X1,X3,X6)
    | ~ c_Type_Otyping(c_Type_Oshift(X1,X4,X6,tc_Type_Otype),X2,X5)
    | c_Type_Otyping(X1,hAPP(hAPP(hAPP(c_Lambda_Osubst,X2),X3),X4),X5) ),
    inference(literals_permutation,[status(thm)],[c_0_2011]) ).

cnf(c_0_2012_0,axiom,
    ( X1 = X2
    | X3 = X4
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat)),c_HOL_Otimes__class_Otimes(X2,X4,tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X1,X4,tc_nat)),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat)) ),
    inference(literals_permutation,[status(thm)],[c_0_2012]) ).

cnf(c_0_2012_1,axiom,
    ( X3 = X4
    | X1 = X2
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat)),c_HOL_Otimes__class_Otimes(X2,X4,tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X1,X4,tc_nat)),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat)) ),
    inference(literals_permutation,[status(thm)],[c_0_2012]) ).

cnf(c_0_2012_2,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat)),c_HOL_Otimes__class_Otimes(X2,X4,tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X1,X4,tc_nat)),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat))
    | X3 = X4
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_2012]) ).

cnf(c_0_2013_0,axiom,
    ( X1 = X2
    | X3 = X4
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat)),c_HOL_Otimes__class_Otimes(X2,X4,tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X1,X4,tc_nat)),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat)) ),
    inference(literals_permutation,[status(thm)],[c_0_2013]) ).

cnf(c_0_2013_1,axiom,
    ( X3 = X4
    | X1 = X2
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat)),c_HOL_Otimes__class_Otimes(X2,X4,tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X1,X4,tc_nat)),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat)) ),
    inference(literals_permutation,[status(thm)],[c_0_2013]) ).

cnf(c_0_2013_2,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat)),c_HOL_Otimes__class_Otimes(X2,X4,tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(X1,X4,tc_nat)),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat))
    | X3 = X4
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_2013]) ).

cnf(c_0_2014_0,axiom,
    ( c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_Divides_Odiv__class_Omod(X2,X4,X1)),c_Divides_Odiv__class_Omod(X3,X4,X1)),X4,X1) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X4,X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2014]) ).

cnf(c_0_2014_1,axiom,
    ( ~ class_Divides_Osemiring__div(X1)
    | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_Divides_Odiv__class_Omod(X2,X4,X1)),c_Divides_Odiv__class_Omod(X3,X4,X1)),X4,X1) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X4,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2014]) ).

cnf(c_0_2015_0,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(X2)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_HOL_Otimes__class_Otimes(X1,X1,X2)),c_HOL_Otimes__class_Otimes(X3,X3,X2)),X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2015]) ).

cnf(c_0_2015_1,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_HOL_Otimes__class_Otimes(X1,X1,X2)),c_HOL_Otimes__class_Otimes(X3,X3,X2)),X2)
    | X1 = c_HOL_Ozero__class_Ozero(X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2015]) ).

cnf(c_0_2015_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_HOL_Otimes__class_Otimes(X1,X1,X2)),c_HOL_Otimes__class_Otimes(X3,X3,X2)),X2)
    | X1 = c_HOL_Ozero__class_Ozero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2015]) ).

cnf(c_0_2016_0,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(X2)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_HOL_Otimes__class_Otimes(X3,X3,X2)),c_HOL_Otimes__class_Otimes(X1,X1,X2)),X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2016]) ).

cnf(c_0_2016_1,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_HOL_Otimes__class_Otimes(X3,X3,X2)),c_HOL_Otimes__class_Otimes(X1,X1,X2)),X2)
    | X1 = c_HOL_Ozero__class_Ozero(X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2016]) ).

cnf(c_0_2016_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_HOL_Otimes__class_Otimes(X3,X3,X2)),c_HOL_Otimes__class_Otimes(X1,X1,X2)),X2)
    | X1 = c_HOL_Ozero__class_Ozero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2016]) ).

cnf(c_0_2017_0,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,c_Divides_Odiv__class_Odiv(X3,X2,X1),X1)),c_Divides_Odiv__class_Omod(X3,X2,X1)) = X3
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2017]) ).

cnf(c_0_2017_1,axiom,
    ( ~ class_Divides_Osemiring__div(X1)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,c_Divides_Odiv__class_Odiv(X3,X2,X1),X1)),c_Divides_Odiv__class_Omod(X3,X2,X1)) = X3 ),
    inference(literals_permutation,[status(thm)],[c_0_2017]) ).

cnf(c_0_2018_0,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X3,X1),X3,X1)),c_Divides_Odiv__class_Omod(X2,X3,X1)) = X2
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2018]) ).

cnf(c_0_2018_1,axiom,
    ( ~ class_Divides_Osemiring__div(X1)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X3,X1),X3,X1)),c_Divides_Odiv__class_Omod(X2,X3,X1)) = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_2018]) ).

cnf(c_0_2019_0,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X1,X3,X2),X3,X2)),c_Divides_Odiv__class_Omod(X1,X3,X2)) = X1
    | ~ class_Divides_Osemiring__div(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2019]) ).

cnf(c_0_2019_1,axiom,
    ( ~ class_Divides_Osemiring__div(X2)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X1,X3,X2),X3,X2)),c_Divides_Odiv__class_Omod(X1,X3,X2)) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_2019]) ).

cnf(c_0_2020_0,axiom,
    ( c_Finite__Set_Osetsum(X1,c_SetInterval_Oord__class_OatLeastLessThan(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat),tc_nat,X3) = c_Finite__Set_Osetsum(X1,c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat),tc_nat,X3)
    | hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Ozero__class_Ozero(X3)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2020]) ).

cnf(c_0_2020_1,axiom,
    ( hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Ozero__class_Ozero(X3)
    | c_Finite__Set_Osetsum(X1,c_SetInterval_Oord__class_OatLeastLessThan(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat),tc_nat,X3) = c_Finite__Set_Osetsum(X1,c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat),tc_nat,X3)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2020]) ).

cnf(c_0_2020_2,axiom,
    ( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
    | hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Ozero__class_Ozero(X3)
    | c_Finite__Set_Osetsum(X1,c_SetInterval_Oord__class_OatLeastLessThan(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat),tc_nat,X3) = c_Finite__Set_Osetsum(X1,c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat),tc_nat,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2020]) ).

cnf(c_0_2021_0,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1)),c_HOL_Otimes__class_Otimes(X2,X4,X1)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X4,X1)),c_HOL_Otimes__class_Otimes(X2,X3,X1))
    | ~ class_Int_Onumber__ring(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2021]) ).

cnf(c_0_2021_1,axiom,
    ( ~ class_Int_Onumber__ring(X1)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1)),c_HOL_Otimes__class_Otimes(X2,X4,X1)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X4,X1)),c_HOL_Otimes__class_Otimes(X2,X3,X1))
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2021]) ).

cnf(c_0_2021_2,axiom,
    ( ~ class_Ring__and__Field_Oidom(X1)
    | ~ class_Int_Onumber__ring(X1)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1)),c_HOL_Otimes__class_Otimes(X2,X4,X1)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X4,X1)),c_HOL_Otimes__class_Otimes(X2,X3,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_2021]) ).

cnf(c_0_2022_0,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1)),c_HOL_Otimes__class_Otimes(X2,X4,X1)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X4,X1)),c_HOL_Otimes__class_Otimes(X2,X3,X1))
    | ~ class_Int_Onumber__ring(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2022]) ).

cnf(c_0_2022_1,axiom,
    ( ~ class_Int_Onumber__ring(X1)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1)),c_HOL_Otimes__class_Otimes(X2,X4,X1)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X4,X1)),c_HOL_Otimes__class_Otimes(X2,X3,X1))
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2022]) ).

cnf(c_0_2022_2,axiom,
    ( ~ class_Ring__and__Field_Oidom(X1)
    | ~ class_Int_Onumber__ring(X1)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1)),c_HOL_Otimes__class_Otimes(X2,X4,X1)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X4,X1)),c_HOL_Otimes__class_Otimes(X2,X3,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_2022]) ).

cnf(c_0_2023_0,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X1,X4,X3),c_Divides_Odiv__class_Omod(X2,X4,X3),X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2023]) ).

cnf(c_0_2023_1,axiom,
    ( ~ class_Divides_Osemiring__div(X3)
    | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X1,X4,X3),c_Divides_Odiv__class_Omod(X2,X4,X3),X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2023]) ).

cnf(c_0_2024_0,axiom,
    ( c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_Divides_Odiv__class_Omod(X2,X4,X1)),X3),X4,X1) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X4,X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2024]) ).

cnf(c_0_2024_1,axiom,
    ( ~ class_Divides_Osemiring__div(X1)
    | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_Divides_Odiv__class_Omod(X2,X4,X1)),X3),X4,X1) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X4,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2024]) ).

cnf(c_0_2025_0,axiom,
    ( c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_Divides_Odiv__class_Omod(X2,X3,X1)),X4),X3,X1) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X3,X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2025]) ).

cnf(c_0_2025_1,axiom,
    ( ~ class_Divides_Osemiring__div(X1)
    | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_Divides_Odiv__class_Omod(X2,X3,X1)),X4),X3,X1) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X3,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2025]) ).

cnf(c_0_2026_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_2026]) ).

cnf(c_0_2026_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_2026]) ).

cnf(c_0_2027_0,axiom,
    ( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X2,X5,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X1,X3),c_Divides_Odiv__class_Odiv(X5,X4,X3),X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X5,X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2027]) ).

cnf(c_0_2027_1,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X2,X5,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X1,X3),c_Divides_Odiv__class_Odiv(X5,X4,X3),X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X5,X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2027]) ).

cnf(c_0_2027_2,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X5,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X2,X5,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X1,X3),c_Divides_Odiv__class_Odiv(X5,X4,X3),X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2027]) ).

cnf(c_0_2027_3,axiom,
    ( ~ class_Divides_Osemiring__div(X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X5,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X2,X5,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X1,X3),c_Divides_Odiv__class_Odiv(X5,X4,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2027]) ).

cnf(c_0_2028_0,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_Divides_Odiv__class_Odiv(X2,X1,X3)),c_Divides_Odiv__class_Odiv(X4,X1,X3)) = c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4),X1,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2028]) ).

cnf(c_0_2028_1,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_Divides_Odiv__class_Odiv(X2,X1,X3)),c_Divides_Odiv__class_Odiv(X4,X1,X3)) = c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4),X1,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2028]) ).

cnf(c_0_2028_2,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_Divides_Odiv__class_Odiv(X2,X1,X3)),c_Divides_Odiv__class_Odiv(X4,X1,X3)) = c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4),X1,X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2028]) ).

cnf(c_0_2028_3,axiom,
    ( ~ class_Divides_Osemiring__div(X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_Divides_Odiv__class_Odiv(X2,X1,X3)),c_Divides_Odiv__class_Odiv(X4,X1,X3)) = c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4),X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2028]) ).

cnf(c_0_2029_0,axiom,
    ( c_Type_Otyping(c_Type_Oshift(X1,X4,X5,tc_Type_Otype),hAPP(hAPP(c_Lambda_Olift,X2),X4),X3)
    | ~ c_Type_Otyping(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2029]) ).

cnf(c_0_2029_1,axiom,
    ( ~ c_Type_Otyping(X1,X2,X3)
    | c_Type_Otyping(c_Type_Oshift(X1,X4,X5,tc_Type_Otype),hAPP(hAPP(c_Lambda_Olift,X2),X4),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2029]) ).

cnf(c_0_2030_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X3,X1),X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2030]) ).

cnf(c_0_2030_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X3,X1),X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
    | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2030]) ).

cnf(c_0_2030_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X1),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X3,X1),X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2030]) ).

cnf(c_0_2030_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X1),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X3,X1),X1),c_Power_Opower__class_Opower(X2,X3,X1),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2030]) ).

cnf(c_0_2031_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,c_Suc(c_Divides_Odiv__class_Odiv(X1,X2,tc_nat)),tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2031]) ).

cnf(c_0_2031_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
    | c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,c_Suc(c_Divides_Odiv__class_Odiv(X1,X2,tc_nat)),tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2031]) ).

cnf(c_0_2032_0,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X5,X6,X3),X4,X3)
    | c_Divides_Odiv__class_Omod(X1,X4,X3) != c_Divides_Odiv__class_Omod(X5,X4,X3)
    | c_Divides_Odiv__class_Omod(X2,X4,X3) != c_Divides_Odiv__class_Omod(X6,X4,X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2032]) ).

cnf(c_0_2032_1,axiom,
    ( c_Divides_Odiv__class_Omod(X1,X4,X3) != c_Divides_Odiv__class_Omod(X5,X4,X3)
    | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X5,X6,X3),X4,X3)
    | c_Divides_Odiv__class_Omod(X2,X4,X3) != c_Divides_Odiv__class_Omod(X6,X4,X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2032]) ).

cnf(c_0_2032_2,axiom,
    ( c_Divides_Odiv__class_Omod(X2,X4,X3) != c_Divides_Odiv__class_Omod(X6,X4,X3)
    | c_Divides_Odiv__class_Omod(X1,X4,X3) != c_Divides_Odiv__class_Omod(X5,X4,X3)
    | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X5,X6,X3),X4,X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2032]) ).

cnf(c_0_2032_3,axiom,
    ( ~ class_Divides_Osemiring__div(X3)
    | c_Divides_Odiv__class_Omod(X2,X4,X3) != c_Divides_Odiv__class_Omod(X6,X4,X3)
    | c_Divides_Odiv__class_Omod(X1,X4,X3) != c_Divides_Odiv__class_Omod(X5,X4,X3)
    | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X5,X6,X3),X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2032]) ).

cnf(c_0_2033_0,axiom,
    ( c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X4,X1) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X5),X6),X4,X1)
    | c_Divides_Odiv__class_Omod(X2,X4,X1) != c_Divides_Odiv__class_Omod(X5,X4,X1)
    | c_Divides_Odiv__class_Omod(X3,X4,X1) != c_Divides_Odiv__class_Omod(X6,X4,X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2033]) ).

cnf(c_0_2033_1,axiom,
    ( c_Divides_Odiv__class_Omod(X2,X4,X1) != c_Divides_Odiv__class_Omod(X5,X4,X1)
    | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X4,X1) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X5),X6),X4,X1)
    | c_Divides_Odiv__class_Omod(X3,X4,X1) != c_Divides_Odiv__class_Omod(X6,X4,X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2033]) ).

cnf(c_0_2033_2,axiom,
    ( c_Divides_Odiv__class_Omod(X3,X4,X1) != c_Divides_Odiv__class_Omod(X6,X4,X1)
    | c_Divides_Odiv__class_Omod(X2,X4,X1) != c_Divides_Odiv__class_Omod(X5,X4,X1)
    | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X4,X1) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X5),X6),X4,X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2033]) ).

cnf(c_0_2033_3,axiom,
    ( ~ class_Divides_Osemiring__div(X1)
    | c_Divides_Odiv__class_Omod(X3,X4,X1) != c_Divides_Odiv__class_Omod(X6,X4,X1)
    | c_Divides_Odiv__class_Omod(X2,X4,X1) != c_Divides_Odiv__class_Omod(X5,X4,X1)
    | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X4,X1) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X5),X6),X4,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2033]) ).

cnf(c_0_2034_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(X2,X1,X3),c_Divides_Odiv__class_Odiv(X4,X1,X3),X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2034]) ).

cnf(c_0_2034_1,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(X2,X1,X3),c_Divides_Odiv__class_Odiv(X4,X1,X3),X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2034]) ).

cnf(c_0_2034_2,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(X2,X1,X3),c_Divides_Odiv__class_Odiv(X4,X1,X3),X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2034]) ).

cnf(c_0_2034_3,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(X2,X1,X3),c_Divides_Odiv__class_Odiv(X4,X1,X3),X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2034]) ).

cnf(c_0_2034_4,axiom,
    ( ~ class_Divides_Osemiring__div(X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(X2,X1,X3),c_Divides_Odiv__class_Odiv(X4,X1,X3),X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2034]) ).

cnf(c_0_2035_0,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X5,X3),X3) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X4,X5,X3),X3),X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2035]) ).

cnf(c_0_2035_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
    | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X5,X3),X3) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X4,X5,X3),X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2035]) ).

cnf(c_0_2036_0,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X5,X3),X3) = c_HOL_Otimes__class_Otimes(X4,c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),X5,X3),X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2036]) ).

cnf(c_0_2036_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
    | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X5,X3),X3) = c_HOL_Otimes__class_Otimes(X4,c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),X5,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2036]) ).

cnf(c_0_2037_0,axiom,
    ( hAPP(c_Type_Oshift(X3,X2,X4,X5),X1) = hAPP(X3,X1)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2037]) ).

cnf(c_0_2037_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | hAPP(c_Type_Oshift(X3,X2,X4,X5),X1) = hAPP(X3,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2037]) ).

cnf(c_0_2038_0,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(X2)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_HOL_Otimes__class_Otimes(X3,X3,X2)),c_HOL_Otimes__class_Otimes(X1,X1,X2)) != c_HOL_Ozero__class_Ozero(X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2038]) ).

cnf(c_0_2038_1,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_HOL_Otimes__class_Otimes(X3,X3,X2)),c_HOL_Otimes__class_Otimes(X1,X1,X2)) != c_HOL_Ozero__class_Ozero(X2)
    | X1 = c_HOL_Ozero__class_Ozero(X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2038]) ).

cnf(c_0_2038_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_HOL_Otimes__class_Otimes(X3,X3,X2)),c_HOL_Otimes__class_Otimes(X1,X1,X2)) != c_HOL_Ozero__class_Ozero(X2)
    | X1 = c_HOL_Ozero__class_Ozero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2038]) ).

cnf(c_0_2039_0,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(X2)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_HOL_Otimes__class_Otimes(X1,X1,X2)),c_HOL_Otimes__class_Otimes(X3,X3,X2)) != c_HOL_Ozero__class_Ozero(X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2039]) ).

cnf(c_0_2039_1,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_HOL_Otimes__class_Otimes(X1,X1,X2)),c_HOL_Otimes__class_Otimes(X3,X3,X2)) != c_HOL_Ozero__class_Ozero(X2)
    | X1 = c_HOL_Ozero__class_Ozero(X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2039]) ).

cnf(c_0_2039_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_HOL_Otimes__class_Otimes(X1,X1,X2)),c_HOL_Otimes__class_Otimes(X3,X3,X2)) != c_HOL_Ozero__class_Ozero(X2)
    | X1 = c_HOL_Ozero__class_Ozero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2039]) ).

cnf(c_0_2040_0,axiom,
    ( hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_Olift,X3),X1)),c_Suc(X2)) = hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_Olift,X3),X2)),X1)
    | ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2040]) ).

cnf(c_0_2040_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),tc_nat)
    | hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_Olift,X3),X1)),c_Suc(X2)) = hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_Olift,X3),X2)),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2040]) ).

cnf(c_0_2041_0,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_Divides_Odiv__class_Omod(X2,X3,X1)),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X3,X1),X3,X1)) = X2
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2041]) ).

cnf(c_0_2041_1,axiom,
    ( ~ class_Divides_Osemiring__div(X1)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_Divides_Odiv__class_Omod(X2,X3,X1)),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X3,X1),X3,X1)) = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_2041]) ).

cnf(c_0_2042_0,axiom,
    ( c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X3,X1),X1),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2042]) ).

cnf(c_0_2042_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
    | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X3,X1),X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2042]) ).

cnf(c_0_2042_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
    | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X3,X1),X1),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2042]) ).

cnf(c_0_2043_0,axiom,
    ( c_HOL_Oord__class_Oless(X4,X3,X2)
    | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Otimes__class_Otimes(X1,X4,X2),X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2043]) ).

cnf(c_0_2043_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | c_HOL_Oord__class_Oless(X4,X3,X2)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Otimes__class_Otimes(X1,X4,X2),X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2043]) ).

cnf(c_0_2043_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Otimes__class_Otimes(X1,X4,X2),X2)
    | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | c_HOL_Oord__class_Oless(X4,X3,X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2043]) ).

cnf(c_0_2043_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Otimes__class_Otimes(X1,X4,X2),X2)
    | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | c_HOL_Oord__class_Oless(X4,X3,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2043]) ).

cnf(c_0_2044_0,axiom,
    ( c_HOL_Oord__class_Oless(X3,X4,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2044]) ).

cnf(c_0_2044_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_HOL_Oord__class_Oless(X3,X4,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2044]) ).

cnf(c_0_2044_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_HOL_Oord__class_Oless(X3,X4,X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2044]) ).

cnf(c_0_2044_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_HOL_Oord__class_Oless(X3,X4,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2044]) ).

cnf(c_0_2045_0,axiom,
    ( c_HOL_Oord__class_Oless(X3,X4,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
    | ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2045]) ).

cnf(c_0_2045_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
    | c_HOL_Oord__class_Oless(X3,X4,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2045]) ).

cnf(c_0_2045_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
    | c_HOL_Oord__class_Oless(X3,X4,tc_nat)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2045]) ).

cnf(c_0_2045_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
    | c_HOL_Oord__class_Oless(X3,X4,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2045]) ).

cnf(c_0_2046_0,axiom,
    ( c_HOL_Oord__class_Oless(X3,X4,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
    | ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2046]) ).

cnf(c_0_2046_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
    | c_HOL_Oord__class_Oless(X3,X4,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2046]) ).

cnf(c_0_2046_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
    | c_HOL_Oord__class_Oless(X3,X4,tc_nat)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2046]) ).

cnf(c_0_2046_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
    | c_HOL_Oord__class_Oless(X3,X4,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2046]) ).

cnf(c_0_2047_0,axiom,
    ( c_Divides_Odiv__class_Omod(X1,X2,tc_nat) = c_Divides_Odiv__class_Omod(X3,X2,tc_nat)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Otimes__class_Otimes(X2,X4,tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Otimes__class_Otimes(X2,X5,tc_nat)) ),
    inference(literals_permutation,[status(thm)],[c_0_2047]) ).

cnf(c_0_2047_1,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Otimes__class_Otimes(X2,X4,tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Otimes__class_Otimes(X2,X5,tc_nat))
    | c_Divides_Odiv__class_Omod(X1,X2,tc_nat) = c_Divides_Odiv__class_Omod(X3,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2047]) ).

cnf(c_0_2048_0,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2048]) ).

cnf(c_0_2048_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | c_HOL_Oord__class_Oless(X2,X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2048]) ).

cnf(c_0_2048_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2048]) ).

cnf(c_0_2049_0,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X2,tc_nat),c_Power_Opower__class_Opower(X1,X3,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2049]) ).

cnf(c_0_2049_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | c_HOL_Oord__class_Oless(X2,X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X2,tc_nat),c_Power_Opower__class_Opower(X1,X3,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2049]) ).

cnf(c_0_2049_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X2,tc_nat),c_Power_Opower__class_Opower(X1,X3,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2049]) ).

cnf(c_0_2050_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2050]) ).

cnf(c_0_2050_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2050]) ).

cnf(c_0_2050_2,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2050]) ).

cnf(c_0_2051_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2051]) ).

cnf(c_0_2051_1,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2051]) ).

cnf(c_0_2051_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2051]) ).

cnf(c_0_2052_0,axiom,
    ( c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X4,X2,X3),c_Power_Opower__class_Opower(X4,X1,X3),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
    | ~ c_HOL_Oord__class_Oless(X4,c_HOL_Oone__class_Oone(X3),X3)
    | ~ class_Ring__and__Field_Oordered__semidom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2052]) ).

cnf(c_0_2052_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X4,X2,X3),c_Power_Opower__class_Opower(X4,X1,X3),X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
    | ~ c_HOL_Oord__class_Oless(X4,c_HOL_Oone__class_Oone(X3),X3)
    | ~ class_Ring__and__Field_Oordered__semidom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2052]) ).

cnf(c_0_2052_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X4,X2,X3),c_Power_Opower__class_Opower(X4,X1,X3),X3)
    | ~ c_HOL_Oord__class_Oless(X4,c_HOL_Oone__class_Oone(X3),X3)
    | ~ class_Ring__and__Field_Oordered__semidom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2052]) ).

cnf(c_0_2052_3,axiom,
    ( ~ c_HOL_Oord__class_Oless(X4,c_HOL_Oone__class_Oone(X3),X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X4,X2,X3),c_Power_Opower__class_Opower(X4,X1,X3),X3)
    | ~ class_Ring__and__Field_Oordered__semidom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2052]) ).

cnf(c_0_2052_4,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X3)
    | ~ c_HOL_Oord__class_Oless(X4,c_HOL_Oone__class_Oone(X3),X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X4,X2,X3),c_Power_Opower__class_Opower(X4,X1,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2052]) ).

cnf(c_0_2053_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
    | c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2053]) ).

cnf(c_0_2053_1,axiom,
    ( c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2053]) ).

cnf(c_0_2053_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
    | c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2053]) ).

cnf(c_0_2053_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
    | c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2053]) ).

cnf(c_0_2054_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
    | c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2054]) ).

cnf(c_0_2054_1,axiom,
    ( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2054]) ).

cnf(c_0_2054_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
    | c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2054]) ).

cnf(c_0_2054_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
    | c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2054]) ).

cnf(c_0_2055_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,X4,X3)
    | c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2055]) ).

cnf(c_0_2055_1,axiom,
    ( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
    | c_HOL_Oord__class_Oless(X1,X4,X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2055]) ).

cnf(c_0_2055_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
    | c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
    | c_HOL_Oord__class_Oless(X1,X4,X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2055]) ).

cnf(c_0_2055_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
    | c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
    | c_HOL_Oord__class_Oless(X1,X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2055]) ).

cnf(c_0_2056_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
    | c_HOL_Oord__class_Oless(X4,X1,X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2056]) ).

cnf(c_0_2056_1,axiom,
    ( c_HOL_Oord__class_Oless(X4,X1,X3)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2056]) ).

cnf(c_0_2056_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
    | c_HOL_Oord__class_Oless(X4,X1,X3)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2056]) ).

cnf(c_0_2056_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
    | c_HOL_Oord__class_Oless(X4,X1,X3)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2056]) ).

cnf(c_0_2057_0,axiom,
    ( c_HOL_Oord__class_Oless(X2,X4,X3)
    | c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2057]) ).

cnf(c_0_2057_1,axiom,
    ( c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
    | c_HOL_Oord__class_Oless(X2,X4,X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2057]) ).

cnf(c_0_2057_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
    | c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
    | c_HOL_Oord__class_Oless(X2,X4,X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2057]) ).

cnf(c_0_2057_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
    | c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
    | c_HOL_Oord__class_Oless(X2,X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2057]) ).

cnf(c_0_2058_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
    | c_HOL_Oord__class_Oless(X4,X2,X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2058]) ).

cnf(c_0_2058_1,axiom,
    ( c_HOL_Oord__class_Oless(X4,X2,X3)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2058]) ).

cnf(c_0_2058_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
    | c_HOL_Oord__class_Oless(X4,X2,X3)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2058]) ).

cnf(c_0_2058_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
    | c_HOL_Oord__class_Oless(X4,X2,X3)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2058]) ).

cnf(c_0_2059_0,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X1,X2,X3),X4,X3),X2,X3) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X4,X3),X2,X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2059]) ).

cnf(c_0_2059_1,axiom,
    ( ~ class_Divides_Osemiring__div(X3)
    | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X1,X2,X3),X4,X3),X2,X3) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X4,X3),X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2059]) ).

cnf(c_0_2060_0,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X1,X4,X3),X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2060]) ).

cnf(c_0_2060_1,axiom,
    ( ~ class_Divides_Osemiring__div(X3)
    | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X1,X4,X3),X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2060]) ).

cnf(c_0_2061_0,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Omod(X2,X4,X3),X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2061]) ).

cnf(c_0_2061_1,axiom,
    ( ~ class_Divides_Osemiring__div(X3)
    | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Omod(X2,X4,X3),X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2061]) ).

cnf(c_0_2062_0,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X5,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2062]) ).

cnf(c_0_2062_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
    | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X5,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2062]) ).

cnf(c_0_2063_0,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(X2)
    | c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),c_HOL_Otimes__class_Otimes(X1,X4,X2)),X1,X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X4),c_Divides_Odiv__class_Odiv(X3,X1,X2))
    | ~ class_Divides_Osemiring__div(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2063]) ).

cnf(c_0_2063_1,axiom,
    ( c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),c_HOL_Otimes__class_Otimes(X1,X4,X2)),X1,X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X4),c_Divides_Odiv__class_Odiv(X3,X1,X2))
    | X1 = c_HOL_Ozero__class_Ozero(X2)
    | ~ class_Divides_Osemiring__div(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2063]) ).

cnf(c_0_2063_2,axiom,
    ( ~ class_Divides_Osemiring__div(X2)
    | c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),c_HOL_Otimes__class_Otimes(X1,X4,X2)),X1,X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X4),c_Divides_Odiv__class_Odiv(X3,X1,X2))
    | X1 = c_HOL_Ozero__class_Ozero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2063]) ).

cnf(c_0_2064_0,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(X2)
    | c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),c_HOL_Otimes__class_Otimes(X4,X1,X2)),X1,X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X4),c_Divides_Odiv__class_Odiv(X3,X1,X2))
    | ~ class_Divides_Osemiring__div(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2064]) ).

cnf(c_0_2064_1,axiom,
    ( c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),c_HOL_Otimes__class_Otimes(X4,X1,X2)),X1,X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X4),c_Divides_Odiv__class_Odiv(X3,X1,X2))
    | X1 = c_HOL_Ozero__class_Ozero(X2)
    | ~ class_Divides_Osemiring__div(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2064]) ).

cnf(c_0_2064_2,axiom,
    ( ~ class_Divides_Osemiring__div(X2)
    | c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),c_HOL_Otimes__class_Otimes(X4,X1,X2)),X1,X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X4),c_Divides_Odiv__class_Odiv(X3,X1,X2))
    | X1 = c_HOL_Ozero__class_Ozero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2064]) ).

cnf(c_0_2065_0,axiom,
    ( c_HOL_Oord__class_Oless(X2,X4,X3)
    | c_HOL_Oord__class_Oless(X4,X2,X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2065]) ).

cnf(c_0_2065_1,axiom,
    ( c_HOL_Oord__class_Oless(X4,X2,X3)
    | c_HOL_Oord__class_Oless(X2,X4,X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2065]) ).

cnf(c_0_2065_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
    | c_HOL_Oord__class_Oless(X4,X2,X3)
    | c_HOL_Oord__class_Oless(X2,X4,X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2065]) ).

cnf(c_0_2065_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
    | c_HOL_Oord__class_Oless(X4,X2,X3)
    | c_HOL_Oord__class_Oless(X2,X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2065]) ).

cnf(c_0_2066_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,X4,X3)
    | c_HOL_Oord__class_Oless(X4,X1,X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2066]) ).

cnf(c_0_2066_1,axiom,
    ( c_HOL_Oord__class_Oless(X4,X1,X3)
    | c_HOL_Oord__class_Oless(X1,X4,X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2066]) ).

cnf(c_0_2066_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
    | c_HOL_Oord__class_Oless(X4,X1,X3)
    | c_HOL_Oord__class_Oless(X1,X4,X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2066]) ).

cnf(c_0_2066_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
    | c_HOL_Oord__class_Oless(X4,X1,X3)
    | c_HOL_Oord__class_Oless(X1,X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2066]) ).

cnf(c_0_2067_0,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1)),c_HOL_Otimes__class_Otimes(X4,X3,X1)) = c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X3,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2067]) ).

cnf(c_0_2067_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1)),c_HOL_Otimes__class_Otimes(X4,X3,X1)) = c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X3,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2067]) ).

cnf(c_0_2068_0,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X4,X1)),c_HOL_Otimes__class_Otimes(X3,X4,X1)) = c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X4,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2068]) ).

cnf(c_0_2068_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X4,X1)),c_HOL_Otimes__class_Otimes(X3,X4,X1)) = c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X4,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2068]) ).

cnf(c_0_2069_0,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X4,X1)),c_HOL_Otimes__class_Otimes(X3,X4,X1)) = c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X4,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2069]) ).

cnf(c_0_2069_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring(X1)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X4,X1)),c_HOL_Otimes__class_Otimes(X3,X4,X1)) = c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X4,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2069]) ).

cnf(c_0_2070_0,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_HOL_Otimes__class_Otimes(X1,X3,X2)),c_HOL_Otimes__class_Otimes(X1,X4,X2)) = c_HOL_Otimes__class_Otimes(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),X4),X2)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2070]) ).

cnf(c_0_2070_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_HOL_Otimes__class_Otimes(X1,X3,X2)),c_HOL_Otimes__class_Otimes(X1,X4,X2)) = c_HOL_Otimes__class_Otimes(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),X4),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2070]) ).

cnf(c_0_2071_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(X2,X1,X3),c_Divides_Odiv__class_Odiv(X4,X1,X3),X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2071]) ).

cnf(c_0_2071_1,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(X2,X1,X3),c_Divides_Odiv__class_Odiv(X4,X1,X3),X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2071]) ).

cnf(c_0_2071_2,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(X2,X1,X3),c_Divides_Odiv__class_Odiv(X4,X1,X3),X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2071]) ).

cnf(c_0_2071_3,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(X2,X1,X3),c_Divides_Odiv__class_Odiv(X4,X1,X3),X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2071]) ).

cnf(c_0_2071_4,axiom,
    ( ~ class_Divides_Osemiring__div(X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(X2,X1,X3),c_Divides_Odiv__class_Odiv(X4,X1,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2071]) ).

cnf(c_0_2072_0,axiom,
    ( c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_Divides_Odiv__class_Omod(X3,X4,X1)),X4,X1) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X4,X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2072]) ).

cnf(c_0_2072_1,axiom,
    ( ~ class_Divides_Osemiring__div(X1)
    | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_Divides_Odiv__class_Omod(X3,X4,X1)),X4,X1) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X4,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2072]) ).

cnf(c_0_2073_0,axiom,
    ( c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_Divides_Odiv__class_Omod(X3,X4,X1)),X4,X1) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X4,X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2073]) ).

cnf(c_0_2073_1,axiom,
    ( ~ class_Divides_Osemiring__div(X1)
    | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_Divides_Odiv__class_Omod(X3,X4,X1)),X4,X1) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X4,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2073]) ).

cnf(c_0_2074_0,axiom,
    ( c_Divides_Odiv__class_Odiv(c_Power_Opower__class_Opower(X2,X4,X3),c_Power_Opower__class_Opower(X1,X4,X3),X3) = c_Power_Opower__class_Opower(c_Divides_Odiv__class_Odiv(X2,X1,X3),X4,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2074]) ).

cnf(c_0_2074_1,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | c_Divides_Odiv__class_Odiv(c_Power_Opower__class_Opower(X2,X4,X3),c_Power_Opower__class_Opower(X1,X4,X3),X3) = c_Power_Opower__class_Opower(c_Divides_Odiv__class_Odiv(X2,X1,X3),X4,X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2074]) ).

cnf(c_0_2074_2,axiom,
    ( ~ class_Divides_Osemiring__div(X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | c_Divides_Odiv__class_Odiv(c_Power_Opower__class_Opower(X2,X4,X3),c_Power_Opower__class_Opower(X1,X4,X3),X3) = c_Power_Opower__class_Opower(c_Divides_Odiv__class_Odiv(X2,X1,X3),X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2074]) ).

cnf(c_0_2075_0,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(X2)
    | X3 = X4
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X5),c_HOL_Otimes__class_Otimes(X1,X3,X2)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X5),c_HOL_Otimes__class_Otimes(X1,X4,X2))
    | ~ class_Int_Onumber__ring(X2)
    | ~ class_Ring__and__Field_Oidom(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2075]) ).

cnf(c_0_2075_1,axiom,
    ( X3 = X4
    | X1 = c_HOL_Ozero__class_Ozero(X2)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X5),c_HOL_Otimes__class_Otimes(X1,X3,X2)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X5),c_HOL_Otimes__class_Otimes(X1,X4,X2))
    | ~ class_Int_Onumber__ring(X2)
    | ~ class_Ring__and__Field_Oidom(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2075]) ).

cnf(c_0_2075_2,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X5),c_HOL_Otimes__class_Otimes(X1,X3,X2)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X5),c_HOL_Otimes__class_Otimes(X1,X4,X2))
    | X3 = X4
    | 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_2075]) ).

cnf(c_0_2075_3,axiom,
    ( ~ class_Int_Onumber__ring(X2)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X5),c_HOL_Otimes__class_Otimes(X1,X3,X2)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X5),c_HOL_Otimes__class_Otimes(X1,X4,X2))
    | X3 = X4
    | X1 = c_HOL_Ozero__class_Ozero(X2)
    | ~ class_Ring__and__Field_Oidom(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2075]) ).

cnf(c_0_2075_4,axiom,
    ( ~ class_Ring__and__Field_Oidom(X2)
    | ~ class_Int_Onumber__ring(X2)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X5),c_HOL_Otimes__class_Otimes(X1,X3,X2)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X5),c_HOL_Otimes__class_Otimes(X1,X4,X2))
    | X3 = X4
    | X1 = c_HOL_Ozero__class_Ozero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2075]) ).

cnf(c_0_2076_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_2076]) ).

cnf(c_0_2076_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_2076]) ).

cnf(c_0_2077_0,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X1),X2,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X1),X3,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2077]) ).

cnf(c_0_2077_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X1),X2,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X1),X3,tc_nat),tc_nat)
    | c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2077]) ).

cnf(c_0_2078_0,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(X3)
    | c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
    | ~ class_Ring__and__Field_Oidom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2078]) ).

cnf(c_0_2078_1,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3)
    | X1 = c_HOL_Ozero__class_Ozero(X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
    | ~ class_Ring__and__Field_Oidom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2078]) ).

cnf(c_0_2078_2,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
    | c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3)
    | X1 = c_HOL_Ozero__class_Ozero(X3)
    | ~ class_Ring__and__Field_Oidom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2078]) ).

cnf(c_0_2078_3,axiom,
    ( ~ class_Ring__and__Field_Oidom(X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
    | c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3)
    | X1 = c_HOL_Ozero__class_Ozero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2078]) ).

cnf(c_0_2079_0,axiom,
    ( X2 = c_HOL_Ozero__class_Ozero(X3)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
    | ~ class_Ring__and__Field_Oidom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2079]) ).

cnf(c_0_2079_1,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
    | X2 = c_HOL_Ozero__class_Ozero(X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
    | ~ class_Ring__and__Field_Oidom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2079]) ).

cnf(c_0_2079_2,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
    | X2 = c_HOL_Ozero__class_Ozero(X3)
    | ~ class_Ring__and__Field_Oidom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2079]) ).

cnf(c_0_2079_3,axiom,
    ( ~ class_Ring__and__Field_Oidom(X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
    | X2 = c_HOL_Ozero__class_Ozero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2079]) ).

cnf(c_0_2080_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X3,X1),X1),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2080]) ).

cnf(c_0_2080_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
    | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X3,X1),X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2080]) ).

cnf(c_0_2080_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
    | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X3,X1),X1),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2080]) ).

cnf(c_0_2081_0,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X2 = X3
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat)) ),
    inference(literals_permutation,[status(thm)],[c_0_2081]) ).

cnf(c_0_2081_1,axiom,
    ( X2 = X3
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat)) ),
    inference(literals_permutation,[status(thm)],[c_0_2081]) ).

cnf(c_0_2081_2,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat))
    | X2 = X3
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2081]) ).

cnf(c_0_2082_0,axiom,
    ( c_HOL_Oord__class_Oless(X2,X4,X1)
    | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3),X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2082]) ).

cnf(c_0_2082_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3),X1)
    | c_HOL_Oord__class_Oless(X2,X4,X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2082]) ).

cnf(c_0_2082_2,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3),X1)
    | c_HOL_Oord__class_Oless(X2,X4,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2082]) ).

cnf(c_0_2083_0,axiom,
    ( c_HOL_Oord__class_Oless(X3,X4,X1)
    | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2083]) ).

cnf(c_0_2083_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
    | c_HOL_Oord__class_Oless(X3,X4,X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2083]) ).

cnf(c_0_2083_2,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
    | c_HOL_Oord__class_Oless(X3,X4,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2083]) ).

cnf(c_0_2084_0,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2084]) ).

cnf(c_0_2084_1,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2084]) ).

cnf(c_0_2084_2,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2084]) ).

cnf(c_0_2085_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2085]) ).

cnf(c_0_2085_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2085]) ).

cnf(c_0_2086_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2086]) ).

cnf(c_0_2086_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2086]) ).

cnf(c_0_2087_0,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2087]) ).

cnf(c_0_2087_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
    | c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2087]) ).

cnf(c_0_2088_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2088]) ).

cnf(c_0_2088_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat)
    | c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2088]) ).

cnf(c_0_2089_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
    | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_HOL_Oord__class_Oless(X3,X4,X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2089]) ).

cnf(c_0_2089_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
    | ~ c_HOL_Oord__class_Oless(X3,X4,X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2089]) ).

cnf(c_0_2089_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(X3,X4,X2)
    | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2089]) ).

cnf(c_0_2089_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
    | ~ c_HOL_Oord__class_Oless(X3,X4,X2)
    | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2089]) ).

cnf(c_0_2090_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_HOL_Oord__class_Oless(X3,X4,X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2090]) ).

cnf(c_0_2090_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
    | ~ c_HOL_Oord__class_Oless(X3,X4,X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2090]) ).

cnf(c_0_2090_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(X3,X4,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2090]) ).

cnf(c_0_2090_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(X3,X4,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2090]) ).

cnf(c_0_2091_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X2,X3),c_HOL_Otimes__class_Otimes(X4,X1,X3),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2091]) ).

cnf(c_0_2091_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X2,X3),c_HOL_Otimes__class_Otimes(X4,X1,X3),X3)
    | ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2091]) ).

cnf(c_0_2091_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X2,X3),c_HOL_Otimes__class_Otimes(X4,X1,X3),X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2091]) ).

cnf(c_0_2091_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
    | ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X2,X3),c_HOL_Otimes__class_Otimes(X4,X1,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2091]) ).

cnf(c_0_2092_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X1,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2092]) ).

cnf(c_0_2092_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X1,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2092]) ).

cnf(c_0_2092_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X1,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2092]) ).

cnf(c_0_2092_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X1,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2092]) ).

cnf(c_0_2093_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_HOL_Oord__class_Oless(X3,X4,X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2093]) ).

cnf(c_0_2093_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
    | ~ c_HOL_Oord__class_Oless(X3,X4,X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2093]) ).

cnf(c_0_2093_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(X3,X4,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2093]) ).

cnf(c_0_2093_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(X3,X4,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2093]) ).

cnf(c_0_2094_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
    | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_HOL_Oord__class_Oless(X3,X4,X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2094]) ).

cnf(c_0_2094_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
    | ~ c_HOL_Oord__class_Oless(X3,X4,X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2094]) ).

cnf(c_0_2094_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(X3,X4,X2)
    | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2094]) ).

cnf(c_0_2094_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
    | ~ c_HOL_Oord__class_Oless(X3,X4,X2)
    | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2094]) ).

cnf(c_0_2095_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X4,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2095]) ).

cnf(c_0_2095_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X4,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
    | ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2095]) ).

cnf(c_0_2095_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X4,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2095]) ).

cnf(c_0_2095_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
    | ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X4,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2095]) ).

cnf(c_0_2096_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2096]) ).

cnf(c_0_2096_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2096]) ).

cnf(c_0_2096_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2096]) ).

cnf(c_0_2096_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2096]) ).

cnf(c_0_2097_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X2,X1),c_HOL_Otimes__class_Otimes(X4,X2,X1),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_HOL_Oord__class_Oless(X3,X4,X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2097]) ).

cnf(c_0_2097_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X2,X1),c_HOL_Otimes__class_Otimes(X4,X2,X1),X1)
    | ~ c_HOL_Oord__class_Oless(X3,X4,X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2097]) ).

cnf(c_0_2097_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(X3,X4,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X2,X1),c_HOL_Otimes__class_Otimes(X4,X2,X1),X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2097]) ).

cnf(c_0_2097_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(X3,X4,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X2,X1),c_HOL_Otimes__class_Otimes(X4,X2,X1),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2097]) ).

cnf(c_0_2098_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X1,X2),c_HOL_Otimes__class_Otimes(X3,X1,X2),X2)
    | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_HOL_Oord__class_Oless(X3,X4,X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2098]) ).

cnf(c_0_2098_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X1,X2),c_HOL_Otimes__class_Otimes(X3,X1,X2),X2)
    | ~ c_HOL_Oord__class_Oless(X3,X4,X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2098]) ).

cnf(c_0_2098_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(X3,X4,X2)
    | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X1,X2),c_HOL_Otimes__class_Otimes(X3,X1,X2),X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2098]) ).

cnf(c_0_2098_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
    | ~ c_HOL_Oord__class_Oless(X3,X4,X2)
    | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X1,X2),c_HOL_Otimes__class_Otimes(X3,X1,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2098]) ).

cnf(c_0_2099_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X1,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2099]) ).

cnf(c_0_2099_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X1,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2099]) ).

cnf(c_0_2099_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X1,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2099]) ).

cnf(c_0_2099_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X1,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2099]) ).

cnf(c_0_2100_0,axiom,
    ( c_Finite__Set_Osetsum(X3,c_SetInterval_Oord__class_OatLeastLessThan(X2,c_Suc(X1),tc_nat),tc_nat,X4) = c_HOL_Ozero__class_Ozero(X4)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_2100]) ).

cnf(c_0_2100_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_Finite__Set_Osetsum(X3,c_SetInterval_Oord__class_OatLeastLessThan(X2,c_Suc(X1),tc_nat),tc_nat,X4) = c_HOL_Ozero__class_Ozero(X4)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_2100]) ).

cnf(c_0_2100_2,axiom,
    ( ~ class_OrderedGroup_Ocomm__monoid__add(X4)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_Finite__Set_Osetsum(X3,c_SetInterval_Oord__class_OatLeastLessThan(X2,c_Suc(X1),tc_nat),tc_nat,X4) = c_HOL_Ozero__class_Ozero(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_2100]) ).

cnf(c_0_2101_0,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2101]) ).

cnf(c_0_2101_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)) = c_HOL_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2101]) ).

cnf(c_0_2102_0,axiom,
    ( c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
    | ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2102]) ).

cnf(c_0_2102_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
    | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1)
    | ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2102]) ).

cnf(c_0_2102_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
    | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2102]) ).

cnf(c_0_2102_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
    | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X3,X1),c_Power_Opower__class_Opower(X2,X4,X1),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2102]) ).

cnf(c_0_2103_0,axiom,
    ( c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X4,X1,X3),c_Power_Opower__class_Opower(X4,X2,X3),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X4,X3)
    | ~ class_Ring__and__Field_Oordered__semidom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2103]) ).

cnf(c_0_2103_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X4,X1,X3),c_Power_Opower__class_Opower(X4,X2,X3),X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X4,X3)
    | ~ class_Ring__and__Field_Oordered__semidom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2103]) ).

cnf(c_0_2103_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X4,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X4,X1,X3),c_Power_Opower__class_Opower(X4,X2,X3),X3)
    | ~ class_Ring__and__Field_Oordered__semidom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2103]) ).

cnf(c_0_2103_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X4,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X4,X1,X3),c_Power_Opower__class_Opower(X4,X2,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2103]) ).

cnf(c_0_2104_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X5,X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2104]) ).

cnf(c_0_2104_1,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X5,X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2104]) ).

cnf(c_0_2104_2,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X5,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2104]) ).

cnf(c_0_2104_3,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X5,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2104]) ).

cnf(c_0_2105_0,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1)),X3) = c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Oone__class_Oone(X1)),X3,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2105]) ).

cnf(c_0_2105_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1)),X3) = c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Oone__class_Oone(X1)),X3,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2105]) ).

cnf(c_0_2106_0,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(X2)
    | c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X3),X1,X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_Divides_Odiv__class_Odiv(X3,X1,X2)),c_HOL_Oone__class_Oone(X2))
    | ~ class_Divides_Osemiring__div(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2106]) ).

cnf(c_0_2106_1,axiom,
    ( c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X3),X1,X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_Divides_Odiv__class_Odiv(X3,X1,X2)),c_HOL_Oone__class_Oone(X2))
    | X1 = c_HOL_Ozero__class_Ozero(X2)
    | ~ class_Divides_Osemiring__div(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2106]) ).

cnf(c_0_2106_2,axiom,
    ( ~ class_Divides_Osemiring__div(X2)
    | c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X3),X1,X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_Divides_Odiv__class_Odiv(X3,X1,X2)),c_HOL_Oone__class_Oone(X2))
    | X1 = c_HOL_Ozero__class_Ozero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2106]) ).

cnf(c_0_2107_0,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(X2)
    | c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),X1),X1,X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_Divides_Odiv__class_Odiv(X3,X1,X2)),c_HOL_Oone__class_Oone(X2))
    | ~ class_Divides_Osemiring__div(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2107]) ).

cnf(c_0_2107_1,axiom,
    ( c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),X1),X1,X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_Divides_Odiv__class_Odiv(X3,X1,X2)),c_HOL_Oone__class_Oone(X2))
    | X1 = c_HOL_Ozero__class_Ozero(X2)
    | ~ class_Divides_Osemiring__div(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2107]) ).

cnf(c_0_2107_2,axiom,
    ( ~ class_Divides_Osemiring__div(X2)
    | c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),X1),X1,X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_Divides_Odiv__class_Odiv(X3,X1,X2)),c_HOL_Oone__class_Oone(X2))
    | X1 = c_HOL_Ozero__class_Ozero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2107]) ).

cnf(c_0_2108_0,axiom,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X5),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X4,X5,X3)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2108]) ).

cnf(c_0_2108_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X5),X3)
    | ~ c_HOL_Oord__class_Oless(X4,X5,X3)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2108]) ).

cnf(c_0_2108_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(X4,X5,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X5),X3)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2108]) ).

cnf(c_0_2108_3,axiom,
    ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
    | ~ c_HOL_Oord__class_Oless(X4,X5,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X5),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2108]) ).

cnf(c_0_2109_0,axiom,
    ( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X4,X3),c_Power_Opower__class_Opower(X2,X4,X3),X3) = c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
    | ~ class_OrderedGroup_Ocomm__monoid__mult(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2109]) ).

cnf(c_0_2109_1,axiom,
    ( ~ class_OrderedGroup_Ocomm__monoid__mult(X3)
    | c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X4,X3),c_Power_Opower__class_Opower(X2,X4,X3),X3) = c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2109]) ).

cnf(c_0_2110_0,axiom,
    ( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X4,X3),c_Power_Opower__class_Opower(X2,X4,X3),X3) = c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2110]) ).

cnf(c_0_2110_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
    | c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X4,X3),c_Power_Opower__class_Opower(X2,X4,X3),X3) = c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2110]) ).

cnf(c_0_2111_0,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X1,X4,X3),X2,X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2111]) ).

cnf(c_0_2111_1,axiom,
    ( ~ class_Divides_Osemiring__div(X3)
    | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X1,X4,X3),X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2111]) ).

cnf(c_0_2112_0,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3) = c_HOL_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Omod(X2,X4,X3),X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2112]) ).

cnf(c_0_2112_1,axiom,
    ( ~ class_Divides_Osemiring__div(X3)
    | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3) = c_HOL_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Omod(X2,X4,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2112]) ).

cnf(c_0_2113_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2113]) ).

cnf(c_0_2113_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2113]) ).

cnf(c_0_2113_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2113]) ).

cnf(c_0_2114_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2114]) ).

cnf(c_0_2114_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2114]) ).

cnf(c_0_2114_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2114]) ).

cnf(c_0_2115_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2115]) ).

cnf(c_0_2115_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2115]) ).

cnf(c_0_2115_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2115]) ).

cnf(c_0_2116_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2116]) ).

cnf(c_0_2116_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2116]) ).

cnf(c_0_2116_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2116]) ).

cnf(c_0_2117_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2117]) ).

cnf(c_0_2117_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2117]) ).

cnf(c_0_2117_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2117]) ).

cnf(c_0_2118_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2118]) ).

cnf(c_0_2118_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2118]) ).

cnf(c_0_2118_2,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2118]) ).

cnf(c_0_2119_0,axiom,
    ( c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Otimes__class_Otimes(X3,X4,X1)),X4,X1) = c_Divides_Odiv__class_Omod(X2,X4,X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2119]) ).

cnf(c_0_2119_1,axiom,
    ( ~ class_Divides_Osemiring__div(X1)
    | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Otimes__class_Otimes(X3,X4,X1)),X4,X1) = c_Divides_Odiv__class_Omod(X2,X4,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2119]) ).

cnf(c_0_2120_0,axiom,
    ( c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Otimes__class_Otimes(X3,X4,X1)),X3,X1) = c_Divides_Odiv__class_Omod(X2,X3,X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2120]) ).

cnf(c_0_2120_1,axiom,
    ( ~ class_Divides_Osemiring__div(X1)
    | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Otimes__class_Otimes(X3,X4,X1)),X3,X1) = c_Divides_Odiv__class_Omod(X2,X3,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2120]) ).

cnf(c_0_2121_0,axiom,
    ( hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
    | ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))) ),
    inference(literals_permutation,[status(thm)],[c_0_2121]) ).

cnf(c_0_2121_1,axiom,
    ( ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)))
    | hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
    inference(literals_permutation,[status(thm)],[c_0_2121]) ).

cnf(c_0_2122_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2122]) ).

cnf(c_0_2122_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2122]) ).

cnf(c_0_2122_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2122]) ).

cnf(c_0_2122_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2122]) ).

cnf(c_0_2123_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2123]) ).

cnf(c_0_2123_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2123]) ).

cnf(c_0_2123_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2123]) ).

cnf(c_0_2123_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2123]) ).

cnf(c_0_2124_0,axiom,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))) ),
    inference(literals_permutation,[status(thm)],[c_0_2124]) ).

cnf(c_0_2124_1,axiom,
    ( ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)))
    | hBOOL(hAPP(X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_2124]) ).

cnf(c_0_2125_0,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2125]) ).

cnf(c_0_2125_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),tc_nat)
    | c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2125]) ).

cnf(c_0_2126_0,axiom,
    ( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X2,X4),c_Power_Opower__class_Opower(X1,X3,X4),X4) = c_Power_Opower__class_Opower(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),X4)
    | ~ class_OrderedGroup_Omonoid__mult(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_2126]) ).

cnf(c_0_2126_1,axiom,
    ( ~ class_OrderedGroup_Omonoid__mult(X4)
    | c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X2,X4),c_Power_Opower__class_Opower(X1,X3,X4),X4) = c_Power_Opower__class_Opower(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_2126]) ).

cnf(c_0_2127_0,axiom,
    ( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X4,X3),X3) = c_Power_Opower__class_Opower(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X4),X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2127]) ).

cnf(c_0_2127_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
    | c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X4,X3),X3) = c_Power_Opower__class_Opower(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X4),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2127]) ).

cnf(c_0_2128_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_2128]) ).

cnf(c_0_2128_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_2128]) ).

cnf(c_0_2129_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_2129]) ).

cnf(c_0_2129_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_2129]) ).

cnf(c_0_2130_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_2130]) ).

cnf(c_0_2130_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_2130]) ).

cnf(c_0_2131_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_2131]) ).

cnf(c_0_2131_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_2131]) ).

cnf(c_0_2132_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_2132]) ).

cnf(c_0_2132_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_2132]) ).

cnf(c_0_2133_0,axiom,
    ( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X2,X4,X3),X1,X3) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X1,X3),X4,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2133]) ).

cnf(c_0_2133_1,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X2,X4,X3),X1,X3) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X1,X3),X4,X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2133]) ).

cnf(c_0_2133_2,axiom,
    ( ~ class_Divides_Osemiring__div(X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X2,X4,X3),X1,X3) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X1,X3),X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2133]) ).

cnf(c_0_2134_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X4)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_Divides_Odiv__class_Omod(X2,X3,X4),X4)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X3,X4)
    | ~ class_Divides_Osemiring__div(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_2134]) ).

cnf(c_0_2134_1,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_Divides_Odiv__class_Omod(X2,X3,X4),X4)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X4)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X3,X4)
    | ~ class_Divides_Osemiring__div(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_2134]) ).

cnf(c_0_2134_2,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X3,X4)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_Divides_Odiv__class_Omod(X2,X3,X4),X4)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X4)
    | ~ class_Divides_Osemiring__div(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_2134]) ).

cnf(c_0_2134_3,axiom,
    ( ~ class_Divides_Osemiring__div(X4)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X3,X4)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_Divides_Odiv__class_Omod(X2,X3,X4),X4)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_2134]) ).

cnf(c_0_2135_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_Divides_Odiv__class_Omod(X4,X2,X3),X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2135]) ).

cnf(c_0_2135_1,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_Divides_Odiv__class_Omod(X4,X2,X3),X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2135]) ).

cnf(c_0_2135_2,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_Divides_Odiv__class_Omod(X4,X2,X3),X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2135]) ).

cnf(c_0_2135_3,axiom,
    ( ~ class_Divides_Osemiring__div(X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_Divides_Odiv__class_Omod(X4,X2,X3),X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2135]) ).

cnf(c_0_2136_0,axiom,
    ( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) = c_Divides_Odiv__class_Odiv(X2,X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2136]) ).

cnf(c_0_2136_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) = c_Divides_Odiv__class_Odiv(X2,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2136]) ).

cnf(c_0_2137_0,axiom,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X4),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2137]) ).

cnf(c_0_2137_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X4),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2137]) ).

cnf(c_0_2137_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X4),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2137]) ).

cnf(c_0_2138_0,axiom,
    ( X1 = c_List_Olist_ONil(X2)
    | c_List_Omap(X3,X1,X2,X4) != c_List_Olist_ONil(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_2138]) ).

cnf(c_0_2138_1,axiom,
    ( c_List_Omap(X3,X1,X2,X4) != c_List_Olist_ONil(X4)
    | X1 = c_List_Olist_ONil(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2138]) ).

cnf(c_0_2139_0,axiom,
    ( X1 = c_List_Olist_ONil(X2)
    | c_List_Omap(X4,X1,X2,X3) != c_List_Olist_ONil(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2139]) ).

cnf(c_0_2139_1,axiom,
    ( c_List_Omap(X4,X1,X2,X3) != c_List_Olist_ONil(X3)
    | X1 = c_List_Olist_ONil(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2139]) ).

cnf(c_0_2140_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_2140]) ).

cnf(c_0_2140_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_2140]) ).

cnf(c_0_2140_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_2140]) ).

cnf(c_0_2141_0,axiom,
    ( c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,c_Suc(X3),X1),c_HOL_Oone__class_Oone(X1),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2141]) ).

cnf(c_0_2141_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,c_Suc(X3),X1),c_HOL_Oone__class_Oone(X1),X1)
    | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2141]) ).

cnf(c_0_2141_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X1),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,c_Suc(X3),X1),c_HOL_Oone__class_Oone(X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2141]) ).

cnf(c_0_2141_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X1),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,c_Suc(X3),X1),c_HOL_Oone__class_Oone(X1),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2141]) ).

cnf(c_0_2142_0,axiom,
    ( c_Lambda_Obeta(hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X3),X4),hAPP(hAPP(hAPP(c_Lambda_Osubst,X2),X3),X4))
    | ~ c_Lambda_Obeta(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2142]) ).

cnf(c_0_2142_1,axiom,
    ( ~ c_Lambda_Obeta(X1,X2)
    | c_Lambda_Obeta(hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X3),X4),hAPP(hAPP(hAPP(c_Lambda_Osubst,X2),X3),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_2142]) ).

cnf(c_0_2143_0,axiom,
    ( c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2143]) ).

cnf(c_0_2143_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
    | c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2143]) ).

cnf(c_0_2143_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
    | c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2143]) ).

cnf(c_0_2144_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X3),X1,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X3),X2,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2144]) ).

cnf(c_0_2144_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X3),X1,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X3),X2,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2144]) ).

cnf(c_0_2145_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X3,X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2145]) ).

cnf(c_0_2145_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
    | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X3,X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2145]) ).

cnf(c_0_2145_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X3,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
    | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2145]) ).

cnf(c_0_2145_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X3,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
    | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2145]) ).

cnf(c_0_2146_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2146]) ).

cnf(c_0_2146_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2146]) ).

cnf(c_0_2146_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2146]) ).

cnf(c_0_2146_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2146]) ).

cnf(c_0_2147_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
    | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2147]) ).

cnf(c_0_2147_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
    | ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2147]) ).

cnf(c_0_2147_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2147]) ).

cnf(c_0_2147_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
    | ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2147]) ).

cnf(c_0_2148_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2148]) ).

cnf(c_0_2148_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2148]) ).

cnf(c_0_2148_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2148]) ).

cnf(c_0_2148_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2148]) ).

cnf(c_0_2149_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2149]) ).

cnf(c_0_2149_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2149]) ).

cnf(c_0_2149_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2149]) ).

cnf(c_0_2149_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2149]) ).

cnf(c_0_2150_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2150]) ).

cnf(c_0_2150_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2150]) ).

cnf(c_0_2150_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
    | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2150]) ).

cnf(c_0_2150_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__semiring__strict(X2)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X3,X2)
    | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2150]) ).

cnf(c_0_2151_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2151]) ).

cnf(c_0_2151_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
    | c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2151]) ).

cnf(c_0_2151_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
    | c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2151]) ).

cnf(c_0_2152_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2152]) ).

cnf(c_0_2152_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
    | c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2152]) ).

cnf(c_0_2152_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
    | c_HOL_Oord__class_Oless(X1,c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2152]) ).

cnf(c_0_2153_0,axiom,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X3),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2153]) ).

cnf(c_0_2153_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X3),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2153]) ).

cnf(c_0_2153_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X3),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2153]) ).

cnf(c_0_2153_3,axiom,
    ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X2)
    | ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X3),c_HOL_Ozero__class_Ozero(X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2153]) ).

cnf(c_0_2154_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2154]) ).

cnf(c_0_2154_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2154]) ).

cnf(c_0_2154_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X1)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2154]) ).

cnf(c_0_2154_3,axiom,
    ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2154]) ).

cnf(c_0_2155_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ class_Ring__and__Field_Oidom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2155]) ).

cnf(c_0_2155_1,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
    | ~ class_Ring__and__Field_Oidom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2155]) ).

cnf(c_0_2155_2,axiom,
    ( ~ class_Ring__and__Field_Oidom(X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2155]) ).

cnf(c_0_2156_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X4,X1,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ class_Ring__and__Field_Oidom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2156]) ).

cnf(c_0_2156_1,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X4,X1,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
    | ~ class_Ring__and__Field_Oidom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2156]) ).

cnf(c_0_2156_2,axiom,
    ( ~ class_Ring__and__Field_Oidom(X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X4,X1,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2156]) ).

cnf(c_0_2157_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(X1,X4,X3),c_Power_Opower__class_Opower(X2,X4,X3),X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2157]) ).

cnf(c_0_2157_1,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(X1,X4,X3),c_Power_Opower__class_Opower(X2,X4,X3),X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2157]) ).

cnf(c_0_2157_2,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(X1,X4,X3),c_Power_Opower__class_Opower(X2,X4,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2157]) ).

cnf(c_0_2158_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2158]) ).

cnf(c_0_2158_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
    | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2158]) ).

cnf(c_0_2158_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
    | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2158]) ).

cnf(c_0_2158_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
    | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2158]) ).

cnf(c_0_2159_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X3,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2159]) ).

cnf(c_0_2159_1,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X3,X2,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2159]) ).

cnf(c_0_2159_2,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X3,X2,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2159]) ).

cnf(c_0_2159_3,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X3,X2,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2159]) ).

cnf(c_0_2159_4,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X1,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X3,X2,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2159]) ).

cnf(c_0_2160_0,axiom,
    ( c_Divides_Odiv__class_Omod(c_Suc(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat)),X1,tc_nat) = c_HOL_Oone__class_Oone(tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2160]) ).

cnf(c_0_2160_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat)
    | c_Divides_Odiv__class_Omod(c_Suc(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat)),X1,tc_nat) = c_HOL_Oone__class_Oone(tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2160]) ).

cnf(c_0_2161_0,axiom,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2161]) ).

cnf(c_0_2161_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4),X3)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2161]) ).

cnf(c_0_2161_2,axiom,
    ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2161]) ).

cnf(c_0_2162_0,axiom,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2162]) ).

cnf(c_0_2162_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4),X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2162]) ).

cnf(c_0_2162_2,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2162]) ).

cnf(c_0_2163_0,axiom,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2163]) ).

cnf(c_0_2163_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2),X3)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2163]) ).

cnf(c_0_2163_2,axiom,
    ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2163]) ).

cnf(c_0_2164_0,axiom,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2164]) ).

cnf(c_0_2164_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2),X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2164]) ).

cnf(c_0_2164_2,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2164]) ).

cnf(c_0_2165_0,axiom,
    ( c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_HOL_Oord__class_Oless(X3,X4,X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2165]) ).

cnf(c_0_2165_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
    | ~ c_HOL_Oord__class_Oless(X3,X4,X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2165]) ).

cnf(c_0_2165_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(X3,X4,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2165]) ).

cnf(c_0_2165_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | ~ c_HOL_Oord__class_Oless(X3,X4,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2165]) ).

cnf(c_0_2166_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2166]) ).

cnf(c_0_2166_1,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2166]) ).

cnf(c_0_2167_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2167]) ).

cnf(c_0_2167_1,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2167]) ).

cnf(c_0_2167_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),tc_nat)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2167]) ).

cnf(c_0_2168_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,c_Divides_Odiv__class_Omod(X4,X2,X3),X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2168]) ).

cnf(c_0_2168_1,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,c_Divides_Odiv__class_Omod(X4,X2,X3),X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2168]) ).

cnf(c_0_2168_2,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,c_Divides_Odiv__class_Omod(X4,X2,X3),X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2168]) ).

cnf(c_0_2168_3,axiom,
    ( ~ class_Divides_Osemiring__div(X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,c_Divides_Odiv__class_Omod(X4,X2,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2168]) ).

cnf(c_0_2169_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,c_Divides_Odiv__class_Omod(X2,X4,X3),X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2169]) ).

cnf(c_0_2169_1,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,c_Divides_Odiv__class_Omod(X2,X4,X3),X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2169]) ).

cnf(c_0_2169_2,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,c_Divides_Odiv__class_Omod(X2,X4,X3),X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2169]) ).

cnf(c_0_2169_3,axiom,
    ( ~ class_Divides_Osemiring__div(X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,c_Divides_Odiv__class_Omod(X2,X4,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2169]) ).

cnf(c_0_2170_0,axiom,
    ( X2 = c_HOL_Oone__class_Oone(tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2170]) ).

cnf(c_0_2170_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | X2 = c_HOL_Oone__class_Oone(tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2170]) ).

cnf(c_0_2170_2,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | X2 = c_HOL_Oone__class_Oone(tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2170]) ).

cnf(c_0_2171_0,axiom,
    ( X2 = c_HOL_Oone__class_Oone(tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2171]) ).

cnf(c_0_2171_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | X2 = c_HOL_Oone__class_Oone(tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2171]) ).

cnf(c_0_2171_2,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | X2 = c_HOL_Oone__class_Oone(tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2171]) ).

cnf(c_0_2172_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2172]) ).

cnf(c_0_2172_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2172]) ).

cnf(c_0_2172_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2172]) ).

cnf(c_0_2173_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4),X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2173]) ).

cnf(c_0_2173_1,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4),X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2173]) ).

cnf(c_0_2173_2,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4),X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2173]) ).

cnf(c_0_2173_3,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2173]) ).

cnf(c_0_2174_0,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(X2)
    | c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Otimes__class_Otimes(X1,X4,X2),X2) = c_Divides_Odiv__class_Odiv(X3,X4,X2)
    | ~ class_Divides_Osemiring__div(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2174]) ).

cnf(c_0_2174_1,axiom,
    ( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Otimes__class_Otimes(X1,X4,X2),X2) = c_Divides_Odiv__class_Odiv(X3,X4,X2)
    | X1 = c_HOL_Ozero__class_Ozero(X2)
    | ~ class_Divides_Osemiring__div(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2174]) ).

cnf(c_0_2174_2,axiom,
    ( ~ class_Divides_Osemiring__div(X2)
    | c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Otimes__class_Otimes(X1,X4,X2),X2) = c_Divides_Odiv__class_Odiv(X3,X4,X2)
    | X1 = c_HOL_Ozero__class_Ozero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2174]) ).

cnf(c_0_2175_0,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(X2)
    | c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X3,X1,X2),c_HOL_Otimes__class_Otimes(X4,X1,X2),X2) = c_Divides_Odiv__class_Odiv(X3,X4,X2)
    | ~ class_Divides_Osemiring__div(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2175]) ).

cnf(c_0_2175_1,axiom,
    ( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X3,X1,X2),c_HOL_Otimes__class_Otimes(X4,X1,X2),X2) = c_Divides_Odiv__class_Odiv(X3,X4,X2)
    | X1 = c_HOL_Ozero__class_Ozero(X2)
    | ~ class_Divides_Osemiring__div(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2175]) ).

cnf(c_0_2175_2,axiom,
    ( ~ class_Divides_Osemiring__div(X2)
    | c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X3,X1,X2),c_HOL_Otimes__class_Otimes(X4,X1,X2),X2) = c_Divides_Odiv__class_Odiv(X3,X4,X2)
    | X1 = c_HOL_Ozero__class_Ozero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2175]) ).

cnf(c_0_2176_0,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Otimes__class_Otimes(X3,X2,X1)) = c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),c_HOL_Oone__class_Oone(X1)),X2,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2176]) ).

cnf(c_0_2176_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Otimes__class_Otimes(X3,X2,X1)) = c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),c_HOL_Oone__class_Oone(X1)),X2,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2176]) ).

cnf(c_0_2177_0,axiom,
    ( c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Odiv(X2,X1,tc_nat),X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2177]) ).

cnf(c_0_2177_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat)
    | c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Odiv(X2,X1,tc_nat),X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2177]) ).

cnf(c_0_2177_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat)
    | c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Odiv(X2,X1,tc_nat),X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2177]) ).

cnf(c_0_2178_0,axiom,
    ( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X2,X3),X1,X3) = c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X3),X3)
    | ~ class_OrderedGroup_Omonoid__mult(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2178]) ).

cnf(c_0_2178_1,axiom,
    ( ~ class_OrderedGroup_Omonoid__mult(X3)
    | c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X2,X3),X1,X3) = c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2178]) ).

cnf(c_0_2179_0,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
    | ~ class_OrderedGroup_Oab__semigroup__mult(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2179]) ).

cnf(c_0_2179_1,axiom,
    ( ~ class_OrderedGroup_Oab__semigroup__mult(X3)
    | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X4,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2179]) ).

cnf(c_0_2180_0,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X4,X3),X2,X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2180]) ).

cnf(c_0_2180_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
    | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X4,X3),X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2180]) ).

cnf(c_0_2181_0,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2181]) ).

cnf(c_0_2181_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
    | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X4,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2181]) ).

cnf(c_0_2182_0,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X4),X3,X4) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_2182]) ).

cnf(c_0_2182_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
    | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X4),X3,X4) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_2182]) ).

cnf(c_0_2183_0,axiom,
    ( c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X1,X3,X4),X4)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_2183]) ).

cnf(c_0_2183_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
    | c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X1,X3,X4),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_2183]) ).

cnf(c_0_2184_0,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X4),X3,X4) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_2184]) ).

cnf(c_0_2184_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
    | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X4),X3,X4) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_2184]) ).

cnf(c_0_2185_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X3,X2,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2185]) ).

cnf(c_0_2185_1,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X3,X2,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2185]) ).

cnf(c_0_2185_2,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X3,X2,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2185]) ).

cnf(c_0_2185_3,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X3,X2,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2185]) ).

cnf(c_0_2185_4,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X3,X2,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2185]) ).

cnf(c_0_2186_0,axiom,
    ( c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(X1,X2,X3),X4,X3) = c_Power_Opower__class_Opower(X1,c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2186]) ).

cnf(c_0_2186_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
    | c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(X1,X2,X3),X4,X3) = c_Power_Opower__class_Opower(X1,c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2186]) ).

cnf(c_0_2187_0,axiom,
    ( c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(X1,X2,X4),X3,X4) = c_Power_Opower__class_Opower(X1,c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X4)
    | ~ class_OrderedGroup_Omonoid__mult(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_2187]) ).

cnf(c_0_2187_1,axiom,
    ( ~ class_OrderedGroup_Omonoid__mult(X4)
    | c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(X1,X2,X4),X3,X4) = c_Power_Opower__class_Opower(X1,c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_2187]) ).

cnf(c_0_2188_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2188]) ).

cnf(c_0_2188_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),X1)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2188]) ).

cnf(c_0_2188_2,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__add(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),X1)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2188]) ).

cnf(c_0_2189_0,axiom,
    ( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2189]) ).

cnf(c_0_2189_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),c_HOL_Ozero__class_Ozero(X1),X1)
    | c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2189]) ).

cnf(c_0_2189_2,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__add(X1)
    | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),c_HOL_Ozero__class_Ozero(X1),X1)
    | c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2189]) ).

cnf(c_0_2190_0,axiom,
    ( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2190]) ).

cnf(c_0_2190_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),c_HOL_Ozero__class_Ozero(X1),X1)
    | c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2190]) ).

cnf(c_0_2190_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),c_HOL_Ozero__class_Ozero(X1),X1)
    | c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2190]) ).

cnf(c_0_2191_0,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) = c_Divides_Odiv__class_Odiv(X2,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2191]) ).

cnf(c_0_2191_1,axiom,
    ( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) = c_Divides_Odiv__class_Odiv(X2,X3,tc_nat)
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2191]) ).

cnf(c_0_2192_0,axiom,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2192]) ).

cnf(c_0_2192_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2192]) ).

cnf(c_0_2193_0,axiom,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2193]) ).

cnf(c_0_2193_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2193]) ).

cnf(c_0_2194_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2194]) ).

cnf(c_0_2194_1,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
    | c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2194]) ).

cnf(c_0_2194_2,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
    | c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2194]) ).

cnf(c_0_2195_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2195]) ).

cnf(c_0_2195_1,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2195]) ).

cnf(c_0_2195_2,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2195]) ).

cnf(c_0_2196_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_2196]) ).

cnf(c_0_2196_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_2196]) ).

cnf(c_0_2197_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_2197]) ).

cnf(c_0_2197_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_2197]) ).

cnf(c_0_2198_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_2198]) ).

cnf(c_0_2198_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_2198]) ).

cnf(c_0_2199_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | X2 = c_HOL_Ozero__class_Ozero(tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Power_Opower__class_Opower(X1,X2,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2199]) ).

cnf(c_0_2199_1,axiom,
    ( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Power_Opower__class_Opower(X1,X2,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2199]) ).

cnf(c_0_2199_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Power_Opower__class_Opower(X1,X2,tc_nat),tc_nat)
    | X2 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2199]) ).

cnf(c_0_2200_0,axiom,
    ( c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X4,X2,X3),X1,X3) = c_Divides_Odiv__class_Omod(X4,X1,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2200]) ).

cnf(c_0_2200_1,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X4,X2,X3),X1,X3) = c_Divides_Odiv__class_Omod(X4,X1,X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2200]) ).

cnf(c_0_2200_2,axiom,
    ( ~ class_Divides_Osemiring__div(X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X4,X2,X3),X1,X3) = c_Divides_Odiv__class_Omod(X4,X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2200]) ).

cnf(c_0_2201_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2201]) ).

cnf(c_0_2201_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2201]) ).

cnf(c_0_2202_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2202]) ).

cnf(c_0_2202_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2202]) ).

cnf(c_0_2203_0,axiom,
    ( hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)))
    | ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
    inference(literals_permutation,[status(thm)],[c_0_2203]) ).

cnf(c_0_2203_1,axiom,
    ( ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
    | hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))) ),
    inference(literals_permutation,[status(thm)],[c_0_2203]) ).

cnf(c_0_2204_0,axiom,
    ( hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)))
    | ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
    inference(literals_permutation,[status(thm)],[c_0_2204]) ).

cnf(c_0_2204_1,axiom,
    ( ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
    | hBOOL(hAPP(X1,c_Divides_Odiv__class_Odiv(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))) ),
    inference(literals_permutation,[status(thm)],[c_0_2204]) ).

cnf(c_0_2205_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2205]) ).

cnf(c_0_2205_1,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2205]) ).

cnf(c_0_2205_2,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2205]) ).

cnf(c_0_2205_3,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X1,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2205]) ).

cnf(c_0_2206_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X3,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2206]) ).

cnf(c_0_2206_1,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X3,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2206]) ).

cnf(c_0_2206_2,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X3,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2206]) ).

cnf(c_0_2206_3,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X1,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X3,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2206]) ).

cnf(c_0_2207_0,axiom,
    ( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X3,X1),X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2207]) ).

cnf(c_0_2207_1,axiom,
    ( ~ class_Divides_Osemiring__div(X1)
    | c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X3,X1),X1) = c_HOL_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2207]) ).

cnf(c_0_2208_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X2),X2),c_HOL_Otimes__class_Otimes(X3,c_HOL_Ozero__class_Ozero(X2),X2),X2)
    | ~ class_Ring__and__Field_Oidom(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2208]) ).

cnf(c_0_2208_1,axiom,
    ( ~ class_Ring__and__Field_Oidom(X2)
    | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X2),X2),c_HOL_Otimes__class_Otimes(X3,c_HOL_Ozero__class_Ozero(X2),X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2208]) ).

cnf(c_0_2209_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X3,X1),X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2209]) ).

cnf(c_0_2209_1,axiom,
    ( ~ class_Ring__and__Field_Oidom(X1)
    | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X3,X1),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2209]) ).

cnf(c_0_2210_0,axiom,
    ( hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)))
    | ~ hBOOL(hAPP(X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_2210]) ).

cnf(c_0_2210_1,axiom,
    ( ~ hBOOL(hAPP(X1,X2))
    | hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))) ),
    inference(literals_permutation,[status(thm)],[c_0_2210]) ).

cnf(c_0_2211_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_Power_Opower__class_Opower(X2,c_Suc(X3),X1),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2211]) ).

cnf(c_0_2211_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
    | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_Power_Opower__class_Opower(X2,c_Suc(X3),X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2211]) ).

cnf(c_0_2211_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1)
    | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_Power_Opower__class_Opower(X2,c_Suc(X3),X1),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2211]) ).

cnf(c_0_2212_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X4) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2212]) ).

cnf(c_0_2212_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
    | c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X4) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2212]) ).

cnf(c_0_2212_2,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X4) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2)
    | ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
    | c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2212]) ).

cnf(c_0_2213_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2213]) ).

cnf(c_0_2213_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X3,tc_nat)
    | c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2213]) ).

cnf(c_0_2214_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2214]) ).

cnf(c_0_2214_1,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1),tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2214]) ).

cnf(c_0_2215_0,axiom,
    ( X1 = X2
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X4,X3)
    | c_Power_Opower__class_Opower(X4,X1,X3) != c_Power_Opower__class_Opower(X4,X2,X3)
    | ~ class_Ring__and__Field_Oordered__semidom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2215]) ).

cnf(c_0_2215_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X4,X3)
    | X1 = X2
    | c_Power_Opower__class_Opower(X4,X1,X3) != c_Power_Opower__class_Opower(X4,X2,X3)
    | ~ class_Ring__and__Field_Oordered__semidom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2215]) ).

cnf(c_0_2215_2,axiom,
    ( c_Power_Opower__class_Opower(X4,X1,X3) != c_Power_Opower__class_Opower(X4,X2,X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X4,X3)
    | X1 = X2
    | ~ class_Ring__and__Field_Oordered__semidom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2215]) ).

cnf(c_0_2215_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X3)
    | c_Power_Opower__class_Opower(X4,X1,X3) != c_Power_Opower__class_Opower(X4,X2,X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),X4,X3)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_2215]) ).

cnf(c_0_2216_0,axiom,
    ( c_Suc(c_Divides_Odiv__class_Omod(X1,X2,tc_nat)) = X2
    | c_Suc(c_Divides_Odiv__class_Omod(X1,X2,tc_nat)) = c_Divides_Odiv__class_Omod(c_Suc(X1),X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2216]) ).

cnf(c_0_2216_1,axiom,
    ( c_Suc(c_Divides_Odiv__class_Omod(X1,X2,tc_nat)) = c_Divides_Odiv__class_Omod(c_Suc(X1),X2,tc_nat)
    | c_Suc(c_Divides_Odiv__class_Omod(X1,X2,tc_nat)) = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_2216]) ).

cnf(c_0_2217_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X3,X2,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2217]) ).

cnf(c_0_2217_1,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X3,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2217]) ).

cnf(c_0_2217_2,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X3,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2217]) ).

cnf(c_0_2217_3,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X3,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2217]) ).

cnf(c_0_2218_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2218]) ).

cnf(c_0_2218_1,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2218]) ).

cnf(c_0_2218_2,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2218]) ).

cnf(c_0_2218_3,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2218]) ).

cnf(c_0_2219_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2219]) ).

cnf(c_0_2219_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2219]) ).

cnf(c_0_2220_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2220]) ).

cnf(c_0_2220_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2220]) ).

cnf(c_0_2220_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2220]) ).

cnf(c_0_2221_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2221]) ).

cnf(c_0_2221_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2221]) ).

cnf(c_0_2221_2,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__add(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2221]) ).

cnf(c_0_2222_0,axiom,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X1),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2222]) ).

cnf(c_0_2222_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X1),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2222]) ).

cnf(c_0_2222_2,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__add(X2)
    | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X1),c_HOL_Ozero__class_Ozero(X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2222]) ).

cnf(c_0_2223_0,axiom,
    ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X1),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2223]) ).

cnf(c_0_2223_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X1),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2223]) ).

cnf(c_0_2223_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X1),c_HOL_Ozero__class_Ozero(X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2223]) ).

cnf(c_0_2224_0,axiom,
    ( X1 = X2
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
    | c_HOL_Otimes__class_Otimes(X3,X1,tc_nat) != c_HOL_Otimes__class_Otimes(X3,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2224]) ).

cnf(c_0_2224_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
    | X1 = X2
    | c_HOL_Otimes__class_Otimes(X3,X1,tc_nat) != c_HOL_Otimes__class_Otimes(X3,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2224]) ).

cnf(c_0_2224_2,axiom,
    ( c_HOL_Otimes__class_Otimes(X3,X1,tc_nat) != c_HOL_Otimes__class_Otimes(X3,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_2224]) ).

cnf(c_0_2225_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X2,c_Power_Opower__class_Opower(X2,X1,X3),X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2225]) ).

cnf(c_0_2225_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X2,c_Power_Opower__class_Opower(X2,X1,X3),X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2225]) ).

cnf(c_0_2225_2,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X2,c_Power_Opower__class_Opower(X2,X1,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2225]) ).

cnf(c_0_2226_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2226]) ).

cnf(c_0_2226_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2226]) ).

cnf(c_0_2226_2,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2226]) ).

cnf(c_0_2227_0,axiom,
    ( c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X1,X3),X1,X3) = X2
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2227]) ).

cnf(c_0_2227_1,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X1,X3),X1,X3) = X2
    | ~ class_Divides_Osemiring__div(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2227]) ).

cnf(c_0_2227_2,axiom,
    ( ~ class_Divides_Osemiring__div(X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X1,X3),X1,X3) = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_2227]) ).

cnf(c_0_2228_0,axiom,
    ( c_HOL_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Odiv(X2,X1,X3),X3) = X2
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2228]) ).

cnf(c_0_2228_1,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | c_HOL_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Odiv(X2,X1,X3),X3) = X2
    | ~ class_Divides_Osemiring__div(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2228]) ).

cnf(c_0_2228_2,axiom,
    ( ~ class_Divides_Osemiring__div(X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | c_HOL_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Odiv(X2,X1,X3),X3) = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_2228]) ).

cnf(c_0_2229_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2229]) ).

cnf(c_0_2229_1,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2229]) ).

cnf(c_0_2229_2,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X2,X4,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2229]) ).

cnf(c_0_2230_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2230]) ).

cnf(c_0_2230_1,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2230]) ).

cnf(c_0_2230_2,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X4,X2,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2230]) ).

cnf(c_0_2231_0,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2) = c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Oone__class_Oone(X1)),c_HOL_Oone__class_Oone(X1)),X2,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2231]) ).

cnf(c_0_2231_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2) = c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Oone__class_Oone(X1)),c_HOL_Oone__class_Oone(X1)),X2,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2231]) ).

cnf(c_0_2232_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2232]) ).

cnf(c_0_2232_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2232]) ).

cnf(c_0_2233_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat),X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2233]) ).

cnf(c_0_2233_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat),X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2233]) ).

cnf(c_0_2234_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Power_Opower__class_Opower(X1,X2,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2234]) ).

cnf(c_0_2234_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Power_Opower__class_Opower(X1,X2,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2234]) ).

cnf(c_0_2235_0,axiom,
    ( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),X1,tc_nat) = X2
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2235]) ).

cnf(c_0_2235_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),X1,tc_nat) = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_2235]) ).

cnf(c_0_2236_0,axiom,
    ( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X1,tc_nat) = X2
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2236]) ).

cnf(c_0_2236_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X1,tc_nat) = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_2236]) ).

cnf(c_0_2237_0,axiom,
    ( c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Omod(X2,X1,tc_nat),X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2237]) ).

cnf(c_0_2237_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Omod(X2,X1,tc_nat),X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2237]) ).

cnf(c_0_2238_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_2238]) ).

cnf(c_0_2238_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_2238]) ).

cnf(c_0_2239_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2239]) ).

cnf(c_0_2239_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2239]) ).

cnf(c_0_2240_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2240]) ).

cnf(c_0_2240_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2240]) ).

cnf(c_0_2241_0,axiom,
    ( c_HOL_Oord__class_Oless(X4,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X4,X1,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2241]) ).

cnf(c_0_2241_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X4,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X4,X1,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2241]) ).

cnf(c_0_2241_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(X4,X1,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X4,X2,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2241]) ).

cnf(c_0_2241_3,axiom,
    ( ~ class_Orderings_Oorder(X3)
    | ~ c_HOL_Oord__class_Oless(X4,X1,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X4,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2241]) ).

cnf(c_0_2242_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,X4,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X2,X4,X3)
    | ~ class_Orderings_Opreorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2242]) ).

cnf(c_0_2242_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X1,X4,X3)
    | ~ c_HOL_Oord__class_Oless(X2,X4,X3)
    | ~ class_Orderings_Opreorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2242]) ).

cnf(c_0_2242_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(X2,X4,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X1,X4,X3)
    | ~ class_Orderings_Opreorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2242]) ).

cnf(c_0_2242_3,axiom,
    ( ~ class_Orderings_Opreorder(X3)
    | ~ c_HOL_Oord__class_Oless(X2,X4,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X1,X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2242]) ).

cnf(c_0_2243_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2243]) ).

cnf(c_0_2243_1,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2243]) ).

cnf(c_0_2243_2,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2243]) ).

cnf(c_0_2243_3,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2243]) ).

cnf(c_0_2244_0,axiom,
    ( c_Divides_Odiv__class_Omod(c_Suc(X1),X2,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_Suc(c_Divides_Odiv__class_Omod(X1,X2,tc_nat)) != X2 ),
    inference(literals_permutation,[status(thm)],[c_0_2244]) ).

cnf(c_0_2244_1,axiom,
    ( c_Suc(c_Divides_Odiv__class_Omod(X1,X2,tc_nat)) != X2
    | c_Divides_Odiv__class_Omod(c_Suc(X1),X2,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2244]) ).

cnf(c_0_2245_0,axiom,
    ( c_HOL_Otimes__class_Otimes(c_Nat_Osemiring__1__class_Oof__nat(X1,X3),c_Nat_Osemiring__1__class_Oof__nat(X2,X3),X3) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X3)
    | ~ class_Ring__and__Field_Osemiring__1(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2245]) ).

cnf(c_0_2245_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring__1(X3)
    | c_HOL_Otimes__class_Otimes(c_Nat_Osemiring__1__class_Oof__nat(X1,X3),c_Nat_Osemiring__1__class_Oof__nat(X2,X3),X3) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2245]) ).

cnf(c_0_2246_0,axiom,
    ( c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X3),X3) = c_Power_Opower__class_Opower(X1,c_Suc(X2),X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2246]) ).

cnf(c_0_2246_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
    | c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X3),X3) = c_Power_Opower__class_Opower(X1,c_Suc(X2),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2246]) ).

cnf(c_0_2247_0,axiom,
    ( c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X3),X3) = c_Power_Opower__class_Opower(X1,c_Suc(X2),X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2247]) ).

cnf(c_0_2247_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
    | c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X3),X3) = c_Power_Opower__class_Opower(X1,c_Suc(X2),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2247]) ).

cnf(c_0_2248_0,axiom,
    ( c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X3),X3) = c_Power_Opower__class_Opower(X1,c_Suc(X2),X3)
    | ~ class_Power_Opower(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2248]) ).

cnf(c_0_2248_1,axiom,
    ( ~ class_Power_Opower(X3)
    | c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X3),X3) = c_Power_Opower__class_Opower(X1,c_Suc(X2),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2248]) ).

cnf(c_0_2249_0,axiom,
    ( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X2,X3),X1,X3) = c_Power_Opower__class_Opower(X1,c_Suc(X2),X3)
    | ~ class_OrderedGroup_Omonoid__mult(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2249]) ).

cnf(c_0_2249_1,axiom,
    ( ~ class_OrderedGroup_Omonoid__mult(X3)
    | c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X2,X3),X1,X3) = c_Power_Opower__class_Opower(X1,c_Suc(X2),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2249]) ).

cnf(c_0_2250_0,axiom,
    ( c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X3),X3) = c_Power_Opower__class_Opower(X1,c_Suc(X2),X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2250]) ).

cnf(c_0_2250_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
    | c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X3),X3) = c_Power_Opower__class_Opower(X1,c_Suc(X2),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2250]) ).

cnf(c_0_2251_0,axiom,
    ( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X2,X3),X1,X3) = c_Power_Opower__class_Opower(X1,c_Suc(X2),X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2251]) ).

cnf(c_0_2251_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
    | c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X2,X3),X1,X3) = c_Power_Opower__class_Opower(X1,c_Suc(X2),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2251]) ).

cnf(c_0_2252_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_Nat_Osemiring__1__class_Oof__nat(X3,X2),X2)
    | ~ class_Ring__and__Field_Oordered__semidom(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2252]) ).

cnf(c_0_2252_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_Nat_Osemiring__1__class_Oof__nat(X3,X2),X2)
    | c_HOL_Oord__class_Oless(X1,X3,tc_nat)
    | ~ class_Ring__and__Field_Oordered__semidom(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2252]) ).

cnf(c_0_2252_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X2)
    | ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_Nat_Osemiring__1__class_Oof__nat(X3,X2),X2)
    | c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2252]) ).

cnf(c_0_2253_0,axiom,
    ( c_Divides_Odiv__class_Odiv(X2,X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2253]) ).

cnf(c_0_2253_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | c_Divides_Odiv__class_Odiv(X2,X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
    | ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2253]) ).

cnf(c_0_2253_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | c_Divides_Odiv__class_Odiv(X2,X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2253]) ).

cnf(c_0_2254_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2254]) ).

cnf(c_0_2254_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2254]) ).

cnf(c_0_2255_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2255]) ).

cnf(c_0_2255_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2255]) ).

cnf(c_0_2256_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2256]) ).

cnf(c_0_2256_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2256]) ).

cnf(c_0_2257_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2257]) ).

cnf(c_0_2257_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2257]) ).

cnf(c_0_2258_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1),tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2258]) ).

cnf(c_0_2258_1,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2258]) ).

cnf(c_0_2259_0,axiom,
    ( c_HOL_Oord__class_Oless(c_Suc(X1),X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2259]) ).

cnf(c_0_2259_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(c_Suc(X1),X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2259]) ).

cnf(c_0_2259_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(c_Suc(X1),X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2259]) ).

cnf(c_0_2260_0,axiom,
    ( c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X1,X2,X3),X2,X3) = c_Divides_Odiv__class_Omod(X1,X2,X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2260]) ).

cnf(c_0_2260_1,axiom,
    ( ~ class_Divides_Osemiring__div(X3)
    | c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X1,X2,X3),X2,X3) = c_Divides_Odiv__class_Omod(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2260]) ).

cnf(c_0_2261_0,axiom,
    ( c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X1,X2,X3),X3) = c_HOL_Otimes__class_Otimes(X1,X2,X3)
    | ~ class_OrderedGroup_Oab__semigroup__idem__mult(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2261]) ).

cnf(c_0_2261_1,axiom,
    ( ~ class_OrderedGroup_Oab__semigroup__idem__mult(X3)
    | c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X1,X2,X3),X3) = c_HOL_Otimes__class_Otimes(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2261]) ).

cnf(c_0_2262_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2262]) ).

cnf(c_0_2262_1,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2262]) ).

cnf(c_0_2262_2,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2262]) ).

cnf(c_0_2263_0,axiom,
    ( c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X3,X1) = c_Divides_Odiv__class_Omod(X2,X3,X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2263]) ).

cnf(c_0_2263_1,axiom,
    ( ~ class_Divides_Osemiring__div(X1)
    | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X3,X1) = c_Divides_Odiv__class_Omod(X2,X3,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2263]) ).

cnf(c_0_2264_0,axiom,
    ( c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X2,X1) = c_Divides_Odiv__class_Omod(X3,X2,X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2264]) ).

cnf(c_0_2264_1,axiom,
    ( ~ class_Divides_Osemiring__div(X1)
    | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X2,X1) = c_Divides_Odiv__class_Omod(X3,X2,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2264]) ).

cnf(c_0_2265_0,axiom,
    ( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_Olift,X1),X2)))
    | ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_2265]) ).

cnf(c_0_2265_1,axiom,
    ( ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
    | hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_Olift,X1),X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_2265]) ).

cnf(c_0_2266_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Oone__class_Oone(X1)),c_HOL_Oone__class_Oone(X1)),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2266]) ).

cnf(c_0_2266_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Oone__class_Oone(X1)),c_HOL_Oone__class_Oone(X1)),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2266]) ).

cnf(c_0_2267_0,axiom,
    ( c_Power_Opower__class_Opower(c_Nat_Osemiring__1__class_Oof__nat(X1,X3),X2,X3) = c_Nat_Osemiring__1__class_Oof__nat(c_Power_Opower__class_Opower(X1,X2,tc_nat),X3)
    | ~ class_Ring__and__Field_Osemiring__1(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2267]) ).

cnf(c_0_2267_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring__1(X3)
    | c_Power_Opower__class_Opower(c_Nat_Osemiring__1__class_Oof__nat(X1,X3),X2,X3) = c_Nat_Osemiring__1__class_Oof__nat(c_Power_Opower__class_Opower(X1,X2,tc_nat),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2267]) ).

cnf(c_0_2268_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(X1)),X2) = c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat))) ),
    inference(literals_permutation,[status(thm)],[c_0_2268]) ).

cnf(c_0_2268_1,axiom,
    ( hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(X1)),X2) = c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)))
    | c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2268]) ).

cnf(c_0_2269_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2269]) ).

cnf(c_0_2269_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1),X1)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2269]) ).

cnf(c_0_2269_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1),X1)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2269]) ).

cnf(c_0_2270_0,axiom,
    ( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X1)),X3),X2) = c_Lambda_OdB_OVar(X1)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2270]) ).

cnf(c_0_2270_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X1)),X3),X2) = c_Lambda_OdB_OVar(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2270]) ).

cnf(c_0_2271_0,axiom,
    ( c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X3),c_Nat_Osemiring__1__class_Oof__nat(X2,X3),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ class_Ring__and__Field_Oordered__semidom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2271]) ).

cnf(c_0_2271_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X3),c_Nat_Osemiring__1__class_Oof__nat(X2,X3),X3)
    | ~ class_Ring__and__Field_Oordered__semidom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2271]) ).

cnf(c_0_2271_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X3),c_Nat_Osemiring__1__class_Oof__nat(X2,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2271]) ).

cnf(c_0_2272_0,axiom,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
    | ~ hBOOL(hAPP(X1,c_Suc(v_sko__List__Xlexn__Xinduct__1(X1)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2272]) ).

cnf(c_0_2272_1,axiom,
    ( ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
    | hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,c_Suc(v_sko__List__Xlexn__Xinduct__1(X1)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2272]) ).

cnf(c_0_2272_2,axiom,
    ( ~ hBOOL(hAPP(X1,c_Suc(v_sko__List__Xlexn__Xinduct__1(X1))))
    | ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
    | hBOOL(hAPP(X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_2272]) ).

cnf(c_0_2273_0,axiom,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
    | ~ hBOOL(hAPP(X1,c_Suc(c_ATP__Linkup_Osko__Nat__Xnat__induct__1__1(X1)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2273]) ).

cnf(c_0_2273_1,axiom,
    ( ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
    | hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,c_Suc(c_ATP__Linkup_Osko__Nat__Xnat__induct__1__1(X1)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2273]) ).

cnf(c_0_2273_2,axiom,
    ( ~ hBOOL(hAPP(X1,c_Suc(c_ATP__Linkup_Osko__Nat__Xnat__induct__1__1(X1))))
    | ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
    | hBOOL(hAPP(X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_2273]) ).

cnf(c_0_2274_0,axiom,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
    | ~ hBOOL(hAPP(X1,c_Suc(v_sko__List__Xreplicate__Xinduct__1(X1)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2274]) ).

cnf(c_0_2274_1,axiom,
    ( ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
    | hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,c_Suc(v_sko__List__Xreplicate__Xinduct__1(X1)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2274]) ).

cnf(c_0_2274_2,axiom,
    ( ~ hBOOL(hAPP(X1,c_Suc(v_sko__List__Xreplicate__Xinduct__1(X1))))
    | ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
    | hBOOL(hAPP(X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_2274]) ).

cnf(c_0_2275_0,axiom,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
    | ~ hBOOL(hAPP(X1,c_Suc(v_sko__List__Xupt__Xinduct__1(X1)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2275]) ).

cnf(c_0_2275_1,axiom,
    ( ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
    | hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,c_Suc(v_sko__List__Xupt__Xinduct__1(X1)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2275]) ).

cnf(c_0_2275_2,axiom,
    ( ~ hBOOL(hAPP(X1,c_Suc(v_sko__List__Xupt__Xinduct__1(X1))))
    | ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
    | hBOOL(hAPP(X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_2275]) ).

cnf(c_0_2276_0,axiom,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
    | ~ hBOOL(hAPP(X1,c_Suc(v_sko__Nat__Xnat__Xinduct__1(X1)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2276]) ).

cnf(c_0_2276_1,axiom,
    ( ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
    | hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,c_Suc(v_sko__Nat__Xnat__Xinduct__1(X1)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2276]) ).

cnf(c_0_2276_2,axiom,
    ( ~ hBOOL(hAPP(X1,c_Suc(v_sko__Nat__Xnat__Xinduct__1(X1))))
    | ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
    | hBOOL(hAPP(X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_2276]) ).

cnf(c_0_2277_0,axiom,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
    | ~ hBOOL(hAPP(X1,c_Suc(v_sko__Nat__Xnat__Xinducts__1(X1)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2277]) ).

cnf(c_0_2277_1,axiom,
    ( ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
    | hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,c_Suc(v_sko__Nat__Xnat__Xinducts__1(X1)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2277]) ).

cnf(c_0_2277_2,axiom,
    ( ~ hBOOL(hAPP(X1,c_Suc(v_sko__Nat__Xnat__Xinducts__1(X1))))
    | ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
    | hBOOL(hAPP(X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_2277]) ).

cnf(c_0_2278_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | X1 = X2
    | c_HOL_Oord__class_Oless(X2,X1,tc_nat)
    | hBOOL(hAPP(hAPP(X3,X2),X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_2278]) ).

cnf(c_0_2278_1,axiom,
    ( X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(X2,X1,tc_nat)
    | hBOOL(hAPP(hAPP(X3,X2),X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_2278]) ).

cnf(c_0_2278_2,axiom,
    ( c_HOL_Oord__class_Oless(X2,X1,tc_nat)
    | X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | hBOOL(hAPP(hAPP(X3,X2),X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_2278]) ).

cnf(c_0_2278_3,axiom,
    ( hBOOL(hAPP(hAPP(X3,X2),X1))
    | c_HOL_Oord__class_Oless(X2,X1,tc_nat)
    | X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2278]) ).

cnf(c_0_2279_0,axiom,
    ( X1 = X2
    | c_HOL_Otimes__class_Otimes(c_Suc(X3),X1,tc_nat) != c_HOL_Otimes__class_Otimes(c_Suc(X3),X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2279]) ).

cnf(c_0_2279_1,axiom,
    ( c_HOL_Otimes__class_Otimes(c_Suc(X3),X1,tc_nat) != c_HOL_Otimes__class_Otimes(c_Suc(X3),X2,tc_nat)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_2279]) ).

cnf(c_0_2280_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(X1),c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X1),X2,X1),X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2280]) ).

cnf(c_0_2280_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
    | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(X1),c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X1),X2,X1),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2280]) ).

cnf(c_0_2281_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_Nat_Osemiring__1__class_Oof__nat(X1,X2),X2)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | ~ class_Ring__and__Field_Oordered__semidom(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2281]) ).

cnf(c_0_2281_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_Nat_Osemiring__1__class_Oof__nat(X1,X2),X2)
    | ~ class_Ring__and__Field_Oordered__semidom(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2281]) ).

cnf(c_0_2281_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X2)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_Nat_Osemiring__1__class_Oof__nat(X1,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2281]) ).

cnf(c_0_2282_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_2282]) ).

cnf(c_0_2282_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_2282]) ).

cnf(c_0_2282_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_2282]) ).

cnf(c_0_2282_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_2282]) ).

cnf(c_0_2283_0,axiom,
    ( c_Lambda_Obeta(hAPP(hAPP(c_Lambda_Olift,X1),X3),hAPP(hAPP(c_Lambda_Olift,X2),X3))
    | ~ c_Lambda_Obeta(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2283]) ).

cnf(c_0_2283_1,axiom,
    ( ~ c_Lambda_Obeta(X1,X2)
    | c_Lambda_Obeta(hAPP(hAPP(c_Lambda_Olift,X1),X3),hAPP(hAPP(c_Lambda_Olift,X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_2283]) ).

cnf(c_0_2284_0,axiom,
    ( c_Lambda_Obeta(hAPP(hAPP(c_Lambda_OdB_OApp,X3),X1),hAPP(hAPP(c_Lambda_OdB_OApp,X3),X2))
    | ~ c_Lambda_Obeta(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2284]) ).

cnf(c_0_2284_1,axiom,
    ( ~ c_Lambda_Obeta(X1,X2)
    | 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_2284]) ).

cnf(c_0_2285_0,axiom,
    ( c_Lambda_Obeta(hAPP(hAPP(c_Lambda_OdB_OApp,X1),X3),hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3))
    | ~ c_Lambda_Obeta(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2285]) ).

cnf(c_0_2285_1,axiom,
    ( ~ c_Lambda_Obeta(X1,X2)
    | 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_2285]) ).

cnf(c_0_2286_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X2,X1,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2286]) ).

cnf(c_0_2286_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X2,X1,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2286]) ).

cnf(c_0_2286_2,axiom,
    ( ~ class_Orderings_Oorder(X3)
    | ~ c_HOL_Oord__class_Oless(X2,X1,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2286]) ).

cnf(c_0_2287_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X2,X1,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2287]) ).

cnf(c_0_2287_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X2,X1,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2287]) ).

cnf(c_0_2287_2,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | ~ c_HOL_Oord__class_Oless(X2,X1,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2287]) ).

cnf(c_0_2288_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X2,X1,X3)
    | ~ class_Orderings_Opreorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2288]) ).

cnf(c_0_2288_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X2,X1,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ class_Orderings_Opreorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2288]) ).

cnf(c_0_2288_2,axiom,
    ( ~ class_Orderings_Opreorder(X3)
    | ~ c_HOL_Oord__class_Oless(X2,X1,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2288]) ).

cnf(c_0_2289_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X2,X1,X3)
    | ~ class_Orderings_Opreorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2289]) ).

cnf(c_0_2289_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X2,X1,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ class_Orderings_Opreorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2289]) ).

cnf(c_0_2289_2,axiom,
    ( ~ class_Orderings_Opreorder(X3)
    | ~ c_HOL_Oord__class_Oless(X2,X1,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2289]) ).

cnf(c_0_2290_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2290]) ).

cnf(c_0_2290_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2290]) ).

cnf(c_0_2291_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),c_HOL_Oone__class_Oone(X2)),X2)
    | ~ class_Ring__and__Field_Oordered__semidom(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2291]) ).

cnf(c_0_2291_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X2)
    | c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),c_HOL_Oone__class_Oone(X2)),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2291]) ).

cnf(c_0_2292_0,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(X2)
    | c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X3,X1,X2),X1,X2) = X3
    | ~ class_Divides_Osemiring__div(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2292]) ).

cnf(c_0_2292_1,axiom,
    ( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X3,X1,X2),X1,X2) = X3
    | X1 = c_HOL_Ozero__class_Ozero(X2)
    | ~ class_Divides_Osemiring__div(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2292]) ).

cnf(c_0_2292_2,axiom,
    ( ~ class_Divides_Osemiring__div(X2)
    | c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X3,X1,X2),X1,X2) = X3
    | X1 = c_HOL_Ozero__class_Ozero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2292]) ).

cnf(c_0_2293_0,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(X2)
    | c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X1,X3,X2),X1,X2) = X3
    | ~ class_Divides_Osemiring__div(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2293]) ).

cnf(c_0_2293_1,axiom,
    ( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X1,X3,X2),X1,X2) = X3
    | X1 = c_HOL_Ozero__class_Ozero(X2)
    | ~ class_Divides_Osemiring__div(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2293]) ).

cnf(c_0_2293_2,axiom,
    ( ~ class_Divides_Osemiring__div(X2)
    | c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X1,X3,X2),X1,X2) = X3
    | X1 = c_HOL_Ozero__class_Ozero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2293]) ).

cnf(c_0_2294_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_2294]) ).

cnf(c_0_2294_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_2294]) ).

cnf(c_0_2294_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_2294]) ).

cnf(c_0_2295_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_2295]) ).

cnf(c_0_2295_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_2295]) ).

cnf(c_0_2295_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_2295]) ).

cnf(c_0_2296_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_2296]) ).

cnf(c_0_2296_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_2296]) ).

cnf(c_0_2296_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_2296]) ).

cnf(c_0_2297_0,axiom,
    ( c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Omod(X1,X2,X3),X2,X3) = c_HOL_Ozero__class_Ozero(X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2297]) ).

cnf(c_0_2297_1,axiom,
    ( ~ class_Divides_Osemiring__div(X3)
    | c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Omod(X1,X2,X3),X2,X3) = c_HOL_Ozero__class_Ozero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2297]) ).

cnf(c_0_2298_0,axiom,
    ( X1 = X2
    | X3 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_HOL_Otimes__class_Otimes(X1,X3,tc_nat) != c_HOL_Otimes__class_Otimes(X2,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2298]) ).

cnf(c_0_2298_1,axiom,
    ( X3 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X1 = X2
    | c_HOL_Otimes__class_Otimes(X1,X3,tc_nat) != c_HOL_Otimes__class_Otimes(X2,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2298]) ).

cnf(c_0_2298_2,axiom,
    ( c_HOL_Otimes__class_Otimes(X1,X3,tc_nat) != c_HOL_Otimes__class_Otimes(X2,X3,tc_nat)
    | X3 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_2298]) ).

cnf(c_0_2299_0,axiom,
    ( X1 = X2
    | X3 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_HOL_Otimes__class_Otimes(X3,X1,tc_nat) != c_HOL_Otimes__class_Otimes(X3,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2299]) ).

cnf(c_0_2299_1,axiom,
    ( X3 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X1 = X2
    | c_HOL_Otimes__class_Otimes(X3,X1,tc_nat) != c_HOL_Otimes__class_Otimes(X3,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2299]) ).

cnf(c_0_2299_2,axiom,
    ( c_HOL_Otimes__class_Otimes(X3,X1,tc_nat) != c_HOL_Otimes__class_Otimes(X3,X2,tc_nat)
    | X3 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_2299]) ).

cnf(c_0_2300_0,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X2 = X3
    | c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_HOL_Otimes__class_Otimes(X1,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2300]) ).

cnf(c_0_2300_1,axiom,
    ( X2 = X3
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_HOL_Otimes__class_Otimes(X1,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2300]) ).

cnf(c_0_2300_2,axiom,
    ( c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_HOL_Otimes__class_Otimes(X1,X3,tc_nat)
    | X2 = X3
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2300]) ).

cnf(c_0_2301_0,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X3),X2,X3) = c_HOL_Ozero__class_Ozero(X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2301]) ).

cnf(c_0_2301_1,axiom,
    ( ~ class_Divides_Osemiring__div(X3)
    | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X3),X2,X3) = c_HOL_Ozero__class_Ozero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2301]) ).

cnf(c_0_2302_0,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X3),X1,X3) = c_HOL_Ozero__class_Ozero(X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2302]) ).

cnf(c_0_2302_1,axiom,
    ( ~ class_Divides_Osemiring__div(X3)
    | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X3),X1,X3) = c_HOL_Ozero__class_Ozero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2302]) ).

cnf(c_0_2303_0,axiom,
    ( X1 = X2
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2303]) ).

cnf(c_0_2303_1,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | X1 = X2
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2303]) ).

cnf(c_0_2303_2,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_2303]) ).

cnf(c_0_2304_0,axiom,
    ( X1 = X2
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2304]) ).

cnf(c_0_2304_1,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | X1 = X2
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2304]) ).

cnf(c_0_2304_2,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_2304]) ).

cnf(c_0_2305_0,axiom,
    ( X1 = X2
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2305]) ).

cnf(c_0_2305_1,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | X1 = X2
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2305]) ).

cnf(c_0_2305_2,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_2305]) ).

cnf(c_0_2306_0,axiom,
    ( X1 = X2
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2306]) ).

cnf(c_0_2306_1,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | X1 = X2
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2306]) ).

cnf(c_0_2306_2,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_2306]) ).

cnf(c_0_2307_0,axiom,
    ( X2 = X1
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2307]) ).

cnf(c_0_2307_1,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | X2 = X1
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2307]) ).

cnf(c_0_2307_2,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | X2 = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_2307]) ).

cnf(c_0_2308_0,axiom,
    ( X1 = X2
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2308]) ).

cnf(c_0_2308_1,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | X1 = X2
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2308]) ).

cnf(c_0_2308_2,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_2308]) ).

cnf(c_0_2309_0,axiom,
    ( X1 = X2
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2309]) ).

cnf(c_0_2309_1,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | X1 = X2
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2309]) ).

cnf(c_0_2309_2,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_2309]) ).

cnf(c_0_2310_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | X2 = X1
    | hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X2)),X3),X1) = c_Lambda_OdB_OVar(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2310]) ).

cnf(c_0_2310_1,axiom,
    ( X2 = X1
    | c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X2)),X3),X1) = c_Lambda_OdB_OVar(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2310]) ).

cnf(c_0_2310_2,axiom,
    ( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X2)),X3),X1) = c_Lambda_OdB_OVar(X2)
    | X2 = X1
    | c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2310]) ).

cnf(c_0_2311_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X2,X1,X3),X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2311]) ).

cnf(c_0_2311_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X2,X1,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2311]) ).

cnf(c_0_2312_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2312]) ).

cnf(c_0_2312_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X1,X2,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2312]) ).

cnf(c_0_2313_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
    | ~ class_Ring__and__Field_Odvd(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2313]) ).

cnf(c_0_2313_1,axiom,
    ( ~ class_Ring__and__Field_Odvd(X3)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X1,X2,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2313]) ).

cnf(c_0_2314_0,axiom,
    ( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X1)),X2),X1) = X2
    | c_HOL_Oord__class_Oless(X1,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2314]) ).

cnf(c_0_2314_1,axiom,
    ( c_HOL_Oord__class_Oless(X1,X1,tc_nat)
    | hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X1)),X2),X1) = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_2314]) ).

cnf(c_0_2315_0,axiom,
    ( c_Type_Otyping(X1,X4,X3)
    | ~ c_Type_Otyping(X1,X2,X3)
    | ~ c_Lambda_Obeta(X2,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_2315]) ).

cnf(c_0_2315_1,axiom,
    ( ~ c_Type_Otyping(X1,X2,X3)
    | c_Type_Otyping(X1,X4,X3)
    | ~ c_Lambda_Obeta(X2,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_2315]) ).

cnf(c_0_2315_2,axiom,
    ( ~ c_Lambda_Obeta(X2,X4)
    | ~ c_Type_Otyping(X1,X2,X3)
    | c_Type_Otyping(X1,X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2315]) ).

cnf(c_0_2316_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X2),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2316]) ).

cnf(c_0_2316_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X2),tc_nat)
    | c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2316]) ).

cnf(c_0_2317_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | c_Divides_Odiv__class_Omod(X2,X1,X3) != c_HOL_Ozero__class_Ozero(X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2317]) ).

cnf(c_0_2317_1,axiom,
    ( c_Divides_Odiv__class_Omod(X2,X1,X3) != c_HOL_Ozero__class_Ozero(X3)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2317]) ).

cnf(c_0_2317_2,axiom,
    ( ~ class_Divides_Osemiring__div(X3)
    | c_Divides_Odiv__class_Omod(X2,X1,X3) != c_HOL_Ozero__class_Ozero(X3)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2317]) ).

cnf(c_0_2318_0,axiom,
    ( c_Divides_Odiv__class_Omod(X2,X1,X3) = c_HOL_Ozero__class_Ozero(X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2318]) ).

cnf(c_0_2318_1,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | c_Divides_Odiv__class_Omod(X2,X1,X3) = c_HOL_Ozero__class_Ozero(X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2318]) ).

cnf(c_0_2318_2,axiom,
    ( ~ class_Divides_Osemiring__div(X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | c_Divides_Odiv__class_Omod(X2,X1,X3) = c_HOL_Ozero__class_Ozero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2318]) ).

cnf(c_0_2319_0,axiom,
    ( hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
    | ~ hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Nat__Xzero__induct__1__1(X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_2319]) ).

cnf(c_0_2319_1,axiom,
    ( ~ hBOOL(hAPP(X1,X2))
    | hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
    | ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Nat__Xzero__induct__1__1(X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_2319]) ).

cnf(c_0_2319_2,axiom,
    ( ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Nat__Xzero__induct__1__1(X1)))
    | ~ hBOOL(hAPP(X1,X2))
    | hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
    inference(literals_permutation,[status(thm)],[c_0_2319]) ).

cnf(c_0_2320_0,axiom,
    ( hBOOL(hAPP(X1,c_Suc(c_ATP__Linkup_Osko__Nat__Xzero__induct__1__1(X1))))
    | hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
    | ~ hBOOL(hAPP(X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_2320]) ).

cnf(c_0_2320_1,axiom,
    ( hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
    | hBOOL(hAPP(X1,c_Suc(c_ATP__Linkup_Osko__Nat__Xzero__induct__1__1(X1))))
    | ~ hBOOL(hAPP(X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_2320]) ).

cnf(c_0_2320_2,axiom,
    ( ~ hBOOL(hAPP(X1,X2))
    | hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
    | hBOOL(hAPP(X1,c_Suc(c_ATP__Linkup_Osko__Nat__Xzero__induct__1__1(X1)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2320]) ).

cnf(c_0_2321_0,axiom,
    ( c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X2),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2321]) ).

cnf(c_0_2321_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X2),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2321]) ).

cnf(c_0_2322_0,axiom,
    ( c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X2),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2322]) ).

cnf(c_0_2322_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X2),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2322]) ).

cnf(c_0_2323_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | X1 = X2
    | ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2323]) ).

cnf(c_0_2323_1,axiom,
    ( X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2323]) ).

cnf(c_0_2323_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
    | X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2323]) ).

cnf(c_0_2324_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | X2 = X1
    | ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2324]) ).

cnf(c_0_2324_1,axiom,
    ( X2 = X1
    | c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2324]) ).

cnf(c_0_2324_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
    | X2 = X1
    | c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2324]) ).

cnf(c_0_2325_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | X1 = X2
    | ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2325]) ).

cnf(c_0_2325_1,axiom,
    ( X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2325]) ).

cnf(c_0_2325_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
    | X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2325]) ).

cnf(c_0_2326_0,axiom,
    ( c_Suc(X1) = X2
    | c_HOL_Oord__class_Oless(c_Suc(X1),X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2326]) ).

cnf(c_0_2326_1,axiom,
    ( c_HOL_Oord__class_Oless(c_Suc(X1),X2,tc_nat)
    | c_Suc(X1) = X2
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2326]) ).

cnf(c_0_2326_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(c_Suc(X1),X2,tc_nat)
    | c_Suc(X1) = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_2326]) ).

cnf(c_0_2327_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_2327]) ).

cnf(c_0_2327_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_2327]) ).

cnf(c_0_2328_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_2328]) ).

cnf(c_0_2328_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_2328]) ).

cnf(c_0_2329_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_2329]) ).

cnf(c_0_2329_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_2329]) ).

cnf(c_0_2330_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_Suc(X1),X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2330]) ).

cnf(c_0_2330_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_Suc(X1),X2,tc_nat)
    | c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2330]) ).

cnf(c_0_2331_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_Ring__and__Field_Oordered__semidom(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2331]) ).

cnf(c_0_2331_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X2)
    | ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2331]) ).

cnf(c_0_2332_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2332]) ).

cnf(c_0_2332_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2332]) ).

cnf(c_0_2333_0,axiom,
    ( c_Divides_Odiv__class_Odiv(X1,X2,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2333]) ).

cnf(c_0_2333_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_Divides_Odiv__class_Odiv(X1,X2,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2333]) ).

cnf(c_0_2334_0,axiom,
    ( c_Divides_Odiv__class_Omod(X1,X2,tc_nat) = X1
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2334]) ).

cnf(c_0_2334_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_Divides_Odiv__class_Omod(X1,X2,tc_nat) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_2334]) ).

cnf(c_0_2335_0,axiom,
    ( hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(X1)),X2) = c_Lambda_OdB_OVar(X1)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2335]) ).

cnf(c_0_2335_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(X1)),X2) = c_Lambda_OdB_OVar(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2335]) ).

cnf(c_0_2336_0,axiom,
    ( hBOOL(hAPP(X1,v_sko__List__Xlexn__Xinduct__1(X1)))
    | hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
    inference(literals_permutation,[status(thm)],[c_0_2336]) ).

cnf(c_0_2336_1,axiom,
    ( hBOOL(hAPP(X1,X2))
    | hBOOL(hAPP(X1,v_sko__List__Xlexn__Xinduct__1(X1)))
    | ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
    inference(literals_permutation,[status(thm)],[c_0_2336]) ).

cnf(c_0_2336_2,axiom,
    ( ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
    | hBOOL(hAPP(X1,X2))
    | hBOOL(hAPP(X1,v_sko__List__Xlexn__Xinduct__1(X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_2336]) ).

cnf(c_0_2337_0,axiom,
    ( hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Nat__Xnat__induct__1__1(X1)))
    | hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
    inference(literals_permutation,[status(thm)],[c_0_2337]) ).

cnf(c_0_2337_1,axiom,
    ( hBOOL(hAPP(X1,X2))
    | hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Nat__Xnat__induct__1__1(X1)))
    | ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
    inference(literals_permutation,[status(thm)],[c_0_2337]) ).

cnf(c_0_2337_2,axiom,
    ( ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
    | hBOOL(hAPP(X1,X2))
    | hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Nat__Xnat__induct__1__1(X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_2337]) ).

cnf(c_0_2338_0,axiom,
    ( hBOOL(hAPP(X1,v_sko__List__Xreplicate__Xinduct__1(X1)))
    | hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
    inference(literals_permutation,[status(thm)],[c_0_2338]) ).

cnf(c_0_2338_1,axiom,
    ( hBOOL(hAPP(X1,X2))
    | hBOOL(hAPP(X1,v_sko__List__Xreplicate__Xinduct__1(X1)))
    | ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
    inference(literals_permutation,[status(thm)],[c_0_2338]) ).

cnf(c_0_2338_2,axiom,
    ( ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
    | hBOOL(hAPP(X1,X2))
    | hBOOL(hAPP(X1,v_sko__List__Xreplicate__Xinduct__1(X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_2338]) ).

cnf(c_0_2339_0,axiom,
    ( hBOOL(hAPP(X1,v_sko__Nat__Xnat__Xinducts__1(X1)))
    | hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
    inference(literals_permutation,[status(thm)],[c_0_2339]) ).

cnf(c_0_2339_1,axiom,
    ( hBOOL(hAPP(X1,X2))
    | hBOOL(hAPP(X1,v_sko__Nat__Xnat__Xinducts__1(X1)))
    | ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
    inference(literals_permutation,[status(thm)],[c_0_2339]) ).

cnf(c_0_2339_2,axiom,
    ( ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
    | hBOOL(hAPP(X1,X2))
    | hBOOL(hAPP(X1,v_sko__Nat__Xnat__Xinducts__1(X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_2339]) ).

cnf(c_0_2340_0,axiom,
    ( hBOOL(hAPP(X1,v_sko__Nat__Xnat__Xinduct__1(X1)))
    | hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
    inference(literals_permutation,[status(thm)],[c_0_2340]) ).

cnf(c_0_2340_1,axiom,
    ( hBOOL(hAPP(X1,X2))
    | hBOOL(hAPP(X1,v_sko__Nat__Xnat__Xinduct__1(X1)))
    | ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
    inference(literals_permutation,[status(thm)],[c_0_2340]) ).

cnf(c_0_2340_2,axiom,
    ( ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
    | hBOOL(hAPP(X1,X2))
    | hBOOL(hAPP(X1,v_sko__Nat__Xnat__Xinduct__1(X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_2340]) ).

cnf(c_0_2341_0,axiom,
    ( hBOOL(hAPP(X1,v_sko__List__Xupt__Xinduct__1(X1)))
    | hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
    inference(literals_permutation,[status(thm)],[c_0_2341]) ).

cnf(c_0_2341_1,axiom,
    ( hBOOL(hAPP(X1,X2))
    | hBOOL(hAPP(X1,v_sko__List__Xupt__Xinduct__1(X1)))
    | ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat))) ),
    inference(literals_permutation,[status(thm)],[c_0_2341]) ).

cnf(c_0_2341_2,axiom,
    ( ~ hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
    | hBOOL(hAPP(X1,X2))
    | hBOOL(hAPP(X1,v_sko__List__Xupt__Xinduct__1(X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_2341]) ).

cnf(c_0_2342_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_2342]) ).

cnf(c_0_2342_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_2342]) ).

cnf(c_0_2342_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_2342]) ).

cnf(c_0_2342_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_2342]) ).

cnf(c_0_2342_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_2342]) ).

cnf(c_0_2342_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_2342]) ).

cnf(c_0_2343_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_2343]) ).

cnf(c_0_2343_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_2343]) ).

cnf(c_0_2343_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_2343]) ).

cnf(c_0_2343_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_2343]) ).

cnf(c_0_2343_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_2343]) ).

cnf(c_0_2344_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | X2 = X1
    | c_Lambda_Osubstn(c_Lambda_OdB_OVar(X2),X3,X1) = c_Lambda_OdB_OVar(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2344]) ).

cnf(c_0_2344_1,axiom,
    ( X2 = X1
    | c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_Lambda_Osubstn(c_Lambda_OdB_OVar(X2),X3,X1) = c_Lambda_OdB_OVar(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2344]) ).

cnf(c_0_2344_2,axiom,
    ( c_Lambda_Osubstn(c_Lambda_OdB_OVar(X2),X3,X1) = c_Lambda_OdB_OVar(X2)
    | X2 = X1
    | c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2344]) ).

cnf(c_0_2345_0,axiom,
    ( X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X2,X1,X3)
    | ~ class_Ring__and__Field_Oordered__idom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2345]) ).

cnf(c_0_2345_1,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,X3)
    | X1 = X2
    | c_HOL_Oord__class_Oless(X2,X1,X3)
    | ~ class_Ring__and__Field_Oordered__idom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2345]) ).

cnf(c_0_2345_2,axiom,
    ( c_HOL_Oord__class_Oless(X2,X1,X3)
    | c_HOL_Oord__class_Oless(X1,X2,X3)
    | X1 = X2
    | ~ class_Ring__and__Field_Oordered__idom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2345]) ).

cnf(c_0_2345_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X3)
    | c_HOL_Oord__class_Oless(X2,X1,X3)
    | c_HOL_Oord__class_Oless(X1,X2,X3)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_2345]) ).

cnf(c_0_2346_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X2,X1,X3)
    | X1 = X2
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2346]) ).

cnf(c_0_2346_1,axiom,
    ( c_HOL_Oord__class_Oless(X2,X1,X3)
    | c_HOL_Oord__class_Oless(X1,X2,X3)
    | X1 = X2
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2346]) ).

cnf(c_0_2346_2,axiom,
    ( X1 = X2
    | c_HOL_Oord__class_Oless(X2,X1,X3)
    | c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2346]) ).

cnf(c_0_2346_3,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | X1 = X2
    | c_HOL_Oord__class_Oless(X2,X1,X3)
    | c_HOL_Oord__class_Oless(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2346]) ).

cnf(c_0_2347_0,axiom,
    ( X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X2,X1,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2347]) ).

cnf(c_0_2347_1,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,X3)
    | X1 = X2
    | c_HOL_Oord__class_Oless(X2,X1,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2347]) ).

cnf(c_0_2347_2,axiom,
    ( c_HOL_Oord__class_Oless(X2,X1,X3)
    | c_HOL_Oord__class_Oless(X1,X2,X3)
    | X1 = X2
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2347]) ).

cnf(c_0_2347_3,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | c_HOL_Oord__class_Oless(X2,X1,X3)
    | c_HOL_Oord__class_Oless(X1,X2,X3)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_2347]) ).

cnf(c_0_2348_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,X3)
    | X1 = X2
    | c_HOL_Oord__class_Oless(X2,X1,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2348]) ).

cnf(c_0_2348_1,axiom,
    ( X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X2,X1,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2348]) ).

cnf(c_0_2348_2,axiom,
    ( c_HOL_Oord__class_Oless(X2,X1,X3)
    | X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2348]) ).

cnf(c_0_2348_3,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | c_HOL_Oord__class_Oless(X2,X1,X3)
    | X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2348]) ).

cnf(c_0_2349_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X2,X1,X3)
    | X2 = X1
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2349]) ).

cnf(c_0_2349_1,axiom,
    ( c_HOL_Oord__class_Oless(X2,X1,X3)
    | c_HOL_Oord__class_Oless(X1,X2,X3)
    | X2 = X1
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2349]) ).

cnf(c_0_2349_2,axiom,
    ( X2 = X1
    | c_HOL_Oord__class_Oless(X2,X1,X3)
    | c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2349]) ).

cnf(c_0_2349_3,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | X2 = X1
    | c_HOL_Oord__class_Oless(X2,X1,X3)
    | c_HOL_Oord__class_Oless(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2349]) ).

cnf(c_0_2350_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_2350]) ).

cnf(c_0_2350_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_2350]) ).

cnf(c_0_2351_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_2351]) ).

cnf(c_0_2351_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_2351]) ).

cnf(c_0_2352_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_2352]) ).

cnf(c_0_2352_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_2352]) ).

cnf(c_0_2353_0,axiom,
    ( c_HOL_Otimes__class_Otimes(X1,X2,X3) = c_HOL_Otimes__class_Otimes(X2,X1,X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2353]) ).

cnf(c_0_2353_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
    | c_HOL_Otimes__class_Otimes(X1,X2,X3) = c_HOL_Otimes__class_Otimes(X2,X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2353]) ).

cnf(c_0_2354_0,axiom,
    ( c_HOL_Otimes__class_Otimes(X1,X2,X3) = c_HOL_Otimes__class_Otimes(X2,X1,X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2354]) ).

cnf(c_0_2354_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
    | c_HOL_Otimes__class_Otimes(X1,X2,X3) = c_HOL_Otimes__class_Otimes(X2,X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2354]) ).

cnf(c_0_2355_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat)
    | c_HOL_Oord__class_Oless(X1,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2355]) ).

cnf(c_0_2355_1,axiom,
    ( c_HOL_Oord__class_Oless(X1,X1,tc_nat)
    | c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2355]) ).

cnf(c_0_2356_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(X2,c_Suc(X1),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2356]) ).

cnf(c_0_2356_1,axiom,
    ( c_HOL_Oord__class_Oless(X2,c_Suc(X1),tc_nat)
    | c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2356]) ).

cnf(c_0_2357_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2357]) ).

cnf(c_0_2357_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2357]) ).

cnf(c_0_2358_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_2358]) ).

cnf(c_0_2358_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_2358]) ).

cnf(c_0_2359_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_2359]) ).

cnf(c_0_2359_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_2359]) ).

cnf(c_0_2360_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_2360]) ).

cnf(c_0_2360_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_2360]) ).

cnf(c_0_2361_0,axiom,
    ( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2361]) ).

cnf(c_0_2361_1,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)
    | X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    inference(literals_permutation,[status(thm)],[c_0_2361]) ).

cnf(c_0_2362_0,axiom,
    ( hAPP(X1,X2) = X3
    | ~ c_Type_Otyping(X1,c_Lambda_OdB_OVar(X2),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2362]) ).

cnf(c_0_2362_1,axiom,
    ( ~ c_Type_Otyping(X1,c_Lambda_OdB_OVar(X2),X3)
    | hAPP(X1,X2) = X3 ),
    inference(literals_permutation,[status(thm)],[c_0_2362]) ).

cnf(c_0_2363_0,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(X2)
    | X3 = c_HOL_Ozero__class_Ozero(X2)
    | c_HOL_Otimes__class_Otimes(X3,X1,X2) != c_HOL_Ozero__class_Ozero(X2)
    | ~ class_Ring__and__Field_Ono__zero__divisors(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2363]) ).

cnf(c_0_2363_1,axiom,
    ( X3 = c_HOL_Ozero__class_Ozero(X2)
    | X1 = c_HOL_Ozero__class_Ozero(X2)
    | c_HOL_Otimes__class_Otimes(X3,X1,X2) != c_HOL_Ozero__class_Ozero(X2)
    | ~ class_Ring__and__Field_Ono__zero__divisors(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2363]) ).

cnf(c_0_2363_2,axiom,
    ( c_HOL_Otimes__class_Otimes(X3,X1,X2) != c_HOL_Ozero__class_Ozero(X2)
    | X3 = c_HOL_Ozero__class_Ozero(X2)
    | X1 = c_HOL_Ozero__class_Ozero(X2)
    | ~ class_Ring__and__Field_Ono__zero__divisors(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2363]) ).

cnf(c_0_2363_3,axiom,
    ( ~ class_Ring__and__Field_Ono__zero__divisors(X2)
    | c_HOL_Otimes__class_Otimes(X3,X1,X2) != c_HOL_Ozero__class_Ozero(X2)
    | X3 = c_HOL_Ozero__class_Ozero(X2)
    | X1 = c_HOL_Ozero__class_Ozero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2363]) ).

cnf(c_0_2364_0,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(X2)
    | X3 = c_HOL_Ozero__class_Ozero(X2)
    | c_HOL_Otimes__class_Otimes(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
    | ~ class_Ring__and__Field_Ono__zero__divisors(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2364]) ).

cnf(c_0_2364_1,axiom,
    ( X3 = c_HOL_Ozero__class_Ozero(X2)
    | X1 = c_HOL_Ozero__class_Ozero(X2)
    | c_HOL_Otimes__class_Otimes(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
    | ~ class_Ring__and__Field_Ono__zero__divisors(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2364]) ).

cnf(c_0_2364_2,axiom,
    ( c_HOL_Otimes__class_Otimes(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
    | X3 = c_HOL_Ozero__class_Ozero(X2)
    | X1 = c_HOL_Ozero__class_Ozero(X2)
    | ~ class_Ring__and__Field_Ono__zero__divisors(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2364]) ).

cnf(c_0_2364_3,axiom,
    ( ~ class_Ring__and__Field_Ono__zero__divisors(X2)
    | c_HOL_Otimes__class_Otimes(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
    | X3 = c_HOL_Ozero__class_Ozero(X2)
    | X1 = c_HOL_Ozero__class_Ozero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2364]) ).

cnf(c_0_2365_0,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(X2)
    | X3 = c_HOL_Ozero__class_Ozero(X2)
    | c_HOL_Otimes__class_Otimes(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
    | ~ class_Ring__and__Field_Oring__no__zero__divisors(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2365]) ).

cnf(c_0_2365_1,axiom,
    ( X3 = c_HOL_Ozero__class_Ozero(X2)
    | X1 = c_HOL_Ozero__class_Ozero(X2)
    | c_HOL_Otimes__class_Otimes(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
    | ~ class_Ring__and__Field_Oring__no__zero__divisors(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2365]) ).

cnf(c_0_2365_2,axiom,
    ( c_HOL_Otimes__class_Otimes(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
    | X3 = c_HOL_Ozero__class_Ozero(X2)
    | X1 = c_HOL_Ozero__class_Ozero(X2)
    | ~ class_Ring__and__Field_Oring__no__zero__divisors(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2365]) ).

cnf(c_0_2365_3,axiom,
    ( ~ class_Ring__and__Field_Oring__no__zero__divisors(X2)
    | c_HOL_Otimes__class_Otimes(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
    | X3 = c_HOL_Ozero__class_Ozero(X2)
    | X1 = c_HOL_Ozero__class_Ozero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2365]) ).

cnf(c_0_2366_0,axiom,
    ( X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2366]) ).

cnf(c_0_2366_1,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | X1 = X2
    | c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2366]) ).

cnf(c_0_2366_2,axiom,
    ( c_HOL_Oord__class_Oless(X2,X1,tc_nat)
    | c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_2366]) ).

cnf(c_0_2367_0,axiom,
    ( X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2367]) ).

cnf(c_0_2367_1,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | X1 = X2
    | c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2367]) ).

cnf(c_0_2367_2,axiom,
    ( c_HOL_Oord__class_Oless(X2,X1,tc_nat)
    | c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_2367]) ).

cnf(c_0_2368_0,axiom,
    ( X2 = c_HOL_Ozero__class_Ozero(X1)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2368]) ).

cnf(c_0_2368_1,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | X2 = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2368]) ).

cnf(c_0_2368_2,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | X2 = c_HOL_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2368]) ).

cnf(c_0_2369_0,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | c_Power_Opower__class_Opower(X2,X1,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    inference(literals_permutation,[status(thm)],[c_0_2369]) ).

cnf(c_0_2369_1,axiom,
    ( X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_Power_Opower__class_Opower(X2,X1,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    inference(literals_permutation,[status(thm)],[c_0_2369]) ).

cnf(c_0_2369_2,axiom,
    ( c_Power_Opower__class_Opower(X2,X1,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2369]) ).

cnf(c_0_2370_0,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2370]) ).

cnf(c_0_2370_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2370]) ).

cnf(c_0_2371_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_2371]) ).

cnf(c_0_2371_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_2371]) ).

cnf(c_0_2371_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_2371]) ).

cnf(c_0_2372_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_2372]) ).

cnf(c_0_2372_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_2372]) ).

cnf(c_0_2372_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_2372]) ).

cnf(c_0_2372_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_2372]) ).

cnf(c_0_2373_0,axiom,
    ( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | c_HOL_Otimes__class_Otimes(X2,X1,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    inference(literals_permutation,[status(thm)],[c_0_2373]) ).

cnf(c_0_2373_1,axiom,
    ( c_HOL_Otimes__class_Otimes(X2,X1,tc_nat) != 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_2373]) ).

cnf(c_0_2374_0,axiom,
    ( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    inference(literals_permutation,[status(thm)],[c_0_2374]) ).

cnf(c_0_2374_1,axiom,
    ( c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != 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_2374]) ).

cnf(c_0_2375_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_2375]) ).

cnf(c_0_2375_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_2375]) ).

cnf(c_0_2375_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_2375]) ).

cnf(c_0_2376_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_2376]) ).

cnf(c_0_2376_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_2376]) ).

cnf(c_0_2376_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_2376]) ).

cnf(c_0_2377_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_2377]) ).

cnf(c_0_2377_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_2377]) ).

cnf(c_0_2377_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_2377]) ).

cnf(c_0_2378_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_2378]) ).

cnf(c_0_2378_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_2378]) ).

cnf(c_0_2378_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_2378]) ).

cnf(c_0_2378_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_2378]) ).

cnf(c_0_2378_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_2378]) ).

cnf(c_0_2378_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_2378]) ).

cnf(c_0_2379_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_2379]) ).

cnf(c_0_2379_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_2379]) ).

cnf(c_0_2379_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_2379]) ).

cnf(c_0_2380_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_2380]) ).

cnf(c_0_2380_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_2380]) ).

cnf(c_0_2380_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_2380]) ).

cnf(c_0_2381_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_2381]) ).

cnf(c_0_2381_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_2381]) ).

cnf(c_0_2381_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_2381]) ).

cnf(c_0_2382_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_2382]) ).

cnf(c_0_2382_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_2382]) ).

cnf(c_0_2382_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_2382]) ).

cnf(c_0_2383_0,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X2 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2383]) ).

cnf(c_0_2383_1,axiom,
    ( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2383]) ).

cnf(c_0_2383_2,axiom,
    ( c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != 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_2383]) ).

cnf(c_0_2384_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
    | ~ class_Orderings_Oorder(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2384]) ).

cnf(c_0_2384_1,axiom,
    ( ~ class_Orderings_Oorder(X2)
    | ~ c_HOL_Oord__class_Oless(X1,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2384]) ).

cnf(c_0_2385_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
    | ~ class_Orderings_Olinorder(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2385]) ).

cnf(c_0_2385_1,axiom,
    ( ~ class_Orderings_Olinorder(X2)
    | ~ c_HOL_Oord__class_Oless(X1,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2385]) ).

cnf(c_0_2386_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
    | ~ class_Orderings_Opreorder(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2386]) ).

cnf(c_0_2386_1,axiom,
    ( ~ class_Orderings_Opreorder(X2)
    | ~ c_HOL_Oord__class_Oless(X1,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2386]) ).

cnf(c_0_2387_0,axiom,
    ( X1 = c_HOL_Oone__class_Oone(tc_nat)
    | X2 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_HOL_Otimes__class_Otimes(X2,X1,tc_nat) != X2 ),
    inference(literals_permutation,[status(thm)],[c_0_2387]) ).

cnf(c_0_2387_1,axiom,
    ( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X1 = c_HOL_Oone__class_Oone(tc_nat)
    | c_HOL_Otimes__class_Otimes(X2,X1,tc_nat) != X2 ),
    inference(literals_permutation,[status(thm)],[c_0_2387]) ).

cnf(c_0_2387_2,axiom,
    ( c_HOL_Otimes__class_Otimes(X2,X1,tc_nat) != X2
    | X2 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X1 = c_HOL_Oone__class_Oone(tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2387]) ).

cnf(c_0_2388_0,axiom,
    ( X1 = c_HOL_Oone__class_Oone(tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2388]) ).

cnf(c_0_2388_1,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
    | X1 = c_HOL_Oone__class_Oone(tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2388]) ).

cnf(c_0_2389_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_2389]) ).

cnf(c_0_2389_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_2389]) ).

cnf(c_0_2389_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_2389]) ).

cnf(c_0_2390_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_2390]) ).

cnf(c_0_2390_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_2390]) ).

cnf(c_0_2390_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_2390]) ).

cnf(c_0_2391_0,axiom,
    ( X1 = c_HOL_Oone__class_Oone(tc_nat)
    | c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_HOL_Oone__class_Oone(tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2391]) ).

cnf(c_0_2391_1,axiom,
    ( c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_HOL_Oone__class_Oone(tc_nat)
    | X1 = c_HOL_Oone__class_Oone(tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2391]) ).

cnf(c_0_2392_0,axiom,
    ( X1 = c_HOL_Oone__class_Oone(tc_nat)
    | c_HOL_Otimes__class_Otimes(X2,X1,tc_nat) != c_HOL_Oone__class_Oone(tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2392]) ).

cnf(c_0_2392_1,axiom,
    ( c_HOL_Otimes__class_Otimes(X2,X1,tc_nat) != c_HOL_Oone__class_Oone(tc_nat)
    | X1 = c_HOL_Oone__class_Oone(tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2392]) ).

cnf(c_0_2393_0,axiom,
    ( X1 = c_HOL_Oone__class_Oone(tc_nat)
    | c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_HOL_Oone__class_Oone(tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2393]) ).

cnf(c_0_2393_1,axiom,
    ( c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) != c_HOL_Oone__class_Oone(tc_nat)
    | X1 = c_HOL_Oone__class_Oone(tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2393]) ).

cnf(c_0_2394_0,axiom,
    ( X1 = c_HOL_Oone__class_Oone(tc_nat)
    | c_HOL_Otimes__class_Otimes(X2,X1,tc_nat) != c_HOL_Oone__class_Oone(tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2394]) ).

cnf(c_0_2394_1,axiom,
    ( c_HOL_Otimes__class_Otimes(X2,X1,tc_nat) != c_HOL_Oone__class_Oone(tc_nat)
    | X1 = c_HOL_Oone__class_Oone(tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2394]) ).

cnf(c_0_2395_0,axiom,
    ( X1 = X2
    | ~ c_fequal(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2395]) ).

cnf(c_0_2395_1,axiom,
    ( ~ c_fequal(X1,X2,X3)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_2395]) ).

cnf(c_0_2396_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_2396]) ).

cnf(c_0_2396_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_2396]) ).

cnf(c_0_2396_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_2396]) ).

cnf(c_0_2397_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_2397]) ).

cnf(c_0_2397_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_2397]) ).

cnf(c_0_2397_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_2397]) ).

cnf(c_0_2397_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_2397]) ).

cnf(c_0_2398_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_2398]) ).

cnf(c_0_2398_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_2398]) ).

cnf(c_0_2399_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_2399]) ).

cnf(c_0_2399_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_2399]) ).

cnf(c_0_2399_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_2399]) ).

cnf(c_0_2400_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_2400]) ).

cnf(c_0_2400_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_2400]) ).

cnf(c_0_2401_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_2401]) ).

cnf(c_0_2401_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_2401]) ).

cnf(c_0_2402_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_2402]) ).

cnf(c_0_2402_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_2402]) ).

cnf(c_0_2403_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_2403]) ).

cnf(c_0_2403_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_2403]) ).

cnf(c_0_2404_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_2404]) ).

cnf(c_0_2404_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_2404]) ).

cnf(c_0_2405_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oone__class_Oone(X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2405]) ).

cnf(c_0_2405_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oone__class_Oone(X1),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2405]) ).

cnf(c_0_2406_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_2406]) ).

cnf(c_0_2406_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_2406]) ).

cnf(c_0_2406_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_2406]) ).

cnf(c_0_2407_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_2407]) ).

cnf(c_0_2407_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_2407]) ).

cnf(c_0_2408_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_2408]) ).

cnf(c_0_2408_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_2408]) ).

cnf(c_0_2409_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_2409]) ).

cnf(c_0_2409_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_2409]) ).

cnf(c_0_2410_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_2410]) ).

cnf(c_0_2410_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_2410]) ).

cnf(c_0_2411_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_2411]) ).

cnf(c_0_2411_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_2411]) ).

cnf(c_0_2412_0,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2412]) ).

cnf(c_0_2412_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
    | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2412]) ).

cnf(c_0_2413_0,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Omult__zero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2413]) ).

cnf(c_0_2413_1,axiom,
    ( ~ class_Ring__and__Field_Omult__zero(X1)
    | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2413]) ).

cnf(c_0_2414_0,axiom,
    ( c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X2),X2) = c_HOL_Ozero__class_Ozero(X2)
    | ~ class_Ring__and__Field_Omult__zero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2414]) ).

cnf(c_0_2414_1,axiom,
    ( ~ class_Ring__and__Field_Omult__zero(X2)
    | c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X2),X2) = c_HOL_Ozero__class_Ozero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2414]) ).

cnf(c_0_2415_0,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Oring__no__zero__divisors(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2415]) ).

cnf(c_0_2415_1,axiom,
    ( ~ class_Ring__and__Field_Oring__no__zero__divisors(X1)
    | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2415]) ).

cnf(c_0_2416_0,axiom,
    ( c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X2),X2) = c_HOL_Ozero__class_Ozero(X2)
    | ~ class_Ring__and__Field_Oring__no__zero__divisors(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2416]) ).

cnf(c_0_2416_1,axiom,
    ( ~ class_Ring__and__Field_Oring__no__zero__divisors(X2)
    | c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X2),X2) = c_HOL_Ozero__class_Ozero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2416]) ).

cnf(c_0_2417_0,axiom,
    ( c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X2),X2) = c_HOL_Ozero__class_Ozero(X2)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2417]) ).

cnf(c_0_2417_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
    | c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X2),X2) = c_HOL_Ozero__class_Ozero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2417]) ).

cnf(c_0_2418_0,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2418]) ).

cnf(c_0_2418_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
    | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2418]) ).

cnf(c_0_2419_0,axiom,
    ( c_Divides_Odiv__class_Odiv(X1,c_HOL_Ozero__class_Ozero(X2),X2) = c_HOL_Ozero__class_Ozero(X2)
    | ~ class_Divides_Osemiring__div(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2419]) ).

cnf(c_0_2419_1,axiom,
    ( ~ class_Divides_Osemiring__div(X2)
    | c_Divides_Odiv__class_Odiv(X1,c_HOL_Ozero__class_Ozero(X2),X2) = c_HOL_Ozero__class_Ozero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2419]) ).

cnf(c_0_2420_0,axiom,
    ( c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2420]) ).

cnf(c_0_2420_1,axiom,
    ( ~ class_Divides_Osemiring__div(X1)
    | c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2420]) ).

cnf(c_0_2421_0,axiom,
    ( c_Divides_Odiv__class_Omod(X1,c_HOL_Oone__class_Oone(X2),X2) = c_HOL_Ozero__class_Ozero(X2)
    | ~ class_Divides_Osemiring__div(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2421]) ).

cnf(c_0_2421_1,axiom,
    ( ~ class_Divides_Osemiring__div(X2)
    | c_Divides_Odiv__class_Omod(X1,c_HOL_Oone__class_Oone(X2),X2) = c_HOL_Ozero__class_Ozero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2421]) ).

cnf(c_0_2422_0,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2422]) ).

cnf(c_0_2422_1,axiom,
    ( ~ class_Divides_Osemiring__div(X1)
    | c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2422]) ).

cnf(c_0_2423_0,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(X2)
    | c_Divides_Odiv__class_Odiv(X1,X1,X2) = c_HOL_Oone__class_Oone(X2)
    | ~ class_Divides_Osemiring__div(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2423]) ).

cnf(c_0_2423_1,axiom,
    ( c_Divides_Odiv__class_Odiv(X1,X1,X2) = c_HOL_Oone__class_Oone(X2)
    | X1 = c_HOL_Ozero__class_Ozero(X2)
    | ~ class_Divides_Osemiring__div(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2423]) ).

cnf(c_0_2423_2,axiom,
    ( ~ class_Divides_Osemiring__div(X2)
    | c_Divides_Odiv__class_Odiv(X1,X1,X2) = c_HOL_Oone__class_Oone(X2)
    | X1 = c_HOL_Ozero__class_Ozero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2423]) ).

cnf(c_0_2424_0,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X1),X2,X1) = X2
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2424]) ).

cnf(c_0_2424_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
    | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X1),X2,X1) = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_2424]) ).

cnf(c_0_2425_0,axiom,
    ( c_HOL_Otimes__class_Otimes(X1,c_HOL_Oone__class_Oone(X2),X2) = X1
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2425]) ).

cnf(c_0_2425_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
    | c_HOL_Otimes__class_Otimes(X1,c_HOL_Oone__class_Oone(X2),X2) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_2425]) ).

cnf(c_0_2426_0,axiom,
    ( c_HOL_Otimes__class_Otimes(X1,c_HOL_Oone__class_Oone(X2),X2) = X1
    | ~ class_OrderedGroup_Omonoid__mult(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2426]) ).

cnf(c_0_2426_1,axiom,
    ( ~ class_OrderedGroup_Omonoid__mult(X2)
    | c_HOL_Otimes__class_Otimes(X1,c_HOL_Oone__class_Oone(X2),X2) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_2426]) ).

cnf(c_0_2427_0,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X1),X2,X1) = X2
    | ~ class_OrderedGroup_Omonoid__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2427]) ).

cnf(c_0_2427_1,axiom,
    ( ~ class_OrderedGroup_Omonoid__mult(X1)
    | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X1),X2,X1) = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_2427]) ).

cnf(c_0_2428_0,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X1),X2,X1) = X2
    | ~ class_OrderedGroup_Ocomm__monoid__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2428]) ).

cnf(c_0_2428_1,axiom,
    ( ~ class_OrderedGroup_Ocomm__monoid__mult(X1)
    | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X1),X2,X1) = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_2428]) ).

cnf(c_0_2429_0,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X1),X2,X1) = X2
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2429]) ).

cnf(c_0_2429_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
    | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X1),X2,X1) = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_2429]) ).

cnf(c_0_2430_0,axiom,
    ( c_Divides_Odiv__class_Odiv(X1,c_HOL_Oone__class_Oone(X2),X2) = X1
    | ~ class_Divides_Osemiring__div(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2430]) ).

cnf(c_0_2430_1,axiom,
    ( ~ class_Divides_Osemiring__div(X2)
    | c_Divides_Odiv__class_Odiv(X1,c_HOL_Oone__class_Oone(X2),X2) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_2430]) ).

cnf(c_0_2431_0,axiom,
    ( c_Divides_Odiv__class_Omod(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1
    | ~ class_Divides_Osemiring__div(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2431]) ).

cnf(c_0_2431_1,axiom,
    ( ~ class_Divides_Osemiring__div(X2)
    | c_Divides_Odiv__class_Omod(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_2431]) ).

cnf(c_0_2432_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_2432]) ).

cnf(c_0_2432_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_2432]) ).

cnf(c_0_2433_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_2433]) ).

cnf(c_0_2433_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_2433]) ).

cnf(c_0_2434_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2434]) ).

cnf(c_0_2434_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ozero__class_Ozero(X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2434]) ).

cnf(c_0_2435_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(X1),X2,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2435]) ).

cnf(c_0_2435_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
    | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(X1),X2,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2435]) ).

cnf(c_0_2436_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_2436]) ).

cnf(c_0_2436_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_2436]) ).

cnf(c_0_2437_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_2437]) ).

cnf(c_0_2437_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_2437]) ).

cnf(c_0_2438_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_2438]) ).

cnf(c_0_2438_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_2438]) ).

cnf(c_0_2439_0,axiom,
    ( c_Power_Opower__class_Opower(X1,c_HOL_Oone__class_Oone(tc_nat),X2) = X1
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2439]) ).

cnf(c_0_2439_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
    | c_Power_Opower__class_Opower(X1,c_HOL_Oone__class_Oone(tc_nat),X2) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_2439]) ).

cnf(c_0_2440_0,axiom,
    ( c_Power_Opower__class_Opower(X1,c_HOL_Oone__class_Oone(tc_nat),X2) = X1
    | ~ class_OrderedGroup_Omonoid__mult(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2440]) ).

cnf(c_0_2440_1,axiom,
    ( ~ class_OrderedGroup_Omonoid__mult(X2)
    | c_Power_Opower__class_Opower(X1,c_HOL_Oone__class_Oone(tc_nat),X2) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_2440]) ).

cnf(c_0_2441_0,axiom,
    ( c_Divides_Odiv__class_Omod(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
    | ~ class_Divides_Osemiring__div(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2441]) ).

cnf(c_0_2441_1,axiom,
    ( ~ class_Divides_Osemiring__div(X2)
    | c_Divides_Odiv__class_Omod(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2441]) ).

cnf(c_0_2442_0,axiom,
    ( c_HOL_Otimes__class_Otimes(X1,X1,X2) = X1
    | ~ class_OrderedGroup_Oab__semigroup__idem__mult(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2442]) ).

cnf(c_0_2442_1,axiom,
    ( ~ class_OrderedGroup_Oab__semigroup__idem__mult(X2)
    | c_HOL_Otimes__class_Otimes(X1,X1,X2) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_2442]) ).

cnf(c_0_2443_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,X1,X2)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2443]) ).

cnf(c_0_2443_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2443]) ).

cnf(c_0_2444_0,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2444]) ).

cnf(c_0_2444_1,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2444]) ).

cnf(c_0_2445_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_2445]) ).

cnf(c_0_2445_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_2445]) ).

cnf(c_0_2445_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_2445]) ).

cnf(c_0_2446_0,axiom,
    ( c_Lambda_Obeta(c_Lambda_OdB_OAbs(X1),c_Lambda_OdB_OAbs(X2))
    | ~ c_Lambda_Obeta(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2446]) ).

cnf(c_0_2446_1,axiom,
    ( ~ c_Lambda_Obeta(X1,X2)
    | c_Lambda_Obeta(c_Lambda_OdB_OAbs(X1),c_Lambda_OdB_OAbs(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_2446]) ).

cnf(c_0_2447_0,axiom,
    ( class_Orderings_Opreorder(tc_fun(X2,X1))
    | ~ class_Orderings_Opreorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2447]) ).

cnf(c_0_2447_1,axiom,
    ( ~ class_Orderings_Opreorder(X1)
    | class_Orderings_Opreorder(tc_fun(X2,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_2447]) ).

cnf(c_0_2448_0,axiom,
    ( class_Orderings_Oorder(tc_fun(X2,X1))
    | ~ class_Orderings_Oorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2448]) ).

cnf(c_0_2448_1,axiom,
    ( ~ class_Orderings_Oorder(X1)
    | class_Orderings_Oorder(tc_fun(X2,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_2448]) ).

cnf(c_0_2449_0,axiom,
    ( c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),X1) = c_HOL_Oone__class_Oone(X1)
    | ~ class_Ring__and__Field_Osemiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2449]) ).

cnf(c_0_2449_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring__1(X1)
    | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),X1) = c_HOL_Oone__class_Oone(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2449]) ).

cnf(c_0_2450_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_2450]) ).

cnf(c_0_2450_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_2450]) ).

cnf(c_0_2451_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_2451]) ).

cnf(c_0_2451_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_2451]) ).

cnf(c_0_2452_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_2452]) ).

cnf(c_0_2452_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_2452]) ).

cnf(c_0_2453_0,axiom,
    ( X1 = X2
    | c_Lambda_OdB_OAbs(X1) != c_Lambda_OdB_OAbs(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2453]) ).

cnf(c_0_2453_1,axiom,
    ( c_Lambda_OdB_OAbs(X1) != c_Lambda_OdB_OAbs(X2)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_2453]) ).

cnf(c_0_2454_0,axiom,
    ( X1 = X2
    | c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OVar(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2454]) ).

cnf(c_0_2454_1,axiom,
    ( c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OVar(X2)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_2454]) ).

cnf(c_0_2455_0,axiom,
    ( X1 = X2
    | c_Suc(X1) != c_Suc(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2455]) ).

cnf(c_0_2455_1,axiom,
    ( c_Suc(X1) != c_Suc(X2)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_2455]) ).

cnf(c_0_2456_0,axiom,
    ( X1 = X2
    | c_Suc(X1) != c_Suc(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2456]) ).

cnf(c_0_2456_1,axiom,
    ( c_Suc(X1) != c_Suc(X2)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_2456]) ).

cnf(c_0_2457_0,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_Suc(c_ATP__Linkup_Osko__Nat__Xnat__Xexhaust__1__1(X1)) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_2457]) ).

cnf(c_0_2457_1,axiom,
    ( c_Suc(c_ATP__Linkup_Osko__Nat__Xnat__Xexhaust__1__1(X1)) = X1
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2457]) ).

cnf(c_0_2458_0,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_Suc(c_ATP__Linkup_Osko__Nat__Xnat__Xnchotomy__1__1(X1)) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_2458]) ).

cnf(c_0_2458_1,axiom,
    ( c_Suc(c_ATP__Linkup_Osko__Nat__Xnat__Xnchotomy__1__1(X1)) = X1
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2458]) ).

cnf(c_0_2459_0,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_Suc(c_ATP__Linkup_Osko__Nat__Xnot0__implies__Suc__1__1(X1)) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_2459]) ).

cnf(c_0_2459_1,axiom,
    ( c_Suc(c_ATP__Linkup_Osko__Nat__Xnot0__implies__Suc__1__1(X1)) = X1
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2459]) ).

% CNF of non-axioms
% Start CNF derivation
fof(c_0_0_771,negated_conjecture,
    ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),c_Lambda_OdB_OVar(c_Suc(v_ia))),c_Suc(v_ja))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(v_ia)),v_ja)),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,c_Lambda_OdB_OVar(v_ia),tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_ja,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
    file('<stdin>',cls_conjecture_4) ).

fof(c_0_1_772,negated_conjecture,
    ! [X1,X2] : hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),c_Lambda_OdB_OVar(c_Suc(X2))),c_Suc(X1))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(X2)),X1)),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,c_Lambda_OdB_OVar(X2),tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),X1,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
    file('<stdin>',cls_conjecture_1) ).

fof(c_0_2_773,negated_conjecture,
    hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),v_s),c_HOL_Ozero__class_Ozero(tc_nat)),v_ss,tc_Lambda_OdB,tc_Lambda_OdB))),
    file('<stdin>',cls_conjecture_0) ).

fof(c_0_3_774,negated_conjecture,
    ! [X1,X2] : hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(X2)),X1))),
    file('<stdin>',cls_conjecture_3) ).

fof(c_0_4_775,negated_conjecture,
    hBOOL(hAPP(c_InductTermi_OIT,v_s)),
    file('<stdin>',cls_conjecture_2) ).

fof(c_0_5_776,negated_conjecture,
    ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),c_Lambda_OdB_OVar(c_Suc(v_ia))),c_Suc(v_ja))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(v_ia)),v_ja)),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,c_Lambda_OdB_OVar(v_ia),tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_ja,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
    inference(fof_simplification,[status(thm)],[c_0_0]) ).

fof(c_0_6_777,negated_conjecture,
    ! [X1,X2] : hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),c_Lambda_OdB_OVar(c_Suc(X2))),c_Suc(X1))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(X2)),X1)),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,c_Lambda_OdB_OVar(X2),tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),X1,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
    c_0_1 ).

fof(c_0_7_778,negated_conjecture,
    hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),v_s),c_HOL_Ozero__class_Ozero(tc_nat)),v_ss,tc_Lambda_OdB,tc_Lambda_OdB))),
    c_0_2 ).

fof(c_0_8_779,negated_conjecture,
    ! [X1,X2] : hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(X2)),X1))),
    c_0_3 ).

fof(c_0_9_780,negated_conjecture,
    hBOOL(hAPP(c_InductTermi_OIT,v_s)),
    c_0_4 ).

fof(c_0_10_781,negated_conjecture,
    ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),c_Lambda_OdB_OVar(c_Suc(v_ia))),c_Suc(v_ja))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(v_ia)),v_ja)),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,c_Lambda_OdB_OVar(v_ia),tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_ja,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
    c_0_5 ).

fof(c_0_11_782,negated_conjecture,
    ! [X3,X4] : hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),c_Lambda_OdB_OVar(c_Suc(X4))),c_Suc(X3))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(X4)),X3)),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,c_Lambda_OdB_OVar(X4),tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),X3,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
    inference(variable_rename,[status(thm)],[c_0_6]) ).

fof(c_0_12_783,negated_conjecture,
    hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),v_s),c_HOL_Ozero__class_Ozero(tc_nat)),v_ss,tc_Lambda_OdB,tc_Lambda_OdB))),
    c_0_7 ).

fof(c_0_13_784,negated_conjecture,
    ! [X3,X4] : hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(X4)),X3))),
    inference(variable_rename,[status(thm)],[c_0_8]) ).

fof(c_0_14_785,negated_conjecture,
    hBOOL(hAPP(c_InductTermi_OIT,v_s)),
    c_0_9 ).

cnf(c_0_15_786,negated_conjecture,
    ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),c_Lambda_OdB_OVar(c_Suc(v_ia))),c_Suc(v_ja))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(v_ia)),v_ja)),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,c_Lambda_OdB_OVar(v_ia),tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_ja,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_16_787,negated_conjecture,
    hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),c_Lambda_OdB_OVar(c_Suc(X1))),c_Suc(X2))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(X1)),X2)),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,c_Lambda_OdB_OVar(X1),tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),X2,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_17_788,negated_conjecture,
    hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),v_s),c_HOL_Ozero__class_Ozero(tc_nat)),v_ss,tc_Lambda_OdB,tc_Lambda_OdB))),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_18_789,negated_conjecture,
    hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(X1)),X2))),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_19_790,negated_conjecture,
    hBOOL(hAPP(c_InductTermi_OIT,v_s)),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_20_791,negated_conjecture,
    ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),c_Lambda_OdB_OVar(c_Suc(v_ia))),c_Suc(v_ja))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(v_ia)),v_ja)),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,c_Lambda_OdB_OVar(v_ia),tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_ja,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
    c_0_15,
    [final] ).

cnf(c_0_21_792,negated_conjecture,
    hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),c_Lambda_OdB_OVar(c_Suc(X1))),c_Suc(X2))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(X1)),X2)),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,c_Lambda_OdB_OVar(X1),tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),X2,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
    c_0_16,
    [final] ).

cnf(c_0_22_793,negated_conjecture,
    hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),v_s),c_HOL_Ozero__class_Ozero(tc_nat)),v_ss,tc_Lambda_OdB,tc_Lambda_OdB))),
    c_0_17,
    [final] ).

cnf(c_0_23_794,negated_conjecture,
    hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(X1)),X2))),
    c_0_18,
    [final] ).

cnf(c_0_24_795,negated_conjecture,
    hBOOL(hAPP(c_InductTermi_OIT,v_s)),
    c_0_19,
    [final] ).

% End CNF derivation

%-------------------------------------------------------------
% Proof by iprover

cnf(c_1469,negated_conjecture,
    ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),c_Lambda_OdB_OVar(c_Suc(v_ia))),c_Suc(v_ja))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(v_ia)),v_ja)),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,c_Lambda_OdB_OVar(v_ia),tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_ja,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
    file('/export/starexec/sandbox/tmp/iprover_modulo_409ec3.p',c_0_20) ).

cnf(c_1824,negated_conjecture,
    ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),c_Lambda_OdB_OVar(c_Suc(v_ia))),c_Suc(v_ja))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(v_ia)),v_ja)),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,c_Lambda_OdB_OVar(v_ia),tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_ja,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
    inference(copy,[status(esa)],[c_1469]) ).

cnf(c_1844,negated_conjecture,
    ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),c_Lambda_OdB_OVar(c_Suc(v_ia))),c_Suc(v_ja))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(v_ia)),v_ja)),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,c_Lambda_OdB_OVar(v_ia),tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_ja,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
    inference(copy,[status(esa)],[c_1824]) ).

cnf(c_1853,negated_conjecture,
    ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),c_Lambda_OdB_OVar(c_Suc(v_ia))),c_Suc(v_ja))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(v_ia)),v_ja)),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,c_Lambda_OdB_OVar(v_ia),tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_ja,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
    inference(copy,[status(esa)],[c_1844]) ).

cnf(c_1854,negated_conjecture,
    ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),c_Lambda_OdB_OVar(c_Suc(v_ia))),c_Suc(v_ja))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(v_ia)),v_ja)),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,c_Lambda_OdB_OVar(v_ia),tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_ja,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
    inference(copy,[status(esa)],[c_1853]) ).

cnf(c_6194,negated_conjecture,
    ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),c_Lambda_OdB_OVar(c_Suc(v_ia))),c_Suc(v_ja))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(v_ia)),v_ja)),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,c_Lambda_OdB_OVar(v_ia),tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_ja,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
    inference(copy,[status(esa)],[c_1854]) ).

cnf(c_1470,negated_conjecture,
    hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),c_Lambda_OdB_OVar(c_Suc(X0))),c_Suc(X1))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(X0)),X1)),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,c_Lambda_OdB_OVar(X0),tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),X1,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
    file('/export/starexec/sandbox/tmp/iprover_modulo_409ec3.p',c_0_21) ).

cnf(c_1826,negated_conjecture,
    hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),c_Lambda_OdB_OVar(c_Suc(X0))),c_Suc(X1))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(X0)),X1)),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,c_Lambda_OdB_OVar(X0),tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),X1,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
    inference(copy,[status(esa)],[c_1470]) ).

cnf(c_1845,negated_conjecture,
    hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),c_Lambda_OdB_OVar(c_Suc(X0))),c_Suc(X1))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(X0)),X1)),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,c_Lambda_OdB_OVar(X0),tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),X1,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
    inference(copy,[status(esa)],[c_1826]) ).

cnf(c_1852,negated_conjecture,
    hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),c_Lambda_OdB_OVar(c_Suc(X0))),c_Suc(X1))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(X0)),X1)),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,c_Lambda_OdB_OVar(X0),tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),X1,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
    inference(copy,[status(esa)],[c_1845]) ).

cnf(c_1855,negated_conjecture,
    hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),c_Lambda_OdB_OVar(c_Suc(X0))),c_Suc(X1))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(X0)),X1)),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,c_Lambda_OdB_OVar(X0),tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),X1,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
    inference(copy,[status(esa)],[c_1852]) ).

cnf(c_6196,negated_conjecture,
    hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),c_Lambda_OdB_OVar(c_Suc(X0))),c_Suc(X1))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(X0)),X1)),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,c_Lambda_OdB_OVar(X0),tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),X1,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
    inference(copy,[status(esa)],[c_1855]) ).

cnf(c_6213,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_6194,c_6196]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : LCL760-1 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.13  % Command  : iprover_modulo %s %d
% 0.13/0.34  % Computer : n015.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Sat Jul  2 16:14:44 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.35  % Running in mono-core mode
% 0.35/0.54  % Orienting using strategy Equiv(ClausalAll)
% 0.35/0.54  % Orientation found
% 0.35/0.54  % 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_43fe78.s --tptp_safe_out true --time_out_real 150 /export/starexec/sandbox/tmp/iprover_modulo_409ec3.p | tee /export/starexec/sandbox/tmp/iprover_modulo_out_653f3f | grep -v "SZS"
% 0.40/0.56  
% 0.40/0.56  %---------------- iProver v2.5 (CASC-J8 2016) ----------------%
% 0.40/0.56  
% 0.40/0.56  % 
% 0.40/0.56  % ------  iProver source info 
% 0.40/0.56  
% 0.40/0.56  % git: sha1: 57accf6c58032223c7708532cf852a99fa48c1b3
% 0.40/0.56  % git: non_committed_changes: true
% 0.40/0.56  % git: last_make_outside_of_git: true
% 0.40/0.56  
% 0.40/0.56  % 
% 0.40/0.56  % ------ Input Options
% 0.40/0.56  
% 0.40/0.56  % --out_options                         all
% 0.40/0.56  % --tptp_safe_out                       true
% 0.40/0.56  % --problem_path                        ""
% 0.40/0.56  % --include_path                        ""
% 0.40/0.56  % --clausifier                          .//eprover
% 0.40/0.56  % --clausifier_options                  --tstp-format  
% 0.40/0.56  % --stdin                               false
% 0.40/0.56  % --dbg_backtrace                       false
% 0.40/0.56  % --dbg_dump_prop_clauses               false
% 0.40/0.56  % --dbg_dump_prop_clauses_file          -
% 0.40/0.56  % --dbg_out_stat                        false
% 0.40/0.56  
% 0.40/0.56  % ------ General Options
% 0.40/0.56  
% 0.40/0.56  % --fof                                 false
% 0.40/0.56  % --time_out_real                       150.
% 0.40/0.56  % --time_out_prep_mult                  0.2
% 0.40/0.56  % --time_out_virtual                    -1.
% 0.40/0.56  % --schedule                            none
% 0.40/0.56  % --ground_splitting                    input
% 0.40/0.56  % --splitting_nvd                       16
% 0.40/0.56  % --non_eq_to_eq                        false
% 0.40/0.56  % --prep_gs_sim                         true
% 0.40/0.56  % --prep_unflatten                      false
% 0.40/0.56  % --prep_res_sim                        true
% 0.40/0.56  % --prep_upred                          true
% 0.40/0.56  % --res_sim_input                       true
% 0.40/0.56  % --clause_weak_htbl                    true
% 0.40/0.56  % --gc_record_bc_elim                   false
% 0.40/0.56  % --symbol_type_check                   false
% 0.40/0.56  % --clausify_out                        false
% 0.40/0.56  % --large_theory_mode                   false
% 0.40/0.56  % --prep_sem_filter                     none
% 0.40/0.56  % --prep_sem_filter_out                 false
% 0.40/0.56  % --preprocessed_out                    false
% 0.40/0.56  % --sub_typing                          false
% 0.40/0.56  % --brand_transform                     false
% 0.40/0.56  % --pure_diseq_elim                     true
% 0.40/0.56  % --min_unsat_core                      false
% 0.40/0.56  % --pred_elim                           true
% 0.40/0.56  % --add_important_lit                   false
% 0.40/0.56  % --soft_assumptions                    false
% 0.40/0.56  % --reset_solvers                       false
% 0.40/0.56  % --bc_imp_inh                          []
% 0.40/0.56  % --conj_cone_tolerance                 1.5
% 0.40/0.56  % --prolific_symb_bound                 500
% 0.40/0.56  % --lt_threshold                        2000
% 0.40/0.56  
% 0.40/0.56  % ------ SAT Options
% 0.40/0.56  
% 0.40/0.56  % --sat_mode                            false
% 0.40/0.56  % --sat_fm_restart_options              ""
% 0.40/0.56  % --sat_gr_def                          false
% 0.40/0.56  % --sat_epr_types                       true
% 0.40/0.56  % --sat_non_cyclic_types                false
% 0.40/0.56  % --sat_finite_models                   false
% 0.40/0.56  % --sat_fm_lemmas                       false
% 0.40/0.56  % --sat_fm_prep                         false
% 0.40/0.56  % --sat_fm_uc_incr                      true
% 0.40/0.56  % --sat_out_model                       small
% 0.40/0.56  % --sat_out_clauses                     false
% 0.40/0.56  
% 0.40/0.56  % ------ QBF Options
% 0.40/0.56  
% 0.40/0.56  % --qbf_mode                            false
% 0.40/0.56  % --qbf_elim_univ                       true
% 0.40/0.56  % --qbf_sk_in                           true
% 0.40/0.56  % --qbf_pred_elim                       true
% 0.40/0.56  % --qbf_split                           32
% 0.40/0.56  
% 0.40/0.56  % ------ BMC1 Options
% 0.40/0.56  
% 0.40/0.56  % --bmc1_incremental                    false
% 0.40/0.56  % --bmc1_axioms                         reachable_all
% 0.40/0.56  % --bmc1_min_bound                      0
% 0.40/0.56  % --bmc1_max_bound                      -1
% 0.40/0.56  % --bmc1_max_bound_default              -1
% 0.40/0.56  % --bmc1_symbol_reachability            true
% 0.40/0.56  % --bmc1_property_lemmas                false
% 0.40/0.56  % --bmc1_k_induction                    false
% 0.40/0.56  % --bmc1_non_equiv_states               false
% 0.40/0.56  % --bmc1_deadlock                       false
% 0.40/0.56  % --bmc1_ucm                            false
% 0.40/0.56  % --bmc1_add_unsat_core                 none
% 0.40/0.56  % --bmc1_unsat_core_children            false
% 0.40/0.56  % --bmc1_unsat_core_extrapolate_axioms  false
% 0.40/0.56  % --bmc1_out_stat                       full
% 0.40/0.56  % --bmc1_ground_init                    false
% 0.40/0.56  % --bmc1_pre_inst_next_state            false
% 0.40/0.56  % --bmc1_pre_inst_state                 false
% 0.40/0.56  % --bmc1_pre_inst_reach_state           false
% 0.40/0.56  % --bmc1_out_unsat_core                 false
% 0.40/0.56  % --bmc1_aig_witness_out                false
% 0.40/0.56  % --bmc1_verbose                        false
% 0.40/0.56  % --bmc1_dump_clauses_tptp              false
% 2.92/3.36  % --bmc1_dump_unsat_core_tptp           false
% 2.92/3.36  % --bmc1_dump_file                      -
% 2.92/3.36  % --bmc1_ucm_expand_uc_limit            128
% 2.92/3.36  % --bmc1_ucm_n_expand_iterations        6
% 2.92/3.36  % --bmc1_ucm_extend_mode                1
% 2.92/3.36  % --bmc1_ucm_init_mode                  2
% 2.92/3.36  % --bmc1_ucm_cone_mode                  none
% 2.92/3.36  % --bmc1_ucm_reduced_relation_type      0
% 2.92/3.36  % --bmc1_ucm_relax_model                4
% 2.92/3.36  % --bmc1_ucm_full_tr_after_sat          true
% 2.92/3.36  % --bmc1_ucm_expand_neg_assumptions     false
% 2.92/3.36  % --bmc1_ucm_layered_model              none
% 2.92/3.36  % --bmc1_ucm_max_lemma_size             10
% 2.92/3.36  
% 2.92/3.36  % ------ AIG Options
% 2.92/3.36  
% 2.92/3.36  % --aig_mode                            false
% 2.92/3.36  
% 2.92/3.36  % ------ Instantiation Options
% 2.92/3.36  
% 2.92/3.36  % --instantiation_flag                  true
% 2.92/3.36  % --inst_lit_sel                        [+prop;+sign;+ground;-num_var;-num_symb]
% 2.92/3.36  % --inst_solver_per_active              750
% 2.92/3.36  % --inst_solver_calls_frac              0.5
% 2.92/3.36  % --inst_passive_queue_type             priority_queues
% 2.92/3.36  % --inst_passive_queues                 [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 2.92/3.36  % --inst_passive_queues_freq            [25;2]
% 2.92/3.36  % --inst_dismatching                    true
% 2.92/3.36  % --inst_eager_unprocessed_to_passive   true
% 2.92/3.36  % --inst_prop_sim_given                 true
% 2.92/3.36  % --inst_prop_sim_new                   false
% 2.92/3.36  % --inst_orphan_elimination             true
% 2.92/3.36  % --inst_learning_loop_flag             true
% 2.92/3.36  % --inst_learning_start                 3000
% 2.92/3.36  % --inst_learning_factor                2
% 2.92/3.36  % --inst_start_prop_sim_after_learn     3
% 2.92/3.36  % --inst_sel_renew                      solver
% 2.92/3.36  % --inst_lit_activity_flag              true
% 2.92/3.36  % --inst_out_proof                      true
% 2.92/3.36  
% 2.92/3.36  % ------ Resolution Options
% 2.92/3.36  
% 2.92/3.36  % --resolution_flag                     true
% 2.92/3.36  % --res_lit_sel                         kbo_max
% 2.92/3.36  % --res_to_prop_solver                  none
% 2.92/3.36  % --res_prop_simpl_new                  false
% 2.92/3.36  % --res_prop_simpl_given                false
% 2.92/3.36  % --res_passive_queue_type              priority_queues
% 2.92/3.36  % --res_passive_queues                  [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 2.92/3.36  % --res_passive_queues_freq             [15;5]
% 2.92/3.36  % --res_forward_subs                    full
% 2.92/3.36  % --res_backward_subs                   full
% 2.92/3.36  % --res_forward_subs_resolution         true
% 2.92/3.36  % --res_backward_subs_resolution        true
% 2.92/3.36  % --res_orphan_elimination              false
% 2.92/3.36  % --res_time_limit                      1000.
% 2.92/3.36  % --res_out_proof                       true
% 2.92/3.36  % --proof_out_file                      /export/starexec/sandbox/tmp/iprover_proof_43fe78.s
% 2.92/3.36  % --modulo                              true
% 2.92/3.36  
% 2.92/3.36  % ------ Combination Options
% 2.92/3.36  
% 2.92/3.36  % --comb_res_mult                       1000
% 2.92/3.36  % --comb_inst_mult                      300
% 2.92/3.36  % ------ 
% 2.92/3.36  
% 2.92/3.36  % ------ Parsing...% successful
% 2.92/3.36  
% 2.92/3.36  % ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e  pe_s  pe_e  snvd_s sp: 0 0s snvd_e % 
% 2.92/3.36  
% 2.92/3.36  % ------ Proving...
% 2.92/3.36  % ------ Problem Properties 
% 2.92/3.36  
% 2.92/3.36  % 
% 2.92/3.36  % EPR                                   false
% 2.92/3.36  % Horn                                  false
% 2.92/3.36  % Has equality                          true
% 2.92/3.36  
% 2.92/3.36  % % ------ Input Options Time Limit: Unbounded
% 2.92/3.36  
% 2.92/3.36  
% 2.92/3.36  Compiling...
% 2.92/3.36  Loading plugin: done.
% 2.92/3.36  Compiling...
% 2.92/3.36  Loading plugin: done.
% 2.92/3.36  Compiling...
% 2.92/3.36  Loading plugin: done.
% 2.92/3.36  Compiling...
% 2.92/3.36  Loading plugin: done.
% 2.92/3.36  Compiling...
% 2.92/3.36  Loading plugin: done.
% 2.92/3.36  Compiling...
% 2.92/3.36  Loading plugin: done.
% 2.92/3.36  Compiling...
% 2.92/3.36  Loading plugin: done.
% 2.92/3.36  Compiling...
% 2.92/3.36  Loading plugin: done.
% 2.92/3.36  Compiling...
% 2.92/3.36  Loading plugin: done.
% 2.92/3.36  Compiling...
% 2.92/3.36  Loading plugin: done.
% 2.92/3.36  Compiling...
% 2.92/3.36  Loading plugin: done.
% 2.92/3.36  Compiling...
% 2.92/3.36  Loading plugin: done.
% 2.92/3.36  Compiling...
% 2.92/3.36  Loading plugin: done.
% 2.92/3.36  Compiling...
% 2.92/3.36  Loading plugin: done.
% 2.92/3.36  Compiling...
% 2.92/3.36  Loading plugin: done.
% 2.92/3.36  Compiling...
% 2.92/3.36  Loading plugin: done.
% 2.92/3.36  Compiling...
% 2.92/3.36  Loading plugin: done.
% 2.92/3.36  Compiling...
% 2.92/3.36  Loading plugin: done.
% 2.92/3.36  Compiling...
% 2.92/3.36  Loading plugin: done.
% 2.92/3.36  % % ------ Current options:
% 2.92/3.36  
% 2.92/3.36  % ------ Input Options
% 2.92/3.36  
% 2.92/3.36  % --out_options                         all
% 2.92/3.36  % --tptp_safe_out                       true
% 2.92/3.36  % --problem_path                        ""
% 2.92/3.36  % --include_path                        ""
% 2.92/3.36  % --clausifier                          .//eprover
% 2.92/3.36  % --clausifier_options                  --tstp-format  
% 2.92/3.36  % --stdin                               false
% 2.92/3.36  % --dbg_backtrace                       false
% 2.92/3.36  % --dbg_dump_prop_clauses               false
% 2.92/3.36  % --dbg_dump_prop_clauses_file          -
% 2.92/3.36  % --dbg_out_stat                        false
% 2.92/3.36  
% 2.92/3.36  % ------ General Options
% 2.92/3.36  
% 2.92/3.36  % --fof                                 false
% 2.92/3.36  % --time_out_real                       150.
% 2.92/3.36  % --time_out_prep_mult                  0.2
% 2.92/3.36  % --time_out_virtual                    -1.
% 2.92/3.36  % --schedule                            none
% 2.92/3.36  % --ground_splitting                    input
% 2.92/3.36  % --splitting_nvd                       16
% 2.92/3.36  % --non_eq_to_eq                        false
% 2.92/3.36  % --prep_gs_sim                         true
% 2.92/3.36  % --prep_unflatten                      false
% 2.92/3.36  % --prep_res_sim                        true
% 2.92/3.36  % --prep_upred                          true
% 2.92/3.36  % --res_sim_input                       true
% 2.92/3.36  % --clause_weak_htbl                    true
% 2.92/3.36  % --gc_record_bc_elim                   false
% 2.92/3.36  % --symbol_type_check                   false
% 2.92/3.36  % --clausify_out                        false
% 2.92/3.36  % --large_theory_mode                   false
% 3.15/3.36  % --prep_sem_filter                     none
% 3.15/3.36  % --prep_sem_filter_out                 false
% 3.15/3.36  % --preprocessed_out                    false
% 3.15/3.36  % --sub_typing                          false
% 3.15/3.36  % --brand_transform                     false
% 3.15/3.36  % --pure_diseq_elim                     true
% 3.15/3.36  % --min_unsat_core                      false
% 3.15/3.36  % --pred_elim                           true
% 3.15/3.36  % --add_important_lit                   false
% 3.15/3.36  % --soft_assumptions                    false
% 3.15/3.36  % --reset_solvers                       false
% 3.15/3.36  % --bc_imp_inh                          []
% 3.15/3.36  % --conj_cone_tolerance                 1.5
% 3.15/3.36  % --prolific_symb_bound                 500
% 3.15/3.36  % --lt_threshold                        2000
% 3.15/3.36  
% 3.15/3.36  % ------ SAT Options
% 3.15/3.36  
% 3.15/3.36  % --sat_mode                            false
% 3.15/3.36  % --sat_fm_restart_options              ""
% 3.15/3.36  % --sat_gr_def                          false
% 3.15/3.36  % --sat_epr_types                       true
% 3.15/3.36  % --sat_non_cyclic_types                false
% 3.15/3.36  % --sat_finite_models                   false
% 3.15/3.36  % --sat_fm_lemmas                       false
% 3.15/3.36  % --sat_fm_prep                         false
% 3.15/3.36  % --sat_fm_uc_incr                      true
% 3.15/3.36  % --sat_out_model                       small
% 3.15/3.36  % --sat_out_clauses                     false
% 3.15/3.36  
% 3.15/3.36  % ------ QBF Options
% 3.15/3.36  
% 3.15/3.36  % --qbf_mode                            false
% 3.15/3.36  % --qbf_elim_univ                       true
% 3.15/3.36  % --qbf_sk_in                           true
% 3.15/3.36  % --qbf_pred_elim                       true
% 3.15/3.36  % --qbf_split                           32
% 3.15/3.36  
% 3.15/3.36  % ------ BMC1 Options
% 3.15/3.36  
% 3.15/3.36  % --bmc1_incremental                    false
% 3.15/3.36  % --bmc1_axioms                         reachable_all
% 3.15/3.36  % --bmc1_min_bound                      0
% 3.15/3.36  % --bmc1_max_bound                      -1
% 3.15/3.36  % --bmc1_max_bound_default              -1
% 3.15/3.36  % --bmc1_symbol_reachability            true
% 3.15/3.36  % --bmc1_property_lemmas                false
% 3.15/3.36  % --bmc1_k_induction                    false
% 3.15/3.36  % --bmc1_non_equiv_states               false
% 3.15/3.36  % --bmc1_deadlock                       false
% 3.15/3.36  % --bmc1_ucm                            false
% 3.15/3.36  % --bmc1_add_unsat_core                 none
% 3.15/3.36  % --bmc1_unsat_core_children            false
% 3.15/3.36  % --bmc1_unsat_core_extrapolate_axioms  false
% 3.15/3.36  % --bmc1_out_stat                       full
% 3.15/3.36  % --bmc1_ground_init                    false
% 3.15/3.36  % --bmc1_pre_inst_next_state            false
% 3.15/3.36  % --bmc1_pre_inst_state                 false
% 3.15/3.36  % --bmc1_pre_inst_reach_state           false
% 3.15/3.36  % --bmc1_out_unsat_core                 false
% 3.15/3.36  % --bmc1_aig_witness_out                false
% 3.15/3.36  % --bmc1_verbose                        false
% 3.15/3.36  % --bmc1_dump_clauses_tptp              false
% 3.15/3.36  % --bmc1_dump_unsat_core_tptp           false
% 3.15/3.36  % --bmc1_dump_file                      -
% 3.15/3.36  % --bmc1_ucm_expand_uc_limit            128
% 3.15/3.36  % --bmc1_ucm_n_expand_iterations        6
% 3.15/3.36  % --bmc1_ucm_extend_mode                1
% 3.15/3.36  % --bmc1_ucm_init_mode                  2
% 3.15/3.36  % --bmc1_ucm_cone_mode                  none
% 3.15/3.36  % --bmc1_ucm_reduced_relation_type      0
% 3.15/3.36  % --bmc1_ucm_relax_model                4
% 3.15/3.36  % --bmc1_ucm_full_tr_after_sat          true
% 3.15/3.36  % --bmc1_ucm_expand_neg_assumptions     false
% 3.15/3.36  % --bmc1_ucm_layered_model              none
% 3.15/3.36  % --bmc1_ucm_max_lemma_size             10
% 3.15/3.36  
% 3.15/3.36  % ------ AIG Options
% 3.15/3.36  
% 3.15/3.36  % --aig_mode                            false
% 3.15/3.36  
% 3.15/3.36  % ------ Instantiation Options
% 3.15/3.36  
% 3.15/3.36  % --instantiation_flag                  true
% 3.15/3.36  % --inst_lit_sel                        [+prop;+sign;+ground;-num_var;-num_symb]
% 3.15/3.36  % --inst_solver_per_active              750
% 3.15/3.36  % --inst_solver_calls_frac              0.5
% 3.15/3.36  % --inst_passive_queue_type             priority_queues
% 3.15/3.36  % --inst_passive_queues                 [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 3.15/3.36  % --inst_passive_queues_freq            [25;2]
% 3.15/3.36  % --inst_dismatching                    true
% 3.15/3.36  % --inst_eager_unprocessed_to_passive   true
% 3.15/3.36  % --inst_prop_sim_given                 true
% 3.15/3.36  % --inst_prop_sim_new                   false
% 3.15/3.36  % --inst_orphan_elimination             true
% 3.15/3.36  % --inst_learning_loop_flag             true
% 3.15/3.36  % --inst_learning_start                 3000
% 3.15/3.36  % --inst_learning_factor                2
% 3.15/3.36  % --inst_start_prop_sim_after_learn     3
% 3.15/3.36  % --inst_sel_renew                      solver
% 3.15/3.36  % --inst_lit_activity_flag              true
% 3.15/3.36  % --inst_out_proof                      true
% 3.15/3.36  
% 3.15/3.36  % ------ Resolution Options
% 3.15/3.36  
% 3.15/3.36  % --resolution_flag                     true
% 3.15/3.36  % --res_lit_sel                         kbo_max
% 3.15/3.36  % --res_to_prop_solver                  none
% 3.15/3.36  % --res_prop_simpl_new                  false
% 3.15/3.36  % --res_prop_simpl_given                false
% 3.15/3.36  % --res_passive_queue_type              priority_queues
% 3.15/3.36  % --res_passive_queues                  [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 3.15/3.36  % --res_passive_queues_freq             [15;5]
% 3.15/3.36  % --res_forward_subs                    full
% 3.15/3.36  % --res_backward_subs                   full
% 3.15/3.36  % --res_forward_subs_resolution         true
% 3.15/3.36  % --res_backward_subs_resolution        true
% 3.15/3.36  % --res_orphan_elimination              false
% 3.15/3.36  % --res_time_limit                      1000.
% 3.15/3.36  % --res_out_proof                       true
% 3.15/3.36  % --proof_out_file                      /export/starexec/sandbox/tmp/iprover_proof_43fe78.s
% 3.15/3.36  % --modulo                              true
% 3.15/3.36  
% 3.15/3.36  % ------ Combination Options
% 3.15/3.36  
% 3.15/3.36  % --comb_res_mult                       1000
% 3.15/3.36  % --comb_inst_mult                      300
% 3.15/3.36  % ------ 
% 3.15/3.36  
% 3.15/3.36  
% 3.15/3.36  
% 3.15/3.36  % ------ Proving...
% 3.15/3.36  % 
% 3.15/3.36  
% 3.15/3.36  
% 3.15/3.36  %  Resolution empty clause
% 3.15/3.36  
% 3.15/3.36  % ------                             Statistics
% 3.15/3.36  
% 3.15/3.36  % ------ General
% 3.15/3.36  
% 3.15/3.36  % num_of_input_clauses:                 1474
% 3.15/3.36  % num_of_input_neg_conjectures:         5
% 3.15/3.36  % num_of_splits:                        0
% 3.15/3.36  % num_of_split_atoms:                   0
% 3.15/3.36  % num_of_sem_filtered_clauses:          0
% 3.15/3.36  % num_of_subtypes:                      0
% 3.15/3.36  % monotx_restored_types:                0
% 3.15/3.36  % sat_num_of_epr_types:                 0
% 3.15/3.36  % sat_num_of_non_cyclic_types:          0
% 3.15/3.36  % sat_guarded_non_collapsed_types:      0
% 3.15/3.36  % is_epr:                               0
% 3.15/3.36  % is_horn:                              0
% 3.15/3.36  % has_eq:                               1
% 3.15/3.36  % num_pure_diseq_elim:                  0
% 3.15/3.36  % simp_replaced_by:                     0
% 3.15/3.36  % res_preprocessed:                     10
% 3.15/3.36  % prep_upred:                           0
% 3.15/3.36  % prep_unflattend:                      0
% 3.15/3.36  % pred_elim_cands:                      0
% 3.15/3.36  % pred_elim:                            0
% 3.15/3.36  % pred_elim_cl:                         0
% 3.15/3.36  % pred_elim_cycles:                     0
% 3.15/3.36  % forced_gc_time:                       0
% 3.15/3.36  % gc_basic_clause_elim:                 0
% 3.15/3.36  % parsing_time:                         0.083
% 3.15/3.36  % sem_filter_time:                      0.
% 3.15/3.36  % pred_elim_time:                       0.
% 3.15/3.36  % out_proof_time:                       0.001
% 3.15/3.36  % monotx_time:                          0.
% 3.15/3.36  % subtype_inf_time:                     0.
% 3.15/3.36  % unif_index_cands_time:                0.
% 3.15/3.36  % unif_index_add_time:                  0.001
% 3.15/3.36  % total_time:                           2.814
% 3.15/3.36  % num_of_symbols:                       121
% 3.15/3.36  % num_of_terms:                         4301
% 3.15/3.36  
% 3.15/3.36  % ------ Propositional Solver
% 3.15/3.36  
% 3.15/3.36  % prop_solver_calls:                    1
% 3.15/3.36  % prop_fast_solver_calls:               15
% 3.15/3.36  % prop_num_of_clauses:                  1262
% 3.15/3.36  % prop_preprocess_simplified:           4598
% 3.15/3.36  % prop_fo_subsumed:                     0
% 3.15/3.36  % prop_solver_time:                     0.
% 3.15/3.36  % prop_fast_solver_time:                0.
% 3.15/3.36  % prop_unsat_core_time:                 0.
% 3.15/3.36  
% 3.15/3.36  % ------ QBF 
% 3.15/3.36  
% 3.15/3.36  % qbf_q_res:                            0
% 3.15/3.36  % qbf_num_tautologies:                  0
% 3.15/3.36  % qbf_prep_cycles:                      0
% 3.15/3.36  
% 3.15/3.36  % ------ BMC1
% 3.15/3.36  
% 3.15/3.36  % bmc1_current_bound:                   -1
% 3.15/3.36  % bmc1_last_solved_bound:               -1
% 3.15/3.36  % bmc1_unsat_core_size:                 -1
% 3.15/3.36  % bmc1_unsat_core_parents_size:         -1
% 3.15/3.36  % bmc1_merge_next_fun:                  0
% 3.15/3.36  % bmc1_unsat_core_clauses_time:         0.
% 3.15/3.36  
% 3.15/3.36  % ------ Instantiation
% 3.15/3.36  
% 3.15/3.36  % inst_num_of_clauses:                  1328
% 3.15/3.36  % inst_num_in_passive:                  0
% 3.15/3.36  % inst_num_in_active:                   0
% 3.15/3.36  % inst_num_in_unprocessed:              1474
% 3.15/3.36  % inst_num_of_loops:                    0
% 3.15/3.36  % inst_num_of_learning_restarts:        0
% 3.15/3.36  % inst_num_moves_active_passive:        0
% 3.15/3.36  % inst_lit_activity:                    0
% 3.15/3.36  % inst_lit_activity_moves:              0
% 3.15/3.36  % inst_num_tautologies:                 0
% 3.15/3.36  % inst_num_prop_implied:                0
% 3.15/3.36  % inst_num_existing_simplified:         0
% 3.15/3.36  % inst_num_eq_res_simplified:           0
% 3.15/3.36  % inst_num_child_elim:                  0
% 3.15/3.36  % inst_num_of_dismatching_blockings:    0
% 3.15/3.36  % inst_num_of_non_proper_insts:         0
% 3.15/3.36  % inst_num_of_duplicates:               0
% 3.15/3.36  % inst_inst_num_from_inst_to_res:       0
% 3.15/3.36  % inst_dismatching_checking_time:       0.
% 3.15/3.36  
% 3.15/3.36  % ------ Resolution
% 3.15/3.36  
% 3.15/3.36  % res_num_of_clauses:                   1431
% 3.15/3.36  % res_num_in_passive:                   0
% 3.15/3.36  % res_num_in_active:                    564
% 3.15/3.36  % res_num_of_loops:                     5
% 3.15/3.36  % res_forward_subset_subsumed:          823
% 3.15/3.36  % res_backward_subset_subsumed:         9
% 3.15/3.36  % res_forward_subsumed:                 0
% 3.15/3.36  % res_backward_subsumed:                0
% 3.15/3.36  % res_forward_subsumption_resolution:   1
% 3.15/3.36  % res_backward_subsumption_resolution:  0
% 3.15/3.36  % res_clause_to_clause_subsumption:     1
% 3.15/3.36  % res_orphan_elimination:               0
% 3.15/3.36  % res_tautology_del:                    0
% 3.15/3.36  % res_num_eq_res_simplified:            0
% 3.15/3.36  % res_num_sel_changes:                  0
% 3.15/3.36  % res_moves_from_active_to_pass:        0
% 3.15/3.36  
% 3.15/3.36  % Status Unsatisfiable
% 3.15/3.36  % SZS status Unsatisfiable
% 3.15/3.36  % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------